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10 Net Radiation
10 NET RADIATION
The net radiation is defined as the difference between the radiant energy absorbed and that emitted by the underlying surface, by the atmosphere, or by the system earth-atmopshere. The net radiation R of the ground surface consists of the direct and diffuse radiation and also of the atmospheric emission (downward atmospheric radiation) absorbed and retained by the underlying surface after heat losses due to the thermal emission of the underlying surface. This can be expressed as the following equation for the net radiation of the underlying surface :
R
=
Q(1 - A )
+ 6Go - Usurf
(10.1)
where Q are the fluxes (or totals) of incoming direct solar and diffuse radiation, A is the albedo of the underlying surface, Go and Usurfare the fluxes (or totals) of atmospheric emission and of the thermal emission of the underlying surface, and 6 is the absorptivity of the underlying surface. Since Usurf- 6G, = F, is the effective radiation of the underlying surface, (10.1) can be written as
R
=
Q(1 - A ) - Fo
(10.1 a)
It should be borne in mind that the concept of the net radiation is to a certain degree abstract. In actual practice we deal with the net radiation of an active layer whose thickness varies within a very wide range. In some cases (smooth underlying surfaces devoid of vegetation) it is very small; in others (plantations or water basins) it reaches high values of the order of meters and tens of meters. The net radiation of the atmosphere, Ra, consists of the direct solar and 655
656
Net Radiation
diffuse radiation q' absorbed by the atmosphere and also of the absorbed thermal radiation UgWfof the underlying surface. The emitted radiation consists of the heat losses due to the atmospheric thermal emission toward the earth's surface and spaceward. The first outgoing component is the atmospheric emission Go and the second is the radiation of the atmosphere U, to space. Thus, the net radiation of the atmosphere is expressed as
If P is the transmissivity of the atmosphere for thermal radiation then the thermal radiation of the underlying surface absorbed by the atmosphere can be presented as Usurf= (1 - P)Uo, where Uo is the upward flux of thermal radiation at ground level. The quantity Uo - Go = Fo , as has already been pointed out, is the effective radiation of the underlying surface, U, = F, is the outgoing radiation to space from both ground and PU,, and atmosphere. In view of this consideration the equation for the net radiation of the atmosphere can have yet another 'form:
+
(10.2)
In the net radiation R, of the system earth-atmosphere the incoming portion consists of the direct solar and diffuse radiation absorbed by the underlying surface and the atmosphere, while the expenditure or loss is determined by the outgoing radiation. The equation for the net radiation of the system earth-atmosphere therefore has the form
(10.3) This equation can also be rewritten: (10.4)
where Q, is the flux of direct solar radiation outside the atmosphere, A , is the albedo of the planet Earth. Let us now turn to the fundamental regularities of the net radiation for the ground surface, the atmosphere, and the system earth-atmosphere in view of their application for meteorological purposes. The importance of radiation data for dynamical meteorology has been discussed in Van Mieghem's work [l].
10.1. Observed Regularities in Variation of Net Radiation
657
10.1. Observed Regularities in Variation of Net Radiation of the Underlying Surface The study of the net radiation of the underlying surface is of extreme importance, as the net radiation is the main determinant of the climate. The magnitude of the net radiation of the underlying surface greatly affects the distribution of temperature in the soil and the adjacent air layers, which accounts for the particular role of the net radiation in the calculation of evaporation and snow melting, and also in a number of problems concerned with weather forecasting, such as the forecasting of late and early frosts and of fog. The study of the net radiation is also important to synoptic meteorology; for example, the lack of data on the net radiation makes it impossible to solve the problem of the formation and transformation of air masses. Finally, the investigation of the net radiation is connected with the effect of radiation on plant and animal life. All this accounts for the great interest in the study of the net radiation of the underlying surface shown by many investigators [2-271. It should, however, be noted that the number of stations engaged in prolonged observations of all the quantities involved in the net radiation or with direct measurements of the total net radiation is very small. This is due to the fact that until quite recently there have been no sufficiently reliable instruments for the direct measurement of the net radiation. Although in recent years satisfactorily constructed balance meters have been developed (such as the Yanishevsky and the Funk net radiometers and others), nevertheless the problem of reliable measurements of the net radiation still lacks solution. It is evident that the main features of the net radiation are determined by the factors that most influence the net radiation components. These include the duration of sunshine, the conditions of cloudiness and atmospheric transparency, the stratification of the atmosphere, and the character and state of the underlying surface. The net radiation of the underlying surface will be positive if the heat gain exceeds its loss, and negative in the reverse case. In the diurnal variation of the net radiation the former is usually observed in daytime and the latter at night. In the annual range for latitudes between 40' N and 4OoS, monthly values of the net radiation are positive for land and sea. In higher latitudes the monthly values become negative in winter months.
1. Diurnal Variation. Let us first characterize the diurnal variation of the net radiation. This problem has been treated in a great number of investi-
658
Net Radiation
gations. Observations show that, as a rule, the maximal positive values of the net radiation occur around noon, and the highest negative values at night. The night variation of the net radiation (the nighttime range of effective radiation) is small in comparison with its variation during the day. The curve of the diurnal cycle of the net radiation is usually asymmetrical in relation to noon; the afternoon values are somewhat lower, for the afternoon effective radiation exceeds the morning values, a feature that is clearly marked in southern and especially so in desert areas. The mentioned regularities in the diurnal variation of the net radiation can be seen in Fig. 10.1, which shows the daily cycle of the net radiation and its components according to Eisenstadt and Zuyev [2] for Tashkent (the measurement employed the Yanishevsky pyranometer and net radiometer). The values of direct solar, diffuse, and the net radiation were averaged from observations on clear summer days (August, 1969) in a sand desert. The other components of the net radiation were obtained by calculation. As seen from Fig. 10.1, in these conditions the leading component of the daytime net radiation is the direct solar radiation. Accordingly, the maximum in the net radiation is observed almost exactly at noon, between 11 and 12 h,
HOUR
FIG. 10.1 Diurnal variation of net radiation components (means of clear days). (1) Net radiation; (2) direct solar radiation; (3) downward atmospheric radiation absorbed by the ground surface; (4) diffuse radiation; (5) reflected shortwave radiation; (6) effective radiation; (7) radiation of the underlying surface.
10.1. Observed Regularities in Variation of Net Radiation
659
and is equal to 0.68 cal/cm2 min. The minimum of -0.15 cal/cm2 min occurs soon after sunset. The zero point in this cycle was observed between 06 and 07 h and between 17 and 18 h. Figure 10.1 shows that these points do not coincide with the moments of sunrise and sunset. In the morning the negative net radiation is observed 40 to 60 min after rise, while the transition from positive to negative values in the evening outruns sunset by about 1.5 h. This can be explained by the fact that the morning influx of heat due to the absorption of direct solar and diffuse radiation can compensate for the loss of heat due to effective radiation only some time after sunrise. In the evening hours the effective radiation predominates over the incoming part of the net radiation before sunset. Observations show that the transition from the positive net radiation to the negative, and vice versa, usually occurs at solar heights of about 5 to 15'. Table 10.1 gives the mean time of the zero point in the net radiation TABLE 10.1 Mean Time of the Setting ( t , ) and End ( t 2 ) of the Positive Net Radiation of the Underlying Surface (in h). After Supozhnikova [ 3 ]
I Month
Latitude, deg
I
40
5-7 5-7 4-6 5-7 5-7 5-7 6-8
April May June July August September October I
16-18 17-19 17-19 17-1 9 17-19 16-18 15-1 7
,
5-7 4-6 4-6 4-6 5-7 5-7 6-8
5-7 4-6 4-6 4-6 5-7 6-8 7-9
16-18 17-19 18-20 17-1 9 16-18 16-18 15-17
1618 17-19 18-20 17-19 17-19 15-17 . -14-16
I
for morning (tl) and evening ( t z ) on the fifteenth day of every month in dependence on latitude. The data were compiled by Sapozhnikova [3] and later corrected in view of more recent observations. It should be remembered that Table 10.1 does not include the case of snow cover, where the positive net radiation is observed at much higher solar altitudes (about 10 to 25'). This is caused by the great snow albedo affecting the net radiation to lesser values. The peculiarities of the dependence of the net radiation upon solar height
660
Net Radiation
at a clear sky can be illustrated by the data of Table 10.2, borrowed from [Chapter 7, Ref. 37bl. Table 10.1 clearly shows a later transition of the net radiation through the zero point and lower net radiation values in the presence of snow. In winter months in the north, and partly in the intermediate latitudes, the net radiation remains negative throughout 24 h. TABLE 10.2 Average Dependence of the Net Radiation (cal/cnz2min) upon Solar Height with Clear Skies. After Kirillova (Chapter 7 [37b])
State of Ground
Albedo,
Snowless
Snow
%
Solar Height, deg 0
5
15-25
-0.07
-0.04
50-80
-0.05
-0.04
10
15
20
25
30
35
0.03 0.12 0.21 0.32 0.41 0.48 -0.01
0.05 0.10 0.17 0.23 0.29
Cloudiness also greatly affects the transition of the net radiation through the zero point. With overcast skies the setting of the negative net radiation is retarded, since in these conditions the effective radiation as a cooling component of the net radiation greatly decreases. Sapozhnikova [3] found a high correlation between the moment of the zero net radiation and the time of the setting and disappearance of the night inversion in the lower air layer of 1.5- to 2-m thickness. Table 10.1 therefore also characterizes the time of appearance (f2) and disappearance ( t l ) of the night inversion in the above air layer. It should be noted that a number of investigations have found a parallelism between the diurnal variation of the net radiation and the vertical temperature gradients near the underlying surface. Sapozhnikova showed a correlation between the net radiation and the temperature difference at 20 to 150 cm above ground. The observations of Eisenstadt and Zuyev [2] give evidence of a parallelism between the net radiation variation and the temperature difference at the level 0 to 20 cm. Eisenstadt [4] also found a close correlation between the net radiation and the temperature of the soil surface. Doubtless, the cause of all these correlations is the close relationship between the temperature of the underlying surface and the adjacent vertical temperature gradients, and the effective radiation as the cooling component of the net radiation.
10.1. Observed Regularities in Variation of Net Radiation
66 1
The smooth diurnal range in the net radiation presented in Fig. 10.1 is observed, naturally, only with clear or fully cloudy skies (in the latter case, of course, the amplitude of the daily variation is notably smaller than with clear skies). In the case of partial cloudiness the daily variation of the net radiation becomes very irregular. This is illustrated by the curves of Fig. 10.2, plotted by Sapozhnikova [3]. The observations made at Koltushy (Leningrad region) on a clear and on a dull day show that the cloudy day gives a smaller range of the diurnal variation in the net radiation, with the variation itself being also more complicated.
-0.21 0
I
I
I
I
I
4
8
12
16
20
Hour
FIG. 10.2 Diurnal variation of net radiation.
(1) June average for Tashkent; (2) at Koltushy (Leningrad region) in a clear July day; (3) at Koltushy in a cloudy July day.
Along with the strong effect of the solar altitude on the direct solar and diffuse radiation, and with the albedo of the underlying surface, the cloud amount is the main factor determining the variability of the net radiation. In daytime the appearance and increase of cloudiness leads to reduction in both global radiation and effective radiation (it should be noted that the global radiation only shows a decrease with increasing cloudiness when averaged; isolated cases can show a reverse picture). At night the variation of cloudiness can affect only the effective radiation. Thus, on the average, the daytime positive values of net radiation with a cloudy sky decrease and the nighttime values also decrease in absolute estimation. However, with the partial cloud and the unobliterated sun when the global radiation is at its highest and the effective radiation is smaller than with a clear sky, the maximal positive values of the net radiation are observed. For instance, Chikirova [ 5 ] found during the observations at
662
Net Radiation
Dolgoprudnaya station (Moscow region) in August, 1947, that the net radiation with partial cloud was equal to 1.07 cal/cm2 min. To characterize the peculiarities in the daily variation of the net radiation with clear and with dull skies, Table 10.3 gives Mukhenberg’s [6] results of observations by means of the Yanishevsky net radiometer at Koltushy (Leningrad region). TABLE 10.3 Seasonal Changes in the Diurnal Variation of Net Radiation (cal/cmzmin). After Mukhenberg [6]
-
Clear
Cloudy
Hour
0 4 8
12 16 20 0
Summer Autumn -0.063 -0.022 0.392 0.632 0.312 -0.042 -0.070
Winter
-0.092 -0.088 -0.070 -0.102 0.045 0.077 0.390 0.028 0.120 -0.064 -0.080 -0.082 -0.079 -0.070
Spring
Summer Autumn
Winter
-0.076 -0.068 0.123 0.355 0.154 -0.048 -0.060
-0.018 -0.018 -0.021 -0.013 0.098 0.053 0.247 0.085 0.175 -0.006 -0.004 -0.012 -0.019 -0.003
-0.034 -0.029 -0.016 -0.024 -0.007 0.054 0.019 0.107 -0.008 0.068 -0.007 0.004 -0.005 -0.019
Spring
It is evident from Table 10.3 that cloudiness in summer leads to a considerable decrease in the net radiation, while on the contrary, cloudiness in winter helps to reduce the negative daily net radiation. The investigations of E. P. Barashkova et al. [Chapter 7, Ref. 37a] show that the averaged dependence of the net radiation upon solar altitude can be described by the following empirical equation :
R
= a(h, -
(10.5)
b)
where a, b are constant and h, is the height of the sun in degrees. For the constants a and b, the dependence on the albedo of the underlying surface is shown below: Albedo, %
a
b
10-20 20-30
0.013 0.012 0.006 0.007 0.004
10.0 9.8 7.4 7.4 8.5
5 W O 60-70 70-80
663
10.1. Observed Regularities in Variation of Net Radiation
With constant solar height (40’) and albedo, the variation of the net radiation in dependence upon cloud amount is characterized by the following data: Cloud amount, in tenths Net radiation, cal/cm* min
3
4
5
6
7
8
0.46 0.45 0.43 0.42 0.40 0.38
We see that with the increase in albedo from 10 to 80 percent, the net radiation shows an almost triple decrease. The increase in cloud amount from 3 to 8 reduces the net radiation by only 0.08 cal/cm2 min, that is, by about 20 percent. Thus we see that the net radiation is more “sensitive” to variations in albedo than to variations in cloud amount. The investigations of Barashkova et al. found a close correlation between the net radiation of a grassy surface and the magnitude of the absorbed shortwave radiation: R,$, - 0.06 (10.6) R= 1.20 At R,, > 0.06 cal/cm2 min this formula enables calculation of the net radiation from the absorbed radiation with an error of about f 10 percent. 2. Annual Variation. In order to characterize the regularities of the annual variation of the net radiation, let us consider Fig. 10.3, which presents isopleths of the net radiation for four points in different climatic zones (Yakutsk, Omsk, Vladivostok, Tashkent). These data of [Chapter 7, Ref. 37a] are also complementary to the daily variation of the net radiation. From examination of Fig. 10.3 it is evident that the maximal net radiation values are usually observed in June to July and are 0.45 to 0.55 cal/cm2 rnin in the north (62 to 64ON lat.) and 0.6 to 0.7 cal/cm2rnin in the south (40’s lat.). The minima fall during December and January, when the obtained values are 0.02 cal/cm2 rnin in the north (Yakutsk) and 0.2 cal/cm2 rnin in the south (Tashkent). In summer the nighttime values of the net radiation of the considered area vary but little and are -0.06 and -0.07 cal/cm2 min. In winter their variation is more pronounced, but the absolute values are very small (from -0.02 to -0.05 cal/cm2 min). The exception is the monsoon area (Vladivostok), where the highest net radiation occurs in April to May, and a small secondary maximum is observed in September.
3. The Effect of Wetting. Observations show that the net radiation of underlying surfaces greatly changes after their wetting by rain or irrigation. Table 10.4 gives the results of measurements of the net radiation over an
664
Net Radiation
-0.05
-0.05
-0.05
FIG. 10.3 Isopleths of net radiation (cal/cm2min). (a) Yakutsk; (b) Omsk; (c) Vladivostok; (d) Tashkent.
irrigated cotton field and over a semidesert in July, 1952 (by means of the Yanishevsky pyrgeometer and balance meter). These results were averaged by Eisenstadt et al. [7] from eight sets of observations on clear days at the state farm “Pakhta Aral” (Uzbek S.S.R.). It is evident from Table 10.4 that at night the net radiation of an irrigated field and a semidesert are approximately equal. In daytime the net radiation of the irrigated field considerably exceeds that of the semidesert. In the hours around midday the difference between these quantities is 0.30 cal/ cmz min. It appears that this difference is determined almost entirely by the inequality of their outgoing components: Owing to the higher surface temperature, the effective radiation of the semidesert exceeds by 0.25 cal/cm2
10.1. Observed Regularities in Variation of Net Radiation
665
TABLE 10.4 Daily Variation of the Net Radiation of an Irrigation Field and a Semidesert (cal/cm2rnin). After Eisenstadt et al. [7]
Area
I
Time, h 0-1
4-5
Irrigated cottonfield -0.07 Semidesert -0.08
6-7
8-9
1 6 1 1 12-13 14-15 16-17
18-19
20-21
-0.06
0.18 0.62 0.89 0.96 0.87 0.46
0.03
-0.07
-0.06
0.13 0.47 0.66 0.66 0.56 0.30
-0.05
-0.10
rnin that of the irrigated field. The remaining 0.05 cal/cm2 min characterizes the difference between the fluxes of global radiation reflected by the two surfaces (the semidesert whose albedo is higher than that of the irrigated cottonfield reflects 0.05 cal/cm2 min more radiation). Thus the reduction of the albedo and temperature of the underlying surface due to irrigation provokes a notable increase in its net radiation. This fact was first stated by Skvortzov [8]. The earlier reversal of sign of the net radiation in the morning and the later in the evening are also due to the reduction in the temperature of the irrigated field and the consequent decrease in its effective radiation, compared with that of the semidesert. Many investigations (see [9-111) have been carried out with the purpose of detailed study of the effect of irrigation on the net radiation. Their results all confirm the notable increase in net radiation due to irrigation. It can be said that in a moderate climate the increase in net radiation due to irrigation averages 20 percent, in steppe and wooded steppe it is 40 percent, and in the semideserts of central Asia 60 percent. It should be noted, however, that the effect of irrigation is strongly dependent on the development of vegetation. Since the change of net radiation by irrigation is caused by a change of albedo and the decrease in effective radiation due to the reduction in the temperature of the underlying surface, Eisenstadt et al. [7] proposed the following formula for the calculation in the net radiation A R (cal/cm2 min):
dR
=
(Q
+ q ) ( A - A') +
B(to
- to')
(10.7)
where Q + q is the global radiation flux, A and A' are the albedos of the ground before and after irrigation, to and to' are the temperatures of the
666
Net Radiation
ground before and after irrigation, and 4, is a coefficient equal to 0.008. Using (10.7), it is easy to explain why A R / R increases southward. This is obviously due to the fact that irrigation in the south causes a stronger reduction of the ground temperature than in the north. Kirillova [12] showed that (10.7) can also be used for the calculation of the difference in net radiation between water and land at two close points. Such calculations as well as observations revealed that in summer the net radiation of water basins, R , , exceeds that of land, RL,while in winter the reverse is the case. The observations of Kirillova at Lake Sevan (Armenia) give the following results: July RwlRL 1.39
Aug. 1.36
Sept. 1.04
Oct. 0.93
This can be accounted for by the fact that the water albedo notably increases in fall as the solar height reduces, and also by the reversal in sign of the temperature difference water-land (water becomes warmer than land, which causes the effective radiation for water to be greater than for land). 4. Effect of Forest. Also important is the variation of net radiation in forests. Under the trees both income (global radiation) and expenditure (effective radiation) in the net radiation will obviously decrease. Observations show that in summer the reduction of global radiation under the trees in daytime by far exceeds the decrease of effective radiation, due to which the net radiation in a forest is much less than in an open place. This conclusion follows, for example, from the observations of Golubova [28, 291 in forest barriers of the Kamennaya Steppe (Ukraine) and in the Saratov region (the Volga area). Table 10.5 displays Golubova’s results [29], obtained by means of the Yanishevsky pyrgeometer for two points of a forest barrier in the Kamennaya Steppe in June-July, 1951. As seen, at small solar heights (in the morning or evening) the net radiation in the forest is, in individual cases, only a few percent of the open field value. At night the net radiation in these cases was practically zero. It is natural that the net radiation under the trees must be strongly dependent on their quality and composition and on the development of foliage. For example, according to Golubova [29], the net radiation inside the forest barrier without foliage on a clear April day was 53 to 88 percent of the open field value. Comparison of these figures with Table 10.5 shows the great influence of leaves on the forest net radiation. In Rauner’s [30] estimation the ratio of the net radiation values over the forest ( R ) and inside ( R 2 , R3) shows strong change during 24 h and
667
10.1. Observed Regularities in Variation of Net Radiation
TABLE 10.5 Net Radiation in Forests. After Golubova [29]
Net Radiation
% in Open Field
cal/cm2min
Hours
Point 1
Point 2
Point 1
08-09
0.02
10-1 1
0.06
4 8
12-13 14-15 1617
0.09 0.03 0.02
18-19
0.01
0.21 0.43 0.04 0.02
Point 2
10
24
4 5
61 10
14
15
is considerably dependent on the phase of vegetation (see Table 10.6 where R2 and R, denote the net radiation values under the coniferous trees with insignificant undergrowth of stand density 0.9, and in a decidious forest with thin young trees and a lower growth of stand density 0.7). It can be seen from Table 10.6 that the “clarification” of the forest after TABLE 10.6 Change in Net Radiation under the Trees Compared with That over the Forest. After Rauner [30]
Period
Time, h
&side -
Rover
4
6
8
10
12
14
16
18
20
22
I0.00 0.09 0.05 0.06 0.05 0.06 0.08 0.07 0.00 0.00
R, R After vegetation (October)
R2 R
0.00 0.17 0.10 0.07 0.16 0.07 0.08 0.11 0.00 0.00
0.33 0 . 3 3 0.00 0.03 0.04 0.10 0.67 0.67
-
0.10 0.15
0.29
-
0.20 0.16 0.33
-
0.40 0.33 0.33
668
Net Radiation
the final period of vegetation is most apparent in the morning and evening hours. A different relationship between the net radiation of a forest and of an open area is observed in winter with snow cover. According to Kuzmin's [Chapter 9, Ref. 1001 observations in the Valdai Hills (W. Russia), the daily net radiation in winter snow-covered forests can be positive, while the open snow field has a negative value of net radiation.
5. Net Radiation Totals. The above data on the diurnal variation of the net radiation show that in the warm half-year, the daytime positive value exceeds the negative value during the night, which leads to the daily net radiation being positive. In winter the opposite picture is observed : the daily net radiation is negative. According to the observations of Pivovarova [Chapter 9, Ref. 371 near Tashkent, the mean diurnal net radiation was 136 cal/cm2 at the end of August and in the first half of September. The fluctuations of the net radiation at times were quite notable. For example, the highest observed daily total was 205 cal/cm2. These are the desert data. At the same area the mean net radiation of a cottonfield was 454 cal/cm2 in July, while for the semidesert it equaled 270 cal/cm2. The reduction in the net radiation of the desert is due to the higher albedo of sand. The results of observations near Leningrad [31] give the daily totals of net radiation in summer of 200 cal/cm2.Table 10.7 (from Barashkova et al. Chapter 7 [37a]) summarizes the observed monthly and annual totals of net radiation. In the annual variation of net radiation the monthly totals usually follow the variation in global radiation. However, in areas with stable snow cover the variation of the surface albedo (especially during spring) is also important. In the north of the territory considered, the negative net radiation is observed during five to six months. To the south of 46' N lat. on the European U.S.S.R. territory and of 43' N lat. on the Asiatic territory, the net radiation is positive throughout the year. During the whole year the totals of net radiation increase southward. Figure 10.4 is a map of the geographical distribution of the annual net radiation totals over the U.S.S.R. territory, plotted by Barashkova et al. [Chapter 7, Ref. 37al. The annual net radiation is seen to be positive everywhere and varies from 20 kcal/cm2 yr in the north to 60 kcal/cm2 yr in the south. This geographical distribution is mainly zonal. However, there is a slight tendency to an increase of net radiation in the west and an opposite tendency in the east of the examined territory.
TABLE
10.7
Meon Latitudinal Totals of Net Radiation (kcallcd). After Barashkova et al. (Chapter 7 [37a])
Latitude, deg
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
Year
38
1.5
2.7
3.8
6.1
8.4
8.8
8.5
7.8
5.4
3.5
1.7
0.8
59.0
40
0.8
2.0
3.6
5.8
8.3
8.8
8.5
7.6
5.3
3.0
1.3
0.5
55.5
42
0.4
1.3
3.4
5.6
8.2
8.8
8.5
7.5
5.2
2.6
0.8
0.1
52.4
0.0
0.8
3.0
5.5
8.1
8.8
8.5
7.3
5.0
2.3
0.5
-0.2
49.6
46
-0.2
0.5
2.7
5.4
8.0
8.8
8.5
7.1
4.7
2.0
0.3
-0.4
47.4
48
-0.4
0.2
2.3
5.3
7.9
8.8
8.5
6.9
4.5
1.8
0.0
-0.5
45.3
50
-0.5
0.0
2.0
5.2
7.8
8.8
8.4
6.7
4.2
1.5
-0.2
-0.7
43.2
52
-0.5
-0.2
1.6
5.1
7.6
8.7
8.3
6.4
3.8
1.1
-0.4
-0.7
40.8
54
-0.6
-0.3
1.2
4.7
7.5
8.5
8.2
6.1
3.4
0.8
-0.5
-0.8
38.2
56
-0.6
-0.4
0.7
4.3
7.4
8.4
8.0
5.8
3.0
0.5
-0.6
-0.8
35.7
58
-0.7
-0.5
0.2
3.7
7.2
8.3
7.9
5.6
2.7
0.3
-0.6
-0.8
33.3
60
-0.8
-0.6
-0.2
3.2
6.9
8.2
7.8
5.4
2.4
0.1
-0.7
-0.8
31 .O
62
-0.8
-0.6
-0.4
2.2
6.5
8.2
7.8
5.3
2.1
-0.1
-0.7
-0.9
28.6
64
-0.7
-0.6
-0.4
1.3
6.0
8.2
7.7
5.1
1.9
-0.2
-0.8
-1
66
-0.7
-0.6
-0.4
0.6
5.5
8.2
7.7
4.9
1.6
-0.4
-0.9
-1.0
68
-0.7
-0.6
-0.4
0.1
5 .O
8.3
7.6
4.5
1.3
-0.7
-0.7
-1
44
.o .o
26.5 24.5 22.7
10.1. Observed Regularities in Variation of Net Radiation
67 1
Of much interest are the results of actinometric measurements in the Arctic and Antarctic, obtained during and after the International Geophysical Year. It appeared, for instance, that even for the major part of the Arctic (except its central area) the mean annual net radiation was positive. According to Chernigovsky’s [32] data, averaged from ten years of observations at six stations, the annual net radiation in the central Arctic was close to zero (0.5 kcal/cm2 yr). In Marshunova’s calculations [33, 341 the maximal annual totals of net radiation occur at Cape Schmidt (1 1.6 kcal/cm2 yr) and at the Chukotskoye Sea (14.4 kcal/cm2 yr). The lowest totals in the central part of the Arctic basin vary from -2.5 kcal/cm2 yr in its western wing to -3.5 kcal/cm2 yr in the east. Interesting data on the net radiation in the Arctic conditions were obtained by Vowinckel and Orwig [35] who contend that there are three main types of the radiation regime of the underlying surface in the Arctic: (1) the Norwegian Sea regime, (2) the continental type, and (3) the regime of pack. The first type is characteristic of the open ocean surface from the Arctic Circle northward. During the year here is observed reciprocal compensation of high positive net radiation values in summer and high negative in winter (the cause for the latter is the relatively high ocean surface temperature; it is of interest that the effect of cold or warm currents is not essential, the primary factor being only the cloud effect). The main feature of this type is a high radiative heat loss of the open ocean surface. The continental type (Siberian continent and western Canada) is entirely different. In winter the radiative heat loss from the surface is small and the downward atmospheric radiation becomes less pronounced owing to scarce cloudiness. As a result the annual net radiation total for the continent is greater than for the ocean. The radiation regime of pack is typical for those ocean areas that are only temporarily free of ice. The contribution of the surface emission to the net radiation here is intermediate compared with that of land and open water. The slow change of the net radiation in spring, due to the high surface albedo, is typical. Contrary to the continental conditions the maximum in net radiation occurs here after the solar culmination. The analysis of observational data performed by Rusin [36] shows that the Antarctic radiation regime is very peculiar. Its annual net radiation is everywhere (except surfaces free of ice and snow) negative. For example, the annual total of net radiation is - 12.2 kcal/cm2 yr at Komsomolskaya station, and from -3.5 to -9.1 kcal/cm2 yr (in different years) at Mirny. With surfaces free of ice and snow the annual net radiation reaches high positive values (over 75 kcal/cm2 yr at Oasis). Thus, on the main part of
672
Net Radiation
the Antarctic territory, the high values of the incoming solar radiation mentioned in Chapter 8 are not “realized” because of the high ground albedo and the long period of radiative cooling during the polar night. In the annual range the monthly net radiation totals are positive for only three to four months. 10.2. Results of Calculations of Net Radiation at the Underlying Surface The relatively small number of observations of the net radiation and its components is not sufficient to give information on the net radiation totals and their temporal and spatial variability. In this connection, theoretical calculations of the net radiation as a whole and of its components are widely used. The methods for such calculations of totals of direct solar, diffuse and global radiation, and also of the effective radiation, have been considered in Chapters 6 , 7, 8, and 9. Calculations show that, as a rule, we deal with a simple annual variation of the net radiation with a summer maximum and a minimum in winter. This is evident, for example, from Table 10.8, compiled by Mukhenberg [ 6 ] from the results of observations and calculations of the net radiation for the Leningrad region. This table shows that the increase of net radiation TABLE 10.8 Annual Variation of Monthly Totals of the Net Radiation and Its Components in the Leningrad Region, kcallcm2. After Mukhenberg [6]
Month
Global Radiation
Radiation Absorbed
Effective Radiation
Net Radiation
January February March April May June July August September October November December
0.4 1.5 4.8 8.1 11.9 13.6 12.8 8.9 5.5 2.0 0.6 0.2
0.2 0.7 4.6 6.8 10.0 11.4 10.6 7.3 4.4 1.6 0.4 0.1
0.7 1 .o 3.4 2.5 3.1 3.5 3.2 2.4 2.1 1.5 0.9 0.7
-0.5 -0.3 1.2 4.3 6.9 7.9 7.4 4.9 2.3 0.1 -0.5 -0.6
Year
70.2
58.1
25.0
33.1
10.2. Results of Calculations of Net Radiation at the Underlying Surface
673
from winter to summer is provoked by the more rapid increase of the absorbed global radiation than of the effective radiation. Although the net radiation in the Leningrad region is negative for six months, for the year as a whole it is positive on account of the higher positive totals in summer. Figure 10.5 shows the annual variation of monthly totals of the net radiation and its components for a number of sites in different climatic zones in Efimova’s estimation [37]. It is evident that the annual range of net CAPE CHELYUSKIN
DUDINKA
BATUMI
SVERDLOVSK
PARAMARIBO
-1-2----3---4
FIG. 10.5 Annual variation of monthly totals of the net radiation and its components in diferent climatic zones. (1) net I.adiation; (2) global radiation; (3) reflected radiation; (4) effective radiation.
674
Net Radiation
radiation usually has a maximum in June to July and a winter minimum. With increasing latitude the duration of the period of positive net radiation values becomes shorter. It is not always, however, that the net radiation has a simple annual cycle. In some cases the special features of the local climatic regime cause the “abnormal” annual variation of net radiation. For example, at Bombay (India) there is a “double” annual range of net radiation, with two maxima in May and October. The minima are observed in December and August. The appearance of the summer minimum is brought about by the increase of monsoon cloudiness at this time of the year, which provokes a considerable decrease in the incoming global radiation (in the preceding section we dealt with a similar case concerning Vladivostok). Interesting results are revealed in the comparison of the values of net radiation and global radiation. At the coast of the Arctic Ocean (Cape Chelyuskin) the annual net radiation of 6.7 kcal/cm2 yr is only about 10 percent of the yearly income of global radiation (63 kcal/cm2 yr). In tundra (Dudinka on the Yenisey near the Kara Sea) the portion of net radiation (17 kcal/cm2 yr) increases to 23 percent (the global radiation being 74 kcal/cm2 yr). An even greater increase of the relative net radiation is observed in the forest zone (Sverdlovsk) to 35 percent, that is, 30 and 86 kcal/cm2 yr. In humid subtropics (Batum) this ratio is 50 percent (64 and 129 kcal/cm2 yr), and in the zone of humid tropical forests (Paramaribo of South America) it is at its highest, about 60 percent (94 and 161 kcal/cm2 yr). The main factor bringing about the change of the relationship between the net and the global radiation is the albedo of the underlying surface (at Cape Chelyuskin of 61 percent and at Paramaribo 18 percent). The relation between the net and the global radiation serves as a spectacular index of the potential energetical possibilities of a given geographical area. For example, irrigation of desert can increase its net radiation by 60 to 70 percent. A still greater effect can’follow the melting of ice or snow in the Arctic. The above data are characteristic of the annual cycle of net radiation at different points of the continent. Table 10.9 gives the results of calculating the net radiation for the Atlantic Ocean and the White Sea, performed by Budyko et al. [38] and by Shiskho [39]. It is natural that the general form of the annual variation of net radiation at sea is the same as that of the inland (maximum in June to July, minimum in January to December). Kirillova [40] has given detailed study to the net radiation of small water basins. Having described in short the peculiarities of the annual variation of
10.2. Results of Calculations of Net Radiation at the Underlying Surface
?
s:
rn
m
I
: I
? 3
I N 3
N m
?
m
? m
? m
\9 3
m 0
I
: I
N I
rn
I
m 0
c
2
675
676
Net Radiation
net radiation at the ground, let us now turn to the examination of its geographical variability. One of the main features of the geographical distribution of net radiation totals is their relatively low latitudinal range in summer and winter and considerable differences during the transitional seasons. This is evident in Table 10.10, borrowed from Alisov et al. [41]. If, for example, the maximal difference between the winter totals of the net radiation is 1.7 kcal/cm2, the corresponding difference will be 16.3 TABLE 10.10 Seasonal and Annual Totals of Net Radiation for Diferent Points in the USSR (kcallcnP). After Alisov et a/. [41]
Place Ust Tzilma Syktyvkar Moscow Kiev Rostov-on-Don Guryev Range of variation
Latitude
Winter
Spring
Summer
Fall
Year
65'27' 61'40'
-7.0 -7.4
15.2 20.0
-6.1 -6 . 9 -5.7 -6.8
23.0 25.5 21.3 23.7 25.7 24.5
-1.7 -1.7
55'45' 50'24' 47'15' 36'01'
0.8 3.6 8.1 11.2 14.5 17.1
...
1.7
16.3
4.4
1.2 2.4 5.6 3.2
24.5 30.4 40.1 38.0
7.3
24.9
kcal/cm2 in spring. It is important that in winter or summer there is no regular variation of net radiation in dependence on latitude, whereas during the transitional seasons, particularly in spring, the net radiation clearly increases southward. The annual net radiation totals are therefore regularly increasing with decreasing latitude. The data of Table 10.10 relate to a relatively limited territory. In the case of vaster areas the winter totals of net radiation show a strong dependence on latitude. According to Sauberer and Dirmhirn [13, 141, in December the diurnal totals of the net radiation of oceans in the Northern Hemisphere vary from -I20 kal/cm2 at 60" to 260-300 kal/cm2 near the equator. Table 10.11 gives the results of calculations of the mean latitudinal distribution of annual net radiation totals for land, oceans, and the entire surface of the globe, obtained by Budyko et al. [38]. The data of Table 10.1I characterize the average distribution of annual net radiation totals over the latitudes. It is evident, however, that in actual fact these totals are also dependent on longitude as well. Let us therefore
10.2. Results of Calculations of Net Radiation at the Underlying Surface
677
turn to consideration of the geographical distribution of annual net radiation totals over the entire global territory. In recent years Soviet investigators were the first to carry out the calculations of the geographical distribution of the net radiation for vast territories and for the entire globe. Budyko et al. [Chapter 7, Ref. 34; 15, 241 have plotted maps of the geographical distribution of monthly and annual net radiation means for the earth as a whole. Figure 10.6 is a map compiled by Efimova [37] and describes the distribution of annual means. One’s attention is drawn by the “jumping” character of the variation of the net radiation in the transition from land to sea, which finds expression in the discontinuity of the isolines at the coastal area. This is due to the sharp change of the ground albedo, as the lesser ocean albedos usually lead to larger net radiation compared with continents. TABLE 10.11 Mean Latitudinal Distribution of Annual Net Radiation Totals over Land, Ocean, and the Earth as a Whole (kcal/cm2yr). After Budyko et al. (Chapter 7 [38]) Net Radiation
Latitude, ON
60-50 5040 40-30 30-20 20-10 10-0
Earth as a whole
1
Latitude,
Ocean
Land
Globe
34 54 78 100 110 107
23 38 56 64 74 79
28 46 69 86 101 101
46
68
77
OS
0-10 10-20 20-30 30-40 40-50 50-60
I 1
Net Radiation Ocean
Land
Globe
107 107 94 73 53 31
75 69 62 55 39 26
99 99
87 71 53 61
It is evident from Fig. 10.6 and Table 10.11 that the annual net radiation is positive over all the globe, varying from values close to zero in the central Arctic and 10 kcal/cm2 yr near the boundary of permanent ice t o 80 to 95 kcal/cm2 yr in tropical latitudes. This does not mean, however, that the annual totals cannot be negative. As has already been mentioned in the preceding section, negative totals may be expected in regions with stable or long-time ice or snow cover, that is, in certain Arctic or Antarctic areas. The distribution of the net radiation over the colder and warmer parts of the globe is roughly zonal (the underlying surface being relatively ho-
10.2. Results of Calculations of Net Radiation at the Underlying Surface
679
mogeneous through large areas in both summer and in winter). I n d r y continental regions (Sahara, deserts of central Asia, etc.) a considerable decrease of the net radiation is observed on account of the high albedo of desert and the great amount of the outgoing radiative heat due to the high desert surface temperatures. Reduced values of net radiation also occur in the monsoon areas and are caused by the increased cloudiness during the warm season. The highest values of the net radiation (over 140 kcal/cm2 yr) are observed in two areas of the Indian Ocean: to the east of the Arabian Peninsula and to the northwest of Australia. On land, the maximal net radiation of about 80 to 95 kcal/cm2 yr is observed in the regions with little cloud but sufficient humidity, such as savanna and evergreen tropical forests. Analysis of the maps of the geographical distribution of net radiation leads to the following conclusions: In January the net radiation is negative north of 45 to 47’N and positive over the rest of the earth (excluding Antarctic). The negative net radiation on land is smaller in absolute value (not more than 1 kcal/cm2 mo) than over the ocean (up to 4 kcal/cm2 mo) because the ocean surface has a higher temperature and loses more heat in radiation. To the south of these latitudes the positive net radiation increases as far as the equator, where it reaches about 8 to 12 kcal/cm2 mo. From the equator southward the net radiation at sea and inland varies little and is respectively 8 to 12 and 6 to 8 kcal/cm2 mo. In January and July the moderate latitudes of the Northern Hemisphere are characterized by a notable homogeneity of the net radiation fields, which accounts for the local formation of continental air masses. In the tropics and at the equator the distribution of net radiation is, on the contrary, rather “motley,” which is due first of all to the inhomogeneity of the geographical distribution of cloudiness. The zero isoline of the net radiation in July passes at 45 to 47’s. According to Sauberer and Dirmhirn [14], the maximal deviations of the geographical distribution of the net radiation of oceans from the zonal norm take place in June. For example, in the middle of the Pacific Ocean there is a sharp minimum of net radiation (240 cal/cm2 day), and in the region where the Gulf Stream originates there is a clear maximum of about 400 cal/cm2 day. The main features of the geographical distribution of the net radiation at sea in summer are determined by cloudiness. The position of the zero line of the net radiation in March is as follows: It passes through Eurasia from northwest to sutheast, through regions of southern Scandinavia, Lithuania, White Russia, northern Ukraine, Saratov region and northern Kazakhstan, and in East Asia passes roughly
680
Net Radiation
along the 48' N circle. In North America it passes through the lower current of the St. Lawrence river and in the west runs up northwards as far as 55'N. 10.3. The Net Radiation of Slopes The results discussed in the preceding sections reveal the regularities of the net radiation of horizontal surfaces. However, agricultural and other important applications demand information on the net radiation of slanting surfaces. In this connection the problem of the laws governing the net radiation of slopes becomes quite vital. Unfortunately, this problem has not been adequately investigated, although much work has been done with respect to the quantity of incoming direct solar and diffuse radiation to slopes and the effective radiation at slopes. The main results concerning incoming shortwave radiation were described in Chapters 5 and 8. The effective radiation on slopes was discussed in Sec. 9.7. Let us now examine some data on the net radiation of the slopes of a sand dune, obtained by Eisenstadt [2] from theoretical calculations based on the following considerations. Let us write the equation for the net radiation R,,of a slope:
where Ssl, DS1and riz are the fluxes of the direct solar diffuse and reflected radiation on the sloping surface, r is the flux of the shortwave radiation reflected from the slope, GSzis the flux of the atmospheric emission on the slope, G,,szis the flux of the emission reflected by the adjacent horizontal surface slopeward, UiUrfis the flux of the thermal radiation of the horizontal surface on the slope, and Us,is the thermal flux emitted by the slope itself. The quantity S,, in (10.8) can be calculated from the familiar equation S,,
= S,[cos
h, sin a cos(A - a )
+ sin h, cos a ]
(10.9)
where S , is the flux of solar radiation incident on the perpendicular to the rays surface, h, is the height of the sun, a is the angle of the slope, A is the azimuth of the sun, and a is the azimuth of the slope. In the considered case it is assumed that for the strewing sand, a = 135', a = 33', and for the windward side, A = 315', a = 16'. If we assume that the diffuse radiation and the radiation reflected by the adjacent horizontal surface and also the thermal radiation of the atmosphere
10.3. The Net Radiation of Slopes
68 1
and of the horizontal surface are isotropic, and that the temperature and optical properties of the slope and the horizontal surface are equal, the following equations for the net radiation components at the slope may easily be obtained (see Chapter 8): a 2 a riZ = r sin2 2 a G,I = Go C O S ~ 2
Dsl
= D COS' -
a G,,sl = (1 - 6 ) sin22 a Uiuri= Usurfsin22
where D, r, G o , Usurf are the fluxes of the diffuse radiation, reflected radiation, downward atmospheric emission, and self-emission for a horizontal surface. All these quantities can be directly measured. Also obvious is the validity of the formulas
where A is the albedo and Tszis the temperature of the slope. Making use of these formulas, Eisenstadt calculated the components of the net radiation of slopes and the net radiation as a whole from data of actinometric observations over a horizontal part on the top of a sand dune carried out on August 22, 1949. The results are summarized in Table 10.12. They should, of course, be treated as very approximate in view of the assumptions adopted. However, even such rough calculations disclose a number of interesting features of the net radiation of slopes. Examination of Table 10.12 shows that the greatest difference between the components of the net radiation for the slopes and the top occurs in the case of the direct solar radiation and the thermal radiation of the underlying surface (see quantities S,, and Us,). The differences of the other components are very small. This means that the peculiarities of the net radiation of slopes compared with a horizontal surface are determined first of all by the differences in the incoming direct solar radiation and the thermal emission of the sloping and horizontal surfaces. It is quite ob-
682
Net Radiation
vious that the difference in thermal emission is due to the difference in surface temperatures. The data of Table 10.12 make it also possible to analyze the special features of the diurnal variation of the net radiation of slopes. This variation is roughly symmetrical with respect to noon on top of the dune, and is considerably asymmetrical for both slopes. The maximum in the net radiation on the leeward side facing southeast takes place before noon (at about lO.OO), while on the windward slope it is observed after noon (at about 13.00). It is easily understandable that the earlier maximum on the leeward slope is caused by a great increase of the temperature of this surface directed to the sun and by the consequent increase in radiative heat loss. Since the steepness of the windward and of the leeward slopes is different, it is also possible to use Table 10.12 for evaluation of the effect of steepness on the peculiarities of the net radiation of slopes. For example, it can be seen that the net radiation of the steeper leeward slope is greater from that of the dune top than in the case of the windward slope. Chizhevskaya [42] measured the net radiation at the north and south slope of the gradient 12 to 17' at Voyeikovo near Leningrad. According to her observations, in spring and fall on clear days the net radiation of the south slope is by 15 percent larger than of the north one. In summer this difference reduces to 5 to 7 percent. Eisenstadt [43, 441 carried out similar measurements at the north, south, east, and west slopes of the Kumbel Pass (the Turkestan mountain range) with angles of 33, 31, 33, and 23O, respectively, and also at the horizontal surface of the ridge of the pass. The revealed differences in the net radiation of the oriented slopes were mainly due to the differences in their thermal emission. The net radiation at the south slope reached 1.01 cal/cm2 min, and at the north slope it was 0.36 cal/cm2 min, on the average. The asymmetry of the daily range of the net radiation at the east and west slopes was quite significant; for example, at 8 h, Rsl = 0.76 cal/cm2 min for the east slope and Rsl = 0 at the west slope. The daytime total of the net radiation of the south slope was by three times and the total during 24 h by 7.5 times greater than for the north slope. The daytime total for the west slope was somewhat larger than for the east, as the latter has a higher temperature during the day and consequently a more intensive radiative cooling. In order to investigate the regularities of the variation of net radiation, Kondratyev and Fedorova [Chapter 8, Refs. 5.9-551 carried out daytime measurements of the net radiation of differently oriented blackened surfaces by means of a ventilated Yanishevsky pyrgeometer. As the result,
TABLE
10.12
Net Radiation of Sloping Sand Dunes and of Horizontal Surfaces on the Top of a Sand Hill (callcm2min). After Eisenstadt and Zuyev [2]
Net Radiation and Its Components
Time, h
6
7
O.OO0 0.125 0.090 0.330 0.365 0.645 0.050 0.085 0.050 0.085 0.045 0.080 0.000 0.000 0.005 0.010 0.010 0.050 0.035 0.100 0.100 0.175 0.390 0.395 0.400 0.405 0.370 0.370 0.000 0.000 0.005 0.005 0.010 0.010 0.040 0.045 0.540 0.585 0.545 0.595 0.560 0.640 -0.100 -0.020 -0.040 0.125 0.170 0.340
8
9
10
11
12
13
14
0.355 0.600 0.940 0.110 0.110 0.100 0.005 0.015 0.015 0.170 0.250 0.470 0.480 0.440 0.000 0.005 0.010 0.050 0.635 0.670 0.730 0.200 0.350 0.570
0.585 0.850 1.165 0.120 0.120 0.110 0,005 0.020 0.170 0.220 0.310 0.515 0.525 0.485 0.000 0.005 0.015 0.055 0.685 0.735 0.830 0.385 0.540 0.700
0.785 1.045 1.305 0.125 0.125 0.115 0.005 0.025 0.220 0.280 0.345 0.565 0.575 0.530 0.000 0.005 0.015 0.060 0.740 0.800 0.925 0.535 0.665 0.770
0.955 1.210 1.350 0.135 0.140 0.130 0.005 0.025 0.265 0.325 0.360 0.535 0.545 0.500 0.000 0.005 0.015 0.060 0.790 0.820 0.995 0.590 0.750 0.715
1.050 1.230 1.275 0.130 0.135 0.125 0.005 0.025 0.285 0.325 0.340 0.560 0.570 0.525 0.000 0.005 0.015 0.060 0.840 0.845 1.025 0.635 0.765 0.650
0.090 1.185 1.090 0.140 0.145 0.135 0.005 0.025 0.295 0.320 0.300 0.600 0.510 0.560 0.000 0.005 0.015 0.060 0.860 0.840 1.005 0.695 0.780 0.570
0.990 1 .ooo 0.780 0.160 0.165 0.150 0.005 0.025 0.275 0.780 0.340 0.560 0.570 0.525 0.000 0.005 0.015 0.055 0.845 0.780 0.980 0.610 0.675 0.330
15
16
17
18
0.840 0.690 0.470 0.080 0.775 0.560 0.310 0.030 0.455 0.170 0.000 0.000 0.175 0.140 0.095 0.065 0.180 0.145 0.095 0.065 0.165 0.135 0.085 0.060 0.005 0.000 0.000 0.000 0.020 0.015 0.010 0.000 0.245 0.200 0.135 0.035 0.230 0.170 0.100 0.025 0.155 0.075 0.025 0.015 0.500 0.475 0.455 0.465 0.510 0.485 0.465 0.475 0.470 0.445 0.430 0.435 0.000 0.000 0.000 0.000 0.005 0.005 0.005 0.005 0.015 0.015 0.010 0.010 0.055 0.055 0.050 0.050 0.805 0.760 0.720 0.685 0.770 0.750 0.710 0.660 0.870 0.758 0.695 0.640 0.485 0.395 0.175 -0.100 0.465 0.270 0.070 -0.115 0.145 -0.035 -0.140 -0.105
Note. Subscript 1 denotes the windward slope, subscript 2 the leeward slope, while the quantities without index refer to the top of the dune.
684
Net Radiation
curves were plotted to represent the dependence of the ratio RslIRh of the net radiation for the slope and for a horizontal surface upon the angle of inclination and the orientation of the slope with various solar heights. Some of these curves are given in Figs. 10.7 and 10.8. As seen from these figures, with increasing height of the sun above the horizon, the dependence of the ratio Rsl/Rhupon surface azimuth becomes less important.
pw
200
a
FIG. 10.7 Dependence of the relative net radiation of the slope Rs,/Rh upon inclination and orientation. July 20, 1956, h, = 27O, yo = 268O, 16.53 h, clear, south-easterly wind of v = 1 mlsec.
For slopes facing the sun, the maximum of Rsl/Rhis observed at a of the order of 90' - h, , being most pronounced at low altitudes of the sun.
40
20 0
N In IU
qn LU
In JU
nn
-ru
cn JV
cn
w
-m
iu
on
ou
J
90
I
a
FIG. 10.8 Dependence of the relative net radiation of the dope Rsl/Rhupon inclination and orientation. June 20, 1956, h, = 66O,yo = 199O, 12.32 h, south-easterly wind, v = I mlsec, clear.
10.3. The Net Radiation of Slopes
685
The curves of Rsl/Rhfor slopes directed opposite to the sun have a minimum, and with certain a the net radiation of the slope is negative when the solar height is not too big. With increasing angle of inclination the net radiation passes through zero at such values of the angle when the direct solar radiation does not hit the sloping surface (a 2 A,). Steep slopes (a> 50') directed opposite to the sun again show positive values, apparently on account of the increasing flux of the reflected radiation to the slope and the reduction in the effective radiation. For slopes with azimuths 90' and 270' relative to the sun, a monotonic decrease of Rsl/Rh with increasing angle of inclination is observed (east and west slopes in Fig. 10.8). It is of interest that with low and moderate solar heights, slopes facing the sun have a far greater net radiation value than do horizontal surfaces. At high elevations of the sun (Fig. 10.8), when the angle of incidence of solar radiation is very large, the net radiation of any oriented surface is either the same or less (in the majority of cases) than that of the horizontal surface. Figure 10.9 gives the results of measurements of the net radiation with continuous cirrus clouds. It is eident from comparison of Figs. 10.7 and 10.9 that the azimuthal dependence of the net radiation in this case tells
I40
a
FIG. 10.9 Dependence of the relative net radiation of the slope RsllRh upon its angle of inclination and orientation. June 16, 1956, h, = 28O, yo = 269O, 16.49 h, cirrus cloud of force 10, south-easterly wind of v = I mlsec.
in a weaker degree than with a clear sky. It is also interesting that in Fig. 10.9 no zone of negative net radiation values appears to be connected with the increase of incoming diffuse radiation and decrease of effective radiation due to the effect of cloud.
686
Net Radiation
The above data are only roughly illustrative with respect to certain regularities of the net radiation of slopes. It should be stressed that there is an extreme need for experimental investigations of the net radiation of slopes and for the perfection of methods for calculating the components of this quantity.
10.4. Net Radiation and Its Components in a Free Atmosphere The boundary atmospheric layer, which is so effective in transforming the integral solar and longwave radiation fluxes, has a thickness of the order of 30 to 50 km. The regularities of the variation of radiant fluxes in the free atmosphere can therefore be investigated by means of instruments mounted on aircrafts, balloons, and rockets. Such investigations provide data on the vertical profiles of the net radiation and its components, which is particularly important in view of the interpretation of satellite measurement data on the outgoing radiation. A special feature of aircraft and balloon investigations is the facility they give in obtaining the information to be used with the purpose of checking the reliability of satellite measurements. Experiments in radiant fluxes in the free atmosphere by means of aircraft and balloons were begun as early as 30 years ago, but only during the past 10 to 15 years has it become possible to conduct them at a sufficiently high level of investigation. In this section we shall first consider the available measurement methods and their accuracy, and then discuss the results of the present investigations. 1. Peculiarities of the Use of the Standard Actinometric Instruments. The standard actinometric instruments mounted on aircraft and balloons were used for measuring radiant fluxes in the free atmosphere in a great number of research works [45-841. It is natural that the use of the standard instruments in such unusual conditions required special methods of measurement and processing, and also careful study of their characteristics with changing parameters of the medium. The most complicated turned out to be the problem of the use of pyranometers and balance meters for measuring global and net radiation. Important investigations of the methods applied in aircraft pyranometric measurements were carried out by Kastrov [51, 531 who had worked out a theory of pyranometers to be installed on aircraft. Omitting the standard corrections (angular, spectral, temperature dependence, etc. ; see
10.4. Net Radiation and Its Components in a Free Atmosphere
687
[Chapter 1, Ref. I]), let us consider only the special features of aircraft or balloon pyranometric measurements. The most important factor controlling the processing of the measurement data is in this case the nonhorizontality of the receiving surfaces. For the lower pyranometer, which measures the upward shortwave radiation flux, the departure of the receiving surface from the horizontal position is of no importance, since the angular distribution of the upward radiation may in the first approximation be considered isotropic. The readings of the upper pyranometer, however, whose receiving surface is exposed to the direct solar radiation as the main component of the global radiation with clear skies, are very sensitive to displacement from the horizontal. Let us assess, following Kastrov [54], how the nonhorizontality of the upper pyranometer affects the angle of incidence of solar radiation and how it changes computation. Let the axis 0.2(Fig. 10.10) correspond to the vertical direction and OZ’ be normal to the pyranometer receiving surface. The position of the sun in the sky is determined by the point M ; a is the azimuth of the plane OZD with respect to the solar vertical (the other designations are evident from the drawing or will be interpreted later on).
FIG. 10.10 The eflect of the nonhorizontality of the pyranometer’s receiving surface.
In the departure from the normal of the receiving surface by angle E relative to the vertical O Z , the solar radiation flux incident on the receiving surface will change by a quantity equal to S (cos (@‘ - cos lo). Here S is (the flux of solar radiation on the surface perpendicular to the rays)
68 8
Net Radiation
the normally incident flux of solar radiation, To is the solar zenith angle, and Cot is the angle of incidence of solar radiation on the receiving surface, defined by the relation
+ sin Co sin
cos lo’= cos Co cos E
E
cos a
When averaging over azimuth the mean error of measurement of the solar radiation flux on the horizontal surface will equal
=
If the angle
E
- S cos lo(l - cos
E)
=
E -2s sin2 cos 2
Co
(10.10)
is small, we have approximately AS’
= -&2 s c o s 50
2
(10.11)
Hence it is evident that the relative measurement error S’ is equal to 2 / 2 ; that is, it is independent of the solar zenith angle to. The obtained result is apparently valid also for the diffuse radiation propagating in a given direction, and therefore (10.1 1) can be easily generalized for evaluating the measurement error with the shortwave net radiation d(F+ - F f ) : E2
d(F4 - F J . )= - (FL - F f ) 2
(10.12)
where F+ and F f are the downward and the upward fluxes of shortwave radiation, respectively. Differentiating (10.12) along the vertical coordinate 2 and introducing the notation q = (d/dz)(FJ.- F f ) for the radiative heat influx, we obtain the following expression for the evaluation of the error in the determination of 9: &2
(10.13)
dq= - - q 2
The above formulas show that at insignificant disturbances of the horizontality of the receiving surface, the measurement error is not important. For example, even at E = 6’ the value (4)~~0.005; that is, the relative error is 0.5 percent. It is essential, however, that the above equations assume azimuthal averaging of the pyranometric readings. In the estimation of random errors from single records their values will be much greater, even at small angles E .
-
10.4. Net Radiation and Its Components in a Free Atmosphere
Let us assume, as before, that
E
= 6’
cos CO’ - cos 5‘0 cos C@
and C0
-
= 60’.
689
In this case
0.2
that is, the relative error will increase up to 20 percent. If To = 70°, the relative error is about 30 percent. At large solar zenith distances, therefore, and without the azimuthal averaging of measurement data (relative to the sun), the errors due to the nonhorizontality of the upper pyranometer receiving surface become very significant. That is why the practice of aircraft pyranometric measurements includes repeated taking of the pyranometric readings for the same “area” from two opposite flight directions; “the left-hand side sun” and “the right-hand side sun.” An even more complicated situation takes place when interpreting the results of measurements from balloons because this method cannot be realized there. In this case, however, the problem is alleviated by the balloon’s rotation around its vertical axis as it ascends. Lopukhin [56] compiled a table for the introduction of corrections for the nonhorizontality of the receiving surface in dependence upon solar height. When the horizontality of the pyranometer receiving surface is disturbed, its sighting field changes: instead of the sky section ABB‘C, the inclined upper pyranometer (Fig. 10.10) views the section AD‘DC positioned below the horizontal plane. The change of the sighting field of the lower instrument is similar. This naturally leads to distortion of the readings. Analyzing the measurement errors in this case, Kastrov [54] came to the conclusion that they are not essential. Aircraft or balloons always give rise to certain “perturbations” in the radiation field considered. In the case of aircraft pyranometric measurements it is more important to take account of the “underlighting” of the pyranometer due to the reflection of radiation from the aircraft surface. In Kastrov’s estimation [54] the errors appearing in this case are of secondary importance. With balloons, one must consider the shading of a portion of the sky the by casing. However, if the suspender, at the end of which the pyranometers are fixed, is long enough, the obliterating effect of the casing may be ignored. The usual purpose of aircraft or balloon measurements of the net radiation is to obtain data on its vertical profile and the components and also to determine the radiative flux divergence. It is natural that in order to obtain such data there are needed, strictly speaking, simultaneous actinometric measurements at different atmospheric levels above the given
690
Net Radiation
underlying surface. The net radiation B ( z ) is determined from the formula B(z) = F J ( z ) - F q z )
(10.14)
The radiative flux divergence q is further calculated from the relation q z - dB dz
(10.15)
derived on assumption of the horizontal optical homogeneity of the atmosphere and underlying surface. In reality, if the condition of the horizontal optical homogeneity is upset, the simultaneous measurements of radiant fluxes at different levels are practically impossible. This fact makes it necessary to solve the following two problems. The first problem is related to the need for evaluating the errors caused by the effect of the horizontal optical nonhomogeneity. Rough estimates of this kind were provided by Kastrov [51]. Suppose that the radiant fluxes are measured over a circular area with the albedo A’, which is surrounded by a surface whose albedo is A . Let the medium between the underlying surface and the level considered be vacuum. Designating 0 as the angle at which the radius r of the area is seen from the given level z, obtain the following relationship between the upward and downward radiant fluxes : F ~ ( z= ) F + ( z ) Asin28
+ F+(z)A’cos28
(10.16)
Further, it can easily be seen that the difference in net radiation at the levels z1 and z2 due to the “parasitic” influence of the horizontal nonhomogeneity of the underlying surface will equal d(z,, z2) = F + ( A - A ’ )
(
+ z22 - + z12 ) ‘12
r2
(10.17)
r2
The value d(z,, z 2 ) is the error sought. Since the radiation transformation by the intermediate layer can only smooth the optical contrasts of the underlying surface, the formula (10.17) gives the upper limit of the error considered. Making use of (10.17), Kastrov evaluated the errors appearing in the measurement of the shortwave net radiation for the case where the shiny snow cover of the Rybinskoye reservoir (near Moscow) with the albedo A = 0.82 was surrounded by a surface with almost melted snow (A’ = 0.27). These calculations showed that the effect of the horizontal optical nonhomogeneity of the underlying surface should be particularly
10.4. Net Radiation and Its Components in a Free Atmosphere
69 1
considered in processing measurement data at elevations above 1 km. In the case where the albedo of the investigated area is lower than that of the environment (reservoir in summer) the effect of the horizontal nonhomogeneity turned out to be insignificant. In the real conditions the horizontal optical nonhomogeneity of the underlying surface and atmosphere can be extremely variegated, which makes difficult the accounting of it in processing measurement data. It should be concluded therefore that the most reliable way to solve the problem of the vertical profile of the net radiation and radiative heat inflow consists in measurements over a homogeneous surface with a clear sky. When applying balloons the horizontal homogeneity must be checked by means of photographing the area considered. In the absence of the horizontal homogeneity the measured net radiation values have a narrow local meaning, and the determination of the radiative heat inflow from (10.15) is related to more or less marked errors whose quantitative evaluation is very difficult. The second problem to be solved when plotting the vertical net radiation profile from aircraft or balloon measurement data consists in the reduction of these data to a given moment of time. In the case of measuring the shortwave radiation fluxes, this problem is solved by using approximate empirical formulas that express the dependence of these fluxes upon solar height. For example, Faraponova and Kastrov [64] used the following formula:
Fl
=
So sin h,
=a-bfi
(10.18)
where So is the solar constant for the given day, h, is the solar height, m is the atmospheric mass in the direction to the sun, and a and b are constant, with b > 0 in the case of the downward and b < 0 in the case of the upward flux. The reduction of the results of measurements of the net radiation or longwave radiation fluxes to a given time presents a problem for which a method of solution is not clearly established. In the case of daytime net radiation measurements it appears to be possible to use empirical formulas similar to (10.18). For the longwave radiation fluxes, variability within 1.5 to 2 h is usually considered insignificant. The correct solution of the problem on the basis of theoretical calculations demands knowledge of the transformation of the vertical temperature and humidity profiles over relatively short time intervals (of the order of several hours), which cannot as yet be obtained.
692
Net Radiation
An important factor to be considered in processing the standard actinometric readings (of pyranometers and net radiometers used in aircraft or balloons) is their dependence on temperature and pressure. The calibration of the instruments in the thermobarochamber, imitating the real conditions of the vertical variation of temperature and pressure, should be taken as the simplest and most reliable. It is obvious that such an artificial “ascent” of the instrument can be accepted only as an approximate standard of atmospheric stratification. This is the kind of calibration that was used at the Chair of Atmospheric Physics of Leningrad University [67-721 in the preparation for balloon measurements. 2. Actinometric Radiosondes. It is obvious that the practical use of data on the net radiation and radiative flux divergence in the free atmosphere is possible only when a sufficient volume of the observational material is available. In this connection many recent attempts have been made to construct simple and light net radiometers that might be launched with the standard radiosondes. Such systems, consisting of standard radiosonde and radiometer, are called actinometric radiosondes. Since the problem of daytime net radiation measurements is very difficult and cannot be solved with the help of radiosonde-borne net radiometers, the latter instruments are used at present for nighttime soundings only. The instrument most widely used with actinometric radiosondes is the so-called economical radiometer of Suomi and Kuhn [84a-89], which will be later indentified as the Suomi net radiometer. This instrument has a multilayer system, schematically presented in Fig. 10.11. Here the surfaces
FIG. 10.11 The scheme of the Suomi net radiometer.
labeled P are polyethylene membranes of 12.7-,u thickness. The inside of the radiometer contains mailar membranes, M , of 6.4-p tnickness. The surfaces of the inner mylar membranes are faced with aluminum. The outer mylar membranes are receiving surfaces and are blackened from the outside and coated with aluminum inside. The polyethylene membranes
10.4. Net Radiation and Its Components in a Free Atmosphere
693
P serve as windshields. The instrument is not in vacuum, and the inside pressure therefore always equals the atmospheric pressure of the corresponding level. The curve T depicts the temperature profile of the net radiometer wall characteristic found for conditions of measurement in the middle troposphere. The casing Z is good thermal insulation. Figure 10.12 presents the outside appearance of the actinometric radiosonde. The net radiometer is Seen to be of triangular form. Note here that the board contacting the net radiometer is coated with aluminum. The
FIG. 10.12 Actinometric radiosonde.
+
vertical dimension of the net radiometer ( D 2 4 = 5.6 cm (the membranes P and A4 are at 0.7-cm distance) and the side of the triangle equals 30 cm. Direct measurement is made of the temperatures Tt and Tb of the receiving surfaces, for which temperature sensors are used. The readings of these sensors are transmitted to the ground in the same way as the readings of the standard air temperature sensor of the radiosonde system. The polyethylene light filters pass from 80 to 90 percent of the integral longwave radiation. The remainder (10 to 20 percent) is dispersed as 90 percent reflected and 10 percent absorbed by the polyethylene film. The latter means that the absorption of radiation can be practically ignored. The elementary theory of the net radiometer [87], based on approximate heat balance equations of the receiving surfaces, leads to the following
694
Net Radiation
expression for the net radiation (effective radiation) :
where u is the Stefan-Boltzmann constant, k = l/a(l - ar) (a = 0.85 is the absorptivity of the receiving surfaces, r = 0.16 is the reflectivity of the polyethylene membranes), ci = (I/D)ki(Tb- T t ) is the heat flux due to the molecular thermal conductivity of air (calculations show that the effect of convection can in this case be ignored), il = 5.10-3 cal/cm2 deg is the thermal capacity of the receiving surfaces, and En is the residual term characterizing the influence of secondary errors. Knowing the constant values of the given instrument, the net radiation sought can be easily determined from the measured Tb and Tt by means of (10.19). Since the receiving surfaces in the Suomi net radiometer are separated by thermal air insulation, it is natural that the temperature difference Tb - Tt is quite high, varying from several degrees near the earth’s surface to scores of degrees in the stratosphere. When deriving (10.19) a number of error sources were not taken into account, such as the radiation of the polyethylene filters and of the radiosonde’s casing, the leaking of air from the inside of the ascending net radiometer, the precipitation of white frost or moisture on the outer surfaces and inside the net radiometer, and the adiabatic air cooling inside the net radiometer in ascension. Calculations show, however, that the first two terms of (10.19) are roughly equal and by far exceed the other terms in the right-hand side of (10.19), whose value is not more than 10 percent of the main terms. It should be noted that almost all secondary factors tend to decrease the temperature difference Tb - Tt , which leads to a small systematic underestimation of the measured net radiation value. The ground testing and comparison of the Suomi net radiometer with other instruments [89] showed that this model may be considered quite reliable for nighttime measurements. It should be noted that the multilayer structure of the net radiometer greatly complicates the interpretation of the obtained results, owing primarily to two causes: First, as seen from (10.19), in processing the measurement data it is necessary to know the value ci characterizing the thermal flux from one receiving surface to another due to the molecular thermal conductivity. In (10.19) this flux is taken account of within the “one-dimensional” theory of thermal conductivity. It is obvious, however, that
10.4. Net Radiation and Its Components in a Free Atmosphere
695
the “side” heat fluxes in the horizontal direction can also be effective. Nor can the influence of the convection inside the net radiometer always be ignored, although its quantitative consideration is extremely difficult. Second, it is clear that the many layers of the net radiometer considerably increase its inertia, which is undesirable. Both unfavorable factors are practically eliminated in the net radiometer of the “disc” type, supplied with wind protection in the form of hemispherical polyethylene covers. It is known that with a disc net radiometer (for example the Yanishevsky type [Chapter 1, Ref. 21) adequately calibrated, there is direct proportionality between the net radiation and the temperature difference of the receiving surfaces, while the time constant can be made sufficiently low. From this standpoint the use of the disc net radiometer is preferable. All these considerations however, have little practical importance. The simultaneous balloon flight [90] of the Suomi and the disc types showed that the results reparted by not more than 2 percent. The ground comparisons of the Suomi net radiometer with the ventilated disc model by the same constructor showed that the ratio of their respective readings was 1.01029, with the mean quadratic deviation of 0.02017. The evaluation of the random errors in the net radiation measurements caused by the errors of the determination of the Suomi, type receiving surface temperature (assumed to equal 0.2OC) led to 0.0027 cal/cm2 min for the upper troposphere and stratosphere, and 0.0041 cal/cm2 min for the lower troposphere. This corresponds to the errors in the determination of the temperature variation in the layers of 50-mb thickness, equal to 0.45 and 0.68 deg/day, respectively. For 100-mb thicknesses these errors decrease by twice. Thus, as.can be judged from these data, the accuracy of measurements by means of the Suomi net radiometer is fairly satisfactory. A number of investigations offered modifications of the Suomi net radiometer. For example, Gayevsky [45] described a similar construction, repeating the pyrgeometer type (the “one-side” net radiometer). Kostianoy [76-781 used the principle of the “multilayer” net radiometer in constructing an actinometric radiosonde. Fritschen and Van Wijk [91, 921 constructed a miniature net radiometer whose receiving surface is a standard thermopile closed on both sides with coupled mica filters of 5-p thickness. The instrument has a cylindrical form of 2.54-cm diameter and about 0.5-cm height. The preference of mica to polyethylene as a filter was dictated by the desire to use the wind protection with steadfast water-repelling properties. However, mica has a strong absorption band in the interval 8.8 to 10.3 ,LA
696
Net Radiation
(where the filter transmission is zero) and a very low transmission in the interval 10.3 to 15 p. In this connection Fritschen [91] concluded that the filter should best be made of the polymer membrane Saran wrap (chemical composition not given). Pohl and Muller [93-961 measured the effective radiation with a miniature heated thermistor net radiometer, substituting it for the temperature sensor in the standard American radiosonde. The variation in the resistance of the thermistors caused by the variation in the effective radiation is used for the frequency modulation of the transmitted radio signal. This allows recording of the vertical variation of the effective radiation during the ascension of the radiosonde. Figure 10.13 presents the scheme of the Pohl net radiometer. As seen, it consists of two disc net radiometers whose receiving surface temperature is measured with the help of thermistors 1, 2, 3, 4. The receiving surface DOWNWARD RADIANT FLUX
U?WARO RADIANT FLUX
FIG. 10.13 The scheme of the Pohl net radiometer.
diameter is 3.9 cm. The upper receiving plate of one net radiometer and the lower of the other have electric heating, which generates H amount of heat in these plates. In order to secure an equal heat exchange between the receiving surfaces and the air, the net radiometer is rotated around its vertical axis in ascension. The fundamental theory of this instrument (see
10.4. Net Radiation and Its Components in a Free Atmosphere
697
[97]) gives the following expression for the net radiation (effective):
(10.20) I
where T I ,T2, T, , T4 are the temperatures of the receiving surfaces, and N is the corrective term for the selectivity of the receiving surfaces, the difference in ventilation of the upper and lower plates, and for the effect of their displacement from horizontal. The value N ’ does not exceed 10 percent of F. Since the directly measured values are the receiving surface temperatures and the strength of current in the heating coils, the accuracy of measurement is much dependent on the reliability of the determination of these quantities. With the accuracy of the temperature difference data of 0.2O and the error in the determination of the strength of current not over 2 percent, the total error in the effective radiation measurement is about 15 percent. An interesting model of net radiometer for the actinometric radiosonde was realized by Aagard [98, 991. His instrument, called by the author “a double radiometer,” consists of two discs (detectors A and B ) of 4-cm diameter and 0.5-mm thickness made by tightly coiling constantan wire insulated with epoxyde resin. The upward receiving surfaces are blackened, while the lower are aluminized and coated with thin quartz protection. The lower receiving surface of one disc is screened by an aluminum membrane positioned at 2-mm distance. The detector A operates in the pyrgeometric regime and serves for measuring the downward radiant fluxes. The deviations of the unscreened detector B are determined by the total of the upward and downward fiuxes. Its lower surface is striped black to keep it cooling even in the case when the radiative heat inflow is positive. In winter the entire receiving surface is blackened. Both detectors are self-compensating : The equality in temperature between the discs and the air is reached by passing the current through the constantan wire (the process of temperature equalization is automatic). Knowing the amount of the joule heat emitted in the discs and the air temperature, it is possible to determine the downward and upward radiant fluxes and their difference (the net radiation). The rough theory of the instrument expresses the net (effective) radiation as
1
+%A* (%+1-)
dT dil
(10.21)
698
Net Radiation
Here H A , HB are the generated heat in the detectors A and B due to heating, a, and a, are the emissivities of the upper receiving surfaces and of the lower surface of the detector By A , is the area of the receiving surfaces; and 1, T are the thermal capacity and temperature of the detectors. According to Aagard [98], the accuracy of measurement of the net radiation during the ascension is 20 percent, while during the horizontal drift the errors decrease to 3 percent. Businger and Kuhn [ 1001 performed simultaneous measurements of the atmospheric thermal radiation by means of the follownig four radiation detectors, launched on an automatic balloon up to the height of 25 km during the night of July 30, 1958, Madison, Wisconsin: (1) a Suomi net radiometer; (2) a disc radiometer with blackened upper and lower receiving surfaces (the resistance thermometer inside the disc measures the mean temperature of the upper and lower surfaces, characterizing the total of the radiant fluxes absorbed by both surfaces); (3) a black sphere; (4)a silver sphere blackened from the outside. In the latter two cases the measured value is the temperature of the black sphere. All the mentioned receiving surfaces are protected from wind by polyethylene film. If the intensity of the atmospheric thermal radiation as a function of the angle between the direction of the beam and the vertical Z(0) is changed for the effective temperature T@), determined from the relation (a/n)T,"(0) = I@), where (T is the Stefan-Boltzmann constant, then it is possible to express all the directly measured temperature values (of the black sphere, disc, or detectors of the net radiometer) in terms of Te(0). The results of measurements are therefore presented in the form of the curves of the vertical temperature distribution. If T,,Tb are the temperatures of the upper and lower surfaces of the net radiometer and Tdis the disc's temperature, then Td4= (1/2)(T: Tb4). The agreement of the measured values Tt, Tb, and Tdshowed that they fully satisfy this relation, and consequently the readings of the net radiometer and of the disc radiometer are in agreement. The temperatures of the black and of the silver spheres turned out to be unequal: in the lower zone of the sounded layer the black sphere is warmer, and in the upper, much colder than the black. The authors explain it by the effect of the convection inside the black sphere on the readings of the resistance thermometer inside the sphere. The net radiometer readings determine the vertical variation of the upward, downward, and effective fluxes of thermal radiation. These data are used to calculate the radiation temperature variations at different heights. The latter are compared with the temperature differences of the black sphere
+
10.4. Net Radiation and Its Components in a Free Atmosphere
699
and the air and also of the silver sphere and the air at the corresponding heights. There is found a similarity between the curves of the vertical distribution of the radiation temperature variations (radiative heat inflow) and the temperature difference of the black sphere and the air.
3. Special Instruments for Balloon and Aircraft Measurements. Since the standard pyranometers and actinometers have proved to be sufficiently reliable in measuring the shortwave radiation in the free atmosphere, up to now there was no great need to construct their special aircraft or balloon modifications. It is otherwise with net radiometers. We know that the errors of ground measurements of the net radiation by means of the standard Yanishevsky net radiometers are quite large. Their use for measuring the net radiation in the free atmosphere is made particularly difficult because in processing the obtained results it is necessary to introduce a correction for wind speed, which demands knowledge of this quantity (because wind currents are inevitably present in horizontal attitudes). For aircraft and balloon measurements (up to now realized during the night only) special net radiometers were constructed whose readings are free of the wind effect. Some of them, applied with actinometric radiosondes, have already been described. We shall now speak of other models used by aircraft or free balloon investigators on board the vehicles. Shliakhov [65] used a compensational Yanishevsky net radiometer to measure the effective radiation (the net radiation at night) from free balloons. The instrument imitates the double pyrgeometer, whose upper receiving lamina is electrically heated to the temperature at which the zero balance takes place. In the first approximation the measured net radiation is simply determined by the quantity of the joule heat generated in the lamina (that is, by strength of current passing through the plate). Investigations of the compensating net radiometer showed that its readings are much dependent on the regime of ventilation. In particular, the vertical ventilation can be greatly effective. If, however, the vertical speed of ascension is low (not more than 1 m/sec), the transfer factor of the instrument varies by not more than f 7 percent. In order to eliminate the varying effect of natural ventilation on the readings of the compensating net radiometer, in a number of flights Shliakhov used artificial ventilation with speed of 4 m/sec. When measuring the longwave radiation fluxes Shliakhov [65] also used his own design of a compensating pyrgeometer with higher sensitivity, resembling the “black shining” Angstrom type (see [l, 21). Depending on the sign of the net radiation the electric current is passed through the black
700
Net Radiation
or shiny (polished constantan) stripes for the purpose of equalizing their temperature by generating the joule heat. The rough theory of the instrument shows that the measured net radiation of the black stripes is directly proportional to the emitted joule heat (to the square of the strength of current). Since the readings of the compensating pyrgeometer depend on the regime of ventilation, a forced ventilation was used to “stabilize” its effect. Investigations showed that with the artificial horizontal ventilation of 3.8 m/sec speed and the vertical speeds of ascension not above 1.5 m/sec, the latter do not affect the results of measurements. It was found experimentally that in ventilating the pyrgeometer, the strength of compensation current must be increased. This means that the temperature of the shining stripes is higher than that of the black stripes. In this connection, to eliminate the wind effect in certain models of the pyrgeometer, Shliakhov also used a method of increasing the thermal resistance between the shining stripes and the connected thermojunctions. The empirical selection of thermal insulation practically allows complete avoidance of the influence of vertical ventilation. The evaluation of errors in the measurement of longwave radiation by means of the compensating net radiometer and pyrgeometer showed that they are never in excess of a few percent. The works of Gayevsky [45-48] described aircraft measurements of longwave radiation fluxes in daytime made with a radiation detector consisting of a linear thermopile assembled in a thick brass casing and supplied with fluoric calcium or KRS-5 filters. The main features of the thermopile are [44] : sensitivity 0.7 V/W; inertia, 3 sec; diameter of the receiving surface, 10 mm; resistance, 22 Q; sighting angle (aperture) 90’ (a later model [45] had an almost hemispherical sighting angle and slightly different parameters). The field and laboratory experiments showed that in this case the measurement errors were not above 0.01 cal/cm2 min. The instruments are fixed in the cockpit against the outlets in the ceiling and floor of the cabin. Since the filter transmits some shortwave radiation, special corrections were introduced to eliminate its “parasitic” effect. For this purpose the daytime measurements employed an auxiliary glass filter. The filter completely excluded the wind effect. The numerous calibrations of the instrument after the blackbody resealed the linearity of its scale in a wide temperature range. Houghton and Brewer [101, 1021, for aircraft measurements of thermal radiation fluxes, constructed a vacuum bolometer with a KRS-5 filter. Investigations showed that its readings were strongly dependent on the filter temperature. At small elevations this source of error is not influential.
10.4. Net Radiation and Its Components in a Free Atmosphere
70 1
The total measurement error varies from a few to 10 percent. The description of their aircraft investigations of the radiant fluxes can be found in [103-1071. The first complex actinometric observations from helicopter were realized by Malevsky-Malevich et al. [108-1101. The preceding discussion shows that only the technique of measuring the shortwave radiation and thermal radiant fluxes may be considered sufficiently refined. As to the net radiation measurement, up to now there have been no daytime attempts in the free atmosphere. The matter stands almost the same with respect to the direct solar radiation. In this connection recently there were first steps made in preparation of the complex automatic instruments for daytime balloon measurements of the net radiation and its components [67-721. The primary stage of such investigations was based on the standard actinometric instruments. 4. The Set of Automatic Instruments for Balloon Measurements of Net
Radiation and Its Components: General Features. These instruments enable continuous measurement and recording of the global, direct solar, and reflected radiation of the net radiation, the full upward and downward radiant fluxes, and also of the air temperature, humidity, and pressure of the temperature of the actinometric and recording instruments and the total ozone content. For measuring the global and reflected radiation two standard Yanishevsky pyranometers are used. The direct solar radiation is measured by means of a thermoelectrical actinometer automatically sighted on the sun with the help of a photoelectric system [I 111. The full upward and downward fluxes and the net radiation are measured by means of Yanishevsky and double net radiometers supplied with special windshields. The air temperature is taken by a platinum resistance thermometer, as is the temperature of the instruments. For measuring the pressure and humidity the respective sensors of the standard radiosonde are used. The ozone content is determined according to the spectroscopic method from the ozone absorption bands, in the ultraviolet spectrum.
Construction of the Instruments. The measurement of the direct solar radiation in a free atmosphere is made possible solely by continuous observation of the sun. The main features of the photoelectric watching system are the following: There is a sun-seeker with an all-round survey and three degrees of accuracy in targeting. The accuracy of the continuous watch is
702
Net Radiation
5 angular minutes. The weight of the installation without the power supply is 8 kg, the consumed capacity 20 W, the range of the working temperatures from -70' to +40°C. There are alternating-current amplifiers with transistors. The use of the standard net radiometer for balloon measurements was made possible only after providing special wind protection. The construction of the windshield is shown in Fig. 10.14. The receiving surfaces, 4
2
FIG. 10.14
The windshield of net radiometers.
10.4. Net Radiation and Its Components in a Free Atmosphere
703
and 5 , of the net radiometer are covered with two polyethylene hemispheres, 2, resting on the wire frames, 3. The rings, 1, press the hemispheres to the base of the framework. The testing of the instrument showed that this protection excludes almost completely the wind effect on the readings, and that the system receiving surface protection satisfies the Lambert law. The upward and downward radiant fluxes are measured by a double net radiometer consisting of two net radiometers positioned in parallel. The space between them is divided into three cavities. The middle one is meant for radiative separation of the upper and lower net radiometers. The side cavities are blackened inside, while the bottom temperature is taken with a platinum resistance thermometer. The net radiometers serve as covers for the intermediate cavities. The other receiving surfaces of the net radiometers are protected by polyethylene filters. The construction of the protection is similar to that of Fig. 10.14. Recording of Measurement Data. As has already been mentioned, the measurement of the radiant fluxes is continuous throughout the flight. The zero is fixed for each sensor regularly (every 36 sec) by disconnecting its circuit. The surrounding air temperature is also measured continuously. The platinum resistance thermometer intended for this measurement contacts the bridge scheme of the self-recorder. The other parameters are measured periodically at 36-sec intervals. All the data, except air temperature, are put on record at the tape of a 13-train oscillograph. The time marks are spaced at I-min intervals. The pressure and humidity are ciphered. Also taped are the train readings taken in the check up of their standard tension and sensitivity. Location of Actinometric Instruments of the Recording and Auxiliary Devices. The instruments are fixed to a frame made of duralumin tubes, and suspended by steel ropes and a strap, which increases the distance from the balloon casing to the center of the frame up to 100 m, thus practically eliminating the shading effect of the balloon. The length of the frame is 8 m (Fig. 10.15). The pyranometers, the net radiometer, and pyrgeometer are placed at the ends of the frame, as far as possible from the container with the recording instruments. The pyranometers are situated at the ends of a short-period pendulum fixed at the gimbals. The receiving surface of one is directed downward; of the other, upward. The pendulum period is about 0.3 sec. Such swings of low amplitude are insignificant for the pyranometers, whose time constant is about 20 sec. The net radiometer and pyrgeometer are stiffly fixed to the frame before the flight.
704
Net Radiation
The watching system with an actinometer and ozonometer is fixed at the cover of the thermoinsulating container positioned at the center of the frame (Fig. 10.15).
/-
FIG. 10.15 Arrangement of instruments on the suspension frame. (1) upper pyranometer; (2) lower pyranometer; (3) cloud photorecorder; (4) ozonometer; (5) actinometer; (6) orienting device; (7) radiosonde; (8) air temperature sensor; (9) net radiometers; (10) ozonometer; (1 1) tracking system.
Outside the container are placed the temperature, pressure, and air humidity sensors, and also an instrument for checking the horizontal plane of the frame and the angular height and position of the sun relative to the longitudinal frame axis. The latter instrument was found to be necessary when examining the actinometric recordings on the tape of the oscillograph. The slowly varying (in dependence on height) values of the global and net radiation were affected by periodical disturbances, with an alternating amplitude and periods of about 10 and 72 sec. The readings of this instrument not only enable determination of the cause for such disturbances but also permit introducing corrections to the readings of the upper pyranometer and net radiometer. Inside the thermoinsulating containter there are the recording devices, the program and order block, the amplifiers of the watching system, and the power source (anode batteries, accumulators).
5. Vertical Projile of Radiant Fluxes in the Free Atmosphere. Let us now give a short review of the results of measurement of the radiant fluxes in the free atmosphere. Consider first the more numerous data on the thermal radiation.
10.4. Net Radiation and Its Components in a Free Atmosphere
705
Thermal Radiation. In 1952-1954 Shliakhov [65] conducted a long series of nighttime balloon flights for the purpose of studying the vertical profile of the net radiation during the night. These measurements were realized by means of a special thermoelectric net radiometer and a pyrgeometer constructed by Shliakhov for balloon flights (the main features of the instruments have been given above). The observations were conducted at “platforms.” During the night the balloon managed from 4 to 6 “platforms” at 1-, 2-, 4-,6-, and 8-km elevations. Along with the actinometric measurements, meteorological observations were made and the measurement of the dust content by means of an impactor. According to Shliakhov, the net radiation F = F f - I;+ increases with height and at the highest elevation (8 km) reaches 0.346 cal/cm2 min. The effective radiation of the blackened receiving surface of the pyrgeometer (F‘ = oT4 - I;+, where T is the temperature of the receiving surface of the pyrgeometer) increases up to a certain level ( 5 to 6 km) and then begins to decrease. The comparison of the observed effective radiation with the values calculated from the Shekhter chart reveals a satisfactory agreement in the case where the effective water vapor mass necessary for the calculation of the radiant fluxes with the chart is made after the formula
dpz,
eZcand p is the absolute humidity and atmospheric where f ( p ) = pressure at the level z; and p o = 1000 mb. Observations show that the introduction of the effective water vapor mass, intended to account for the dependence of the absorption upon pressure, is quite important in the conditions of a free atmosphere. It should be noted, however, that the aircraft measurements by Gayevsky [45] showed that above 1 to 2 km the observed longwave radiation fluxes appeared to be by 15 percent more, on the average, than those computed with the help and that of the Shekhter chart (the correction for pressure f ( p ) = the departure of the computed values from the observed values increases with height. This conclusion was justified by the results of the actinometric radiosonde measurements obtained by Kostianoy [76]. It is therefore possible that Shliakhov’s data can be accounted for by the compensation of systematic errors in the calculation of the upward and downward thermal fluxes. Thus the problem of the actually justified form of the correction for the pressure cannot be considered clarified. Gayevsky’s data clearly show that the cause for the increase of the effective radiation with height is a
G),
706
Net Radiation
more rapid vertical decrease of the downward long-wave radiation flux rather than of the upward. Similar results are revealed in Lopukhin’s work [57]. Given in Table 10.13 are the ratios of the downward to upward fluxes with clear skies according to Lopukhin [57]. TABLE 10.13 Ratios of Downward to Upward FIuxes Pressure, mb: 966 FJ/Ff :
965
950
900
814
800
748
697
600
505
422
0.82 0.87 0.81 0.75 0.59 0.69 0.64 0.60 0.53 0.41 0.38
Shliakhov’s values of the radiative air cooling were from a few hundredths to 0.25 deg/h, which means that the corresponding quantities calculated from the Shekhter chart are in a good agreement with the experimental data. The measurements of the dust content at different heights, conducted by Shliakhov [65], showed it to be insignificant over all cases. The effect of dust on the longwave radiation absorption could not therefore be traced. The theoretical calculations confirmed the conclusion that during the night observations, the dust effect cannot be notable. The above investigations refer to the conditions of a clear sky. It is natural that with cloudy skies the vertical profile of the thermal radiation fluxes undergoes considerable transformation. For instance, according to the aircraft measurements of Lopukhin [58], the nighttime vertical increase of the net radiation is not so clear with overcast skies as without clouds. Inside the dense cloud cover of the lower level, as a rule there is the state of radiative equilibrium; the net radiation is either very small or zero. The last conclusion was justified by the results of aircraft measurements of longwave radiation fluxes obtained by Gayevsky [47]. Since near the cloud boundaries the observed vertical gradients of the longwave radiation fluxes are large, the radiative temperature variations, especially above the clouds, are greater than with clear skies. With net radiation in the region of lower clouds decreasing, observations indicate radiative heating in this area. At the upper cloud boundary a strong radiative cooling takes place. For example, Lopukhin [58] observed the radiative heating under the lower stratus clouds equal to 0.06 deg/h; and above the cloud tops, the cooling of 0.28 deg/h. The above results of aircraft and balloon measurements of the longwave radiation fluxes relate to comparatively small heights. Certain recent investigations have been busy with measuring the thermal radiation fluxes
10.4. Net Radiation and Its Components in a Free Atmosphere
707
at different atmospheric heights, including the stratosphere. They were realized mainly by means of actinometric radiosondes. The data on the stratosphere give some experimental information about the outgoing radiation. Kuhn et al. [112], for example, obtained the following thermal radiation flux values at 20 km on a clear summer night: F f = 0.36 cal/cm2 min, and FC = 0.04 cal/cm2 min. On a clear winter night at 12 km, F f = 0.27 and F J = 0.08 cal/cm2 min. The authors of [112] assume that the outgoing radiation Fm = F f - FC. On this assumption the experimental data for the outgoing radiation considerably depart from the theoretical calculation of the upward thermal radiation flux at the level of the tropopause. It appears that the assumption F, FT', where FTf is the upward thermal flux at the tropopause, should be considered better substantiated than the identification of the outgoing radiation with the flux difference F f - FC. This is justified not only by theoretical calculations but also by experiments. Actually, according to Kuhn et al. [112], in all cases F f F J . This means that the upward flux is only slightly transformed by the stratosphere and the difference F, - F t is clearly less than F J . In Kagan's estimation [113] the outgoing longwave radiation may be identified with the upward flux at the level of 100 mb. As given in [112], with a clear sky the observed effective radiation increases with height up to the stratosphere. It is natural though that the vertical gradient of the effective radiation should decreases as the height increases, especially in winter. For example, the actinometric radiosonde launched on February 17, 1958, showed that already in the layer 200 to 300 mb there is a radiative equilibrium (the vertical gradient of the effective radiation is zero). Kuhn and Suomi [114] published the results of 15 simultaneous launchings of actinometric radiosondes made at different points on the territory of the central and western United States on July 29, 1959. Thus the first experimental data characterizing the geographical variability of the outgoing radiation were obtained. At a later date similar results were derived by Kostianoy and Pakhomova [77] and by Kostianoy [115, 1161. The authors of [114] used two vertical cross sections to characterize the spatial distribution of the effective radiation flux F f - F J in the layer from the earth's surface to about 30 km elevation. Figure 10.16 gives a vertical cross section of the effective radiation field (expressed in hundredths of cal/cm2 min) for 0600 h of July, 1959 from Las Vegas to the International Falls (Minnesota). Analysis of the vertical sections shows that the effective radiation distribution near the ceiling of sounding is similar to the field of radiation in the
-
>
Net Radiation
708 km
FIG. 10.16
mb
Vertical cross section of the net radiation field (lo-$ calJcrnemin) between Yegas and I n t e ~ ~ ~ Fa& ~ o n~a~~ ~ n ~ s July o f a29,) ,1959, ~6~ h.
troposphere in that it is determined first of all by the rne~eorolo~cal regime of the troposphere. For example, the minimal effective radiation i s observed in the frontal region. The radiation field is found to be greatly variable at 25 to 30 krn elevation, depending on the type of air masses. With tropical sea air the mean value of the effective radiation at 25 km is 0.35 cal/cm2 mia. With conditions of a weak front, the measurements reveal a variation in
10.4. Net Radiation and Its Components in a Free Atmosphere
709
the effective radiation of 22 percent in the passage from one air mass to another. The maximal heat influx due to the longwave radiation occurs in the lower half of the troposphere. For the layer, for example, situated between the earth’s surface and the 400-mb level, the mean difference in effective radiation at the borderline is 0.20 cal/cm2 min, whereas the corresponding value for the layer from 400 to 15 mb is only 0.07 cal/cm2 min. Thus, about three-quarters of the total heat influx takes place in the tropospheric layer below 7 km. Figure 10.17 illustrates the data characterizing the vertical section of the radiative flux divergence (in cal/cm2min for a 100-mb layer) and clearly
SOUNDING POINTS
FIG. 10.17
cal/cm2min, for a Vertical cross section of the radiative divergence 100-mb layer) under the same conditions as in Fig. 10.16.
710
Net Radiation
shows the complexity of the spatial structure of the radiative heat inflow field. Here the regions of radiative cooling are marked C and those of heating are W . Staley and Kuhn [90] carried out two launchings of actinometric sondes in the area of intensive baroclynic zones in the middle troposphere. One of the ascents (April 5, 1958, southwestern United States) revealed an anomalous vertical profile of the effective radiation and the upward longwave radiant flux. Beginning from the upper boundary of the temperature inversion in the baroclynic zone to the ceiling of sounding (near 125 mb), the upward flux increases with height in spite of the monotonic decrease of the air temperature. Analysis of the possible causes for this abnormality shows that the most probable of them is the transfer of the radiosonde from the area obliterated by clouds to the cloudless atmosphere with a warm underlying surface. This justifies the importance of taking into account the horizontal nonhomogeneity of the atmosphere and underlying surface in the interpretation of the measurement data on the radiant fluxes in the free atmosphere. This also makes it possible to expect, in particular, that the results of measurements of the radiant fluxes from satellites and from balloons will be different. The calculation of the vertical profiles of the radiative temperature variations in both cases yielded quantitatively similar results. The obtained vertical dependences of the radiative temperature variations were sharply nonmonotonic with a transition from radiative cooling to heating in the baroclynic zones. The radiative cooling above and below these zones very from 0 to 4-5 deg/day. The radiative heating in the baroclynic zones is slightly less, but with a maximum of 4 deg/day. The curves of the vertical distribution of the radiative temperature variations at maximal height enables us to suppose that radiative heating occurs in the tropopause. The qualitative comparison of the experimental data with the results of theoretical calculations reveals a satisfactory agreement (except that the measurements do not show the radiative cooling at the upper inversion layer boundary predicted by theory). This may be explained by the low “resolving power” of the instruments, which does not allow detection of the radiative temperature variations in relatively thin atmospheric layers. According to 50 actinometric radiosoundings (with a Pohl net radiometer) performed by Ronicke [I171 at San Salvador (Central America) in different seasons, the mean vaules of the upward longwave radiation flux in the lower stratosphere is 0.35 cal/cm2 min in the dry season, 0.32 cal/cm2 min in the transitional period, and 0.29 cal/cm2 min during the rainy season. In all cases the observed effective radiation increased up to
10.4. Net Radiation and Its Components in a Free Atmosphere
71 1
about the tropopause and then slightly decreased with height in the lower stratosphere. According to the measurements of Fenn and Weickmann [97] in the Thule area (Greenland), made on February 14, 1959, the effective radiant flux at about 30-km height was approximately 0.16 cal/cm2 min. The vertical profile of the effective radiation is characterized by its increase with height from 0.05 cal/cm2 rnin at ground level to 0.20 cal/cm2 rnin within 15 to 20 km. Above 20 km the effective radiation was observed to decrease with height. Comparison of the results of these measurements with the above data for the intermediate latitudes shows that the Arctic values of the effective radiation are much smaller. It is obviously explained, in the main, by the low temperature of the underlying surface during the polar night. The actinometric radiosounding carried out by Muller [93], mostly in the cloudless conditions, showed, that on May 4, 1959 (18.21 to 20.20 GMT), the net longwave radiation increased from 0.075 cal/cm2 rnin at ground level to 0.315 cal/cm2 rnin at the height of 10.2 km (this level does not coincide with the minimal temperature level in the tropopause), then decreased to 0.195 cal/cm2 min at 13.75 km, and finally increased to 0.210 cal/cm2 rnin near 24 km. Comparison with the calculations from the Moller chart shows that the agreement in the troposphere is good but that the calculations do not reveal the inversion in the variation of the net longwave radiation in the stratosphere. The mean (over 46 launchings) vertical profile of the net radiation clearly demonstrates the above-mentioned inversion in the net radiation variation in the stratosphere. Analysis of the averaged profiles of the net longwave radiation relating to different circulation types showed that the minimal values of the outgoing radiation are observed with the zonal circulation ; the maximal, with the meridional. Mantis [118] studied the regularities in the variation of the outgoing radiation from measurement data on the temperature T R of a black sphere. The sounding with the black-sphere method showed that above 60 mb, the temperature TR had no vertical variation (the decrease with height of the downward longwave radiation flux in the stratosphere appears to be compensated by the increase of the upward flux). For the determination of the outgoing radiation it was therefore possible to use the following empirical formula F, = 2.12aTR4(50 mb) (10.22) where a is the Stefan-Boltzmann constant, and T R (50 mb) is the temperature of the black sphere at 50-mb level. Using this formula for the calcula-
712
Net Radiation
tion of F,, Mantis found out a strong decrease of the outgoing radiation connected with the increase in the upper cloud amount. Since the cirrus cloud has little effect on the incoming shortwave radiation, the net radiation of the system earth-atmosphere should therefore be expected to increase with the upper level clouds. With clear skies the outgoing radiation showed little variation, although the total water vapor content in a vertical column of atmosphere was greatly varying. The temperature dependence of the outgoing radiation was likewise weakly expressed. Three nighttime soundings at different places were used to plot charts of the isolines of the outgoing radiation over the eastern United States. These charts clearly show that cloudiness is the main factor that determines the variability of radiation. The latitudinal dependence of the outgoing radiation is characterized by a decrease northward. The obtained values of the outgoing radiation are in satisfactory agreement with the results of theoretical calculations. The averaging of all observational data gave a value of 0.345 cal/cm2 min. The mean effective radiation of the earth’s surface is 0.064 cal/cm2 min. Thus the heat loss due to the radiative cooling of the entire atmospheric thickness is 0.281 cal/cm2 min. The accuracy of these determinations is about 5 percent. Shortwave Radiation. Although the measurements of shortwave radiation fluxes in the free atmosphere are fairly numerous, all relate to relatively low heights. Since 1946-1947 the Central Aerological Observatory and then the Geophysical Observatory of Tashkent as well as some other local geophysical observatories (in Kiev, Minsk, Odessa) have been undertaking investigations of various elements of the net radiation in the free atmosphere, of the shortwave radiant fluxes above all. A great contribution to the development and direction of these studies was made by an outstanding Soviet specialists in actinometry and atmospheric optics, V. G. Kastrov, whose work dealt with the methods for measurements and with a number of important actinometric problems concerning the free atmosphere. The above research employed free balloons, automatic stratostats, and aircraft. The first stage of the investigations was devoted mainly to the vertical profiles of shortwave (global and reflected) radiation. Observations were usually conducted only during clear or almost clear days. The purpose of this research was to study the factors of the shortwave radiation attenuation in the atmosphere and to obtain information on the radiant heat inflow due to shortwave radiation at different atmospheric levels.
10.4. Net Radiation and Its Components in a Free Atmosphere
713
The applied instruments were standard actinometers used with surface measurements (pyranometers, actinometers, pyrheliometers). In the measurements from free balloons the pyranometers were fixed on gimbals and dropped from a cord at 50 to 70 m below the balloon cabin. The balloon ceiling was usually 7 to 9 km. The heights reached by aircraft varied from 3 to 6 km. In all cases along with the actinometric measurements recorded were the temperature, pressure, and humidity of the air. In 1953-1954 Piatovskaya [60, 61 ] conducted aircraft measurements of shortwave radiation fluxes up to 3 km, over various homogeneous surfaces with clear skies and with clouds of force 2, not more (Leningrad region). In the observation of the global radiation a standard Yanishevksy pyranometer was used. To measure the reflected radiation a special high sensitivity pyranometer was applied. The readings were taken at 200,500,1000,1500,2000,2500, and 3000 m. The technique of processing the readings was usually in combination with Kastrov’s method, which takes into account the peculiarities of aircraft actinometric measurements. According to [60], the global radiation almost always increases with height. Its decrease occurred only in the cases where the sun was obscured by cirrus clouds invisible to the eye. The gradient of the increase was in all cases decreasing with height, especially above 2 km. For example, in the layer 0 to 1 km it averaged 0.076 cal/cm2 min km, while for 2 to 3 km it decreased to 0.034 cal/cm2 min km. The dependence of the global radiation fluxes upon the altitude of the sun is in all cases nonlinear, The attenuation of the global radiation in the 0- to 3-km layer has an annual mean of 0.18 cal/cm2 min. The measurements of the reflected radiation (upward flux) were made above Lake Ladoga (Leningrad region) over all seasons and above a homogeneous area with crop planting (in winter a smooth snow field). The reflected radiation almost always increased with height, and its vertical profile depended upon the underlying surface type. As did global radiation, the reflected radiation showed a notable vertical increase only in the layer 1.5 to 2 km thick, above which it either rapidly slowed down or completely stopped. The vertical gradient of the reflected radiation was greatly variable. The maximal gradients were observed in the layer 1 to 2 km. For example, averaged over a year, the vertical gradient in this layer is 0.018 cal/cm2 min km, while in the underlying layer 0 to 1 km, it is 0.009 kal/cm2 min km and 0.008 kal/cm2 min km for the 2- to 3-km level. Calculations of the net shortwave radiation as a difference between the global and reflected radiation give, as a rule, an increase of the net radiation with height. The net radiation difference between two levels was used to
714
Net Radiation
calculate the shortwave radiation absorption by l-km layers. The absorbed radiation greatly varies in dependence upon season and decreases with height. For a year the absorbed radiation in the entire 0- to 3-km layer was, on the average, 0.135 cal/cm2 min. Calculations of the shortwave radiation absorption by water vapor from the Moller and Kastrov formulas showed that it decreased with height, and had a summer maximum and a winter minimum, averaging 0.042 cal/cm2 min for a year in the 0- to 3-km layer. The ratio of the measured absorbed radiation to that calculated by taking account of the absorption by water vapor only decreases with height. In the 0- to 3-km layer, its mean shows little seasonal variation, and the above ratio is, on the average, 3.2 for a year. The absorbed radiation values were used to calculate the radiative heating. Individual values of the radiative heating vary within a wide range from hundredths to 0.3 deg/h. Averaged over a year, the radiative heating is 0.1 deg/h in the 0- to 3-km layer. When calculated, taking into account the absorption by water vapor only, it was 0.03 deg/h. Interesting aircraft measurements of the shortwave radiation fluxes up to relatively high elevations (13 km) were carried out by Roach [119]. The data of these observations were processed to obtain the albedo and radiative heat inflow due to the absorption of shortwave radiation. Similarly to the above mentioned Soviet results, Roach found a considerable residual absorption of the shortwave radiation caused by aerosols. In atmospheric layers strongly polluted with aerosols, the radiative air heating can exceed 10 deg/day. Brewer and Wilson [120] have carried out measurements of solar ultraviolet radiation in a free atmosphere.
The Net Radiation and Its Components. Above has been described a set of automatic balloon instruments intended for daytime measurements of the net radiation and its components. Let us now consider some results of the balloon measurements, as given in [67-771. The daytime sounding with actionometric balloons up to 25 to 32 km was started in 1961. The data on the radiant flux profiles, obtained in 19611962 are summarized in [55, 681. We shall treat the results of 1963-1964 [71]. Knowledge of the radiant flux profiles makes it possible to study the energy transformation in the atmosphere, to find the seasonal peculiarities in the variation of the radiant fluxes, and to estimate the outgoing radiation. The gradients of the radiant fluxes enable calculation of the radiative flux divergence over each atmospheric component in the thermal regime. One of the soundings with a set of actinometric instruments was perfor-
715
10.4. Net Radiation and Its Components in a Free Atmosphere
med on October 23, 1964. The ascension took 2 h 30 min. The variation in the solar height during this period was 4' (from 26'21' to 22'36'). The area was exposed to the influence of a high-pressure ridge expanding over the eastern European territory of the U.S.S.R. in the zone of the washed out polar front that separated the continental temperature air from the continental tropical air. The branch of the Arctic front was near the polar. For this reason at some elevation there was observed a zone of close pressure isolines. It represented the stream flow passing from Tselinograd (North Kazakh, S.S.R.) to the southern Urals-Kuibyshev (on theVo1ga)Syktyvkar (on the N. Dvina). The launching was carried out in the outer anticyclonic area of the stream flow. Radiant Fluxes. Direct Solar Radiation S (Fig. 10.18). After the instruments were removed from the cloud at 1.9-km altitude, the actionometer was automatically targeted on the sun. The value S at this altitude was 1.22 cal/cm2 min. In the layer from 2 to 5 km, the solar radiation increased by a quantity AS = 0.35 cal/cm2 min. The increase of S then slowed down, but continued up to a height of 22 km, where S = 1.94 cal/cm2 min. Above 22 km, the flux of direct solar radiation was practically constant.
The Reflected Radiation Rk (Fig. 10.18). The ground value of the reflected radiation flux was 0.035 cal/cm2 min. It was the same up to the level of the continuous cloudiness (1 km).
Q
------ --___-__
-- _-__
6 18 20 22 24 26 28 H, km
FIG. 10.18
30
Q-R -R
B
32
Vertical profiles of net radiation and its components measured in the ascent on October 23, 1964.
716
Net Radiation
In the cloud layer, Rk increased with a gradient 0.086 cal/cm2 rnin km in the lower part, with 0.187 cal/cm2 rnin km in the middle, and with 0.16 cal/cm2 rnin km in the upper layer. The maximal value during the given flight was 0.5 cal/cm2 min. With increasing balloon elevation above the cloud the reflected radiation decreased of 0.3 cal/cm2 rnin at the heights over 24 km (h, = 23'). The fall of 0.05 cal/cm2 rnin at the very end of the ascension related to the discontinuity in the cloud underlying the balloon.
The Net Radiation B (Fig. 10.18). Two types of net radiometer with a polyethylene wind protection were used for measuring B with the usual Yanishevsky and a double net radiometers. The vertical profiles of the net radiation obtained by means of both instruments fully coincide, but the range of fluctuations of B as shown by the double net radiometer was probably due to the use of gimbals. The systematic deviation between the respective net radiation readings was 15 to 20 percent. Those of the usual net radiometer were taken to be the principal readings because it was calibrated in the wind channel, whereas the double net radiometer was calibrated with respect to the sun at the horizontal position of its receiving surface. The ground value of the net radiation was 0.125 cal/cm2 min and did not vary in the space below the cloud nor even up to the middle cloud level. At about 7 km there was a small minimum of 0.1 cal/cm2 min, while above this altitude the observed B gradually increased to 0.24 cal/cm2 rnin at 28.5 km, which can be explained mainly by the changing properties of the underliyng surface. The Albedo A (Fig. 10.19, curve 3). In the layer under the cloud the albedo varied from 18 to 20 percent. The " peak " albedo inside the cloud reached 85 percent, after which it showed a monotonic decrease. At 20 km its value was already 42 percent, remaining at that up to 27 km and then decreasing slowly (with a decrease in R k ) down to 35 percent at the level of 31.5 km. The decrease of the albedo over 27 km resulted from the change in the nature of the underlying surface (cloud conditions). The Global Radiation Q (Fig. 10.18). The global radiation value at ground level equaled 0.2 cal/cm2 min. In the layer below the cloud and in the lower cloud, Q was practically constant. It increased to 0.66 cal/cm2 min. closer to the upper cloud boundary and was equal to 0.65 cal/cm2 rnin above the cloud top. The variation of the global radiation flux in the layer from 2 to 6 km was by about 0.12 cal/cm2 min. From 8 to 20 km it increased only by 0.03 cal/cm2 min, which is explained by the increase of S and the vertical decrease of the diffuse radiation. Above 26 km, Q was slowly increasing.
10.4. Net Radiation and Its Components in a Free Atmosphere
717
The value of the global radiation at the level of the sounding ceiling (31.5 km) was fully determined by S' = S sin h, , that is, the contribution of the diffuse radiation was insignificant. A 100
90
80 70 60
$. 50 a 40
O'
2
4
6 8 10 I2 14 16 18 20 22 24 26 28 30 32H, km
FIG. 10.19 Vertical albedo profiles. (1,2) for clear weather; (3) for cloudiness.
Net Shortwave Radiation Q - Rk (Fig. 10.18). This flux was calculated from the profiles Q and R k and was characteristic of the shortwave radiation transfer. The values Q - Rk within the cloud and below fluctuate near 0.15 cal/cm2 min. Their minimum in the middle cloud was 0.08 cal/cm2 min. In the upper layer Q - Rk reached 0.18 cal/cm2 min, while closer to the upper cloud boundary it decreased to 0.14 cal/cm2 min. Above the cloud the variation of the net shortwave radiation is caused by the increase of Q (up to 10 km) and decrease of Rk (within 10 to 20 km). Analysis of the results of a number of soundings reveals some general regularities in the transformation of the radiant fluxes and the fields of the meteorological elements during the summer and fall periods. Let us consider the profiles of the net radiation and its main components typical of these seasons, obtained in the soundings of 1963-1964.
The Net Radiation with a summer homogeneous underlying surface is transformed chiefly in the troposphere (Fig. 10.20). A state close to radiative equilibrium was observed in the morning hours at the solar height h, = = 25 to 30' (curves 1,2). Here the dashes indicate a probable variation of the net radiation for a homogeneous underlying surface. In fall the profile of the net radiation is likewise little variable (curve 3). With solar heights
718
Net Radiation
25 to 30°, the change in the net radiation usually occurred only within the lower 5-km layer. The exceptions are the data corresponding to the curve 3. The increase of the net radiation in the 8- to 21-km layer from 0.1 to 0.24
0
2
FIG. 10.20 (1,2) summer, h,
4
6
8
-
10 12 14 16 18 20 22 24 26 28 30 32 H,km
Vertical profiles of net radiation for summer and autumn. (3) autumn, h, = 26'; (4) summer, h, = 58'.
= 26-30';
cal/cm2 min was related to the decrease of the global radiation (see Fig. 10.18). It should be noted that the profiles 1 to 3 are reduced to the fixed solar altitudes. The profile 3, for example, is reduced to 26'32'. The minimal net radiation was obtained at low altitudes of the sun and with snow cover in November ( B = 0.07 cal/cm2 min). The Direct Solar Radiation (Fig. 10.21) undergoes changes up to about 15 to 22 km. Its vertical profile depends on the content and vertical distribution of the attenuating components : water vapor and aerosol particles.
0.8 0.6
/ *
Figure 10.21 gives four profiles of the direct solar radiation plotted from the data for the summer (curves 1, 2, 3) and fall (curve 4) periods. The air masses whose attenuating properties are characterized by the considered profiles are essentially different with respect to the content of water vapor and aerosol particles. Curve 1 was plotted with a mean atmospheric mois-
10.4. Net Radiation and Its Components in a Free Atmosphere
719
ture content equal to 2.4 " cm " of precipitated water. Profile 2 refers to the air mass of the type " warm sea," with the moisture content of 4.7 cm of precipitated water. The profiles 3 and 4 correspond to 3.5 and 1.78 cm, respectively. The considerable turbidity of the troposphere was an almost constant peculiarity of the zone of sounding. The exception was the case where there was an air mass of high transparency (profile 1) above the layer of the continuous lower cloud. The aerosol layers in the lower atmosphere are usually situated at 1 to 2 and 3 to 5 km, which is indicated by the change in the inclination of the direct solar radiation profiles of these obtained at different solar altitudes in July (1963-1964). It should be noted that differences between individual profiles disappeared above 21 km. The difference between the fluxes of solar radiation near the ceiling of sounding for the summer and fall measurements is determined by the variation in the sun-earth distance. The solar radiation profiles obtained at the heights of the sun 55' to 60' were characterized by variation of S only within the troposphere (curves 1,2). A notable increase of the direct solar radiation at h, = 25' to 30' continued up to 21 km. Above that height the increase of S continued by about 0.007 cal/cm2 min km. The measured S at the peak point of sounding was 1.87 cal/cm2 min in summer and 1.97 cal/cm2 min in fall. Reducing these values to the mean sun-earth distance, we have 1.93 and 1.94 cal/cm2 min, respectively. The given S profiles were obtained with the use of new corrections for the effect of surrounding temperature on the readings of the actinometer. Laboratory investigations revealed that the temperature correction is very important and that the correction for the joint effect of temperature and pressure cannot be determined with sufficient accuracy. The value of the mean temperature correction to the sensitivity of the actinometer is 0.0875 percent per degree.
Global Radiation Q (Fig. 10.22). The global radiation fluxes obtained at the altitudes of the sun close to 30' (curves 2,3,4) undergo transformation practically only in the lower 10-km layer. In the 10- to 15-km layer the decrease in the diffuse radiation is compensated by an increase of the direct solar radiation, and in this layer Q remains constant. Above 15 km the global radiation slowly increases with a decreasing attenuating air mass. The contribution of the diffuse radiation above 16 km can be ignored. The vertical global radiation profiles 2, 3, 4 are reduced to the fixed solar altitudes. Profile 2, for example, is reduced to h, = 30°, the other two to h, = 26'10'. The difference of the global radiation fluxes in the stratosphere results from the inequality of the solar altitudes during the measurements.
720
Net Radiation
Profiles 1 and 4 were obtained with complete cloud at the heights 2 to 3 and 1 to 2 km, respectively.
L
,
.
0
2
4
8
6
10 12
14
16
18 20 22 24 26 28 3032-
Y km
FIG. 10.22 Vertical profiles of global radiation for summer and fall. (1) summer, h, = 60°; (2, 3) summer, h, = 26-30'; (4) fall, h, = 2 6 O .
Reflected Radiation Rk (Fig. 10.23). The reflected radiation fluxes with clear skies depend more on solar altitude than on cloud. For example, the close profiles 2, 4, and 5 were obtained at a clear sky, but the profile 2
0
2
4
6
8
10 12
14
16 18 20 22 2 4 26 28 30 32 H, km
FIG. 10.23 Vertical profiles of reflected shortwave radiation. (1) summer, h, = 5 8 O , Sc force 10; (2) summer, h, = 5 5 O , clear; (3) summer, h, = 53O, cloud of three layers; (4) summer, h, = 30°, clear; (5) summer, h, = 2S0, clear; (6) autumn, h, = 2 6 O , Sc force 10.
corresponds to h, = 56' to 60°, while the profiles 4, 5 correspond to h, = 30' to 35'. The profiles 1, 3, and 6, relating to the conditions of a cloudy sky, are notably different because the profiles 1 and 3 correspond to greater solar heights than does profile 6. With an increasing height the value Rk in the sounding zone for a clear sky increased by 20 to 25 percent, and
10.4. Net Radiation and Its Components in a Free Atmosphere
72 1
for an overcast sky increased by 30 to 40 percent above the cloud level. Near the upper cloud boundary, Rk reached 0.9 cal/cm2 min. This value appears to be the highest possible for the temperate latitudes. At ground level, Rk varied from 0.04 to 0.2 cal/cm2 min. Profile 3 characterizes the variation of Rkwith three level clouds. The decrease of Rk above 10 km resulted from the variation in the underlying clouds. The same factor influenced the variation of Rk near the ceiling of sounding in the case of curves 5 and 6. The Albedo (Fig. 10.19). The variation of albedo with height is represented by only three profiles, all obtained at h, = 25' to 35'. Profile 1 is typical of the summer season, although its values are slightly higher than the usual summer means. As to the strong variability of the albedo represented by curve 3, this, as has already been mentioned, is caused by the cloud effect. Radiative Flux Divergence. The set of measurements compiled for net radiation and its components made it possible to obtain detailed profiles of the shortwave and longwave radiant fluxes. The vertical profiles of the total shortwave and longwave net radiation were used to calculate the radiative flux divergence and also the radiation temperature variations for 50-mb layers.t At this point certain details of the profiles of the radiant fluxes related to the effect of the horizontal nonhomogeneity of the underlying surface were corrected. Figure 10.24 displays the vertical profiles of the
t
1
408
V
H. km
FIG. 10.24 Radiation temperature variations for 50-mb layers from measurements of the integral net radiation. (1,2) summer; (3) autumn. t Kostianoy has discussed possibilities of direct measurements of the radiative flux divergence in his work [121].
722
Net Radiation
radiation temperature variations calculated from the total net radiation. Profiles 1 and 2 determine (ar/at),&d for the morning hours (h, = 25' to 35') on a clear July day. Profile 3 refers to the noon (h, = 25') of October 23, 1964. As is evident, the profiles of the radiation temperature variations in the considered cases are very different, although there are some common features expressed in the transition from the zones of radiative heating to the zones of cooling. Since the vertical net radiation profile varies only slightly, the values (aT/at),&dare small (except profile 3, obtained with an anomalous variation of the net radiation) and fluctuate near zero (radiative equilibrium). In the 3- to E-km layer there occurred insignificant cooling of about 0.02 deg/h, while in the 8- to 28-km layer a tendency to heating was observed. Figures 10.25 and 10.26 present the vertical profiles of the 3
0.30
0.14 0.12 0.10 0.0 0.6 0.4 0.2
0.0 -0.02 -0,06t -0.10
I
0
1,II I$II
IIII
4 6
6
I0
12
I4
16
I6
20 22 24 26 28 30 32
H , km
-0.14
- 0 26
-0.30
FIG. 10.25 Radiative heating for 50-mb layers due to absorption of shortwave radiation. (1,2) summer; (3) autumn.
radiation temperature variations, calculated from the shortwave and longwave net radiation. Here the sharp variations of (aT/at),,, for profile 3 relating to a cloud layer should be noted. It should also be noted that the great variations of (ar/at),,d calculated from Q - Rk correspond to a notable variation of the opposite sign for (aT/at),&d,calculated from Blw. Thus, in the majority of cases, the marked radiative cooling due to the
10.4. Net Radiation and Its Components in a Free Atmosphere
723
longwave radiation relate to the atmospheric layers that strongly absorb shortwave radiation.
c 0 24 0 20 0 16 0 12
0 08 0.l -34
0 02
-0.02 -006 -010 -0.14
-0.18
-0.22
FIG. 10.26 Radiation temperature variation for 50-mb layers due to longwave radiation. (1) summer; (2) autumn.
As has already been mentioned, the total net radiation in the sounding zone varied little, especially at low solar altitudes. Therefore the effect of the nonhomogeneity of the underlying surface (for instance, the underlying cloud variation) would lead to a notable exaggeration or underestimation of the radiation temperature variations. Such distortions appear to have taken place for the case described by profile 3. For the profiles (b’T/b’t)rad calculated from Q - R, negative values were at times obtained. For example, during the measurements inside a cloud layer there were obtained considerable values of -0.26 deg/h (the cloud layer is dashed). Such results can be explained by two causes: (1) by the horizontal nonhomogeneity of the shortwave radiation field inside the cloud; (2) by the precipitation of moisture on the protecting covers of the instruments during the passage through clouds. Rocket Measurements. Recent years have seen the first steps in devoloping rocket methods for investigation of outgoing radiation. Kasatkin [1221 described the construction of a high-altitude optical
724
Net Radiation
station designed for complex investigations of the radiative field at great elevations, in a wide spectral region. The station was envisaged as comprising a great number of instruments, such as telephotometers, teleradiometers, telespectrometers, spectroanalyzers, and net radiometers. Liventzov et al. [I231 made a rocket radiometer for measuring the integral longwave outgoing radiation. The radiation detector of this instrument, based on the principle of differentiation (the outgoing radiation is measured as the difference in the radiation of the earth and space), is a bismuth bolometer. Table 10.14 gives the results of the measurements carried out by Liventzov et al. [123] in 1958-1961. For comparison (which should be considered only conditional) are also given certain theoretical calculations. The outgoing radiation values are expressed in watts per square meter and also through the effective temperature TOK. Although comparison of the results of measurements and calculations is conditional (the latter are of climatological nature), it may still be noted that the measured values are in all cases less than those calculated. Since 1958 Markov et al. [124, 1251 have been carrying out systematic investigations of the outgoing infrared radiation by means of rocket- and balloon-borne instruments. The angular distribution of the outgoing radiation intensity was measured from rockets in the 0.8- to 40-p spectral region at 100 to 400 km, and simultaneously in the atmospheric thickness up to 30 km from geophysical balloons (about 50 measurements in all). The angular resolving power of the instruments was 2 x rad. The authors of [I241 have made the following conclusions of their research: (1) The observed agreement between the results of measurements and calculations is satisfactory. (2) The contribution of the upper atmospheric layers to the outgoing radiation is considerably greater than it was supposed (the height of the radiating thickness in the atmosphere can reach 150 km, and the vertical distribution of contributions to the radiation takes place over the layers, in particular, for the 2.5- to 8-p spectral region over 280, 430, and 500 km). (3) The angular distribution of the outgoing radiation does not show any small-scale nonhomogeneities. (4) There is no marked daily variation in the angular distribution of the outgoing radiation (of chief importance are the meteorological conditions of the moment).
Recently [124, 126, 1271 detailed investigations of the angular and spectral distribution of the outgoing longwave radiation have been made. Using instruments mounted on geophysical rockets that were launched to 500
TABLE 10.14 Results of Rocket Measurements and Theoretical Calculations of the Integral Longwave Outgoing Radiation. Afrer Liventzov et a!. [123 1
Theoretical Calculations
Experiments Conditions of Measurement
Clear
~
1
Kondratyev Filipovich
1.2x1O2 216
2 . 2 ~ 1 0250 ~
Moderate cloud
...
...
Complete cloud
...
...
0 . 9 ~ 1 0200 ~
...
...
2.1 x102 248
1 . 4 ~ 1 0224 ~
...
.. .
1 . 8 ~ 1 0238 ~
470
200
200
20
16
15
Date
8/27/58
7110159
6/15/60
2/15/61
Moscow time
0.8, 0.6
0.4, 12
0.5, 42
Near noon
Elevation, km Mean ground temperature, O C
100
-2
Simpson
Bauer, Philipps
1 . 9 ~ 1 0242 ~
1 . 8 ~ 1 0238 ~
726
Net Radiation
km on November 18, 1962, and June 18, 1963, Markov et al. [124, 126, 1281 realized simultaneous measurements of the spectral composition (wavelength interval 4 to 38 p ) and angular distribution (range of angles f90’ relative to the nadir) of the outgoing radiation. The measurements were made during both upward and downward flight by means of an impulse infrared rocket spectrometer. The spectral resolution of the radiation was performed with the help of modulation filters that transmitted in the region of the absorption bands of the modulating materials (quartz, lithium fluoride, fluorite, and nontransparent metallic membrane). In this case the measured value was the difference in radiation between the earth and the modulator. Since the temperature of the modulator was not fixed, in order to check its constancy and also to take account of the “parasitic” radiation of the inlets and other optical elements, the radiation of the space in the direction close to horizontal (the radiation of space is assumed to be zero) was recorded as standard. The constancy of the sensitivity of the detectingamplifying scheme was achieved by calibration to the standard incandescent lamp. The use of filters allows reaching a spectral resolving power of the order of several microns. The channels of the spectrometer embrace the following wavelength intervals : 4.5-38, 12.5-38, 4.5-8.5 p. To increase the amount of energy reaching the instrument, a slit diaphragm with the side ratios of 1:lO or 1:30 was used with the minimal resolvable angle of 2 x rad. A low inertia bolometer served as a radiation detector. All joints of the instrument with moving details were hermeticized. The spectrometer was calibrated to the black radiators with the temperatures from 77 to 350’K. The sensitivity threshold in the flying conditions was 1.5 x 10” W/cm-2, which corresponds to the resolution with respect to the effective temperature of 2.7’K. The measurement data showed that in the range of 200 to 500 km heights, the shape of the angular distribution curves are little dependent on altitude. For wide spectral regions the angular distribution was close to isotropic and almost without small-scale fluctuations. In the narrow regions the outgoing radiation intensity fluctuations were much greater (up to 50 percent). In the majority of cases the maximum in the spectral radiation distribution was observed in the 4.5- to 8.5-,u region, with the effective temperature of 270 to 280’K, whereas in the transparency window it was about 240’K (the meteorological conditions were determined by variable cloud from 1 to 2 to 7 to 8 tenths, with the lower boundary from 1 to 7 km). Comparison of the effective temperatures with the real values at various
10.4. Net Radiation and Its Components in a Free Atmosphere
727
levels revealed that in the case of the integral radiation, the effective temperature corresponded to air temperature at the 6-km level. For the region of the water vapor absorption band (4.5 to 8 . 5 ~ this ) level was 20 km. However, the high effective temperatures should in this case be attributed to the fact that the source of radiation lay in the upper atmospheric layers. In this connection the intensive infrared radiation of the atmosphere, as observed by the authors of [124, 1261, is of greatest importance. With different conditions of investigation the intensive infrared radiation of the atmospheric layers was observed at 250 to 300, 420 to 450, and about 500 km. This radiation was concentrated mainly in the wavelength range of 2.5 to 8 p and in the part of the atmosphere illuminated by the sun. The radiant flux in the sighting along the tangent, when the ray’s path through the atmosphere extended over 1000 km, reached (3 to 7) x lo2 W m-’. The radiant intensity was increasing during the maximal solar activity. Careful analysis of the conditions of instrument functioning showed that the above conclusions are not affected by any measurement errors but are quite objective. Concerning the nature of the emission it is assumed in [I261 that it was due to the excitation by the corpuscular solar radiation of certain gas molecules contained in the ionosphere. One of these gases appears to be NO (in any case with respect to 280 km). Calculations showed that with the observed radiant intensity the effected temperature must be about 2000OK. In the given case, however, it is impossible to compare the effective and the kinetic temperatures in view of the absence of the state of thermodynamic equilibrium. Lebedinsky et al. [129] carried out measurements of the spectral composition of the outgoing thermal radiation in the wavelength range of 7 to 38 p by means of a diffraction scanning spectrometer mounted on the satellite “Cosmos 45” (206-km perigee, 327-km apogee, 65’ orbital angle of inclination). The terrestrial radiation in the direction of the nadir was measured as the difference with respect to the space radiation at the satellite level in the horizontal direction. The type of cloud underlying the satellite was determined photometrically by measuring the nadir radiance in the spectral region of 0.6 to 0.8 p (the spatial resolving power of the photometer was about 30 km). The infrared spectrophotometer consisted of two monochromators with plane reflecting diffraction gratings of 24 lines/mm (of 7- to 20-p wavelength) and 12 lines/mm (14 to 38 p). In the first wavelength range the spectral resolution was increasing with an increase in wavelength from 1.4 to 1.1 p ; in the second, it varied from 2.8 to 2.1 p. The instrument angle of
728
Net Radiation
sighting field was 1'46' x 2'20', which corresponds to a ground area of 75 km2 with a mean orbital altitude of 250 km. Radiation was detected by a bolometer with a 1 x 1 mm2 surface. The instrument was calibrated to blackbody characteristics. The duration of a complete measurement cycle was 81 sec. The readings were recorded on a 35-mm tape of the sixtrain oscillograph (container with the tape was landed). The operation of the instruments produced 2880 recordings. Typical curves of outgoing radiation spectral distribution with cloudy and clear skies clearly indicated the 9.6-,u ozone band and the 15-,u carbon dioxide band. The observed correlation between photometric readings and measurement data for the 8-7 to 12-,u transparency window was markedly negative, which reflects the opposite effect of clouds on the shortwave and the longwave outgoing radiation. A similar negative correlation was observed with the outgoing radiation of 18.5-,u wavelength. The effect of clouds was found to be considerable in all the studied intervals of the spectrum. This is due to the fact that the main contribution to the outgoing radiation of the considered wavelength range is made by the lower troposphere. The temporal variability of the radiation in the region of the 9.6-,u ozone absorption band was observed to be very great, which resulted from the variations of the ozone content in the atmosphere. It is supposed that the radiation in the 14.1-,u ozone band may greatly contribute to the outgoing radiation corresponding to this wavelength. Interesting spectral measurements of the infrared outgoing radiation were made by Band and Block [129a]. Many investigations (for example, [130-1321) were devoted measurements of the ultraviolet (solar and diffuse) radiation. Important information on the outgoing radiation in the 3.4- to 4.2-,u transparency window was obtained by means of a high-resolution infrared radiometer during the operation of the Nimbus I meteorological satellite (see [133]).
10.5. Climatology of Net Radiation of the Earth The first measurements of the net radiation of the atmosphere and the system earth-atmosphere (to be considered in the next section) are quite recent. For this reason various methods of their theoretical calculation are used in the determination of these quantities, particularly when the investigation is concerned with the climatology of the net radiation. We shall consider later some results of such theoretical calculations, mainly following the works [134-1411.
10.5. Climatology of Net Radiation of the Earth
729
1. Net Radiation of the Atmosphere. Equation (10.2), which determines the atmospheric net radiation, contains three components : the effective radiation F,, the outgoing radiation F,, and the solar radiation absorbed by the atmosphere, 4'. Calculations and observations show that the latter value. is much smaller than the other components. The atmospheric net radiation is therefore determined mainly by the thermal radiative influx I;, - F,. It is easy to see that, on the average, F,, < Fm , and consequently the atmospheric net radiation is negative. This is due to the fact that the atmosphere absorbs only the earth's thermal radiation (and considerably less so the solar radiation), while its emission is directed toward the earth's surface and toward space. Kondratyev and Dyachenko [1351 calculated the longwave net radiation of the atmosphere as Fa = F,, - F,, which made possible the plotting of charts to show its geographical distribution (the given longwave radiation values are absolute throughout the section). For these charts the data of 260 points (165 continental and 95 maritime) equally spaced over the earth's surface were used. The polar latitudes (over 80" N and 70" S ) and high altitudes were not considered because of the lack of a necessary amount of data. The total area of the investigated surface is 460.1 million km2 out of the earth's 510 million km2. The isolines of the chart of the distribution of the annual longwave net radiation totals are plotted at 20 kcal/cm2. The monthly isolines have a 2 kcal/cm2 spacing. The work [135] gives a map of the distribution of the annual totals of the atmospheric longwave net radiation (Fig. 10.27) and 12 monthly charts. It follows from considerations of the charts that the field of the atmospheric longwave net radiation is farly homogeneous, with a small range of the monthly and even the annual totals variation. The considered values show a monotonic increase from the poles equatorward in all the charts. Analysis of the chart of the annual longwave net radiation totals (Fig. 10.27) reveals that these totals vary from less than 100 kcal/cm2 yr in the polar latitudes to 160 kcal/cm2 yr at the equator. The isolines are mostly in the latitudinal direction. At the sea-continent border, discontinuities of the isolines result from the horizontal nonhomogeneity of the temperature field. A certain break of zonality in the variation of the isolines is observed over cold and warm ocean currents. With the cold currents the longwave net radiation of the atmosphere Fa decreases. This occurs, for example, over the cold Peruvian current or above the currents caused by the westerlies near the southwestern coasts of Australia. The warm currents are connected
730
Net Radiation
10.5. Climatology of Net Radiation of the Earth
731
with an increase in the longwave net radiation totals. Such an increase is observed over the warm Gulf Stream, over a branch of the northern Pacific ocean current, and over the warm currents in the Indian ocean. These data reveal a possibility of satellite detection of ocean currents, since the fields of the outgoing radiation and radiative flux divergence in the atmosphere indicate their presence. The great ocean area of the Southern hemisphere and the position of the thermal equator north of the geographical borderline causes the mean heat inflow to the atmosphere of the Southern hemisphere to be larger than that of the Northern hemisphere. The maximal longwave net radiation of 140 to 160 kcal/cm2 yr takes place over the warm equatorial currents with a frequent recurrence of clouds. The absolute maximum in the longwave radiative heat influx to the atmosphere was observed over the Pacific Ocean and equaled 163 kcal/cm2 yr. Comparison of the geographical distribution charts for the longwave net radiation of the atmosphere, F,, with analogous charts for the outgoing radiation F, and for the effective radiation of the underlying surface, Fo ,shows that the distribution of the longwave net radiation over the ocean is largely determined by the influence of the outgoing radiation. On continents the longwave radiation is determined by the effective radiation of the earth’s surface. In this connection it should be noted that the minimal F, values are related to deserts, where the observed effective radiation of the surface, Fo ,is at its highest (due to the high temperatures, low atmospheric moisture content, and insignificant cloud). For example, in the Northern hemisphere a notable decrease of the annual totals, F, , was observed in the deserts of North Africa and Arabia, where F, was less than 120 kcal/cm2 yr. In the Southern hemisphere the longwave net radiation was observed to decrease considerably over the Great Sandy Desert of Australia and over the deserts of South Africa. The absolute minimum was noted over the Kalahari desert (South Africa), with F, less than 100 kcal/cm2 yr. The mean atmospheric longwave net radiation for the globe is 131.5 kcal/cm2 yr (Table 10.15). The mean continental value is 119.0 kcal/cm2 yr, and the maritime is 136.0 kcal/cm2 yr. These values were calculated with account taken of the fact that the land and the sea areas are 29 and 71 percent of the globe, respectively. The authors of [I351 also obtained the annual totals of the atmospheric longwave net radiation for different latitudinal zones (Table 10.15). In their determination the sea-land proportionality for each latitudinal belt was taken into account. The mean annual total for a zone was calculated
732
Net Radiation
from the formula
where S is the total zonal area, S, and S, are the respective area of land and sea, and (Fa)L and (Fa)sare the atmospheric longwave net radiation over land and sea, respectively. The analysis of Table 10.15 shows that the longwave radiative heat inflow for the whole atmospheric thickness increases from the poles equatorwards. Note here that the mean net radiation for the Southern hemisphere is slightly larger than for the Northern hemisphere. This is due to the great ocean area of the former. Let us now characterize the results of the analysis of the monthly distribution charts of the atmospheric longwave net radiation (Figs. 10.28 and 10.29 give the January and July maps). The monthly maps of the longwave net radiation distribution are to some degree similar to the annual charts. In winter the Northern hemisphere has a clear minimum of F, in the area of the Siberian anticyclone, while the Gulf Stream somewhat increases the heat inflow to the atmosphere of the North Atlantic region. The tropical maxima slightly displace from season to season. In summer they are observed near the tropics; in winter, closer to the equator. From the consideration of these maps it is possible to state that the maximal absolute values of the monthly totals Fa occur over the equatorial ocean. In July the maximum of the heat inflow displaces north of the equator and is more than 12 kcal/cm2 mo(in the Pacificocean more than 13 kcal/cm2 mo). A reverse picture is observed in January. The F, maxima displace from the equator southward and exceed 12 kcal/cm2 mo (13 kcal/cm2 mo in the Pacific Ocean). Further analysis of the monthly charts shows that the maxima in the longwave radiative heat inflow to the atmosphere in this case are also connected with the maximal outgoing radiation (F, N 16 kcal/cm2 mo) observed over ocean. This is evident from the comparison of the above charts and also from a graph of the dependence of the atmospheric longwave net radiation on the outgoing radiation plotted for oceans (Fig. 10.30). The relationship is farly close and linear. The correlation coefficient r = 0.94. The effective radiation of the surface appears to have little influence on the radiative heat inflow to the atmosphere over the ocean. This is explained by the fact that the maritime Fa values are little variable and relatively small (3 to 4 kcal/cm2 mo) as compared with F,.
TABLE 10.15 Mean Latitudinal Values Fa (kcal/cm2yr). Afrer Kondratyev and Dyachenko [135]
Latitude, deg
90-80 80-70 70-60 60-50 5040 40-30 30-20 20-10 10-0 0-10 10-20 20-30 3040 40-50 50-60 60-70 70-80 80-90 From 80' N lat. to 70" S lat.
Land Area,
Sea Area,
Total Zonal Area, mln (lo6) km2
%
%
10 29 72 57 52 43 38 26 23 24 22 23 12 3 1 10 78
90 71 28 43 48 57 62 74 77 76 78 77 88 97 99 90 22
3.9 11.6 18.9 25.6 31.5 36.4 40.2 42.8 44.1 44.1 42.8 40.2 36.4 31.5 25.6 18.9 11.6 3.9
71
460.1
119.0
Mean Zonal
Mean
Mean
Fa
Fo
over Land, kcal/cm2 yr
over Sca, kcal/cm2 yr
kcal/cm2 yr
115 114 112 110 119 126 132 131 131 113 111 114 118
118 121 120 129 139 150 150 151 147 135 127 125 120
116 117 116 121 131 144 146 146 144 130 125 124 120
136.0
131.5
Fa
C Fa Zonal, kcal/cm2 yr
L
0 01
111 21.9 x 1OI8 30.0 x 1OI8 36.6 x los8 44.1 x 10'8 52.7 x 1Ol8 61.7 x 1OI8 64.5 x 10'8 64.5 x los8 61.7 X 1Ol8 52.3 x lor8 45.6 x 39.1 x 1Ol8 30.8 x 1Ol8
s z z
s
w
4
w w
FIG. 10.28 Geographical distribution of monthly totals of the atmospheric longwave budget, January.
10.5. Climatology of Net Radiation of the Earth
736
Net Radiation
..
.... . ..... ... .... .
.. . . :.: .
.. ... ...:....... .... .. .
. ...
i
*
e
1301~~
120
110
130
140
150
160
FIG. 10.30 Dependence between the longwave budget and the outgoing radiation.
The continental Fa values are strongly affected by the effective radiation of the earth's surface, whose influence becomes less only with a complete low cloud cover. In this case the temperatures of the earth's surface and the lower cloud boundary are equalized, which leads to almost zero values of the effective radiation. The relationship between the atmospheric longwave net radiation, Fa, and the continental outgoing radiation F, is not simple. Let us consider the graphs of Fig. 10.31 for the purpose of analyzing the annual variation in the atmospheric longwave net radiation. The presented
(0)
Fig. 10.31
737
I............ I I U P r n I x x I
-
MONTH (d 1
7
I
mnnrrIxxI month
(e 1
t
13
7 1 . . . . . . . - - . . -
r m s ! m l x s I
&
MONTH (9)
FIG. 10.31 Annual variation of the longwave net radiation in different landscape and climatic zones.
(a) tundra [(l) Amderma, Siberian Arctic; (2) Cape Barrow]; (b) forest of the temperate latitudes [(l) Sverdlovsk, (2) Forth Nelson]; (c) wooded steppe and forest of the temperate latitudes [(l) Rostov-on-Don, (2) El Passo]; (d) arid zones of the subtropical latitudes and the Mediterranean area [(l) Tashkent, (2) Rome]; (e) region of subequatorial monsoons [(l) Fort Larni, (2) Calcutta]; (f) tropical deserts [(I) Vadi Halfa, (2) Alice Springs]; (g) equatorial climate of the tropical forests [(l) Sao Gabriel, (2) Batavia, (3) Singapore].
738
Net Radiation
curves depict the annual variation of Fa with different climatological and local features. To secure direct comparison of Fa and F, throughout the year, the selected points were coincident or close climatologically to those used in the work of Yefimova and Strokina [37]. It is evident from the consideration of Fig. 10.31 that the annual variation of the atmospheric longwave net radiation in tundra has a May and September maxima of 10.5 kcal/cm2 mo at Amderma (Siberian Arctic) and 9.5 kcal/cm2 mo at Point Barrow (N. Alaska). These maxima are due to a considerable cloud amount and the resulting low F, values. During the warm period the observed minimum is fairly deep (9.0 to 9.2 kcal/ cm2 mo) and is due to the maximal F,. Figure 10.31(b) presents the annual variation of the longwave net radiation for the wooded area of the temperature latitudes. The curves are rather smooth, with a summer maximum of 10.2 to 10.5 and a winter minimum of 8.7 to 9.0 kcal/cm2 mo. In the zone of wooded steppe, and the steppe presented in Fig. 10.31(c), the quantity considered has a deep spring minimum (at Rostov-on-Don, 9.1 kcal/cm2 mo; at El Paso, 8.0 kcal/cm2 mo). This period is characterized by large effective radiation values. In early summer (June and July) a maximum Fa is observed (9.7 to 10.2 kcal/cm2 mo). The atmospheric longwave net radiation decreases notably closer toward fall. Figure 10.31(d) gives the curves of the annual Fa variation for the dry areas of the temperate latitudes (Tashkent) and for the Mediterranean (Rome). The annual variation of Fa is here quite great, with a range of about 2 kcal/cm2 mo. The minimum Fa occurs in summer and is due to the high values of the effective radiation of the earth’s surface, resulting from hot and cloudless weather. The great monthly F, totals in the dry temperate zones are caused by the high temperatures and the presence of cloud. A similar increase of Fa in the Mediterranean follows the considarable cloud amount and increased humidity during winter. In the dry temperate zone (Tashkent) the maximal Fa is observed in spring, with low F, and high F, values. In summer there is a minimum of Fa due to the maximal F,, though in this period the outgoing radiation F, exceeds 16 kcal/cm2 mo. Returning to the analysis of the charts of the longwave net radiation geographical distribution, we note that in deserts (Sahara, Kalahari, Arabian) the January Fa values are fairly large (6 to 8 kcal/cm2 mo), which can be accounted for by the high temperatures and little cloud. The F, values here are small, with minima less than 10 kcal/cm2 mo (less than 8 kcal/cm2 mo in Australia).
739
10.5. Climatology of Net Radiation of the Earth
In the Northern hemisphere, in America as well as in Eurasia, the longwave net radiation of the atmosphere in January is little variable, with a range from 9 to 10 kcal/cm2 mo, lowering to about 8 kcal/cm2 mo only in the area of the Siberian anticyclone. This Fa minimum is the result of the great cooling of the underlying surface, which causes the outgoing radiation to fall to 10 kcal/cm2 mo. In July in Eurasia there is a washed-out field of the atmospheric longwave net radiation. In the high latitudes (behind the Artic Circle), Fais of the order of 9 kcal/cm2 mo. The rest of the continent has Fa less than 10 kcal/cm2 mo. In North America at the same latitudes, Fa has the same values. The exception is the Arctic regions, where Fa is about 8 to 9 kcal/cm2 mo. In the zone of deserts and semideserts the minimal F, of less than 10 kcal/ cm2 mo are observed in July, which is caused by the high effective radiation. The areas of the equatorial monsoons are presented in Fig. 10.31(e). We see a considerable range of the annual F, variation. The maxima of Fa are observed in fall (11.8 to 12.6 kcal/cm2) and the minima in winter (9.2 to 9.6 kcal/cm2 mo). A small-range annual variation of Fa takes place in the tropical deserts (see Fig. 10.31(f)). In African deserts Fa is 9.0 to 10.5 kcal/cm2, while in Australian deserts, it is somewhat lower (8.5 to 9.0 kcal/cm2 mo). Figure 10.31 (g) displays the curves of the annual variation of the quantity considered for areas with the climate of the equatorial tropical woods, where the cloud amount is significant and humidity high. The range of Fa here is smooth throughout the year, with large values of the order of 11.0 kcal/cm2 mo (San Gabriel, California). On the islands of the same climatic zone (Batavia and Singapore) the variation of F, has a large amplitude of the order of 1.0 to 1.5 kcal/cm2 mo. Calculations of the shortwave (incoming) component of the atmospheric net radiation are rather few, which results in limited information for the total net radiation of the atmosphere. This subject has been given most detailed treatment by Vinnikov [142]. According to Budyko (137), the latitudinal distribution of the annual atmospheric net radiation totals in the Northern hemisphere is characterized by the following values: Latitude, deg:
0-10
R, , kcal/cm2yr :
-56
10-20 20-30
-54
-50
30-40 40-50 50-60 60-90 0-90
-59
-69
-76
-73
-60
As seen, the atmospheric net radiation slightly decreases in absolute value within the latitudinal belt from the equator to about 25' and then increases
740
Net Radiation
again up to about 60' latitude. To the north of 60' the absolute value is again observed to decrease. The mean annual net radiation in the Northern Hemisphere is -60 kcal/cm2 yr. Its components are Fa = 50, F, = 145, q' = 35 kcal/cm2 yr. Later, these components were calculated for the Southern hemisphere. The calculation of the atmospheric net radiation components for the earth as a whole gives the following values: F, = 150, Fa = 43, q' = 39, R, = 68 kcal/cm2 yr. In Budyko's estimation the negative pet radiation of the atmosphere is by about three-quarters compensated by the heat gain due to condensation, and by one-quarter by that due to the turbulent heat loss of the underlying surface. Moller [143] studied the regularities in the annual variation of the atmospheric net radiation in various climatic zones to find that the maximal absolute value always occurred in November and was equal to 250 to 300 cal/cm2 day. The minima were observed from May to July and varied from 140 to 190 cal/cm2 day. Table 10.16, compiled by Moller, compares the results of the calculation of the annual means of the atmospheric net radiation and its components for various latitudinal zones performed by different authors. TABLE 10.16 Comparison of the Calculations of the Aimospheric Nei Radiaiion and Its Components (cal/cm2day). After Moller [143] Calculation
30-50'N
40-60'N
60-90'N
90 217 127
82 233 151
81 227 146
121 359 238
99 333 234
59 287 228
96 305 209
83 280 197
65 230 165
92 300 208
79 29 1 212
55 262 207
1. Baur and Philipps (1934) q'
Fo
- Fa
I Ra I
2. Houghton (1954)
d Fo - Fm I Ra I
3. London (1957) q'
Fo - Fa
IRa I 4. Moller (1959)
d Fo - Fa
I Ra I
741
10.5. Climatology of Net Radiation of the Earth
This comparison shows that the data of the recent calculations are in fairly good agreement, whereas those obtained earlier are either underestimated (Baur and Philipps) or exaggerated (Houghton). Vinnikov’s calculations of the components of the net and thermal atmospheric radiation [144-1461 are, as was already mentioned, the most detailed. Table 10.17, borrowed from Vinnikov [146], gives the mean latitudinal distribution of the annual totals of the thermal balance components for various latitudinal belts. Here P denotes the turbulent heat loss of the underlying surface toward the atmosphere, L, is the heat income due to condensation, C is the advective heat transfer caused by the horizontal movement in the atmosphere. We see that the data of this table reveal a low latitudinal variability of the atmospheric net radiation. TABLE 10.17 Components of the Atmospheric Thermal Balance (kcal/cm2yr). After Vinnikov [I461
I Ra I
P
Lr
C
9 13 17 23 24 15 9 8 11 15
11 9 8
29 45 46 45 44 72 119 94 71 53 57 63 61
-32
40-50 50-60
70 60 60 69 82 83 76 74 16 74 71 64 57
Earth as a whole
72
13
59
0
Latitude
70-60’ N 60-50 50-40
40-30 30-20 20-10 10-0
O-loo s
10-20 20-30 30-40
-2 3 -1 - 14 4 52 28 12 -6 -3 8 12
Berland [138] plotted the annual and monthly (for the four seasons) maps of the geographical distribution of the atmospheric net radiation for the Northern hemisphere. Analysis of these maps likewise reveals a comparatively low spatial variation of the net radiation. The field of the net radiation is particularly “washed out” in summer in view of the small latitudinal variations of the absorbed solar and outgoing radiation (the net radiation is about 4 to 6 kcal/cm2 mo). In December the variation of the net radiation is from - 10 kcal/cm2 mo in the high latitudes and to 4 kcal/cm2 mo in the
742
Net Radiation
low latitudes. The annual net radiation also has a notable geographical variation. Similar results are obtained by Vinnikov [146] for the entire globe. The annual totals on the global scale vary approximately from -40 to - 100 kcal/ cm2yr. The smallest (in absolute value) totals are observed in the intermediate and high latitudes in summer, where the atmosphere absorbs the largest amount of solar radiation.
2. The Outgoing Radiation. The investigations of the outgoing radiation have a long history (see [l, 21). We shall consider here only the more complete and recent results of Vinnikov’s study [ 1441. Vinnikov proposed an approximate method for calculating the outgoing longwave radiation, and plotted monthly and annual charts of the planetary distribution of the outgoing radiation. Figure 10.32 gives one of his charts, the global distribution of the annual totals of the outgoing radiation. Analyzing these monthly and annual maps we see that the field of the outgoing radiation is fairly homogeneous. The outgoing radiation varies within a relatively small range of monthly and annual total. In all maps, F, is seen to increase from the poles toward the tropics. This is explained first by the increasing mean temperature of the troposphere, and second by the decrease in cloud in the high-pressure belts. At the equator there is a minimum of the outgoing radiation, due to the increasing cloud amount. The monthly 10, totals in January vary from 10 kcal/cm2 mo in the high latitudes to 16 kcal/cm2 mo in the tropics, while in July this variation is from 12 to 18 kcal/cm2 mo, respectively. The annual totals vary from less than 140 kcal/cm2 in the polar latitudes to over 200 kcal/cm2yr in North Africa and Arabia. The maxima in the outgoing radiation are observed over the low-latitude deserts with high air temperatures and insignificant moisture content and cloud. At places where the cloud amount and air humidity are high (equator) the outgoing radiation has considerably smaller values, but there is no continuance of small F., The variation of F, is dependent on atmospheric moisture and cloudiness. The zonal distribution of the outgoing radiation is seen to be broken by the effect of cold and warm ocean currents. With powerful currents the isolines are strongly fractured. The warm ocean currents cause an increase, whereas the cold currents effect a decrease of both monthly and annual totals of the outgoing radiation. This is evident from the effect of the warm Gulf Stream and the cold Peruvian current. Also effective with respect to the outgoing radiation field distribution are
10.5. Climatology of Net Radiation of the Earth
744
Net Radiation
the displacement of the thermal equator north of the geographical and the great ocean area of the Southern Hemisphere. As a result the thermal radiation of the Southern Hemisphere is less, on the average, than that of the Northern Hemisphere.
3. The Net Radiation of the Earth-Atmosphere System. As seen from (10.3), the net incoming radiation of this system is determined by the direct solar and diffuse radiation absorbed by the atmosphere and of the losses from the outgoing radiation. Calculations show that the quantity considered can be both positive and negative. In its annual range net radiation of the system in the intermediate latitudes is positive in summer and negative throughout the remainder of the year. Table 10.18 gives Vinnikov's calculations [1461, which are characteristic of the latitudinal and seasonal variability of the net radiation. (One can also consult Shneerov's work [147].) TABLE 10.18 Mean Latitudinal Distribution of the Net Radiation of the Earth-Atmosphere System (kcaI/cm2).After Vinnikov [146J
Latitude
January
July
Year
70-60' N 60-50
-10 -8.7 -6.8 -4.7 -2.6 -0.5 1.5 3.4 4.9 6.1 6.8 6.7
3.9 4.4 4.9 4.8 4 3.2 2.4 1
-49 -30 -12 4 14 23 29
50-40
40-30 30-20 20-10 10-0 &loo 10-20 20-30 3 0 40-50 50-60
s
-1 -3 -5.3 -7.3
-
31 28 20 9 -8 -29
It is evident from Table 10.18 that the transition from positive to negative values (northward) takes place near 40'. An interesting conclusion reached from consideration of the above data is that the net radiation of the Southern Hemisphere exceeds that of the Northern Hemisphere. Since there are no marked variations in the thermal regime of the earth
id
>
0
TABLE 10.19 Mean Annual Latitudinal Distributionof the Net Radiation and Its Components of the Earth-Atmosphere System (wlfcmamin). Afrer London 11391 N Latitudes, deg
Net Radiation Component 0-10
10-20
20-30
30-40
40-50
5060
60-70
70-80
80-90
Mean
Absorbed solar radiation
0.403
0.409
0.387
0.341
0.276
0.224
0.169
0.122
0.160
0.324
Outgoing radiation
0.347
0.354
0.353
0.327
0.306
0.287
0.270
0.253
0.245
0.324
Net radiation
0.056
0.055
0.034
0.014 -0.030
0.139
0.OOO
-0.063
-0.101
-0.131
746
Net Radiation
as a whole, it follows that the mean annual net radiation (identical with the thermal balance) of the earth-atmosphere system must be zero. The same conclusion is reached by London [I391 in particular, whose data are given in Table 10.19. At the same time Table 10.19 gives an idea of the relationship among the components of the net radiation of the earth-atmosphere system. Berland’s data on the mean latitudinal range of the monthly net radiation and its componets for the same system are presented in Table 10.20. Comparison with Vinnikov’s data (Table 10.18) reveals a satisfactory agreement between these results. TABLE 10.20 Mean Latitudinal Variation of the Monthly Net Radiation and Its Components for the Earth-Atmosphere System (kcaI/cm2).After Berland [138]
December
June N Lat., deg
70 60 50
40 30 20 10 0
15.4 17.2 18.3 19 19.1 18.5 17.2 15.5
12.9 13.4 13.6 14.1 14.6 14.2 13.3 12.7
2.5 3.8 4.7 4.9 4.5 4.3 3.9 2.8
0.0 0.7 2.6 5.7 9.6 12.8 15.5 16.9
11.4 11.7 12.3 13.1 14.3 14.8 14.1 13.1
-11.4 -11 - 9.7 - 7.4 - 4.7 - 2 1.4 3.8
London [I391 has also calculated the seasonal and annual net radiation and its components of the system averaged for the entire Northern hemisphere (Table 10.21). The data of Table 10.21 make it possible to analyze the relation between the net radiation components. As seen, the main contribution to the income of the net radiation is made by the absorption of shortwave radiation by the earth’s surface. A significantly smaller portion of the radiation is absorbed by the atmosphere and even less by clouds. Accordingly, the greatest losses of the shortwave radiation are due to its scattering spaceward by the atmosphere and clouds. All absorbed (reflected) radiation components have an annual variation. For example, a radiant flux scattered by the atmosphere and clouds is maximal in summer, which is caused by the maximum of isolation outside the earth and an increasing cloud amount during this period. As to the reflection of radion by the earth’s
747
10.5. Climatology of Net Radiation of the Earth
TABLE 10.21 Seasonal Distribution of the Mean Net Radiation and Its Components for the Northern Hemisphere in the Average Cloud Conditions (cal/cmzmin). After London [139]
Net Radiation Components
Winter
Spring
0.348
0.580
Summer Autumn
Year
I. Incoming shortwave radiation Insolation at the upper boundary of the atmosphere
0.645
0.424
0.500
Radiation absorption in the atmosphere: (a) by ozone (b) by water vapor and dust (c) by clouds
0.011 0.044
0.016
0.019
0.010
0.014
0.067
0.092
0.057
0.065
0.005
0.010
0.011
0.007
0.008
Total absorption
0.060
0.093
0.122
0.074
0.087
0.023 0.078
0.037 0.141
0.015
0.029
0.048 0.162 0.024
0.028 0.103 0.018
0.034 0.121 0.021
0.116
0.207
0.234
0.149
0.176
0.085
0.142
0.129
0.045 0.043
0.091 0.050
0.090 0.070
0.091 0.064 0.048
0.112 0.072 0.053
0.173
0.283
0.289
0.203
0.237
0.530
0.564
0.614
0.581
0.572
0.439 0.091
0.473 0.091
0.523 0.091
0.494 0.087
0.482 0.090
Reflection and scattering of radiation spaceward: (a) by atmosphere (b) by clouds (c) by earth’s surface Total reflection Absorption of radiation by the earth’s surface : (a) of direct solar (b) of transmitted by clouds (c) of diffuse Total absorption by earths’ surface 11. Longwave radiation
Effective radiation of earth’s surface: (a) thermal terrestrial radiation (b) downward atmospheric radiation (c) effective radiation
748
Net Radiation
TABLE 10.21 (continued) Net Radiation Components
Winter
Spring Summer Autumn
Year
Thermal radiation of troposphere: (a) thermal radiation absorbed by troposphere (b) tropospheric thermal radiation
0.501
0.535
0.588
0.555
0.545
0.716
0.749
0.817
0.778
0.765
Longwave net radiation of troposphere
0.215
0.214
0.229
0.223
0.220
0.029 0.277 0.011
0.029 0.276 0.016
0.026 0.294 0.019
0.026 0.283 0.010
0.027 0.283 0.014
0.317
0.321
0.339
0.319
0.324
Thermal radiation spaceward: (a) of earth’s surface (in transparency windows) (b) of troposphere (c) of stratosphere Total outgoing radiation
surface, it has a spring maximum. Although the albedo is maximal in winter, the lowest insolation value at this time causes the reflected radiation to reach maximum only in the spring, with greater insolation values and the snow cover remaining on the major part of the hemisphere. The heat losses of the earth-atmosphere system are determined first of all by the thermal radiation of the troposphere, which makes the largest contribution to the outgoing radiation. The radiation of the earth’s surface (in the transparency windows) is less than 10 percent of the outgoing radiation, while the stratospheric contribution is still less, not exceeding 3 to 6 percent. The seasonal variability of the outgoing radiation and its components is seen to be very low. In the Northern Hemisphere the mean outgoing radiation is 0.324 cal/cm2 min, which corresponds to the effective temperature of -22’. The seasonal values of the outgoing radiation depart from the mean by not more than 2 to 5 percent. The low variability of the radiation of the earth’s surface is explained by the mutually compensating effects of its temperature increase from winter to summer, on the one hand, and by the increasing cloud amount and decreasing atmospheric transparency due to the increase of the total water vapor content, on the other. It is important to note, however, that the conclusion about the low variability of the out-
10.5. Climatology of Net Radiation of the Earth
749
going radiation holds good only with respect to the outgoing radiation values averaged over the whole Northern Hemisphere. As is evident from Table 10.21, the net radiation of the earth-atmosphere system for the Northern Hemisphere is positive in spring and summer, and negative in autumn and winter. The maximum summer value is 0.072 cal/ cm2 min, while the winter minimum is 0.084 cal/cm2 min. Vinnikov [ 1461 plotted monthly (for all months) and annual charts of the geographical distribution of the net radiation of the considered system. The most characteristic feature of this geographical distribution is its closeness to the zonal, which gives evidence of the leading role of the astronomical factors in the radiation regime. The zonality is seen to be broken in the desert areas. Also evident in the net radiation field is the nonhomogeneity of the underlying surface at the ocean-land division, which is indicated by the discontinuity of isolines. The net radiation of the earth-atmosphere system is positive throughout the year only in a narrow equatorial zone of f 10’ latitudes. At all other places the net radiation changes sign twice a year. For about three months (in summer) the net radiation is positive over the entire hemisphere (souhern and northern). The zone of negative values appears at the poles in summer and then gradually expands southwards, occupying the territory south of 30’ for five months. In spring the zero isoline begins to recede toward the north. The maximal positive values reach 40 kcal/cm2 yr, while the negative become 60 kcai/cm2 yr. Making use of the charts given in the “Atlas of the heat balance of the globe” [141], it is possible to determine all components of the thermal and water balances for the land, ocean, and the earth as a whole. Calculations show that the earth as a planet absorbs 168 kcal/cm2 yearly. Of this, 112 kcal/cm2 yr, or two-thirds, is absorbed at the earth’s surface and 56 kcal/ cm2 yr, or one-third, in the atmosphere. The earth‘s surface loses yearly, on the average, 40 kcal/cm2, owing to the long-wave effective radiation, which results in its mean net radiation being 72 kcal/cm2 yr. Of this, 59 kcal/cm2 yr is spent in evaporation and 13 kcal/cm2 yr is given to the atmosphere in the turbulent heat loss. It should be noted that the heat expenditure in evaporation is 82 percent of the net radiation for the whole earth, this expenditure constitutes 90 percent for the ocean and almost 50 percent for land. In accordance with the amount of heat lost in evaporation the mean annual total of evaporation from the earth’s surfaces appears to equal 100 cm. This is, at the same time, the annual total of precipitation at the earth’s surface. The numerical values of the main components of the thermal and water
750
Net Radiation
balances of the earth’s surface obtained in the recent investigations somewhat exceed the formerly found values. In particular, the majority of the earlier studies would give the annual precipitation and evaporation for the whole earth equal to 80 to 90 cm. Their increase to 100 cm/yr is explained mainly by the greater accuracy in determining the normal precipitation on oceans, where it was not sufficient in the former years. As is known, the solar radiation is the chief climate-forming factor. It is of interest, however, that even now the amount of energy used by man is comparable with the net radiation value (see Budyko’s work [140]. According to latest data, the mean net radiation of the total continental surface is 49 kcal/cm2 yr, while the energy consumed by mankind is about 0.02 kcal/cm2 yr, with almost 1 kcal/cm2 for large areas in individual countries. Assuming that the annual increase of the energy generation be 10 percent we may expect that the total amount of energy due to man’s efforts will exceed the net radiation in less than a hundred years. In such conditions the role of the main climate-forming factor will pass to the energy generated by mankind. It is natural to expect, then, considerable changes in the regularities of the radiation regime and climate. The above-considered calculations performed by different authors show certain discrepancies, which stresses the necessity of experimental investigations of the quantity considered. An important step in this direction has been made by using data on the outgoing radiation obtained from meteorological satellites. Let us now discuss these data. 10.6. Investigations of the Earth’s Net Radiation by Means of Satellites The instruments used with the TIROS and NIMBUS meteorological satellites to measure the outgoing radiation in various spectral regions and the first results of these measurements are described by this author (see [148]). This author’s other work [149] is devoted to the practical application of such data. In the present section we shall reduce the subject to consideration of the recent satellite data on the componentes of the net radiation of the earth-atmosphere system (the significance of degradation errors in satellite radiometers must be mentioned, as for example, in [150, 1511). In accordance with the theoretical calculations discussed in the preceding paragraph the satellite data show that the outgoing longwave radiation has an equatorial minimum, almost symmetrical maxima in the subtropics, and a monotonic decrease polewards. Such results were obtained, for example, by Winston and Rao [152, 1531 (five-channel radiometer of Tiros 11; see Fig. 10.33), House [I541 (hemispheric sensors of the outgoing radiation in Tiros
10.6. Investigations of the Earth’s Net Radiation by Means of Satellites
751
550 I
Y.
500 “E
2 450 8 c
._ 5 5 400
7
.z 0
350
c
a 0
300 50
40
30
10 0 Latitude
20
S
10
20 30
40
50 N
FIG. 10.33 Mean latitudinal distribution of the outgoing Iongwave radiation measured from TIROS II over 26 days in comparison with theoretical calculations, (1) data of Houghton (annual means; (2) Retien (winter); (3) London (winter); (4) TIROS I1 (November-January); (5) Simpson (November-December); (6) Baur and Philipps (January).
IV; see Fig. 10.34),Bandeen et al. [ I S ] , and others. An interesting research in this field belongs to Hanel and Stroud [156].
.‘6
e
z
0.35
3
P
a 0.300 . 2 5 ~ 1I 1 I I 9060 30
0s
(II) 510 (I) so1 I
I
I
0
I
I
I
30
I
I
I I L
6090
ON
FIG. 10.34 Latitudinal variation of the outgoing longwave radiation measured from TIROS I V (semispherical sensors). (I) Feb. 8-Apr. 10, 1962; (11) Apr. 11-June 10, 1962.
The main factors of the mentioned peculiarities of the latitudinal distribution of the outgoing radiation are the earth’s cloud and temperature. For example, the outgoing radiation maxima in the subtropics are caused by the high temperature of the earth’s surface and the relatively small cloud amount (subtropical high-pressure zones). The equatorial minimum is con-
752
Net Radiation
nected with the area of the intertropical convergence zone. The results of measurements and calculations are seen to depart in a rather marked way (Figs. 10.33 and 10.34). Rao [157] investigated the Tiros I1 and Tiros I11 data on the outgoing thermal radiation relating to the belt 55' S to 55' N lat. (see Fig. 10.35).
LAT
FIG. 10.35 Latitudinal variation of the outgoing longwave radiation in summer and autumn. (1) from data of TIROS I1 (over 26 days, Nov.-Dec. 1960 and Jan. 1961); (2) data of TIROS I11 (9 days of July 1961).
As seen, in the intermediate latitudes of the Northern hemisphere the outgoing radiation increases from winter to summer, which can be caused by both a decrease in cloud and increase in the temperatue of the underlying surface. The inverse varibility of the outgoing radiation is observed in the southern intermediate latitudes. The two decreases of the outgoing radiation near the equator as observed by Tiros I1 can be explained by two local zones of greater cloudiness. The most detailed investigation of the variability of the net radiation components of the earth-atmosphere system has been made by Bandeen et al. [155] on the basis of 14 months of continuous Tiros VII operation. The method for processing observational data used in [155] is characterized in [149]. Table 10.22 gives seasonal totals of the net radiation components for the earth as a whole. Figures 10.36 and 10.37 present the curves of the latitudinal variation in the mean annual outgoing longwave radiation and albedo compared with London's calculations [ 1391. The seasonal variation of the outgoing long-wave radiation totals is seen to vary little (Table 10.22). The seasonal range of the latitudinal profile of the outgoing radiation as presented in [I551 shows that the tropical mini-
10.6. Investigations of the Earth's Net Radiation by Means of Satellites
753
TABLE 10.22 Seasonal and Annual Totals of the Net Radiation Components for the Earth. After Bandeen et al. 11551
Monthly Period
June-July Sept.-Nov. Dec.-Feb. Mar.-May
Outgoing Longwave Radiation 10l6 cal/min 1725.2 1725.2 1712.2 1746.5
Solar Radiation loz6cal/min
Albedo of Earth,
Reflected
Incident
%
699.0 922.2 859.7 796.0
2457.8 2574.8 2609.8 2544.2
28.4 35.8 32.9 31.3
mum occurs in the Northern hemisphere during most of the year, except from December to February. This causes the minimum in Fig. 10.36 to take place at 5' N lat., thus presenting asymmetry between the hemispheres.
FIG. 10.36 Latitudinal variation of annual means of the outgoing radiation (the scale of the axis of abscissas is proportional to the area of the latitudinal belts). (1) data of TIROS VII (region 8-12 p, June 1963-May 1964); (2) calculations of J. London.
The Northern hemisphere also contains the absolute maximum of outgoing radiation during as long a period (except from June to August), which asymmetry is clearly evident from Fig. 10.36. As a rule, the outgoing radiation in the northern latitudes outside the tropics is greater than in the southern, but the equatorial zones reveal an inverse relationship, which balances the heat losses in radiation by the two hemispheres.
754
Net Radiation
FIG. 10.37 Latitudinal variation of annual means of the planetary albedo (the scale of the axis of abscissae proportional to the income of solar radiation outside the atmosphere and corresponding latitudinal belts). (1) data of TIROS VII (spectral region 0.55-0.75 p , June 1963-May 1964); (2) calculations of J. London.
The latitudinal variation of albedo is almost directly opposite to that of the outgoing radiation and is caused by the cloud effect (see Fig. 10.37 and also Fig. 10.38, borrowed from [154]). The dashed curves of Fig. 10.38
--I
10
;i
.\
x)
20 10
011 I 9060
I
1
I
I
I
0 OS
I
I
I
30
1
1
1
1
6090
ON
FIG. 10.38 Latitudinal variation of albedo measuredfrom TIROS IV (sensing halfspheres). (I) Feb. 8-Apr. 10, 1962; (11) Apr. 11-June 10, 1962, [averaged area 48ON48OS; albedo: (I) 28.9 percent, (11) 37.2 percent; reflected radiation: (I) 598 cal/cma day, (11) 500 cal/crna day).
10.6. Investigations of the Earth's Net Radiation by Means of Satellites
755
characterize a possible measurement errors influence. The maximal albedo near the equator takes place at about 5' N lat. (Fig. 10.37)' coinciding with the minimum of the outgoing long-wave radiation. The minimal albedo is, however, observed at 16' N lat., that is, is somewhat displaced south of the outgoing radiation maximum. The albedo of the Northern Hemisphere exceeds that of the southern within the latitudinal belt from the equator to 12' and is smaller at higher latitudes. Analysis of the annual albedo variation reveals that its minima occur approximately in July, and maxima in October. This finds reflection in the variability of the seasonal means as well (Table 10.22). The average latitudinal distribution of the net radiation of the earth-atmosphere system shows asymmetry in relation to the equator, which results in the transition from positive values in the low latitudes to negative in the high, taking place in different latitudinal belts of the Northern and Southern Hemispheres. This is clearly seen in Fig. 10.39 [154]. 0.20
1
0.15 .E
0.10
; 2
0.05
0
H
0
3
-0.05
I-
-0.10
2 W
2
-0.1 5 -0.20
90 60
30 OS
0 LATITUDE
30
60 90
ON
FIG. 10.39 Latitudinal variation of net radiation measured from TIROS IV (sensing half-spheres). (1) data of Simpson (1928) for March-May; (2) London (autumn and spring of 1957); (3) Tiros IV (March-May, 1962).
Astling and Horn [ 1581 used the Tiros I1 measurement data for 27 days (November 26, 1960 to January 6, 1961) to plot the mean latitudinal distributions of the outgoing longwave radiation for the entire global surface and separately for continent and ocean. The measurements were concerned with the zone 50' S to 50' N lat., except a part of central Asia and northern South America, including the adjacent regions of the Pacific and Atlantic
756
Net Radiation
Oceans. The initial data for each 24 h were averages (over at least 10 values) with respect to squares of 2.5' equatorial side and then used in plotting charts of geographical distribution of the outgoing radiation for every day of the 27 days. All data relate to the angles with respect to nadir not less than 56'. The averaged meridional profiles of the outgoing radiation were calculated by reading the charted values (there were 7269 points) and the mean latitudinal magnitudes were calculated for zones of 5' width. The obtained meridional profile represents, as in the above-mentioned works, an equatorial minimum, maxima in the warm and relatively cloudless subtropical zones and decreasing radiation with a further increase in latitude. The absolute outgoing radiation values appeared to be less (especially in the zone from 5' N to 10' S Iat.) than the earlier data of the Explorer VII satellite and actinometric radiosondes. Such deviation should evidently be explained by the inaccurate consideration of the effect of the edgeward darkening of the planet's disk in processing the Tiros I1 data (the outgoing radiation measured at large angles relative to the nadir appears to be underestimated due to the effect of darkening as compared with the corresponding "undersatellite" values). This conclusion is confirmed by the fact that comparison of the outgoing radiation values, averaged over all the measurements with the values selected for the nadir angles less than 26', revealed the former's underestimation. Since, however, even the "undersatellite" values obtained with Tiros I1 are less than the Explorer VII data, it should be believed that one of the causes for this deviation is the different calibration of the respective instruments. According to data for nadir angles less than 26', the outgoing radiation in the subtropical minimal zone (15-25' N, 10-35" S lat.) is about 480 cal/cm2 day. Astling and Horn [158] found a notable difference between the meridional outgoing radiation profiles relating to continent and ocean. With continents there is a sharp minimum of the outgoing radiation within 5' N to 15' S lat., while with ocean this minimum is weaker and displaces to the interval 5' to 10" N lat. It appears that the continental displacement of the minimum southward is due to the effect of clouds related to the intertropical convergence zone. Another important difference is observed in the subtropics and relates to the influence of the underlying surface temperature in these relatively cloudless areas. Over ocean (low variability of temperature) the outgoing radiation in both hemispheres in the subtropics is about 500 cal/cm2 day, while the corresponding continental values are 540 cal/cm2 day (the summer hemisphere with high temperatures) and 475 cal/cm2 day (the winter hemisphere with low temperatures). The data of [158] on the variation of the outgoing radiation relative to
10.6. Investigations of the Earth’s Net Radiation by Means of Satellites
757
its mean show that this variation is most marked over the continents. Recently there have been attempts made at investigation of the diurnal range of the outgoing longwave radiation. Astling and Horn, for example, in processing the Tiros I1 data for 27 selected days (Nov. 26, 1960 to Jan. 6, 1961) found a notable daily variation over both continents and oceans. In the case of continents, the daytime values exceeded the diurnal means by 0.04 cal/ cm2 min, while the nighttime values were systematically lower by 0.02 cal/cm2 min. With oceans, the daily variation appeared to be less marked though still notable. The statement of daily variation in the outgoing radiation over the ocean whose surface temperature is stable enough was quite unexpected and required careful analysis of the measurement errors. So far the effect of errors has not been taken sufficiently into account, which does not allow acceptance of the above conclusion on the daily variation of the outgoing radiation for ocean as being reliable. It has been noted above that the main factors determining the outgoing longwave radiation are clouds and atmospheric stratification. The recent calculations and measurements reveal a considerable effect of the aerosol layers on the outgoing radiation (see [159]). The available experimental data are, however, contradictory. For example, Gupta [160] analyzed the daily totals (averaged over 5 days) of the outgoing longwave radiation for various Indian stations as given by the Tiros IV meteorological satellite in April, May, and June of 1962. The obtained values were then compared with the calculations of the outgoing radiation with a clear sky from the averaged aerological sounding data derived by means of the Elsasser chart. The deviation between the measured and calculated values was not more than 10 percent. Such good agreement gives evidence, in particular, of the insignificant effect of aerosol dust particles on the longwave radiation transfer. This, however, does not change the conclusion about the notable influence of aerosol on the radiative heat inflow, reached on the basis of measurements and calculations of the radiative temperature variations due to longwave radiation. The attempt to use the Tiros I1 data for evaluating the outgoing radiation and albedo means for the earth as a whole with calculated high-latitudes Values led to the planetary outgoing radiation of 0.31 1 cal/cm2min and albedo of 0.38 [158]. It should be noted that the albedo is usually assumed to equal 0.34, while according to the Explorer VII data, it is 0.33. This discrepancy should be attributed to the limited (with respect to the time interval) use of data and also to measurement errors. In processing the Tiros I11 data, Wexler [25] evaluated albedo at from 4 to 10 percent (with clear skies) to 30 percent with continuous cloud (in the
758
Net Radiation
Sahara region the albedo reaches 20 percent in clear weather). The albedo attained 54 percent for channel 5 and 47 percent for channel 3 only during the first five orbits. The mean value for this period was 20 percent. Considering that the mean cloud albedo as measured from aircraft is 50 percent with individual values of 80 percent, it becomes clear that the satellite data should be regarded as underestimated. Conover [I611 worked out a method for determining the albedo of the earth-atmosphere system based on the use of television data (cloud cover and terrestrial photographs) obtained from meteorological satellites. This method was applied in the processing of satellite pictures and the simultaneous photographs made from a U-2 aircraft at 20 km elevation. The spectral sensitivity of the satellite TV camera and of the aerophotographing instrument was approximately the same. The TV system (including video recording) was calibrated by successive irradiation of the screen from three tungsten incandescent lamps (the use of several sources was caused by the necessity to model a wide range of radiances). The determination of the absolute cloud radiance (in energy units) from the signals recorded at the ground-receiving video installation was carried out by comparing with the amplitude of signals recorded in the irradiation of the TV camera during the calibration before the fight. As shown in [161], in the photometric film processing it is necessary to consider the following factors : (1) picture-to-picture variation in exposition; (2) effect of temperature variations on the TV functioning; (3) nonhomogeneous distribution of blackening density even with homogeneous lighting; and (4) non homogeneity of the film. When calculating the albedo from cloud radiances it was assumed that the radiation reflection by clouds is isotropic; the atmosphere overlying the cloud was taken into account solely by computing the contribution of the Rayleigh scattering for the nadir angle 22’ (the angular dependence of multiply scattered light ignored) and of the absorption by ozone, whose total content was 0.28 “cm”. The values of cloud and of terrestrial radiance in satellite and aircraft estimation agree satisfactorily. The averaged satellite albedo values vary from 7 percent (the Pacific, cloudless) to 92 percent (dense and extensive cumulonimbus clouds). The snow albedo was found to decrease from 70 to 51 percent four days after snowfall. For the White Sands Desert (New Mexico) the albedo was recorded at 68 percent with solar altitude of 78’ and nadir angles from 17 to 28’. Comparison with albedo data known from literature shows that similar satellite and aircraft measurements yield exaggerated values. Nordberg et al. [I621 analyzed the results of the effective temperature and
10.6. Investigations of the Earth's Net Radiation by Means of Satellites
759
albedo determination from the Tiros 111measurement data on the outgoing radiation by making use of simultaneous wide-angle photographs of cloud distribution. The three typical situations considered in [162] relate to the Atlantic Ocean and North Africa (two representing a cloudless atmosphere) and also to the eastern United States (cloudy sky). All data were obtained for local noon. It is of essence that in all the three case the TV cameras and wide-angle radiometer were almost exactly oriented with respect to the nadir. The nadir sighting angle for the five-channel radiometer varied from 0 to 45'. The results obtained by the authors of El621 are discussed in [148, 1491. Rasool and Prabhakara [I631 were the first to realize the climatological processing of the Tiros data for 1962-63; their purpose was to derive information on the average planetary distribution of the net radiation components for the esrth-atmosphere system in the zone 60' S to 60' N lat. For more accuracy with respect to the five-channel radiometer data, only those readings were used which related to the solar zenith angles of less than 60' and nadir sighting angles less than 45'. The Tiros IV data from February to June of 1962 averaged for 5' lat 5' long squares were used to plot the planetary albedo chart. In this plot only such points were considered that corresponded to not less than a hundred individual albedo values (most often 500). The albedo calculation was made from the channel 3 readings (spectral region 0.2 to 5 p ) on the assumption of isotropy of the solar radiation reflection by the earth. In processing the results, the temporal variation of the radiometer's sensitivity was taken into account. The most characteristic features of the geographical albedo distribution may be summarized as follows: The ocean albedo, especially in subtropics, is about 20 percent. The continental albedo varies from 30 to 40 percent. On the average, the albedo is 26 and 34 percent, respectively. The mean albedo of the earth-atmosphere system within the investigated zone is 31 percent. The albedo isolines follow the oceanic contours. At the coastal line, large albedo gradients were observed. In the Southern Hemisphere the longitudinal variation of albedo is weak, except the subtropical zone with three minima over oceans. During the whole period of measurements the albedo for the Sahara and Arabian Deserts is about 45 percent and comparable with that of Central Africa and South America where the intensive cloud was observed (these data are justified by the Tiros I11 and Tiros IV results). Such a high albedo value leads to believe that the earlier estimations of the absorbed solar radiation for desert areas were exaggerated. Since the outgoing longwave radiation
760
Net Radiation
in this case is quite great, it turns out that in the Sahara conditions, the net radiation of the earth-atmosphere system approaches zero, which contradicts the familiar calculations that present a positive value. Figure 10.40 gives the isopleths of absorbed radiation q', plotted by Rasool and Prabhakara [123a, 1631 from the Tiros IV and Tiros VII data and considered as annual means. It is evident that the q' values in the temperate and subtropical northern latitudes in June and July are unusually high. Also notable is the zone of maximal absorbed radiation in the southern subtropical latitudes in summer. Both peculiarities in the absorbed radiation variation are due mainly to the effect of the low ocean albedo.
FIG. 10.40 Isopleths of daily totals of absorbed solar radiation (cal/cm2day).
The data of Fig. 10.41 characterize the latitudinal and annual variation of the outgoing longwave radiation. Hence it is clear that the latitudinal range of considered means is very weak. A still weaker range is observed with the annual variation. Nevertheless these data, as well as the above considered results, confirm the presence of two weak subtropical maxima of the outgoing radiation along the equator, observed in August, September, and October (in the same months in spite of the opposite seasonal phases). The equatorial minimum indicates the intertropical convergence zone with more cloud.
10.6. Investigations of the Earth’s Net Radiation by Means of Satellites
761
FIG. 10.41 Zsopleths of daily totals of the outgoing longwave radiation (callcine day).
In Fig. 10.42 are given isopleths of the net radiation for the earth-atmosphere system. Since the outgoing longwave radiation field is very “diluted,” these isopleths are similar to those of the absorbed solar radiation of Fig. 10.40. It is evident from Fig. 10.42 that the maximal net radiation zones occupy the belts 20 to 40’ in both hemispheres in summer. Within 20’ N to 15’s lat. the net radiation is positive throughout the year. In Rasool and Prabhakara’s estimation [163] the net radiation of the earth as a whole is practically zero. In the Northern hemisphere this quantity is -77 x 10l8 and +81 x 10ls cal/day to the north and south of the 50’ parallel, respectively. In the Southern Hemisphere the analogous values are -92.5 x 10l8 and +94 x 10ls cal/day. Vowinckel and Orvig [35] used calculations of the solar and outgoing longwave radiation absorbed by the atmosphere and also the known values of the net radiation and its components for the underlying surface, to obtain the net radiation of the atmosphere and the earth-atmosphere system. Extremal evaluation of the effect of errors in the determination of the cloudless atmosphere moisture content on the calculation of the absorbed shortwave radiation showed that they were not in excess of 4 percent. The absorption by stratus clouds was taken into account with the help of corrections‘
762
Net Radiation
FIG. 10.42 Zsopleths of daily totals of the net radiation for the system earth's surface atmosphere (cal/cm8day).
determined from the familiar literature data. With respect to cirrus clouds, it was assumed that they would not affect the absorption. The outgoing longwave radiation was calculated from the Elsasser chart, considering water vapor only and assuming identity of the outgoing radiation and of the upward longwave radiation flux at the 300-mb level. The altitudes of the lower, middle, and upper clouds were taken respectively as 1.2, 4.0, and 5.5. km. Consideration of the calculations of the annual variation in the atmospheric net radiation and its components for various points with clear skies and in the real cloud conditions showed that its main difference from the net radiation of the underlying surface consists in a smaller amplitude due to the low value of the shortwave component as compared with the stable longwave. In all cases the atmospheric net radiation is negative, being lowest in late summer and autumn and highest in spring and early summer. All components are maximal in summer. The most characteristic feature is an exceptional stability of the outgoing longwave radiation during the year. As a rule, the negative net radiation of the atmosphere increases with cloud, since the radiation toward the earth's surface increases with the appearance of clouds and is not compensated by an increase in the absorped shortwave
10.6. Investigations of the Earth’s Net Radiation by Means of Satellites
763
radiation (an inverse situation may be observed only in the conditions of a very dry atmosphere). An unusual Arctic feature, compared with the temperate latitudes, is the increase in the outgoing radiation due to inversions with the appearance of clouds, and consequently the increasing radiative cooling of the entire atmospheric thickness. The amount of atmospheric net radiation consists mainly of radiation from the underlying surface. The zonal and meridional sections of the net radiation for the earthatmosphere system repeat the main features of the corresponding sections for the underlying surface. Monthly charts of its geographical distribution reveal a very low latitudinal variability in winter. The differences are greatest for land and oceans. In midwinter the maximum of net radiation occurs in the Norwegian Sea and moves toward the zone of pack ice closer to spring. The maximal cooling is observed over the pole only in late summer. In spring there is a notable increase of the meridional net radiation gradients (under the influence of the albedo nonhomogeneity). The typical winter contrast between ocean and continent disappears in summer. In midsummer and early autumn the regional and latitudinal variation of the net radiation strongly smooths out. In August and September the net radiation distribution presents a rather simple picture: its negative values decrease from the pole with increasing latitude. Along with the climatological characteristics of the net radiation and its components for the earth-atmosphere system, it is of interest to know their variability. Such information obtained in processing the Tiros I11 and Tiros IV data with its four orbits (middle July, 1961) and by using theoretical data is given by Davis [164] and Kennedy [165]. Table 10.23 summarizes the atmospheric net radiation values of the total radiative heat influx to the whole thickness of the atmosphere and its components (the longwave radiative heat influx and the absorbed solar radiation) and also the outgoing longwave radiation and the reflected solar radiation. It is evident from this table that these quantities have relatively small variations. The exception is the reflected solar radiation (outgoing shortwave radiation) whose greater variation is due to the effect of cloud nonhomogeneity . The outgoing longwave radiation was found to have a more “motley” field than given in [I641 by Gergen [166], who used actinometric radiosoundings at 25 United States locations during May 26 to 30, 1959. In his estimation the outgoing longwave radiation varied from 15.6 to 26.6 mW/ cm2, that is, almost by twice, which was mainly due to the cloud cover nonhomogeneity. An interesting example of the spatial variability of the outgoing radiation in the transparency window 8 to 12 p, from the Tiros
TABLE 10.23 Mean Values and Standard Deviations of the Components of the Radiative Heat Inflow for the Whole Atmospheric Thickness, of the Outgoing Longwave Radiations, and of the Reflected Solar Radiation. After Davis 11641 ~
~~
~~~
Orbit 3
Orbit 4
Measurement Mean
Std' Deviation
Mean
Std' Deviation
Orbit 29 Mean
Std' Deviation
Orbit 44 Mean
Std. Deviation
z
s w L Total radiative heat inflow, cal/cm2 min
0.1347
0.0277
0.1408
0.0228
0.1394
0.0262
0.1454
0.0233
Longwave radiative heat inflow, cal/cm2 min
0.2436
0.0258
0.2551
0.0219
0.2578
0.0231
0.2535
0.0327
Absorbed solar radiation, cal/cmz min
0.1090
0.0155
0.1143
0.0187
0.1183
0.0128
0.1084
0.0192
Outgoing longwave radiation, cal/cm2 min
0.3580
0.0513
0.3633
0.0481
0.3359
0.0360
0.3846
0.0494
Reflected solar radiation (channel 3, W/mZ)
94.4
46.7
29.6
62.2
E B'
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System 765
I11 data on July 16, 1961, is considered by Allison et al. [167]. According to their data, the effective temperature (measured in the transparency window) varies from 225 to 300’k and more in the belt 55’ N to 5 5 ’ s lat. The isolated character of the available data on the variation of the net radiation components in the earth-atmosphere system underlines the necessity of further investigations in this direction.
10.7. Statistical Features of the Net Radiation of the Earth-Atmosphere System At present the available satellite data on the outgoing radiation are so numerous as to make any complete “individual” analysis impossible, not even with high-speed electronic computers. Certain statistical methods of analysis are therefore needed to represent and generalize the material of observations that iiust be processed. This problem is also essentially interesting from the viewpoint of using outgoing radiation data as a field of random values. Statistical methods for analyzing satellite meteorological information are in their infancy (see [167a, 168-1721). We shall consider here some results obtained by Borisenkov et al. [167a, 1681, who in analyzing the outgoing radiation fields used the statistical theory of turbulence. The need to know the structure of the thermal terrestrial radiation field is essential because the strict solution of certain problems of the methods for observation and objective analysis of the radiation field is possible only if the structural characteristics of the field is known. Such knowledge, for example, can help to pinpoint the expedient frequency of satellite measurements of the outgoing radiation. It can also be used in objective analysis of radiation fields, in their comparison with the fields of other meteorological elements (temperature, for example), and so on. Even the first results of the outgoing radiation, as obtained by satellite measurements characterize the radiative field structure to a certain degree. In the work [167a] are considered the statistics of the outgoing radiation fields as obtained by the Tiros I1 meteorological satellite. The authors made use of the information summarized in the Tiros I1 radiation data catalog [173]. Tiros 11, launched on November 23, 1960, was supplied with two TV cameras for recording cloud, ice, and other ground objects, and was designed for measuring the earth’s outgoing radiation in different spectral regions. Two wide-angle sensors measured the integral fluxes of long- and short-
766
Net Radiation
wave radiation within the 50' sighting angle. For spectral measurements, a five-channel radiometer with a sighting angle of 5' and supplied with filters to isolate certain spectral regions was used. The five channels corresponded to the following intervals:
No. 1 to NO. 2 to NO. 3 to NO. 4 to No. 5 to
6-6.15 p : 8-12 PFC: 0.2-6 p : 8-30 p : 0.55-0.75 p :
water vapor absorption band atmospheric transparency window region of the reflected solar radiation integral thermal radiation region of the camera's spectral sensitivity
The above-mentioned catalog gives the results of radiation measurements by each channel for 52 orbits in the interpolation with a grid step of 40 miles. Besides, the channel 2 data are plotted on polar stereographic charts (scale 1 :50,000,000) with a grid step of 200 miles. Later, the catalog was followed by additional limitations to use of the given material [1741. It appeared that the geographical correspondence of the data had to be corrected in view of the errors in the determination of the scanning angle as a function of time. Besides, there were errors in the deciphering of the transmitted signals, due to radio noises. The distortion of signals was especially strong in channels 3 and 5. The supplement thus recommended that channel 5 data be ignored and those of channel 3 be used with great care. Only the results for channels 1,2, and 4 were therefore considered in [167a]. However, errors for these channels, apart from error in geographical location, were still great. According to [174], the mean error in the determination of the outgoing radiation for the 6 to 6.5 p region was f0.06 W/m2, which corresponds to the effective temperature error of f2' (at T = 240'K). With the channel 2 region, it was f 1.6 W/m2 (f2O at T = 270OK). With channel 4, it was f 1.7 W/m2 (31 2' at T = 260'K). The finite errors in the determination of radiation values by channels 1, 2, and 4 were f0.18 W/m2 (f 6' at T = 240'K), f4 W/m2 (f 5' at T = 270°K), and f5.6 W/m2 (f6' at T = 260'K), respectively. The errors in the water vapor absorption band (channel 1) may be still greater, owing to certain effects, which results in their finite value of & 0.2425 W/m2 (f8' at T = 240OK). In spite of quite a few shortcomings of the observational data given in the catalog, they are still valuable for some preliminary conclusions about the radiative field structure. The data were processed according to the following logic. Let us select rectangular surfaces with small latitudinal extension along the regular grids
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System 767
of the observational charts. Let the number of columns m and lines n that determine the selected grids be fixed for each surface. Denoting the radiation value in the grid r through F(r), we have the following mean value for a field of m bars and n lines : (10.23) In the case for determination of the spatial structural function of the element f, we can use the formula
bf(l)
1 sn
= -
z 8n
i=l
[f@i
+4 -
(10.24)
wheref(ri) = F(ri) - F and s = m/2 is rounded off with respect to the lesser side. The autocorrelational moment mf(/) and the normalized autocorrelational moment (autocorrelation factor) kf(l)for the element f were determined from the formulas :
The value I of the shift between the grid with the correlated elements varied from h to sh (h is the grid step; in this case h z 40 miles). Since, as has already been mentioned, the radiation measurements included considerable errors, we should try to evaluate the reliability of the obtained structural and correlation functions, taking into account these errors. Let f(ri) contain a random error E . In this case, f(ri
+ 1)
=f‘(ri
f(ri) = f ’ ( r i )
+ 1) + &(Ti+ I> +
&(Ti)
(10.27a) (10.27b)
where f ‘ is the true f value. If we assume that the measurement errors are in no way connected with the true ,f’ values and at various points of the field are statistically independent of each other, the following equation is easily obtained from (10.24) and (10.27): (10.28) bf(l) = bf’(Z) 2 2
+
768
Net Radiation
where
Substituting (10.27) in to (10.26) and considering the above assumptions, we have in the numerator: 1
nn.
1
an
+
The denominc’ior of (10.26) is (of)2 2, where
In this case
[ I
at
/=o
where k f fis the true value of the autocorrelation factor and (of)2is the true dispersion. Since in the given case there is the following relationship between the calculated and the true dispersion,
the expression for kf can be rewritten as
It is easy to see from (10.29) that the observational errors cause the true autocorrelation moment always to exceed the kf obtained from the data with a random error E. It also follows from (10.29) that with the error E~ small compared with the dispersion u2, the true autocorrelation factor is little different from that calculated. For example, for the pressure at sea level, E is of the order of
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System 769
0.1 mb and cr 21 10 mb. It is obvious that such an error in the determination of the autocorrelation factor is negligible. In the investigation of the correlation moments of radiative fields, however, the error cannot be ignored, since the ratio &/cr is 0.4 to 0.5 at best, while for individual fields E and cr are comparable. The derived formulas enable certain correction of the structural and autocorrelation functions. Note here that at a given &, the autocorrelation factors obtained for orbits with higher (T values are more trustworthy, since in this case the calculated kf(l) are closer to the true values. The calculated structural characteristics of radiative fields for channels 1, 2, and 4 are given below, but analysis of them should take into consideration the preceding remarks. The structural and correlation functions were calculated for 50 fields of channel l , 56 of channel 2, and 62 of channel 4. The number of cases here exceeds the number of orbits, since the radiation fields for several orbits were divided into two regions. Figures 10.43 through 10.45 give the mean, maximal and minimal structural functions, and autocorrelation factors for the mentioned fields. All calculations were made with a Ural2 electronic digital computer. Q060L
a-0.040
a020
-
xil 0
(b)
P
-04 -02
FIG. 10.43 Structural functions ( a ) and autocorrelation factors (b) of the radiation field. Channel I. (1) maximum; (2) mean; (3) minimum.
770
Net Radiation
-0.2 -0.4
-0.6 b
FIG. 10.44 Structural functions ( a ) and autocorrelation factors (b) of the radiation field. Channel 2. Numbered as in Fig. 10.43. a
100
'n
20 2
4
6
8
10
12
Ii
I6
IbL
I .ol-
' r
-0.4
-
FIG. 10.45 Structural functions ( a ) and autocorrelation factors (b) of the radiation field. Channel 4. Numbered as in Fig. 10.43.
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System 771
To obtain the structural and correlation functions, the values of all functions for each Z were plotted on the graphs, the means were calculated, and the average b(1) and k(Z) lines were drawn. The maxima and minima with b(Z) and k(Z) were simply drawn by a smooth curve around the field of points obtained, and isolated large departures were ignored. In order to check the function isotropy, analogous calculations were made, with selections taken from the radiation values in the grids perpendicular to the initial direction. The first calculations were concerned with the linear grids but now they included the vertical columns. The linear values are plotted in solid lines and the vertical in dashes. Since the columns contain less grids than lines, the latter calculations ended with smaller 1. It is evident from the figures that, on the average, isotropy is best fulfilled for the integral radiation and is worse, for the radiation in the water vapor absorption band. It will be shown further that for individually selected radiation fields, there may be no isotropy, even in the 8- to 30-p region. We see that the variation of the structural functions first shows a rapid increase and then a practical stability with certain 1. Let us designate the distance at which b, reaches “saturation” by d. On the average, for the radiation fields of each channel, d w 16 h. The radiant flux in the 6- to 6.5-p region is practically determined by the atmospheric water vapor radiation, with a maximum at about the 400-mb area level. The structural functions of the radiant flux in this region will thus characterize the spatial structure of the water vapor distribution and its temperature. The Tiros I1 data on the channel 1 range, as was already metioned, contain far greater relative errors than on the radiation of channels 2 and 4. For this reason the channel 1 information should be considered very rough. It is possible that the considerable dispersion of points for the field k,(Z) and relatively large deviations from the conditions of isotropy may be partly explained by the low accuracy of these data. The obtained nonstandard values of the structural function for each Z are naturally less in the given case than b,(Z) and b,(l) because the absolute value of radiation for the 6- to 6.5-p region is small compared with the radiation in the 8- to 12 and 8 to 30 p regions. The field of points b,(Z) is, however, more compact than with b,(Z) and b4(Z). Thus, since the ratio of the maximal structural function to the minimal (from the rounding lines) at distances close to finite is of the order of 7 to 8, it is about 20 for b,(d) and b,(d). This fact may be explained by the more uniform spatial distribution of water vapor in comparison with that of cloudiness, which strongly affects the value and nature of the structural functions b,(Z) and b4(Z). Considering the variation of the autocorrelation factor k,(l) with distance, it is
772
Net Radiation
evident that it shows a slower decrease than in the other two channels. In the initial interval (for Z < 3h), however, the decrease of k,(Z) is more rapid than that of k2(Z)and k4(I). Besides, the difference between the maximal and minimal lines of the k,(l) field is considerably larger than for channels 2 and 4. This appears to be caused by the low accuracy of the obtained values of radiation in this spectral region. From the determination of the structural function it follows that b’, 0 = 0. Therefore we have, on the basis of (10.28),
b,(O)
= 2&2
Extrapolating the mean b,(l) value (Fig. 10.43(a)) up to I = 0, we have 2 2 N 0.006 W2/m4. As seen, the average error determined by zero extrapolation equals the average error in the radiation measurement given by the supplement to the Tiros I1 catalog [174]. At present the greatest attention is drawn to the 8- to 12-,u atmospheric window (of all the five spectral regions). The radiation detected from the satellite in this interval is by 75 percent due to the radiation of the earth’s underlying surface or clouds. It can thus be used to determine their temperature. Since the cloud surface temperature is usually much lower than that of the underlying surface, the radiation field in the 8- to 12-,u region can be used to estimate the cloud distribution and the pressure systems involving considerable cloud amount. The structural radiation functions for this part of the spectrum will therefore be strongly dependent upon the character of cloud fields. The same dependence must take place for channel 4. Comparing the structural and correlations functions of radiation of channels 2 and 4, we see that they have a close resemblance. Especially close are the mean b,(Z) and b4(Z), although the isotropy of the average radiative field for the 8- to 12-,u window is considerably more than for the 8- to 30-,u region. Comparison of the autocorrelation factors shows that the connection between radiation over different points of channels 2 and 4 undergoes approximately the same extinction. Such agreement between the structural and correlation funtions of radiation for channels 2 and 4 enables attempting transition from b(I) and k(Z) of the one channel to those of the other. Figure 10.46 is a graph of the relation between the structural functions of these radiative fields for a selected value I = 1Oh. The relationship is linear and is represented by the equation of regression : b4(II0)= o.71b2(Il,,)
+ 4.67
(10.30)
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System 773
with a relatively high correlation coefficient of 0.89. This justifies the great closeness of the connection. 80 I-
70 60
50
-*
40
-
30 20 10
0
I
10
I
I
l
20 30 40
I
I
50
60 70 80
1
1
b2
FIG. 10.46 Relationship between structural functions of the radiation fields (Channels 2 and 4, I = 10 h).
Since the radiative fields can, on the average, be considered isotropic, the following simple relationship is established between the structural function and the autocorrelation factor on the basis of (10.24)and (10.25),provided the condition for homogeneity is fulfilled : bf(l) = 20; [l - kf(Z)]
(10.31)
It follows from the expression (10.31)that closer relations between the investigated characteristics lead to a decrease of the structural function, while their separation makes it increase. In particular, if such distances L are selected for which k f ( L ) = 0, then b f ( L )= 2aP.To check the fulfillment of this relation, the data of Figs. 10.43 to 10.45 were used to determine L, for which kf = 0, and the values bf(L) = 2a2 were taken from the mean curve. The f-value dispersion was directly determined for each field and later averaged. The obtained E~ values are given in Table 10.24. It is evident from Table 10.24 that the coincidence of the obtained c2 is quite satisfactory, which justifies the validity of the statement about the isotropy and homogeneity of the mean radiative field in the above spectral intervals. Let us further consider some applications of the derived structural characteristics. Since in plotting charts the observational data are interpolated in
774
Net Radiation TABLE 10.24 Dispersion of the Radiative Field. After published data [174]
Spectral Region, p
az (from Figs. 10.43-10.44)
6-6.5 8-12 8-30
0.0118 20.0 17.5
a2 Averaged with Respect to Isolated Fields 0.0126 21.90 16.85
the grids of the regular net, it is natural to inquire about the optimal frequency of radiation measurements made from the satellite, which would have an interpolation error not exceeding the given one. The scheme for analyzing the meteorological fields in general and radiative fields in particular (adopted in the United States) did not until recently consider the structure of the analyzed fields. The interpolated value of the element f at every regular grid interesection was determined as a mean weight among several values ; the weight factor taken to be inversely proportional (without sufficient justification) to the square distance between the grid intersection and the initial point of interpolation. Such was the logic of radiation data processing as presented in the catalog [173]. If the structural and correlation functions had been taken into account, this interpolation would have been more accurate. According to Drozdov and Shepelevsky, the mean square error in the linear interpolation can be determined from the formula given in Gandin's work [175]:
Substituting the expression (10.3 1) into this formula, we have &I2 - - 6 = 2-
a '
r
I
[l - kf(f - r ) ]
+2 (10.33)
At the ends of the segment I, the error 6 is defined by the error kf.If the interpolation is performed with respect to the middle of the segment f (r = (l/2)), then (10.34)
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System
775
If we know the radiative field structure, it is obviously easy to state the finite distai-cu at which 6 will become larger than the given error. Gandin [I751 proposed a formula for interpolation which considered the minimal error condition. The interpolated fo value is thus sought in the form of a linear combination: n
fo =
c Pifi
(i = 1 , 2
- . a
n)
(10.35)
i=l
in which the weights Piare so selected that they have the minimal mean square error for interpolation with (10.35): n
E~~
=
[fo
-
x Pifil2
= min
(10.36)
i=1
In the transition from thefvalue to the autocorrelation factors, equations for determining the coefficients Pi by way of the structural characteristics of the field f are derived. The interpolation error here is defined from the formula n
6=1-
x koiPi
(10.37)
i=1
where the koi are the autocorrelation factors between the element foand the knownfi element at points i. In the case of interpolation over two points with respect to the middle of the 1 segment,
6
=
I -2Pkf(f)
(10.38)
where
The error calculated with (10.38)is slightly less, all other conditions being equal, than the error of the linear interpolation. The admissible measurement frequency in the second case therefore appears to be somewhat lower than in the first. However, for small distances, both formulas yield close results. For example, to secure an error in the integral radiation interpolation not exceeding the mean of 1.7 W/m2, the distances between the measurement points must not be larger than 60 to 70 miles. The same evolution is obtained with (10.34).It is evident that the radiation measurement errors as well as the interpolation error will affect the autocorrelation factor. More accurate estimates of the admissible I can therefore be obtained by
776
Net Radiation
taking into account the errors in the determination of k,. Depending on the position of basic points, the interpolation error can be evaluated prior to the derivation of the weight factors Pii by making use of the normalized correlation functions k,(Z). Let us present the following analogy with (10.35):
where the subscript 1 indicates the number of points at which the interpolated f value is calculated. Let us have the following system of normal equations to find the weight factors Pij by the least squares method:
(10.40)
---
where u is the dispersion with el = u2 = = on for homogeneous fields, and kii are the correlation funtions (conjugate correlation factors) dependent on the reciprocal position of the basic points only. The mean quadratic error of such a representation will be defined by the formula (10.41) where k12
kl?l
1 ... k2n ............... ...............
k21
D=
k13
kn1
k23
kna
kn3
*.'
(10.42)
1
is the determinant composed of conjugate correlation factors and D is the corresponding minor. The correlation functions can be used with (10.41) foi, the evaluation of the interpolation error and the expedient measurement frequency without preliminary knowledge of the weight factors P,. The values of the correlation function should first be corrected as noted above.
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System 777
The spatial radiation structure must be known for the calculation of radiation means in a certain satellite-orbit interval and also for the evaluation of the accuracy of such calculations. Lichtman and Kagan [I761 derived formuls for the determination of the accuracy in defining the mean for the infinitely great distance on the basis of measurement data in its final section Z : E~~ =
bAm,
+ 22 lorb,(r) dr 1
2
1
1:'
b,(r) dr
(10.43)
In addition, if a limited number of measurements n is performed in this section at points ri (i = 1, 2 n), according to the work cited, there will appear an additional error due to the limitation of the number of measurements :
If there are several parallel itineraries spaced at d or greater distance it is possible to consider that the measurements at one route are independent of those at others, and that their total length will be equal to the summed itineraries. If the distance between the routes is less than d, the second and subsequent routes must obviously be summarized with the weights proportional to b(r)/b(d),where in the given case r is the distance between the successive itineraries. Making use of the above structural functions and taking account of the admissible errors in the determination of the mean, it is easy to find with (10.43) and (10.44) the expedient dimensions of the area with respect to which the averaging should be performed. Presenting, for example, the structural function of the radiation in the 8- to 30-p region in the form b4(r) b4(d)(1 - [exp(- 0.0758r4'3)]}
-
and substituting it in (10.43), we find that for a rectangular area of 20h length and 1% width, the error in the determination of the mean radiation is approximately equal to a single measurement error. The above examples made use of the mean structural characteristics of radiative fields. However, those of individual fields can also be useful in certain investigations. When analyzing the structural functions of radiative fields, their variability in time and from region to region was noted. The authors of [I681 made an attempt at qualitative analysis of the dependence
778
Net Radiation
of the variability of b4Q upon the state of the atmospheric thermobaric field. It was assumed that, on the average, the type and character of cloud and humidi-y d i s ~ b u t i o nwould be reffected by the nature of the thermoba~c field. To perform this analysis the areas employed in the calculation of the structural radiation functions were plotted on charts of absolute topography of the 500-mb isobaric surface. The baric features were then compared with the structural radiation function of the given region. Figures 10.41 and
FIG. 10.47 Absolute topography chart of a 500-mb isobaric surface, Dec. 13, 1960.
10.48 give an exemplary baric field at the level of 500 mb (December 13, 1960) and the structural radiation functions for three regions of this field. It appears that the greater the field's horizonta~homogeneity, the smal~erthe value b,(d), and the best is the fulfillment of radiation isotropy. In region 3 the therrnobaric field is at its calmest, with corresponding and relatively small b4(d)=S 10. The fulfillment of isotropy of the radiation field is satisfactory here. In regions 2 and I the thermal field and baric features are not horizontally homogeneous. This possibly accounts for the great values and
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System
779
anisotropy of the structural characteristics of the radiative field. The anisotropy is especially marked in region 2. Apart from the physical causes it may be due to the great difference in the number of intersections along the columns and lines of the area considered. Analogous comparison of the
L
FIG. 10.48 Structural functions of the integral radiation fields. (1) 0554 hr, orbit 290; (2) 0739 hr, orbit 291 ; (3) 1240 hr, orbit 294.
structural radiation functions with thermobaric fields was made for five days. The general picture is similar to the one described above, with respect to analysis of the structural and correlation functions. Thus, even the magnitude and nature of the spatial variation of the structural (correlation) functions and the fulfillment of the isotropy conditions can, to a certain degree, be indicators of the state of the thermobaric field. Further researh in this direction will enable further verification and provide more detail to this statement. Of considerable interest is the determination of the spectral density of the most energetically important perturbations. The spectral density S(o) calculated in [168] from the formula
Irn
S(w) = k ( t ) cos W T d t n o
(10.45)
where k ( t ) is the correlation function, is presented in Fig. 10.49. The calculation was based on the Tiros I1 and Tiros I11 data and performed with the Ural 2 electronic digital computer by making use of the correlation functions of radiative fields for various spectral intervals. The spectral func-
780
(a 1
0.41
400
1200
2000
2000
3600
krn
-cn
0.3
1
3 0.2
km
km
0.41
(e 1
400
1200
2000 km
2000
3600
FIG. 10.49 Spectral density of the radiation field with using radiation data selected from intersections of the 40 miles grid step (2), of 1.25’ (2) and of 2 . F (3). (a) Channel 1 ; (b) Channel 2 ; (c) Channel 3; (d) Channel 4; (e) Channel 5.
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System 781
-.
tions were obtained for w corresponding to I = h, 2h -,with h different for each satellite. It should be noted that since the correlation function at I > 10h is not realiably determined, the values S(1) at I > 10 must not be much trusted. Figure 10.49 presents three curves characterizing the spectral density of the integral outgoing radiation field for three types of correlation function, computed with a grid step of 40 miles and 1.25' and 2.5' of the meridional arc. It follows from this figure that the most probable scales of the integral outgoing radiation perturbations at h = 40 miles are 350 and 800 km. Taking into account the limits of the correlation function fluctuations, the minimal scale of perturbations is placed at 200 to 500 km, and the maximal scale at 600 to 800 km. Perturbations on such scales are observed in the fields of other meteorological elements-of pressure and geopotential, in particular. If the radiation data are selected at a grid step h = 1.25', the calculated spectral functions (curve 2) also reveal two scales of perturbations of 400 and 700 km. Taking account of possible departures of the correlation function from the means, the scale of lesser perturbations varies within 250 to 700 km; for greater perturbations it is within 700 to 900 km. In addition, still greater perturbations are revealed whose scale is of the order of 1100 to 1700 km. It is easy to see that, in spite of the notable discrepancy between the channel 4 data with the Tiros I1 and Tiros 111, the spectral characteristics of perturbations turned out to be fairly close. The same figure gives a curve of the spectral density for the outgoing radiation field as observed at channel 4 of the Tiros I11 satellite with a grid step of 2.5'. It is obvious that in the given case the authors could not isolate the spectrum of perturbations on the 200 to 500-km scale, but then revealed in more detail perturbations on the 800-1000 km scale and even greater perturbations on the planetary scale whose dimesions were from 1600-2000 to 2500-3500 km. The radiant flux in the 6- to 6.5-p region is practically determined by the atmospheric water vapor radiation, with a maximum at 7 to 8 km. The spectral density of these radiative field (Fig. 10.49) therefore makes it possible to evaluate the scales of the energetically significant perturbations at about 400,700, and also 1100 to 1700 km (curve 2). However, curve 3 of the spectral radiation density from the Tiros I11 data at h = 2.5' has only one maximum at I 21 800 km, coinciding with a similar curve of Fig. 10.45. The two curves are then almost specular. The absence of any perturbations as shown by the Tiros I1 curve of spectral density is strange. Curve 1, however
782
Net Radiation
(Fig. 10.45), has exceptionally clear maxima at distances of the order of 350 and 800 km. Also perturbations of the radiative field appear in the atmospheric window, with a scale of about 1500 km. In calculating from the radiation data with h = 1.25', though, the spectral density has but a weak perturbation only for I 800 km. According to the curve 3, there are notable perturbations on the 1200 to 1600-km scale in this spectral interval. These perturbations are generally less marked than for the fields of the integral and water vapor radiation. It is possible that cloud fields are the important factor causing the perturbations in the atmospheric window region. The large perturbations on the plantary scale are most pronounced with radiative fields formed mainly by the whole tropospheric thickness, that is, in the spectral region isolated by channels 1 and 4. In the region of the integral shortwave radiation (Fig. 10.49) curve 2 shows two scales of perturbations, of 500 to 1000 and 1200 to 1500 km. The same order of values is revealed in the perturbation of radiative fields when channel 5 uses the selections from the intersections with a grid step 2.5' (curve 3 of Fig. 10.45). The same curve shows another maximum at I 2400 km. Two other curves, curve 3 in Fig. 10.49 and curve 2 in Fig. 10.49, have least notable perturbations. The first, curve 3, shows them only with I = 500 to 1300 and 1500 to 2100 km, while with curve 2 it is practically impossible to trace any perturbations. Since the initial measurement data on the radiation with these two channels are particularly erratic, it is natural to expect great errors in the calculated spectral density. For example, the spectral density curves for channel 3 at h = 2.5' and for channel 5 at h = 1.25', calculated from the maximal and minimal surrounding lines of the autocorrelation factors field, are almost specular. The spectral density calculated from the mean k is thus very smooth. Similar spectral analysis may appear to be very useful in comparing the radiative fields plotted from satellite data with the fields of the basic meteorological elements of pressure and temperature in particular.
-
-
REFERENCES 1. Van Mieghern, J. (1958). Radiation data needed in dynamical meteorology. Arch. Meteorol., Geophys. Bioklimatol. A10, No. 4. 2. Eisenstadt, B. A., and Zuyev, M. V. (1952). Some features of the heat budget of a sand desert. Trans. Tashkent Geophys. Obs. No. 6. 3. Sapozhnikova, S. A. (1950). "Microclimate and Local Climate." Gidrometeoizdat, Moscow. 4. Eisenstadt, B. A. (1957). Net radiation and the soil surface temperature at Tashkent. Trans. Tashkent Geophys. Obs. No. 13.
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5. Chikirova, G. A. (1949). Net radiation as observed at the railway station Dolgoprudnaya (Moscow). Trans. Main Geophys. Obs. No. 16 (78). 6. Mukhenberg, V. V. (1953). Net radiation and heat budget of the Leningrad region. Meteorol. Hydrol. No. 4. 7. Eisenstadt, B. A., Kirillova, T. V., Lichtman, D. L., Ogneva T. A., Timofeyev, M. P., and Zeitin, G. H. (1953). Variation in the heat budget of an active surface with irrigation. Trans. Main Geophys. Obs. No. 39 (101). 8. Skvortzov, A. A. (1930). On the climate of oasis and desert and certain peculiarities of their heat budget. Papers Agr. Meteorol. No. 21. 9. Kirillova, T. V., and Timofeyev, M. P. 11959). On the calculation of the net radiation of water reservoirs from the net radiation of land. Meteorol. Hydrol. No. 11. 10. Timofeyev, M. P. (1963). “The Meteorological Regime of Reservoirs.” Gidrometeoizdat, Moscow. 11. Kirillova, T. V. (1963). The formation of the net radiation of the underlying surface. Proc. All-Union Meteorol. Conf, 1961 Vol. VII. 12. Kirillova, T. V. (1958). The net radiation of Lake Sevan. Trans. Main Geophys. Obs. No. 78. 13. Sauberer, F. (1956). Uber die Strahlungsbilanz verschiedener Oberflachen und deren Messung. Wetter Leben 8, Nos. 1 and 2. 14. Sauberer, F., and Dirmhirn, I. (1954). uber der Strahlungshaushalt der Ozeane auf der Nordhalbkugel. Arch. Meteorol. Geophys. Bioklimatol. B6, Nos. 1 and 2. 15. Budyko, M. I., and Efimova, N. A. (1964). Variability of the radiation factors in the heat balance of the Earth’s surface. Meteorol. Hydrof. No. 4. 16. Kraus, H. (1963). Der Tagesgang des Energiehaushaltes der bodennahen Luftschicht. Arch. Meteorol. Geophys. Bioklimatof. B12, Nos. 3 and 4. 17. Monteith, J. L., and Szeicz, G. (1961). The radiation balance of bare soil and vegetation. Quart. J. Roy. Meteorol. Soc. 87, No. 372. 18. Orvig, S. (1961). Net radiation flux over sub-arctic surfaces. J. Meteorol. 18, No. 2. 19. Pivovarova, 2. I., and Pleshkova, T. T. (1962). On the radiation regime of the USSR as observed at a network of stations. Proc. All-Union Meteorol. Conf., 1961 Vol. IV. 20. Fleischer, R. (1959). Vier Jahre Strahlungsbilanz-Registrierungen am Meteorologischen Observatorium Hamburg. Ber. Deut. Wetterdienstes 7 , No. 51. 21. Goisa, N. I., and Sakali, L. I. (1963). On the relationship between the radiation and meteorological regimes of the atmospheric boundary layer. Trans. Ukrainian Hydrometeorol. Znst. No. 35. 22. Bossolasco, M., Cicconi, G., Dagnino, I., Flocchini, A. E., and Flocchini, G. (1965). Ricerche sulla radiazione solare. Contrib. Znst. Geofis. Geodet. Univ. Genova, Mem. No. 3. 23. Robinson, G. D. (1964). Surface measurements of solar and terrestrial radiation during the ICY and IGC. Ann. Intern. Geophys. Yr. 32, 17-61. 24. Budyko, M. I., Kagan, R. L., and Strokina, L. A. (1966). On anomalies of the ocean heat balance components. Meteorol. Hydrol. No. 1. 25. Wexler, R. (1964). Infrared and visual radiation measurements from TIROS 111. Appl. Opt. 3, No. 2. 26. Wyrtki, K. (1965). The average annual heat balance of the North Pacific Ocean and its relation to ocean circulation. J. Geophys. Res. 70, No. 18. 27. Chernigovsky, N. T., and Marshunova, M. S. (1965). “The Climate of Soviet Arctic.” Gidrometeoizdat, Leningrad.
784
Net Radiation
28. Golubova, T. A. (1952). On the radiation regime inside a field-protection forest barrier. Trans. Main Geophys. Obs. No. 36 (98). 29. Golubova, T. A. (1954). Radiation regime under the foliage of forest barriers. Trans. Main Geophys. Obs. No. 44 (106). 30. Rauner, Y. L., and Rudnev, N. I. (1960). The forest heat budget. Proc. Acad. Sci.
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786
Net Radiation
72. Kondratyev, K. Ya., Nikolsky, G. A., and Esipova, E. N. (1966). The components of solar radiation attenuation in the troposphere and lower stratosphere. Probl. Atmospheric Phys., Leningrad Univ. Publ. No. 4. 73. Belov, V. F. (1962). Attenuation of solar radiation in a free atmosphere over the Davis Sea and antarctic slopes. Trans. Centr. Aerol. Obs. No. 45. 74. Belayeva, I. P. (1964). The results of aircraft albedo measurements for mountains. Trans. Central Asia Hydrometeorol. Znst. No. 18. 75. Koptev, A. P. (1961). Albedo of clouds, water and the surface under snow and ice (from data of a “flying observatory”). Trans. Arct. Antarct. Znst. No. 229. 76. Kostianoy, G. N. (1963). Preliminary results of an actinometric sounding of the atmosphere in 1961 under anticyclonic conditions. Trans. Centr. Aerol. Obs. No. 49. 77. Kostianoy, G. N., and Pakhomova, L. A. (1964). Actinometric radiosounding of the atmosphere over the Pacific Ocean. Meteorol. Hydro/. No. 11. 78. Kostianoy, G. N. (1963). An actinometric radiosonde. Meteorol. Hydrol. No. 7. 79. Lopukhin, E. A. (1963). Investigation of distribution of the net radiation components over Central Asia. Trans. Central Asia Hydrometeorol. Znst. No. 16 (31). 80. Lopukhin, E. A. (1963). Vertical profiles of the net radiation components in Uzbekistan. Trans. Central Asia Hydrometeorol. Znst. No. 1 1 (26). 81. Baner, K. G., and Dutton, J. A. (1962). Albedo variations measured from an airplane over several types of surfaces. J. Geophys. Res. 67, No. 6. 82. Girault, P. (1964). RCalisation d‘une sonde de mesure du bilan radiatif de I’atmosphitre. Ann. Telecommun. 19, Nos. 9-10. 83. Clarke, D. B. (1963). Radiation measurements with an airborne radiometer over the ocean east of Trinidad. J. Geophys. Res. 68, No. 1. 84. Katulin, V. A., Kozyrev, B. P., Malkevich, M. S., Rosenberg, G. V., and Faraponova, G. P. (1964). An aircraft instrument for measuring net radiation and some results of the measurements. Zn “Actinometry and Atmospheric Optics.” Acad. Sci. U.S.S.R., Moscow. 84a. Kuhn, P. M. (1963). Radiometersonde observations of infrared flux emissivity of water vapor. J. Appl. Meteorol. 2, No. 3. 85. Kuhn, P. M. (1963). Measured effective long-wave emissivity of clouds. Month. Weather Rev. 91, Nos. 10-12. 86. Kuhn, P. M. (1963). Soundings of observed and computed infrared flux. J. Geophys. Res. 68, No. 5. 87. Suomi, V. E., Staley, D. O., and Kuhn, P. M. (1958). A direct measurement of infrared radiation divergence to 160 mb. Quart. J. Roy. Meteorol. SOC.84, No. 360. 88. Suomi, V. E., and Kuhn, P. M. (1958). An economical net radiometer. Tellus 10, No. 1 . 89. Tanner, C. B., Businger, J. A., and Kuhn, P. M. (1960). The economical net radiometer. J. Geophys. Res. 65, No. 65. 99. Staley, D. O., and Kuhn, P. M. (1961). Measurements of radiative cooling through two intense baroclinic zones in the middle troposphere. J. Meteorol. 18, No. 2. 91. Fritschen, L. G. (1960). Construction and calibration details of the thermal transducer-type net radiometer. Bull. Am. Meteorol. SOC.41, No. 4. 92. Fritschen, L. G., and Van Wijk, W. R. (1959). Use of an economical thermal transducer as a net radiometer. Bull. Am. Meteorol. SOC.40, No. 6. 93. Miiller, H.-G. (1964). Radiation measurements in the free atmosphere during the IGY and IGC. Ann. Intern. Geophys. Yr.
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94. Miiller, H.-G. (1961). Einige Radiosonde zur Messung der kurzwelligen Strahlung und der Albedo in der freien Atmosphare. Beitr. Phys. Atmosphare 34,Nos. 1 and 2. 95. Miiller, H.-G., and Pohl, W. (1956). Messungen des Ultraroten Strahlungsstromes in der freien Atmosphare. Sitzber. Math.-Naturw. KI. Bayer. Akad. Wiss. Munchen. 96. Pohl, W. (1957). Der Ultrarotstralungsstrom in der freien Atmosphare. Umschau 5, No. 15. 97. Fenn, R. W., and Weickmann, H. K. (1960). Atmospheric net radiation flux during winter in the Thule area, Greenland. J. Geophys. Res. 65, No. 11. 98. Aagard, R. L. (1960). Measurements of infrared radiation divergence in the atmosphere with the double-radiometer and the black ball. J. Meteorol. 17, No. 9. 99. Aagard, R. L. (1958). Convection free instrument for measuring infrared radiation in the atmosphere. Rev. Sci. Znstr. 30, No. 11. 100. Businger, J. A., and Kuhn, P. M. (1960). On the observation of total and net atmospheric radiation. J. Meteorol. 17, No. 4. 101. Brewer, A. W., and Houghton, J. T. (1956). Some measurements of the flux of infrared radiation in the atmosphere. Proc. Roy. SOC.A236, No. 1205. 102. Houghton, J. T., and Brewer, A. W. (1954). A new radiometer. J. Sci. Znstr. 31, No. 5. 103. Hanson, K. J., and Viebrock, H. J. (1964). Albedo measurements over the northeastern United States. Monthl. Weather Rev., 92, No. 5. 104. Williamson, E. J., and Houghton, J. T. (1965). Radiometric measurements of emission from stratospheric water vapour. Quart. J. Roy. Meteorol. SOC.91, No. 389. 105. Chapursky, L. I. (1965). Detection of clouds against snow. In “Application of Radiophysical Methods to Oceanographical and Ice Investigations.” Arctic and Antarctic Inst. Publ., Leningrad. 106. Mani, A., Sreedharan, C. R., and Srinivasan, V. (1965). Measurements of infrared radiation fluxes over India. J. Geophys. Res. 70, No. 18. 106a. Kuhn, P. M., and Johnson, D. R. (1966). Improved radiometersonde observations of atmospheric infrared radiance. J. Geophys. Res. 71, No. 2. 107. Williamson, E. J., and Houghton, J. T. (1966). A radiometersonde for observing emission from atmospheric water vapor. Appl. Opt. 5, No. 3. 108. Malevsky-Malevich, S. P. (1965). To the method of actinometric observations from a helicopter. Trans. Main Geophys. Obs. No. 167. 109. Malevsky-Malevich, S. P., and Serova, N. V. (1965). Some results of measurements of net radiation over water basins during spring. Trans. Main Geophys. Obs. No. 167. 110. Kirillova, T. V., and Malevsky-Malevich, S. P. (1965). On the profile of upward fluxes of long-wave radiation over water basins. Trans. Main Geophys. Obs. No. 167. 1 1 1. Badinov, I. Y. (1962). Three-stage photoelectrical tracking system on transistors. Art. Earth Satellite, No. 14. 112. Kuhn, P. M., Suomi, V. E., and Darkow, G. I. (1959). Soundings of terrestrial radiation flux. Monthly Weather Rev. 87, No. 4. 113. Kagan, R. L. (1965). On the calculation of thermal radiation fluxes in a cloudless atmosphere. Trans. Main Geophys. Obs. No. 174. 114. Kuhn, P. M., and Suomi, V. E. (1960). Infrared radiometer soundings on a synoptic scale. J. Geophys. Res. 65, No. 11. 115. Kostianoy, G. N. (1965). On the relation between the field of long-wave radiation and synoptic conditions in summer. Meteorol. Hydrol. No. 10.
788
Net Radiation
116. Kostianoy, G. N. (1965). On the variation of the long-wave radiation field in a free winter atmosphere. Proc. Acad. Sci. USSR 1, No. 8. 117. Ronicke, G. (1961). uber Messungen des Verlaufs der Warmestrahlungs Bilanz in der freien Atmosphare in San Salvador. 2. Meteorol. 15, Nos. 1-6. 118. Mantis, H. T. (1962). Observations of infrared cooling of a tropical air mass. J. Geophys. Res. 66, No. 2. 119. Roach, W. T. (1961). Some aicraft observations of fluxes of solar radiation in the atmosphere. Quart. Roy. Meteorol. SOC. 87, No. 373. 120. Brewer, A. W., and Wilson, A. W. (1965). Measurements of solar ultraviolet radiation in the stratosphere. Quart. J. Roy. Meteorol. SOC.91,No. 390. 121. Kostianoy, G. N. (1966). On the relation between the radiative temperature of a non-transparent body and the environmental radiative temperature variation. Proc. Acad. Sci. USSR, Ser. Phys. Atmosphere Ocean 2, No. 5 . 122. Kasatkin, A. M. (1963). High-altitude optical station for atmospheric research. Art. Earth. Satellite No. 15. 123. Liventzov, A. V., Markov, M. N., and Merson, Y. I. (1964). Experimental determination of the outgoing terrestrial radiation to space during a total solar eclipse from high-altitude geophysical rockets. In “Actinometry and Atmospheric Optics.” Acad. Sci. U.S.S.R., Moscow. 123a. Rasool, S. I., and Prabhakara, C. (1965). Heat budget of the southern hemisphere. Presentation at the COSPAR Symp., Argentina, 1965. 124. Markov, M. N., Merson, Ya. I., and Shamilev, M. R. (1965). Investigation of the angular distribution of the earth and terrestrial atmosphere emission from geophysical rockets and balloons. In “Investigation of Space.” Nauka, Moscow. 125. Markov, M. N., Merson, I. Y., and Shamilev, M. R. (1966). Emission of ionospheric layers in the infrared spectrum. Rept. Acad. Sci. USSR 167, No. 4. 126. Markov, M. N., Merson, I. Y., and Shamilev, M. R. (1965). Upper atmospheric layers emitting in the infrared. In “Investigation of Space.” Nauka, MOSCOW. 127. Rao, P. K., Astling, E. G., and Winninghoff, F. J. (1965). An investigation of degradation errors in Tiros IV scanning radiometer data and the determination of correction factors. Meteorol, Satellite Lab. Rept. No. 34. 128. Bazhulin, P. A., Kartashev, A. V., and Markov, M. N. (1965). Angular and spectral distribution of terrestrial radiation in the infrared. In “Investigation of Space.” Nauka, Moscow. 129. Lebedinsky, A. I., Glovatsky, D. N., Tulupov, V. I., Hlopov, B. V., Fomichev, A. A., and Shuster, G. I. (1945). Infrared spectrophotometry of thermal terrestrial radiation. In “Invesigation of Space.” Nauka, Moscow. 129a. Band, H. E., and Block, L. C. (1965). Spectral radiance measurements of the Earth from high altitudes. Appl. Opt. 4, No. 3. 130. Neupert, W. M. (1965). Intensity variations in the solar extreme ultraviolet spectrum observed by OSO-1. Ann. Astrophys. 28, No. 2. 131. Hall, L. A., Schweizer, W. and Hinterregger, H. E. (1965). Long-term variation of solar extreme ultraviolet fluxes. J. Geophys. Res. 70, No. 90. 132. Miller, D. H., and Stewart, K. H. (1965). Observations of atmospheric ozone from an artificial Earth satellite. Proc. Roy. SOC.A288, No. 1415. 133. Observations from the Nimbus I Meteorological Satellite (1965). NASA SP-89. 134. Budyko, M. I., and Kondratyev, K. Ya. (1964). The heat budget of the earth. Space Invest. 2, No. 1.
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135. Kondratyev, K. Ya., and Dyachenko, L. N. (1965). Distribution of long-wave net radiation of the atmosphere over the globe. Trans. Main Geophys. Obs No. 170. 136. Kondratyev, K. Ya., and Dyachenko, L. N. (1966). Correlations between atmospheric net radiation and outgoing radiation. Trans. Main Geophys. Obs. No. 184. 137. Budyko, M. I. (1949). The heat balance of the northern hemisphere. Trans. Main Geophys. Obs. No. 18 (80). 138. Berland, T. G. (1956). The heat balance of the atmosphere in the northern hemisphere. In “A. I. Voyeikov and Modern Problems of Climatology.” Gidrometeoizdat, Moscow. 139. London, J. (1957). A study of atmopsheric heat balance. Final Rept. Contract, No. AF19(122)-165, New York University. 140. Budyko, M. I. (1962). Some ways of affecting the climate. Meteorol. Hydrol. No. 2. 141. “Atlas of the Heat Balance of the Globe.” ed. (1963). Budyko, Moscow. 142. Vinnikov, K. Y. (1965). Albedo of the earth-atmosphere system and the field of outgoing short-wave radiation. Trans. Main Geophys. Obs. No. 170. 143. Moller, F. (1960). Der Strahlungshaushalt der Troposphare. Meteorol. Rundschau 13, No. 3. 144. Vinnikov, K. Y. (1965). Outgoing radiation of the earth-atmosphere system. Trans. Main Geophys. Obs. No. 168. 145. Vinnikov, K. Y. (1965). Albedo of the earth-atmosphere system and the field of outgoing shortwave radiation. Trans. Main Geophys. Obs. No. 170. 146. Vinnikov, K. Y. (1965). A new calculation of the heat balance of the erath-atmosphere system. Meteorol. Hydrol. No. 8. 147. Shneerov, B. E. (1963). Calculation of the net radiation of the earth-atmosphere system and of its components. Meteorol. Hydrol. No. 7. 148. Kondratyev, K. Ya. (1963). “Meteorological Satellites.” Gidrometeoizdat, Moscow. (see NASA, Tech. Transl. F177). 149. Kondratyev, K. Ya., Borisenkov, E. P., and Morozkin, A. A. (1966). “Practical Application of Meteorological Satellite Data.” Gidrometeoizdat, Moscow. 150. Dirmhirn, I. (1966). A recalibration of Tiros infrared radiometers using meteorological radiation instruments. NASA X-622-66-176. 151. Davis, P. A. (1966). Tiros radiation measurements and variations in atmospheric heating. Contract NASA 5-9540, Stanford Res. Inst. 152. Winston, J. S., and Rao, P. K. (1962). Preliminary study of planetary-scale outgoing long-wave radiation as measured from Tiros I1 measurements. Monthly Wearher Rev. 90, No. 8. 153. Winston, J. S., and Rao, P. K. (1963). Variations in the planetary-scale outgoing long-wave radiation as derived from Tiros I1 measurements. Monthly Weather Rev. 91, Nos. 10-12. 154. House, F. B. (1964). The Earth’s radiation budget as seen by Tiros IV satellite. Presentation at he Radiation Symp., Leningrad, 1964. 155. Bandeen, W. R., Halev, M., and Strange, J. (1964). A radiation climatology in the visible and infrared from the Tiros meteorological satellites. NASA X-651-64218. Goddard Space Flight Center, Washington, D.C. 156. Hanel, R. A., and Stroud, W. G. (1961). Infrared imaging from satellites. J. Geophys. Res. 89, No. 8. 157. Rao, P. K. (1964). Seasonal variations of outgoing long-wave radiation as observed by Tiros I1 and Tiros 111 satellites. Weather 19, No. 3.
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158. Astling, E. S., and Horn, L. H. (1964). Some geophysical variations of terrestrial radiation measured by Tiros 11. J. Atmospheric Sci. 21, No. 1. 158a. Wexler, H. (1964). Infrared and visual radiation measurements from Tiros 11. Appl. Opt. 3, No. 2. 159. Zdunkowski, W., Henderson, D., and Hales, J. (1965). The influence of haze on infrared radiation measurements detected by space vehicles. Tellus 17, No. 2. 160. Gupta, M. G. (1965). Outgoing long-wave radiation from Indian stations. Nature 207, No. 4999. 161. Conover, J. H. (1965). Cloud and terrestrial albedo determination from Tiros satellite pictures. J. Appl. Meteorol. 4, No. 3. 162. Nordberg, W., Bandeen, W. R., Conrath, B. J., Kunde, V., and Persano, J. (1961). Preliminary results of radiation measurements from the Tiros 111 meteorological satellite. J. Atmospheric Sci. 19, No. 1. 163. Rasool, S. I., and Prabhakara, C. (1965). Radiation studies from meteorological satellites. New York Univ. Geophys. Sci. Lab. Rept. No. 65. 164. Davis, P. A. (1964). Satellite radiation measurements and the atmospheric heat balance. NASA Final Rept. Contract 5-2919, Stanford Res. Inst. 165. Kennedy, J. S. (1964). Energy generation through radiative processes in the lower stratosphere. Planet, Circ. Proj. Rept. No. 11. 166. Gergen, J. L. (1965). Atmospheric energy calculations related to radiation observations. J. Atmospheric Sci. 22, No. 2. 167. Allison, L. J., Gray, T. Y., Jr., and Warnecke, G. (1966). A quasi-global presentation of Tiros I11 radiation data. NASA Goddard Space Flight Center, Washington,
D.C. 167a. Borisenkov, E. P., Doronin, Y. P., and Kondratyev, K. Ya. (1963). Structural characteristics of the radiation field of the earth as a planet. Space Invest. 1, No. 1. 168. Borisenkov, E. P., Doronin, Y. P., and Kondratyev, K. Ya. (1965). Structural characteristics of the outgoing radiation fields as measured from the Tiros I1 and Tiros 111 satellites and their interpretation. Space Invest. 3, No. 3. 169. Baryshev, V. A. (1965). The mesostructure of the integral radiation field of the earth as a planet. Proc. Acad. Sci. USSR, Ser. Phys. Atmosphere Ocean No. 8. 170. Malkevich, M. S., Monin, A. S., and Rosenberg, G. V. (1964). The spatial structure of a radiative field as a source of meteorological information. Proc. Acad. Sci. USSR, Ser. Geophys. No. 3. 171. Malkevich, M. S., Malkov, I. P., Pakhomova, L. A., Rosenberg, G. V., and Faraponova, G. P. (1964). Determination of statistical characteristics of radiative fields over clouds. Space Invest. 2, No. 2. 172. Malkevich, M. S. (1966). On the spatial structure of the atmospheric long-wave radiation field. Proc. Acad. Sci. USSR,Ser. Phys. Atmosphere Ocean, 2, NO. 4. 173. Tiros I1 Radiation Data Catalogue. I. Goddard Space Flight Center, NASA and U.S. Dept. of Commerce Weather Bureau, Washington, D.C., 1961. 174. Tiros I1 Radiation Data Users’ Manual Supplement. Goddard Space Flight Center, Washington, D.C., 1962. 175. Gandin, L. S. (1960). On the optimal interpolation and extrapolation of meteorological fields. Trans. Main Geophys. Obs. No. 114. 176. Lichtman, D. L., and Kagan, R. L. (1960). Some problems of rationalizing snow W i n g . Trans. Main Geophys. Obs. No. 108.
The net radiation is defined as the difference between the radiant energy absorbed and that emitted by the underlying surface, by the atmosphere, or by the system earth-atmopshere. The net radiation R of the ground surface consists of the direct and diffuse radiation and also of the atmospheric emission (downward atmospheric radiation) absorbed and retained by the underlying surface after heat losses due to the thermal emission of the underlying surface. This can be expressed as the following equation for the net radiation of the underlying surface :
R
=
Q(1 - A )
+ 6Go - Usurf
(10.1)
where Q are the fluxes (or totals) of incoming direct solar and diffuse radiation, A is the albedo of the underlying surface, Go and Usurfare the fluxes (or totals) of atmospheric emission and of the thermal emission of the underlying surface, and 6 is the absorptivity of the underlying surface. Since Usurf- 6G, = F, is the effective radiation of the underlying surface, (10.1) can be written as
R
=
Q(1 - A ) - Fo
(10.1 a)
It should be borne in mind that the concept of the net radiation is to a certain degree abstract. In actual practice we deal with the net radiation of an active layer whose thickness varies within a very wide range. In some cases (smooth underlying surfaces devoid of vegetation) it is very small; in others (plantations or water basins) it reaches high values of the order of meters and tens of meters. The net radiation of the atmosphere, Ra, consists of the direct solar and 655
656
Net Radiation
diffuse radiation q' absorbed by the atmosphere and also of the absorbed thermal radiation UgWfof the underlying surface. The emitted radiation consists of the heat losses due to the atmospheric thermal emission toward the earth's surface and spaceward. The first outgoing component is the atmospheric emission Go and the second is the radiation of the atmosphere U, to space. Thus, the net radiation of the atmosphere is expressed as
If P is the transmissivity of the atmosphere for thermal radiation then the thermal radiation of the underlying surface absorbed by the atmosphere can be presented as Usurf= (1 - P)Uo, where Uo is the upward flux of thermal radiation at ground level. The quantity Uo - Go = Fo , as has already been pointed out, is the effective radiation of the underlying surface, U, = F, is the outgoing radiation to space from both ground and PU,, and atmosphere. In view of this consideration the equation for the net radiation of the atmosphere can have yet another 'form:
+
(10.2)
In the net radiation R, of the system earth-atmosphere the incoming portion consists of the direct solar and diffuse radiation absorbed by the underlying surface and the atmosphere, while the expenditure or loss is determined by the outgoing radiation. The equation for the net radiation of the system earth-atmosphere therefore has the form
(10.3) This equation can also be rewritten: (10.4)
where Q, is the flux of direct solar radiation outside the atmosphere, A , is the albedo of the planet Earth. Let us now turn to the fundamental regularities of the net radiation for the ground surface, the atmosphere, and the system earth-atmosphere in view of their application for meteorological purposes. The importance of radiation data for dynamical meteorology has been discussed in Van Mieghem's work [l].
10.1. Observed Regularities in Variation of Net Radiation
657
10.1. Observed Regularities in Variation of Net Radiation of the Underlying Surface The study of the net radiation of the underlying surface is of extreme importance, as the net radiation is the main determinant of the climate. The magnitude of the net radiation of the underlying surface greatly affects the distribution of temperature in the soil and the adjacent air layers, which accounts for the particular role of the net radiation in the calculation of evaporation and snow melting, and also in a number of problems concerned with weather forecasting, such as the forecasting of late and early frosts and of fog. The study of the net radiation is also important to synoptic meteorology; for example, the lack of data on the net radiation makes it impossible to solve the problem of the formation and transformation of air masses. Finally, the investigation of the net radiation is connected with the effect of radiation on plant and animal life. All this accounts for the great interest in the study of the net radiation of the underlying surface shown by many investigators [2-271. It should, however, be noted that the number of stations engaged in prolonged observations of all the quantities involved in the net radiation or with direct measurements of the total net radiation is very small. This is due to the fact that until quite recently there have been no sufficiently reliable instruments for the direct measurement of the net radiation. Although in recent years satisfactorily constructed balance meters have been developed (such as the Yanishevsky and the Funk net radiometers and others), nevertheless the problem of reliable measurements of the net radiation still lacks solution. It is evident that the main features of the net radiation are determined by the factors that most influence the net radiation components. These include the duration of sunshine, the conditions of cloudiness and atmospheric transparency, the stratification of the atmosphere, and the character and state of the underlying surface. The net radiation of the underlying surface will be positive if the heat gain exceeds its loss, and negative in the reverse case. In the diurnal variation of the net radiation the former is usually observed in daytime and the latter at night. In the annual range for latitudes between 40' N and 4OoS, monthly values of the net radiation are positive for land and sea. In higher latitudes the monthly values become negative in winter months.
1. Diurnal Variation. Let us first characterize the diurnal variation of the net radiation. This problem has been treated in a great number of investi-
658
Net Radiation
gations. Observations show that, as a rule, the maximal positive values of the net radiation occur around noon, and the highest negative values at night. The night variation of the net radiation (the nighttime range of effective radiation) is small in comparison with its variation during the day. The curve of the diurnal cycle of the net radiation is usually asymmetrical in relation to noon; the afternoon values are somewhat lower, for the afternoon effective radiation exceeds the morning values, a feature that is clearly marked in southern and especially so in desert areas. The mentioned regularities in the diurnal variation of the net radiation can be seen in Fig. 10.1, which shows the daily cycle of the net radiation and its components according to Eisenstadt and Zuyev [2] for Tashkent (the measurement employed the Yanishevsky pyranometer and net radiometer). The values of direct solar, diffuse, and the net radiation were averaged from observations on clear summer days (August, 1969) in a sand desert. The other components of the net radiation were obtained by calculation. As seen from Fig. 10.1, in these conditions the leading component of the daytime net radiation is the direct solar radiation. Accordingly, the maximum in the net radiation is observed almost exactly at noon, between 11 and 12 h,
HOUR
FIG. 10.1 Diurnal variation of net radiation components (means of clear days). (1) Net radiation; (2) direct solar radiation; (3) downward atmospheric radiation absorbed by the ground surface; (4) diffuse radiation; (5) reflected shortwave radiation; (6) effective radiation; (7) radiation of the underlying surface.
10.1. Observed Regularities in Variation of Net Radiation
659
and is equal to 0.68 cal/cm2 min. The minimum of -0.15 cal/cm2 min occurs soon after sunset. The zero point in this cycle was observed between 06 and 07 h and between 17 and 18 h. Figure 10.1 shows that these points do not coincide with the moments of sunrise and sunset. In the morning the negative net radiation is observed 40 to 60 min after rise, while the transition from positive to negative values in the evening outruns sunset by about 1.5 h. This can be explained by the fact that the morning influx of heat due to the absorption of direct solar and diffuse radiation can compensate for the loss of heat due to effective radiation only some time after sunrise. In the evening hours the effective radiation predominates over the incoming part of the net radiation before sunset. Observations show that the transition from the positive net radiation to the negative, and vice versa, usually occurs at solar heights of about 5 to 15'. Table 10.1 gives the mean time of the zero point in the net radiation TABLE 10.1 Mean Time of the Setting ( t , ) and End ( t 2 ) of the Positive Net Radiation of the Underlying Surface (in h). After Supozhnikova [ 3 ]
I Month
Latitude, deg
I
40
5-7 5-7 4-6 5-7 5-7 5-7 6-8
April May June July August September October I
16-18 17-19 17-19 17-1 9 17-19 16-18 15-1 7
,
5-7 4-6 4-6 4-6 5-7 5-7 6-8
5-7 4-6 4-6 4-6 5-7 6-8 7-9
16-18 17-19 18-20 17-1 9 16-18 16-18 15-17
1618 17-19 18-20 17-19 17-19 15-17 . -14-16
I
for morning (tl) and evening ( t z ) on the fifteenth day of every month in dependence on latitude. The data were compiled by Sapozhnikova [3] and later corrected in view of more recent observations. It should be remembered that Table 10.1 does not include the case of snow cover, where the positive net radiation is observed at much higher solar altitudes (about 10 to 25'). This is caused by the great snow albedo affecting the net radiation to lesser values. The peculiarities of the dependence of the net radiation upon solar height
660
Net Radiation
at a clear sky can be illustrated by the data of Table 10.2, borrowed from [Chapter 7, Ref. 37bl. Table 10.1 clearly shows a later transition of the net radiation through the zero point and lower net radiation values in the presence of snow. In winter months in the north, and partly in the intermediate latitudes, the net radiation remains negative throughout 24 h. TABLE 10.2 Average Dependence of the Net Radiation (cal/cnz2min) upon Solar Height with Clear Skies. After Kirillova (Chapter 7 [37b])
State of Ground
Albedo,
Snowless
Snow
%
Solar Height, deg 0
5
15-25
-0.07
-0.04
50-80
-0.05
-0.04
10
15
20
25
30
35
0.03 0.12 0.21 0.32 0.41 0.48 -0.01
0.05 0.10 0.17 0.23 0.29
Cloudiness also greatly affects the transition of the net radiation through the zero point. With overcast skies the setting of the negative net radiation is retarded, since in these conditions the effective radiation as a cooling component of the net radiation greatly decreases. Sapozhnikova [3] found a high correlation between the moment of the zero net radiation and the time of the setting and disappearance of the night inversion in the lower air layer of 1.5- to 2-m thickness. Table 10.1 therefore also characterizes the time of appearance (f2) and disappearance ( t l ) of the night inversion in the above air layer. It should be noted that a number of investigations have found a parallelism between the diurnal variation of the net radiation and the vertical temperature gradients near the underlying surface. Sapozhnikova showed a correlation between the net radiation and the temperature difference at 20 to 150 cm above ground. The observations of Eisenstadt and Zuyev [2] give evidence of a parallelism between the net radiation variation and the temperature difference at the level 0 to 20 cm. Eisenstadt [4] also found a close correlation between the net radiation and the temperature of the soil surface. Doubtless, the cause of all these correlations is the close relationship between the temperature of the underlying surface and the adjacent vertical temperature gradients, and the effective radiation as the cooling component of the net radiation.
10.1. Observed Regularities in Variation of Net Radiation
66 1
The smooth diurnal range in the net radiation presented in Fig. 10.1 is observed, naturally, only with clear or fully cloudy skies (in the latter case, of course, the amplitude of the daily variation is notably smaller than with clear skies). In the case of partial cloudiness the daily variation of the net radiation becomes very irregular. This is illustrated by the curves of Fig. 10.2, plotted by Sapozhnikova [3]. The observations made at Koltushy (Leningrad region) on a clear and on a dull day show that the cloudy day gives a smaller range of the diurnal variation in the net radiation, with the variation itself being also more complicated.
-0.21 0
I
I
I
I
I
4
8
12
16
20
Hour
FIG. 10.2 Diurnal variation of net radiation.
(1) June average for Tashkent; (2) at Koltushy (Leningrad region) in a clear July day; (3) at Koltushy in a cloudy July day.
Along with the strong effect of the solar altitude on the direct solar and diffuse radiation, and with the albedo of the underlying surface, the cloud amount is the main factor determining the variability of the net radiation. In daytime the appearance and increase of cloudiness leads to reduction in both global radiation and effective radiation (it should be noted that the global radiation only shows a decrease with increasing cloudiness when averaged; isolated cases can show a reverse picture). At night the variation of cloudiness can affect only the effective radiation. Thus, on the average, the daytime positive values of net radiation with a cloudy sky decrease and the nighttime values also decrease in absolute estimation. However, with the partial cloud and the unobliterated sun when the global radiation is at its highest and the effective radiation is smaller than with a clear sky, the maximal positive values of the net radiation are observed. For instance, Chikirova [ 5 ] found during the observations at
662
Net Radiation
Dolgoprudnaya station (Moscow region) in August, 1947, that the net radiation with partial cloud was equal to 1.07 cal/cm2 min. To characterize the peculiarities in the daily variation of the net radiation with clear and with dull skies, Table 10.3 gives Mukhenberg’s [6] results of observations by means of the Yanishevsky net radiometer at Koltushy (Leningrad region). TABLE 10.3 Seasonal Changes in the Diurnal Variation of Net Radiation (cal/cmzmin). After Mukhenberg [6]
-
Clear
Cloudy
Hour
0 4 8
12 16 20 0
Summer Autumn -0.063 -0.022 0.392 0.632 0.312 -0.042 -0.070
Winter
-0.092 -0.088 -0.070 -0.102 0.045 0.077 0.390 0.028 0.120 -0.064 -0.080 -0.082 -0.079 -0.070
Spring
Summer Autumn
Winter
-0.076 -0.068 0.123 0.355 0.154 -0.048 -0.060
-0.018 -0.018 -0.021 -0.013 0.098 0.053 0.247 0.085 0.175 -0.006 -0.004 -0.012 -0.019 -0.003
-0.034 -0.029 -0.016 -0.024 -0.007 0.054 0.019 0.107 -0.008 0.068 -0.007 0.004 -0.005 -0.019
Spring
It is evident from Table 10.3 that cloudiness in summer leads to a considerable decrease in the net radiation, while on the contrary, cloudiness in winter helps to reduce the negative daily net radiation. The investigations of E. P. Barashkova et al. [Chapter 7, Ref. 37a] show that the averaged dependence of the net radiation upon solar altitude can be described by the following empirical equation :
R
= a(h, -
(10.5)
b)
where a, b are constant and h, is the height of the sun in degrees. For the constants a and b, the dependence on the albedo of the underlying surface is shown below: Albedo, %
a
b
10-20 20-30
0.013 0.012 0.006 0.007 0.004
10.0 9.8 7.4 7.4 8.5
5 W O 60-70 70-80
663
10.1. Observed Regularities in Variation of Net Radiation
With constant solar height (40’) and albedo, the variation of the net radiation in dependence upon cloud amount is characterized by the following data: Cloud amount, in tenths Net radiation, cal/cm* min
3
4
5
6
7
8
0.46 0.45 0.43 0.42 0.40 0.38
We see that with the increase in albedo from 10 to 80 percent, the net radiation shows an almost triple decrease. The increase in cloud amount from 3 to 8 reduces the net radiation by only 0.08 cal/cm2 min, that is, by about 20 percent. Thus we see that the net radiation is more “sensitive” to variations in albedo than to variations in cloud amount. The investigations of Barashkova et al. found a close correlation between the net radiation of a grassy surface and the magnitude of the absorbed shortwave radiation: R,$, - 0.06 (10.6) R= 1.20 At R,, > 0.06 cal/cm2 min this formula enables calculation of the net radiation from the absorbed radiation with an error of about f 10 percent. 2. Annual Variation. In order to characterize the regularities of the annual variation of the net radiation, let us consider Fig. 10.3, which presents isopleths of the net radiation for four points in different climatic zones (Yakutsk, Omsk, Vladivostok, Tashkent). These data of [Chapter 7, Ref. 37a] are also complementary to the daily variation of the net radiation. From examination of Fig. 10.3 it is evident that the maximal net radiation values are usually observed in June to July and are 0.45 to 0.55 cal/cm2 rnin in the north (62 to 64ON lat.) and 0.6 to 0.7 cal/cm2rnin in the south (40’s lat.). The minima fall during December and January, when the obtained values are 0.02 cal/cm2 rnin in the north (Yakutsk) and 0.2 cal/cm2 rnin in the south (Tashkent). In summer the nighttime values of the net radiation of the considered area vary but little and are -0.06 and -0.07 cal/cm2 min. In winter their variation is more pronounced, but the absolute values are very small (from -0.02 to -0.05 cal/cm2 min). The exception is the monsoon area (Vladivostok), where the highest net radiation occurs in April to May, and a small secondary maximum is observed in September.
3. The Effect of Wetting. Observations show that the net radiation of underlying surfaces greatly changes after their wetting by rain or irrigation. Table 10.4 gives the results of measurements of the net radiation over an
664
Net Radiation
-0.05
-0.05
-0.05
FIG. 10.3 Isopleths of net radiation (cal/cm2min). (a) Yakutsk; (b) Omsk; (c) Vladivostok; (d) Tashkent.
irrigated cotton field and over a semidesert in July, 1952 (by means of the Yanishevsky pyrgeometer and balance meter). These results were averaged by Eisenstadt et al. [7] from eight sets of observations on clear days at the state farm “Pakhta Aral” (Uzbek S.S.R.). It is evident from Table 10.4 that at night the net radiation of an irrigated field and a semidesert are approximately equal. In daytime the net radiation of the irrigated field considerably exceeds that of the semidesert. In the hours around midday the difference between these quantities is 0.30 cal/ cmz min. It appears that this difference is determined almost entirely by the inequality of their outgoing components: Owing to the higher surface temperature, the effective radiation of the semidesert exceeds by 0.25 cal/cm2
10.1. Observed Regularities in Variation of Net Radiation
665
TABLE 10.4 Daily Variation of the Net Radiation of an Irrigation Field and a Semidesert (cal/cm2rnin). After Eisenstadt et al. [7]
Area
I
Time, h 0-1
4-5
Irrigated cottonfield -0.07 Semidesert -0.08
6-7
8-9
1 6 1 1 12-13 14-15 16-17
18-19
20-21
-0.06
0.18 0.62 0.89 0.96 0.87 0.46
0.03
-0.07
-0.06
0.13 0.47 0.66 0.66 0.56 0.30
-0.05
-0.10
rnin that of the irrigated field. The remaining 0.05 cal/cm2 min characterizes the difference between the fluxes of global radiation reflected by the two surfaces (the semidesert whose albedo is higher than that of the irrigated cottonfield reflects 0.05 cal/cm2 min more radiation). Thus the reduction of the albedo and temperature of the underlying surface due to irrigation provokes a notable increase in its net radiation. This fact was first stated by Skvortzov [8]. The earlier reversal of sign of the net radiation in the morning and the later in the evening are also due to the reduction in the temperature of the irrigated field and the consequent decrease in its effective radiation, compared with that of the semidesert. Many investigations (see [9-111) have been carried out with the purpose of detailed study of the effect of irrigation on the net radiation. Their results all confirm the notable increase in net radiation due to irrigation. It can be said that in a moderate climate the increase in net radiation due to irrigation averages 20 percent, in steppe and wooded steppe it is 40 percent, and in the semideserts of central Asia 60 percent. It should be noted, however, that the effect of irrigation is strongly dependent on the development of vegetation. Since the change of net radiation by irrigation is caused by a change of albedo and the decrease in effective radiation due to the reduction in the temperature of the underlying surface, Eisenstadt et al. [7] proposed the following formula for the calculation in the net radiation A R (cal/cm2 min):
dR
=
(Q
+ q ) ( A - A') +
B(to
- to')
(10.7)
where Q + q is the global radiation flux, A and A' are the albedos of the ground before and after irrigation, to and to' are the temperatures of the
666
Net Radiation
ground before and after irrigation, and 4, is a coefficient equal to 0.008. Using (10.7), it is easy to explain why A R / R increases southward. This is obviously due to the fact that irrigation in the south causes a stronger reduction of the ground temperature than in the north. Kirillova [12] showed that (10.7) can also be used for the calculation of the difference in net radiation between water and land at two close points. Such calculations as well as observations revealed that in summer the net radiation of water basins, R , , exceeds that of land, RL,while in winter the reverse is the case. The observations of Kirillova at Lake Sevan (Armenia) give the following results: July RwlRL 1.39
Aug. 1.36
Sept. 1.04
Oct. 0.93
This can be accounted for by the fact that the water albedo notably increases in fall as the solar height reduces, and also by the reversal in sign of the temperature difference water-land (water becomes warmer than land, which causes the effective radiation for water to be greater than for land). 4. Effect of Forest. Also important is the variation of net radiation in forests. Under the trees both income (global radiation) and expenditure (effective radiation) in the net radiation will obviously decrease. Observations show that in summer the reduction of global radiation under the trees in daytime by far exceeds the decrease of effective radiation, due to which the net radiation in a forest is much less than in an open place. This conclusion follows, for example, from the observations of Golubova [28, 291 in forest barriers of the Kamennaya Steppe (Ukraine) and in the Saratov region (the Volga area). Table 10.5 displays Golubova’s results [29], obtained by means of the Yanishevsky pyrgeometer for two points of a forest barrier in the Kamennaya Steppe in June-July, 1951. As seen, at small solar heights (in the morning or evening) the net radiation in the forest is, in individual cases, only a few percent of the open field value. At night the net radiation in these cases was practically zero. It is natural that the net radiation under the trees must be strongly dependent on their quality and composition and on the development of foliage. For example, according to Golubova [29], the net radiation inside the forest barrier without foliage on a clear April day was 53 to 88 percent of the open field value. Comparison of these figures with Table 10.5 shows the great influence of leaves on the forest net radiation. In Rauner’s [30] estimation the ratio of the net radiation values over the forest ( R ) and inside ( R 2 , R3) shows strong change during 24 h and
667
10.1. Observed Regularities in Variation of Net Radiation
TABLE 10.5 Net Radiation in Forests. After Golubova [29]
Net Radiation
% in Open Field
cal/cm2min
Hours
Point 1
Point 2
Point 1
08-09
0.02
10-1 1
0.06
4 8
12-13 14-15 1617
0.09 0.03 0.02
18-19
0.01
0.21 0.43 0.04 0.02
Point 2
10
24
4 5
61 10
14
15
is considerably dependent on the phase of vegetation (see Table 10.6 where R2 and R, denote the net radiation values under the coniferous trees with insignificant undergrowth of stand density 0.9, and in a decidious forest with thin young trees and a lower growth of stand density 0.7). It can be seen from Table 10.6 that the “clarification” of the forest after TABLE 10.6 Change in Net Radiation under the Trees Compared with That over the Forest. After Rauner [30]
Period
Time, h
&side -
Rover
4
6
8
10
12
14
16
18
20
22
I0.00 0.09 0.05 0.06 0.05 0.06 0.08 0.07 0.00 0.00
R, R After vegetation (October)
R2 R
0.00 0.17 0.10 0.07 0.16 0.07 0.08 0.11 0.00 0.00
0.33 0 . 3 3 0.00 0.03 0.04 0.10 0.67 0.67
-
0.10 0.15
0.29
-
0.20 0.16 0.33
-
0.40 0.33 0.33
668
Net Radiation
the final period of vegetation is most apparent in the morning and evening hours. A different relationship between the net radiation of a forest and of an open area is observed in winter with snow cover. According to Kuzmin's [Chapter 9, Ref. 1001 observations in the Valdai Hills (W. Russia), the daily net radiation in winter snow-covered forests can be positive, while the open snow field has a negative value of net radiation.
5. Net Radiation Totals. The above data on the diurnal variation of the net radiation show that in the warm half-year, the daytime positive value exceeds the negative value during the night, which leads to the daily net radiation being positive. In winter the opposite picture is observed : the daily net radiation is negative. According to the observations of Pivovarova [Chapter 9, Ref. 371 near Tashkent, the mean diurnal net radiation was 136 cal/cm2 at the end of August and in the first half of September. The fluctuations of the net radiation at times were quite notable. For example, the highest observed daily total was 205 cal/cm2. These are the desert data. At the same area the mean net radiation of a cottonfield was 454 cal/cm2 in July, while for the semidesert it equaled 270 cal/cm2. The reduction in the net radiation of the desert is due to the higher albedo of sand. The results of observations near Leningrad [31] give the daily totals of net radiation in summer of 200 cal/cm2.Table 10.7 (from Barashkova et al. Chapter 7 [37a]) summarizes the observed monthly and annual totals of net radiation. In the annual variation of net radiation the monthly totals usually follow the variation in global radiation. However, in areas with stable snow cover the variation of the surface albedo (especially during spring) is also important. In the north of the territory considered, the negative net radiation is observed during five to six months. To the south of 46' N lat. on the European U.S.S.R. territory and of 43' N lat. on the Asiatic territory, the net radiation is positive throughout the year. During the whole year the totals of net radiation increase southward. Figure 10.4 is a map of the geographical distribution of the annual net radiation totals over the U.S.S.R. territory, plotted by Barashkova et al. [Chapter 7, Ref. 37al. The annual net radiation is seen to be positive everywhere and varies from 20 kcal/cm2 yr in the north to 60 kcal/cm2 yr in the south. This geographical distribution is mainly zonal. However, there is a slight tendency to an increase of net radiation in the west and an opposite tendency in the east of the examined territory.
TABLE
10.7
Meon Latitudinal Totals of Net Radiation (kcallcd). After Barashkova et al. (Chapter 7 [37a])
Latitude, deg
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
Year
38
1.5
2.7
3.8
6.1
8.4
8.8
8.5
7.8
5.4
3.5
1.7
0.8
59.0
40
0.8
2.0
3.6
5.8
8.3
8.8
8.5
7.6
5.3
3.0
1.3
0.5
55.5
42
0.4
1.3
3.4
5.6
8.2
8.8
8.5
7.5
5.2
2.6
0.8
0.1
52.4
0.0
0.8
3.0
5.5
8.1
8.8
8.5
7.3
5.0
2.3
0.5
-0.2
49.6
46
-0.2
0.5
2.7
5.4
8.0
8.8
8.5
7.1
4.7
2.0
0.3
-0.4
47.4
48
-0.4
0.2
2.3
5.3
7.9
8.8
8.5
6.9
4.5
1.8
0.0
-0.5
45.3
50
-0.5
0.0
2.0
5.2
7.8
8.8
8.4
6.7
4.2
1.5
-0.2
-0.7
43.2
52
-0.5
-0.2
1.6
5.1
7.6
8.7
8.3
6.4
3.8
1.1
-0.4
-0.7
40.8
54
-0.6
-0.3
1.2
4.7
7.5
8.5
8.2
6.1
3.4
0.8
-0.5
-0.8
38.2
56
-0.6
-0.4
0.7
4.3
7.4
8.4
8.0
5.8
3.0
0.5
-0.6
-0.8
35.7
58
-0.7
-0.5
0.2
3.7
7.2
8.3
7.9
5.6
2.7
0.3
-0.6
-0.8
33.3
60
-0.8
-0.6
-0.2
3.2
6.9
8.2
7.8
5.4
2.4
0.1
-0.7
-0.8
31 .O
62
-0.8
-0.6
-0.4
2.2
6.5
8.2
7.8
5.3
2.1
-0.1
-0.7
-0.9
28.6
64
-0.7
-0.6
-0.4
1.3
6.0
8.2
7.7
5.1
1.9
-0.2
-0.8
-1
66
-0.7
-0.6
-0.4
0.6
5.5
8.2
7.7
4.9
1.6
-0.4
-0.9
-1.0
68
-0.7
-0.6
-0.4
0.1
5 .O
8.3
7.6
4.5
1.3
-0.7
-0.7
-1
44
.o .o
26.5 24.5 22.7
10.1. Observed Regularities in Variation of Net Radiation
67 1
Of much interest are the results of actinometric measurements in the Arctic and Antarctic, obtained during and after the International Geophysical Year. It appeared, for instance, that even for the major part of the Arctic (except its central area) the mean annual net radiation was positive. According to Chernigovsky’s [32] data, averaged from ten years of observations at six stations, the annual net radiation in the central Arctic was close to zero (0.5 kcal/cm2 yr). In Marshunova’s calculations [33, 341 the maximal annual totals of net radiation occur at Cape Schmidt (1 1.6 kcal/cm2 yr) and at the Chukotskoye Sea (14.4 kcal/cm2 yr). The lowest totals in the central part of the Arctic basin vary from -2.5 kcal/cm2 yr in its western wing to -3.5 kcal/cm2 yr in the east. Interesting data on the net radiation in the Arctic conditions were obtained by Vowinckel and Orwig [35] who contend that there are three main types of the radiation regime of the underlying surface in the Arctic: (1) the Norwegian Sea regime, (2) the continental type, and (3) the regime of pack. The first type is characteristic of the open ocean surface from the Arctic Circle northward. During the year here is observed reciprocal compensation of high positive net radiation values in summer and high negative in winter (the cause for the latter is the relatively high ocean surface temperature; it is of interest that the effect of cold or warm currents is not essential, the primary factor being only the cloud effect). The main feature of this type is a high radiative heat loss of the open ocean surface. The continental type (Siberian continent and western Canada) is entirely different. In winter the radiative heat loss from the surface is small and the downward atmospheric radiation becomes less pronounced owing to scarce cloudiness. As a result the annual net radiation total for the continent is greater than for the ocean. The radiation regime of pack is typical for those ocean areas that are only temporarily free of ice. The contribution of the surface emission to the net radiation here is intermediate compared with that of land and open water. The slow change of the net radiation in spring, due to the high surface albedo, is typical. Contrary to the continental conditions the maximum in net radiation occurs here after the solar culmination. The analysis of observational data performed by Rusin [36] shows that the Antarctic radiation regime is very peculiar. Its annual net radiation is everywhere (except surfaces free of ice and snow) negative. For example, the annual total of net radiation is - 12.2 kcal/cm2 yr at Komsomolskaya station, and from -3.5 to -9.1 kcal/cm2 yr (in different years) at Mirny. With surfaces free of ice and snow the annual net radiation reaches high positive values (over 75 kcal/cm2 yr at Oasis). Thus, on the main part of
672
Net Radiation
the Antarctic territory, the high values of the incoming solar radiation mentioned in Chapter 8 are not “realized” because of the high ground albedo and the long period of radiative cooling during the polar night. In the annual range the monthly net radiation totals are positive for only three to four months. 10.2. Results of Calculations of Net Radiation at the Underlying Surface The relatively small number of observations of the net radiation and its components is not sufficient to give information on the net radiation totals and their temporal and spatial variability. In this connection, theoretical calculations of the net radiation as a whole and of its components are widely used. The methods for such calculations of totals of direct solar, diffuse and global radiation, and also of the effective radiation, have been considered in Chapters 6 , 7, 8, and 9. Calculations show that, as a rule, we deal with a simple annual variation of the net radiation with a summer maximum and a minimum in winter. This is evident, for example, from Table 10.8, compiled by Mukhenberg [ 6 ] from the results of observations and calculations of the net radiation for the Leningrad region. This table shows that the increase of net radiation TABLE 10.8 Annual Variation of Monthly Totals of the Net Radiation and Its Components in the Leningrad Region, kcallcm2. After Mukhenberg [6]
Month
Global Radiation
Radiation Absorbed
Effective Radiation
Net Radiation
January February March April May June July August September October November December
0.4 1.5 4.8 8.1 11.9 13.6 12.8 8.9 5.5 2.0 0.6 0.2
0.2 0.7 4.6 6.8 10.0 11.4 10.6 7.3 4.4 1.6 0.4 0.1
0.7 1 .o 3.4 2.5 3.1 3.5 3.2 2.4 2.1 1.5 0.9 0.7
-0.5 -0.3 1.2 4.3 6.9 7.9 7.4 4.9 2.3 0.1 -0.5 -0.6
Year
70.2
58.1
25.0
33.1
10.2. Results of Calculations of Net Radiation at the Underlying Surface
673
from winter to summer is provoked by the more rapid increase of the absorbed global radiation than of the effective radiation. Although the net radiation in the Leningrad region is negative for six months, for the year as a whole it is positive on account of the higher positive totals in summer. Figure 10.5 shows the annual variation of monthly totals of the net radiation and its components for a number of sites in different climatic zones in Efimova’s estimation [37]. It is evident that the annual range of net CAPE CHELYUSKIN
DUDINKA
BATUMI
SVERDLOVSK
PARAMARIBO
-1-2----3---4
FIG. 10.5 Annual variation of monthly totals of the net radiation and its components in diferent climatic zones. (1) net I.adiation; (2) global radiation; (3) reflected radiation; (4) effective radiation.
674
Net Radiation
radiation usually has a maximum in June to July and a winter minimum. With increasing latitude the duration of the period of positive net radiation values becomes shorter. It is not always, however, that the net radiation has a simple annual cycle. In some cases the special features of the local climatic regime cause the “abnormal” annual variation of net radiation. For example, at Bombay (India) there is a “double” annual range of net radiation, with two maxima in May and October. The minima are observed in December and August. The appearance of the summer minimum is brought about by the increase of monsoon cloudiness at this time of the year, which provokes a considerable decrease in the incoming global radiation (in the preceding section we dealt with a similar case concerning Vladivostok). Interesting results are revealed in the comparison of the values of net radiation and global radiation. At the coast of the Arctic Ocean (Cape Chelyuskin) the annual net radiation of 6.7 kcal/cm2 yr is only about 10 percent of the yearly income of global radiation (63 kcal/cm2 yr). In tundra (Dudinka on the Yenisey near the Kara Sea) the portion of net radiation (17 kcal/cm2 yr) increases to 23 percent (the global radiation being 74 kcal/cm2 yr). An even greater increase of the relative net radiation is observed in the forest zone (Sverdlovsk) to 35 percent, that is, 30 and 86 kcal/cm2 yr. In humid subtropics (Batum) this ratio is 50 percent (64 and 129 kcal/cm2 yr), and in the zone of humid tropical forests (Paramaribo of South America) it is at its highest, about 60 percent (94 and 161 kcal/cm2 yr). The main factor bringing about the change of the relationship between the net and the global radiation is the albedo of the underlying surface (at Cape Chelyuskin of 61 percent and at Paramaribo 18 percent). The relation between the net and the global radiation serves as a spectacular index of the potential energetical possibilities of a given geographical area. For example, irrigation of desert can increase its net radiation by 60 to 70 percent. A still greater effect can’follow the melting of ice or snow in the Arctic. The above data are characteristic of the annual cycle of net radiation at different points of the continent. Table 10.9 gives the results of calculating the net radiation for the Atlantic Ocean and the White Sea, performed by Budyko et al. [38] and by Shiskho [39]. It is natural that the general form of the annual variation of net radiation at sea is the same as that of the inland (maximum in June to July, minimum in January to December). Kirillova [40] has given detailed study to the net radiation of small water basins. Having described in short the peculiarities of the annual variation of
10.2. Results of Calculations of Net Radiation at the Underlying Surface
?
s:
rn
m
I
: I
? 3
I N 3
N m
?
m
? m
? m
\9 3
m 0
I
: I
N I
rn
I
m 0
c
2
675
676
Net Radiation
net radiation at the ground, let us now turn to the examination of its geographical variability. One of the main features of the geographical distribution of net radiation totals is their relatively low latitudinal range in summer and winter and considerable differences during the transitional seasons. This is evident in Table 10.10, borrowed from Alisov et al. [41]. If, for example, the maximal difference between the winter totals of the net radiation is 1.7 kcal/cm2, the corresponding difference will be 16.3 TABLE 10.10 Seasonal and Annual Totals of Net Radiation for Diferent Points in the USSR (kcallcnP). After Alisov et a/. [41]
Place Ust Tzilma Syktyvkar Moscow Kiev Rostov-on-Don Guryev Range of variation
Latitude
Winter
Spring
Summer
Fall
Year
65'27' 61'40'
-7.0 -7.4
15.2 20.0
-6.1 -6 . 9 -5.7 -6.8
23.0 25.5 21.3 23.7 25.7 24.5
-1.7 -1.7
55'45' 50'24' 47'15' 36'01'
0.8 3.6 8.1 11.2 14.5 17.1
...
1.7
16.3
4.4
1.2 2.4 5.6 3.2
24.5 30.4 40.1 38.0
7.3
24.9
kcal/cm2 in spring. It is important that in winter or summer there is no regular variation of net radiation in dependence on latitude, whereas during the transitional seasons, particularly in spring, the net radiation clearly increases southward. The annual net radiation totals are therefore regularly increasing with decreasing latitude. The data of Table 10.10 relate to a relatively limited territory. In the case of vaster areas the winter totals of net radiation show a strong dependence on latitude. According to Sauberer and Dirmhirn [13, 141, in December the diurnal totals of the net radiation of oceans in the Northern Hemisphere vary from -I20 kal/cm2 at 60" to 260-300 kal/cm2 near the equator. Table 10.11 gives the results of calculations of the mean latitudinal distribution of annual net radiation totals for land, oceans, and the entire surface of the globe, obtained by Budyko et al. [38]. The data of Table 10.1I characterize the average distribution of annual net radiation totals over the latitudes. It is evident, however, that in actual fact these totals are also dependent on longitude as well. Let us therefore
10.2. Results of Calculations of Net Radiation at the Underlying Surface
677
turn to consideration of the geographical distribution of annual net radiation totals over the entire global territory. In recent years Soviet investigators were the first to carry out the calculations of the geographical distribution of the net radiation for vast territories and for the entire globe. Budyko et al. [Chapter 7, Ref. 34; 15, 241 have plotted maps of the geographical distribution of monthly and annual net radiation means for the earth as a whole. Figure 10.6 is a map compiled by Efimova [37] and describes the distribution of annual means. One’s attention is drawn by the “jumping” character of the variation of the net radiation in the transition from land to sea, which finds expression in the discontinuity of the isolines at the coastal area. This is due to the sharp change of the ground albedo, as the lesser ocean albedos usually lead to larger net radiation compared with continents. TABLE 10.11 Mean Latitudinal Distribution of Annual Net Radiation Totals over Land, Ocean, and the Earth as a Whole (kcal/cm2yr). After Budyko et al. (Chapter 7 [38]) Net Radiation
Latitude, ON
60-50 5040 40-30 30-20 20-10 10-0
Earth as a whole
1
Latitude,
Ocean
Land
Globe
34 54 78 100 110 107
23 38 56 64 74 79
28 46 69 86 101 101
46
68
77
OS
0-10 10-20 20-30 30-40 40-50 50-60
I 1
Net Radiation Ocean
Land
Globe
107 107 94 73 53 31
75 69 62 55 39 26
99 99
87 71 53 61
It is evident from Fig. 10.6 and Table 10.11 that the annual net radiation is positive over all the globe, varying from values close to zero in the central Arctic and 10 kcal/cm2 yr near the boundary of permanent ice t o 80 to 95 kcal/cm2 yr in tropical latitudes. This does not mean, however, that the annual totals cannot be negative. As has already been mentioned in the preceding section, negative totals may be expected in regions with stable or long-time ice or snow cover, that is, in certain Arctic or Antarctic areas. The distribution of the net radiation over the colder and warmer parts of the globe is roughly zonal (the underlying surface being relatively ho-
10.2. Results of Calculations of Net Radiation at the Underlying Surface
679
mogeneous through large areas in both summer and in winter). I n d r y continental regions (Sahara, deserts of central Asia, etc.) a considerable decrease of the net radiation is observed on account of the high albedo of desert and the great amount of the outgoing radiative heat due to the high desert surface temperatures. Reduced values of net radiation also occur in the monsoon areas and are caused by the increased cloudiness during the warm season. The highest values of the net radiation (over 140 kcal/cm2 yr) are observed in two areas of the Indian Ocean: to the east of the Arabian Peninsula and to the northwest of Australia. On land, the maximal net radiation of about 80 to 95 kcal/cm2 yr is observed in the regions with little cloud but sufficient humidity, such as savanna and evergreen tropical forests. Analysis of the maps of the geographical distribution of net radiation leads to the following conclusions: In January the net radiation is negative north of 45 to 47’N and positive over the rest of the earth (excluding Antarctic). The negative net radiation on land is smaller in absolute value (not more than 1 kcal/cm2 mo) than over the ocean (up to 4 kcal/cm2 mo) because the ocean surface has a higher temperature and loses more heat in radiation. To the south of these latitudes the positive net radiation increases as far as the equator, where it reaches about 8 to 12 kcal/cm2 mo. From the equator southward the net radiation at sea and inland varies little and is respectively 8 to 12 and 6 to 8 kcal/cm2 mo. In January and July the moderate latitudes of the Northern Hemisphere are characterized by a notable homogeneity of the net radiation fields, which accounts for the local formation of continental air masses. In the tropics and at the equator the distribution of net radiation is, on the contrary, rather “motley,” which is due first of all to the inhomogeneity of the geographical distribution of cloudiness. The zero isoline of the net radiation in July passes at 45 to 47’s. According to Sauberer and Dirmhirn [14], the maximal deviations of the geographical distribution of the net radiation of oceans from the zonal norm take place in June. For example, in the middle of the Pacific Ocean there is a sharp minimum of net radiation (240 cal/cm2 day), and in the region where the Gulf Stream originates there is a clear maximum of about 400 cal/cm2 day. The main features of the geographical distribution of the net radiation at sea in summer are determined by cloudiness. The position of the zero line of the net radiation in March is as follows: It passes through Eurasia from northwest to sutheast, through regions of southern Scandinavia, Lithuania, White Russia, northern Ukraine, Saratov region and northern Kazakhstan, and in East Asia passes roughly
680
Net Radiation
along the 48' N circle. In North America it passes through the lower current of the St. Lawrence river and in the west runs up northwards as far as 55'N. 10.3. The Net Radiation of Slopes The results discussed in the preceding sections reveal the regularities of the net radiation of horizontal surfaces. However, agricultural and other important applications demand information on the net radiation of slanting surfaces. In this connection the problem of the laws governing the net radiation of slopes becomes quite vital. Unfortunately, this problem has not been adequately investigated, although much work has been done with respect to the quantity of incoming direct solar and diffuse radiation to slopes and the effective radiation at slopes. The main results concerning incoming shortwave radiation were described in Chapters 5 and 8. The effective radiation on slopes was discussed in Sec. 9.7. Let us now examine some data on the net radiation of the slopes of a sand dune, obtained by Eisenstadt [2] from theoretical calculations based on the following considerations. Let us write the equation for the net radiation R,,of a slope:
where Ssl, DS1and riz are the fluxes of the direct solar diffuse and reflected radiation on the sloping surface, r is the flux of the shortwave radiation reflected from the slope, GSzis the flux of the atmospheric emission on the slope, G,,szis the flux of the emission reflected by the adjacent horizontal surface slopeward, UiUrfis the flux of the thermal radiation of the horizontal surface on the slope, and Us,is the thermal flux emitted by the slope itself. The quantity S,, in (10.8) can be calculated from the familiar equation S,,
= S,[cos
h, sin a cos(A - a )
+ sin h, cos a ]
(10.9)
where S , is the flux of solar radiation incident on the perpendicular to the rays surface, h, is the height of the sun, a is the angle of the slope, A is the azimuth of the sun, and a is the azimuth of the slope. In the considered case it is assumed that for the strewing sand, a = 135', a = 33', and for the windward side, A = 315', a = 16'. If we assume that the diffuse radiation and the radiation reflected by the adjacent horizontal surface and also the thermal radiation of the atmosphere
10.3. The Net Radiation of Slopes
68 1
and of the horizontal surface are isotropic, and that the temperature and optical properties of the slope and the horizontal surface are equal, the following equations for the net radiation components at the slope may easily be obtained (see Chapter 8): a 2 a riZ = r sin2 2 a G,I = Go C O S ~ 2
Dsl
= D COS' -
a G,,sl = (1 - 6 ) sin22 a Uiuri= Usurfsin22
where D, r, G o , Usurf are the fluxes of the diffuse radiation, reflected radiation, downward atmospheric emission, and self-emission for a horizontal surface. All these quantities can be directly measured. Also obvious is the validity of the formulas
where A is the albedo and Tszis the temperature of the slope. Making use of these formulas, Eisenstadt calculated the components of the net radiation of slopes and the net radiation as a whole from data of actinometric observations over a horizontal part on the top of a sand dune carried out on August 22, 1949. The results are summarized in Table 10.12. They should, of course, be treated as very approximate in view of the assumptions adopted. However, even such rough calculations disclose a number of interesting features of the net radiation of slopes. Examination of Table 10.12 shows that the greatest difference between the components of the net radiation for the slopes and the top occurs in the case of the direct solar radiation and the thermal radiation of the underlying surface (see quantities S,, and Us,). The differences of the other components are very small. This means that the peculiarities of the net radiation of slopes compared with a horizontal surface are determined first of all by the differences in the incoming direct solar radiation and the thermal emission of the sloping and horizontal surfaces. It is quite ob-
682
Net Radiation
vious that the difference in thermal emission is due to the difference in surface temperatures. The data of Table 10.12 make it also possible to analyze the special features of the diurnal variation of the net radiation of slopes. This variation is roughly symmetrical with respect to noon on top of the dune, and is considerably asymmetrical for both slopes. The maximum in the net radiation on the leeward side facing southeast takes place before noon (at about lO.OO), while on the windward slope it is observed after noon (at about 13.00). It is easily understandable that the earlier maximum on the leeward slope is caused by a great increase of the temperature of this surface directed to the sun and by the consequent increase in radiative heat loss. Since the steepness of the windward and of the leeward slopes is different, it is also possible to use Table 10.12 for evaluation of the effect of steepness on the peculiarities of the net radiation of slopes. For example, it can be seen that the net radiation of the steeper leeward slope is greater from that of the dune top than in the case of the windward slope. Chizhevskaya [42] measured the net radiation at the north and south slope of the gradient 12 to 17' at Voyeikovo near Leningrad. According to her observations, in spring and fall on clear days the net radiation of the south slope is by 15 percent larger than of the north one. In summer this difference reduces to 5 to 7 percent. Eisenstadt [43, 441 carried out similar measurements at the north, south, east, and west slopes of the Kumbel Pass (the Turkestan mountain range) with angles of 33, 31, 33, and 23O, respectively, and also at the horizontal surface of the ridge of the pass. The revealed differences in the net radiation of the oriented slopes were mainly due to the differences in their thermal emission. The net radiation at the south slope reached 1.01 cal/cm2 min, and at the north slope it was 0.36 cal/cm2 min, on the average. The asymmetry of the daily range of the net radiation at the east and west slopes was quite significant; for example, at 8 h, Rsl = 0.76 cal/cm2 min for the east slope and Rsl = 0 at the west slope. The daytime total of the net radiation of the south slope was by three times and the total during 24 h by 7.5 times greater than for the north slope. The daytime total for the west slope was somewhat larger than for the east, as the latter has a higher temperature during the day and consequently a more intensive radiative cooling. In order to investigate the regularities of the variation of net radiation, Kondratyev and Fedorova [Chapter 8, Refs. 5.9-551 carried out daytime measurements of the net radiation of differently oriented blackened surfaces by means of a ventilated Yanishevsky pyrgeometer. As the result,
TABLE
10.12
Net Radiation of Sloping Sand Dunes and of Horizontal Surfaces on the Top of a Sand Hill (callcm2min). After Eisenstadt and Zuyev [2]
Net Radiation and Its Components
Time, h
6
7
O.OO0 0.125 0.090 0.330 0.365 0.645 0.050 0.085 0.050 0.085 0.045 0.080 0.000 0.000 0.005 0.010 0.010 0.050 0.035 0.100 0.100 0.175 0.390 0.395 0.400 0.405 0.370 0.370 0.000 0.000 0.005 0.005 0.010 0.010 0.040 0.045 0.540 0.585 0.545 0.595 0.560 0.640 -0.100 -0.020 -0.040 0.125 0.170 0.340
8
9
10
11
12
13
14
0.355 0.600 0.940 0.110 0.110 0.100 0.005 0.015 0.015 0.170 0.250 0.470 0.480 0.440 0.000 0.005 0.010 0.050 0.635 0.670 0.730 0.200 0.350 0.570
0.585 0.850 1.165 0.120 0.120 0.110 0,005 0.020 0.170 0.220 0.310 0.515 0.525 0.485 0.000 0.005 0.015 0.055 0.685 0.735 0.830 0.385 0.540 0.700
0.785 1.045 1.305 0.125 0.125 0.115 0.005 0.025 0.220 0.280 0.345 0.565 0.575 0.530 0.000 0.005 0.015 0.060 0.740 0.800 0.925 0.535 0.665 0.770
0.955 1.210 1.350 0.135 0.140 0.130 0.005 0.025 0.265 0.325 0.360 0.535 0.545 0.500 0.000 0.005 0.015 0.060 0.790 0.820 0.995 0.590 0.750 0.715
1.050 1.230 1.275 0.130 0.135 0.125 0.005 0.025 0.285 0.325 0.340 0.560 0.570 0.525 0.000 0.005 0.015 0.060 0.840 0.845 1.025 0.635 0.765 0.650
0.090 1.185 1.090 0.140 0.145 0.135 0.005 0.025 0.295 0.320 0.300 0.600 0.510 0.560 0.000 0.005 0.015 0.060 0.860 0.840 1.005 0.695 0.780 0.570
0.990 1 .ooo 0.780 0.160 0.165 0.150 0.005 0.025 0.275 0.780 0.340 0.560 0.570 0.525 0.000 0.005 0.015 0.055 0.845 0.780 0.980 0.610 0.675 0.330
15
16
17
18
0.840 0.690 0.470 0.080 0.775 0.560 0.310 0.030 0.455 0.170 0.000 0.000 0.175 0.140 0.095 0.065 0.180 0.145 0.095 0.065 0.165 0.135 0.085 0.060 0.005 0.000 0.000 0.000 0.020 0.015 0.010 0.000 0.245 0.200 0.135 0.035 0.230 0.170 0.100 0.025 0.155 0.075 0.025 0.015 0.500 0.475 0.455 0.465 0.510 0.485 0.465 0.475 0.470 0.445 0.430 0.435 0.000 0.000 0.000 0.000 0.005 0.005 0.005 0.005 0.015 0.015 0.010 0.010 0.055 0.055 0.050 0.050 0.805 0.760 0.720 0.685 0.770 0.750 0.710 0.660 0.870 0.758 0.695 0.640 0.485 0.395 0.175 -0.100 0.465 0.270 0.070 -0.115 0.145 -0.035 -0.140 -0.105
Note. Subscript 1 denotes the windward slope, subscript 2 the leeward slope, while the quantities without index refer to the top of the dune.
684
Net Radiation
curves were plotted to represent the dependence of the ratio RslIRh of the net radiation for the slope and for a horizontal surface upon the angle of inclination and the orientation of the slope with various solar heights. Some of these curves are given in Figs. 10.7 and 10.8. As seen from these figures, with increasing height of the sun above the horizon, the dependence of the ratio Rsl/Rhupon surface azimuth becomes less important.
pw
200
a
FIG. 10.7 Dependence of the relative net radiation of the slope Rs,/Rh upon inclination and orientation. July 20, 1956, h, = 27O, yo = 268O, 16.53 h, clear, south-easterly wind of v = 1 mlsec.
For slopes facing the sun, the maximum of Rsl/Rhis observed at a of the order of 90' - h, , being most pronounced at low altitudes of the sun.
40
20 0
N In IU
qn LU
In JU
nn
-ru
cn JV
cn
w
-m
iu
on
ou
J
90
I
a
FIG. 10.8 Dependence of the relative net radiation of the dope Rsl/Rhupon inclination and orientation. June 20, 1956, h, = 66O,yo = 199O, 12.32 h, south-easterly wind, v = I mlsec, clear.
10.3. The Net Radiation of Slopes
685
The curves of Rsl/Rhfor slopes directed opposite to the sun have a minimum, and with certain a the net radiation of the slope is negative when the solar height is not too big. With increasing angle of inclination the net radiation passes through zero at such values of the angle when the direct solar radiation does not hit the sloping surface (a 2 A,). Steep slopes (a> 50') directed opposite to the sun again show positive values, apparently on account of the increasing flux of the reflected radiation to the slope and the reduction in the effective radiation. For slopes with azimuths 90' and 270' relative to the sun, a monotonic decrease of Rsl/Rh with increasing angle of inclination is observed (east and west slopes in Fig. 10.8). It is of interest that with low and moderate solar heights, slopes facing the sun have a far greater net radiation value than do horizontal surfaces. At high elevations of the sun (Fig. 10.8), when the angle of incidence of solar radiation is very large, the net radiation of any oriented surface is either the same or less (in the majority of cases) than that of the horizontal surface. Figure 10.9 gives the results of measurements of the net radiation with continuous cirrus clouds. It is eident from comparison of Figs. 10.7 and 10.9 that the azimuthal dependence of the net radiation in this case tells
I40
a
FIG. 10.9 Dependence of the relative net radiation of the slope RsllRh upon its angle of inclination and orientation. June 16, 1956, h, = 28O, yo = 269O, 16.49 h, cirrus cloud of force 10, south-easterly wind of v = I mlsec.
in a weaker degree than with a clear sky. It is also interesting that in Fig. 10.9 no zone of negative net radiation values appears to be connected with the increase of incoming diffuse radiation and decrease of effective radiation due to the effect of cloud.
686
Net Radiation
The above data are only roughly illustrative with respect to certain regularities of the net radiation of slopes. It should be stressed that there is an extreme need for experimental investigations of the net radiation of slopes and for the perfection of methods for calculating the components of this quantity.
10.4. Net Radiation and Its Components in a Free Atmosphere The boundary atmospheric layer, which is so effective in transforming the integral solar and longwave radiation fluxes, has a thickness of the order of 30 to 50 km. The regularities of the variation of radiant fluxes in the free atmosphere can therefore be investigated by means of instruments mounted on aircrafts, balloons, and rockets. Such investigations provide data on the vertical profiles of the net radiation and its components, which is particularly important in view of the interpretation of satellite measurement data on the outgoing radiation. A special feature of aircraft and balloon investigations is the facility they give in obtaining the information to be used with the purpose of checking the reliability of satellite measurements. Experiments in radiant fluxes in the free atmosphere by means of aircraft and balloons were begun as early as 30 years ago, but only during the past 10 to 15 years has it become possible to conduct them at a sufficiently high level of investigation. In this section we shall first consider the available measurement methods and their accuracy, and then discuss the results of the present investigations. 1. Peculiarities of the Use of the Standard Actinometric Instruments. The standard actinometric instruments mounted on aircraft and balloons were used for measuring radiant fluxes in the free atmosphere in a great number of research works [45-841. It is natural that the use of the standard instruments in such unusual conditions required special methods of measurement and processing, and also careful study of their characteristics with changing parameters of the medium. The most complicated turned out to be the problem of the use of pyranometers and balance meters for measuring global and net radiation. Important investigations of the methods applied in aircraft pyranometric measurements were carried out by Kastrov [51, 531 who had worked out a theory of pyranometers to be installed on aircraft. Omitting the standard corrections (angular, spectral, temperature dependence, etc. ; see
10.4. Net Radiation and Its Components in a Free Atmosphere
687
[Chapter 1, Ref. I]), let us consider only the special features of aircraft or balloon pyranometric measurements. The most important factor controlling the processing of the measurement data is in this case the nonhorizontality of the receiving surfaces. For the lower pyranometer, which measures the upward shortwave radiation flux, the departure of the receiving surface from the horizontal position is of no importance, since the angular distribution of the upward radiation may in the first approximation be considered isotropic. The readings of the upper pyranometer, however, whose receiving surface is exposed to the direct solar radiation as the main component of the global radiation with clear skies, are very sensitive to displacement from the horizontal. Let us assess, following Kastrov [54], how the nonhorizontality of the upper pyranometer affects the angle of incidence of solar radiation and how it changes computation. Let the axis 0.2(Fig. 10.10) correspond to the vertical direction and OZ’ be normal to the pyranometer receiving surface. The position of the sun in the sky is determined by the point M ; a is the azimuth of the plane OZD with respect to the solar vertical (the other designations are evident from the drawing or will be interpreted later on).
FIG. 10.10 The eflect of the nonhorizontality of the pyranometer’s receiving surface.
In the departure from the normal of the receiving surface by angle E relative to the vertical O Z , the solar radiation flux incident on the receiving surface will change by a quantity equal to S (cos (@‘ - cos lo). Here S is (the flux of solar radiation on the surface perpendicular to the rays)
68 8
Net Radiation
the normally incident flux of solar radiation, To is the solar zenith angle, and Cot is the angle of incidence of solar radiation on the receiving surface, defined by the relation
+ sin Co sin
cos lo’= cos Co cos E
E
cos a
When averaging over azimuth the mean error of measurement of the solar radiation flux on the horizontal surface will equal
=
If the angle
E
- S cos lo(l - cos
E)
=
E -2s sin2 cos 2
Co
(10.10)
is small, we have approximately AS’
= -&2 s c o s 50
2
(10.11)
Hence it is evident that the relative measurement error S’ is equal to 2 / 2 ; that is, it is independent of the solar zenith angle to. The obtained result is apparently valid also for the diffuse radiation propagating in a given direction, and therefore (10.1 1) can be easily generalized for evaluating the measurement error with the shortwave net radiation d(F+ - F f ) : E2
d(F4 - F J . )= - (FL - F f ) 2
(10.12)
where F+ and F f are the downward and the upward fluxes of shortwave radiation, respectively. Differentiating (10.12) along the vertical coordinate 2 and introducing the notation q = (d/dz)(FJ.- F f ) for the radiative heat influx, we obtain the following expression for the evaluation of the error in the determination of 9: &2
(10.13)
dq= - - q 2
The above formulas show that at insignificant disturbances of the horizontality of the receiving surface, the measurement error is not important. For example, even at E = 6’ the value (4)~~0.005; that is, the relative error is 0.5 percent. It is essential, however, that the above equations assume azimuthal averaging of the pyranometric readings. In the estimation of random errors from single records their values will be much greater, even at small angles E .
-
10.4. Net Radiation and Its Components in a Free Atmosphere
Let us assume, as before, that
E
= 6’
cos CO’ - cos 5‘0 cos C@
and C0
-
= 60’.
689
In this case
0.2
that is, the relative error will increase up to 20 percent. If To = 70°, the relative error is about 30 percent. At large solar zenith distances, therefore, and without the azimuthal averaging of measurement data (relative to the sun), the errors due to the nonhorizontality of the upper pyranometer receiving surface become very significant. That is why the practice of aircraft pyranometric measurements includes repeated taking of the pyranometric readings for the same “area” from two opposite flight directions; “the left-hand side sun” and “the right-hand side sun.” An even more complicated situation takes place when interpreting the results of measurements from balloons because this method cannot be realized there. In this case, however, the problem is alleviated by the balloon’s rotation around its vertical axis as it ascends. Lopukhin [56] compiled a table for the introduction of corrections for the nonhorizontality of the receiving surface in dependence upon solar height. When the horizontality of the pyranometer receiving surface is disturbed, its sighting field changes: instead of the sky section ABB‘C, the inclined upper pyranometer (Fig. 10.10) views the section AD‘DC positioned below the horizontal plane. The change of the sighting field of the lower instrument is similar. This naturally leads to distortion of the readings. Analyzing the measurement errors in this case, Kastrov [54] came to the conclusion that they are not essential. Aircraft or balloons always give rise to certain “perturbations” in the radiation field considered. In the case of aircraft pyranometric measurements it is more important to take account of the “underlighting” of the pyranometer due to the reflection of radiation from the aircraft surface. In Kastrov’s estimation [54] the errors appearing in this case are of secondary importance. With balloons, one must consider the shading of a portion of the sky the by casing. However, if the suspender, at the end of which the pyranometers are fixed, is long enough, the obliterating effect of the casing may be ignored. The usual purpose of aircraft or balloon measurements of the net radiation is to obtain data on its vertical profile and the components and also to determine the radiative flux divergence. It is natural that in order to obtain such data there are needed, strictly speaking, simultaneous actinometric measurements at different atmospheric levels above the given
690
Net Radiation
underlying surface. The net radiation B ( z ) is determined from the formula B(z) = F J ( z ) - F q z )
(10.14)
The radiative flux divergence q is further calculated from the relation q z - dB dz
(10.15)
derived on assumption of the horizontal optical homogeneity of the atmosphere and underlying surface. In reality, if the condition of the horizontal optical homogeneity is upset, the simultaneous measurements of radiant fluxes at different levels are practically impossible. This fact makes it necessary to solve the following two problems. The first problem is related to the need for evaluating the errors caused by the effect of the horizontal optical nonhomogeneity. Rough estimates of this kind were provided by Kastrov [51]. Suppose that the radiant fluxes are measured over a circular area with the albedo A’, which is surrounded by a surface whose albedo is A . Let the medium between the underlying surface and the level considered be vacuum. Designating 0 as the angle at which the radius r of the area is seen from the given level z, obtain the following relationship between the upward and downward radiant fluxes : F ~ ( z= ) F + ( z ) Asin28
+ F+(z)A’cos28
(10.16)
Further, it can easily be seen that the difference in net radiation at the levels z1 and z2 due to the “parasitic” influence of the horizontal nonhomogeneity of the underlying surface will equal d(z,, z2) = F + ( A - A ’ )
(
+ z22 - + z12 ) ‘12
r2
(10.17)
r2
The value d(z,, z 2 ) is the error sought. Since the radiation transformation by the intermediate layer can only smooth the optical contrasts of the underlying surface, the formula (10.17) gives the upper limit of the error considered. Making use of (10.17), Kastrov evaluated the errors appearing in the measurement of the shortwave net radiation for the case where the shiny snow cover of the Rybinskoye reservoir (near Moscow) with the albedo A = 0.82 was surrounded by a surface with almost melted snow (A’ = 0.27). These calculations showed that the effect of the horizontal optical nonhomogeneity of the underlying surface should be particularly
10.4. Net Radiation and Its Components in a Free Atmosphere
69 1
considered in processing measurement data at elevations above 1 km. In the case where the albedo of the investigated area is lower than that of the environment (reservoir in summer) the effect of the horizontal nonhomogeneity turned out to be insignificant. In the real conditions the horizontal optical nonhomogeneity of the underlying surface and atmosphere can be extremely variegated, which makes difficult the accounting of it in processing measurement data. It should be concluded therefore that the most reliable way to solve the problem of the vertical profile of the net radiation and radiative heat inflow consists in measurements over a homogeneous surface with a clear sky. When applying balloons the horizontal homogeneity must be checked by means of photographing the area considered. In the absence of the horizontal homogeneity the measured net radiation values have a narrow local meaning, and the determination of the radiative heat inflow from (10.15) is related to more or less marked errors whose quantitative evaluation is very difficult. The second problem to be solved when plotting the vertical net radiation profile from aircraft or balloon measurement data consists in the reduction of these data to a given moment of time. In the case of measuring the shortwave radiation fluxes, this problem is solved by using approximate empirical formulas that express the dependence of these fluxes upon solar height. For example, Faraponova and Kastrov [64] used the following formula:
Fl
=
So sin h,
=a-bfi
(10.18)
where So is the solar constant for the given day, h, is the solar height, m is the atmospheric mass in the direction to the sun, and a and b are constant, with b > 0 in the case of the downward and b < 0 in the case of the upward flux. The reduction of the results of measurements of the net radiation or longwave radiation fluxes to a given time presents a problem for which a method of solution is not clearly established. In the case of daytime net radiation measurements it appears to be possible to use empirical formulas similar to (10.18). For the longwave radiation fluxes, variability within 1.5 to 2 h is usually considered insignificant. The correct solution of the problem on the basis of theoretical calculations demands knowledge of the transformation of the vertical temperature and humidity profiles over relatively short time intervals (of the order of several hours), which cannot as yet be obtained.
692
Net Radiation
An important factor to be considered in processing the standard actinometric readings (of pyranometers and net radiometers used in aircraft or balloons) is their dependence on temperature and pressure. The calibration of the instruments in the thermobarochamber, imitating the real conditions of the vertical variation of temperature and pressure, should be taken as the simplest and most reliable. It is obvious that such an artificial “ascent” of the instrument can be accepted only as an approximate standard of atmospheric stratification. This is the kind of calibration that was used at the Chair of Atmospheric Physics of Leningrad University [67-721 in the preparation for balloon measurements. 2. Actinometric Radiosondes. It is obvious that the practical use of data on the net radiation and radiative flux divergence in the free atmosphere is possible only when a sufficient volume of the observational material is available. In this connection many recent attempts have been made to construct simple and light net radiometers that might be launched with the standard radiosondes. Such systems, consisting of standard radiosonde and radiometer, are called actinometric radiosondes. Since the problem of daytime net radiation measurements is very difficult and cannot be solved with the help of radiosonde-borne net radiometers, the latter instruments are used at present for nighttime soundings only. The instrument most widely used with actinometric radiosondes is the so-called economical radiometer of Suomi and Kuhn [84a-89], which will be later indentified as the Suomi net radiometer. This instrument has a multilayer system, schematically presented in Fig. 10.11. Here the surfaces
FIG. 10.11 The scheme of the Suomi net radiometer.
labeled P are polyethylene membranes of 12.7-,u thickness. The inside of the radiometer contains mailar membranes, M , of 6.4-p tnickness. The surfaces of the inner mylar membranes are faced with aluminum. The outer mylar membranes are receiving surfaces and are blackened from the outside and coated with aluminum inside. The polyethylene membranes
10.4. Net Radiation and Its Components in a Free Atmosphere
693
P serve as windshields. The instrument is not in vacuum, and the inside pressure therefore always equals the atmospheric pressure of the corresponding level. The curve T depicts the temperature profile of the net radiometer wall characteristic found for conditions of measurement in the middle troposphere. The casing Z is good thermal insulation. Figure 10.12 presents the outside appearance of the actinometric radiosonde. The net radiometer is Seen to be of triangular form. Note here that the board contacting the net radiometer is coated with aluminum. The
FIG. 10.12 Actinometric radiosonde.
+
vertical dimension of the net radiometer ( D 2 4 = 5.6 cm (the membranes P and A4 are at 0.7-cm distance) and the side of the triangle equals 30 cm. Direct measurement is made of the temperatures Tt and Tb of the receiving surfaces, for which temperature sensors are used. The readings of these sensors are transmitted to the ground in the same way as the readings of the standard air temperature sensor of the radiosonde system. The polyethylene light filters pass from 80 to 90 percent of the integral longwave radiation. The remainder (10 to 20 percent) is dispersed as 90 percent reflected and 10 percent absorbed by the polyethylene film. The latter means that the absorption of radiation can be practically ignored. The elementary theory of the net radiometer [87], based on approximate heat balance equations of the receiving surfaces, leads to the following
694
Net Radiation
expression for the net radiation (effective radiation) :
where u is the Stefan-Boltzmann constant, k = l/a(l - ar) (a = 0.85 is the absorptivity of the receiving surfaces, r = 0.16 is the reflectivity of the polyethylene membranes), ci = (I/D)ki(Tb- T t ) is the heat flux due to the molecular thermal conductivity of air (calculations show that the effect of convection can in this case be ignored), il = 5.10-3 cal/cm2 deg is the thermal capacity of the receiving surfaces, and En is the residual term characterizing the influence of secondary errors. Knowing the constant values of the given instrument, the net radiation sought can be easily determined from the measured Tb and Tt by means of (10.19). Since the receiving surfaces in the Suomi net radiometer are separated by thermal air insulation, it is natural that the temperature difference Tb - Tt is quite high, varying from several degrees near the earth’s surface to scores of degrees in the stratosphere. When deriving (10.19) a number of error sources were not taken into account, such as the radiation of the polyethylene filters and of the radiosonde’s casing, the leaking of air from the inside of the ascending net radiometer, the precipitation of white frost or moisture on the outer surfaces and inside the net radiometer, and the adiabatic air cooling inside the net radiometer in ascension. Calculations show, however, that the first two terms of (10.19) are roughly equal and by far exceed the other terms in the right-hand side of (10.19), whose value is not more than 10 percent of the main terms. It should be noted that almost all secondary factors tend to decrease the temperature difference Tb - Tt , which leads to a small systematic underestimation of the measured net radiation value. The ground testing and comparison of the Suomi net radiometer with other instruments [89] showed that this model may be considered quite reliable for nighttime measurements. It should be noted that the multilayer structure of the net radiometer greatly complicates the interpretation of the obtained results, owing primarily to two causes: First, as seen from (10.19), in processing the measurement data it is necessary to know the value ci characterizing the thermal flux from one receiving surface to another due to the molecular thermal conductivity. In (10.19) this flux is taken account of within the “one-dimensional” theory of thermal conductivity. It is obvious, however, that
10.4. Net Radiation and Its Components in a Free Atmosphere
695
the “side” heat fluxes in the horizontal direction can also be effective. Nor can the influence of the convection inside the net radiometer always be ignored, although its quantitative consideration is extremely difficult. Second, it is clear that the many layers of the net radiometer considerably increase its inertia, which is undesirable. Both unfavorable factors are practically eliminated in the net radiometer of the “disc” type, supplied with wind protection in the form of hemispherical polyethylene covers. It is known that with a disc net radiometer (for example the Yanishevsky type [Chapter 1, Ref. 21) adequately calibrated, there is direct proportionality between the net radiation and the temperature difference of the receiving surfaces, while the time constant can be made sufficiently low. From this standpoint the use of the disc net radiometer is preferable. All these considerations however, have little practical importance. The simultaneous balloon flight [90] of the Suomi and the disc types showed that the results reparted by not more than 2 percent. The ground comparisons of the Suomi net radiometer with the ventilated disc model by the same constructor showed that the ratio of their respective readings was 1.01029, with the mean quadratic deviation of 0.02017. The evaluation of the random errors in the net radiation measurements caused by the errors of the determination of the Suomi, type receiving surface temperature (assumed to equal 0.2OC) led to 0.0027 cal/cm2 min for the upper troposphere and stratosphere, and 0.0041 cal/cm2 min for the lower troposphere. This corresponds to the errors in the determination of the temperature variation in the layers of 50-mb thickness, equal to 0.45 and 0.68 deg/day, respectively. For 100-mb thicknesses these errors decrease by twice. Thus, as.can be judged from these data, the accuracy of measurements by means of the Suomi net radiometer is fairly satisfactory. A number of investigations offered modifications of the Suomi net radiometer. For example, Gayevsky [45] described a similar construction, repeating the pyrgeometer type (the “one-side” net radiometer). Kostianoy [76-781 used the principle of the “multilayer” net radiometer in constructing an actinometric radiosonde. Fritschen and Van Wijk [91, 921 constructed a miniature net radiometer whose receiving surface is a standard thermopile closed on both sides with coupled mica filters of 5-p thickness. The instrument has a cylindrical form of 2.54-cm diameter and about 0.5-cm height. The preference of mica to polyethylene as a filter was dictated by the desire to use the wind protection with steadfast water-repelling properties. However, mica has a strong absorption band in the interval 8.8 to 10.3 ,LA
696
Net Radiation
(where the filter transmission is zero) and a very low transmission in the interval 10.3 to 15 p. In this connection Fritschen [91] concluded that the filter should best be made of the polymer membrane Saran wrap (chemical composition not given). Pohl and Muller [93-961 measured the effective radiation with a miniature heated thermistor net radiometer, substituting it for the temperature sensor in the standard American radiosonde. The variation in the resistance of the thermistors caused by the variation in the effective radiation is used for the frequency modulation of the transmitted radio signal. This allows recording of the vertical variation of the effective radiation during the ascension of the radiosonde. Figure 10.13 presents the scheme of the Pohl net radiometer. As seen, it consists of two disc net radiometers whose receiving surface temperature is measured with the help of thermistors 1, 2, 3, 4. The receiving surface DOWNWARD RADIANT FLUX
U?WARO RADIANT FLUX
FIG. 10.13 The scheme of the Pohl net radiometer.
diameter is 3.9 cm. The upper receiving plate of one net radiometer and the lower of the other have electric heating, which generates H amount of heat in these plates. In order to secure an equal heat exchange between the receiving surfaces and the air, the net radiometer is rotated around its vertical axis in ascension. The fundamental theory of this instrument (see
10.4. Net Radiation and Its Components in a Free Atmosphere
697
[97]) gives the following expression for the net radiation (effective):
(10.20) I
where T I ,T2, T, , T4 are the temperatures of the receiving surfaces, and N is the corrective term for the selectivity of the receiving surfaces, the difference in ventilation of the upper and lower plates, and for the effect of their displacement from horizontal. The value N ’ does not exceed 10 percent of F. Since the directly measured values are the receiving surface temperatures and the strength of current in the heating coils, the accuracy of measurement is much dependent on the reliability of the determination of these quantities. With the accuracy of the temperature difference data of 0.2O and the error in the determination of the strength of current not over 2 percent, the total error in the effective radiation measurement is about 15 percent. An interesting model of net radiometer for the actinometric radiosonde was realized by Aagard [98, 991. His instrument, called by the author “a double radiometer,” consists of two discs (detectors A and B ) of 4-cm diameter and 0.5-mm thickness made by tightly coiling constantan wire insulated with epoxyde resin. The upward receiving surfaces are blackened, while the lower are aluminized and coated with thin quartz protection. The lower receiving surface of one disc is screened by an aluminum membrane positioned at 2-mm distance. The detector A operates in the pyrgeometric regime and serves for measuring the downward radiant fluxes. The deviations of the unscreened detector B are determined by the total of the upward and downward fiuxes. Its lower surface is striped black to keep it cooling even in the case when the radiative heat inflow is positive. In winter the entire receiving surface is blackened. Both detectors are self-compensating : The equality in temperature between the discs and the air is reached by passing the current through the constantan wire (the process of temperature equalization is automatic). Knowing the amount of the joule heat emitted in the discs and the air temperature, it is possible to determine the downward and upward radiant fluxes and their difference (the net radiation). The rough theory of the instrument expresses the net (effective) radiation as
1
+%A* (%+1-)
dT dil
(10.21)
698
Net Radiation
Here H A , HB are the generated heat in the detectors A and B due to heating, a, and a, are the emissivities of the upper receiving surfaces and of the lower surface of the detector By A , is the area of the receiving surfaces; and 1, T are the thermal capacity and temperature of the detectors. According to Aagard [98], the accuracy of measurement of the net radiation during the ascension is 20 percent, while during the horizontal drift the errors decrease to 3 percent. Businger and Kuhn [ 1001 performed simultaneous measurements of the atmospheric thermal radiation by means of the follownig four radiation detectors, launched on an automatic balloon up to the height of 25 km during the night of July 30, 1958, Madison, Wisconsin: (1) a Suomi net radiometer; (2) a disc radiometer with blackened upper and lower receiving surfaces (the resistance thermometer inside the disc measures the mean temperature of the upper and lower surfaces, characterizing the total of the radiant fluxes absorbed by both surfaces); (3) a black sphere; (4)a silver sphere blackened from the outside. In the latter two cases the measured value is the temperature of the black sphere. All the mentioned receiving surfaces are protected from wind by polyethylene film. If the intensity of the atmospheric thermal radiation as a function of the angle between the direction of the beam and the vertical Z(0) is changed for the effective temperature T@), determined from the relation (a/n)T,"(0) = I@), where (T is the Stefan-Boltzmann constant, then it is possible to express all the directly measured temperature values (of the black sphere, disc, or detectors of the net radiometer) in terms of Te(0). The results of measurements are therefore presented in the form of the curves of the vertical temperature distribution. If T,,Tb are the temperatures of the upper and lower surfaces of the net radiometer and Tdis the disc's temperature, then Td4= (1/2)(T: Tb4). The agreement of the measured values Tt, Tb, and Tdshowed that they fully satisfy this relation, and consequently the readings of the net radiometer and of the disc radiometer are in agreement. The temperatures of the black and of the silver spheres turned out to be unequal: in the lower zone of the sounded layer the black sphere is warmer, and in the upper, much colder than the black. The authors explain it by the effect of the convection inside the black sphere on the readings of the resistance thermometer inside the sphere. The net radiometer readings determine the vertical variation of the upward, downward, and effective fluxes of thermal radiation. These data are used to calculate the radiation temperature variations at different heights. The latter are compared with the temperature differences of the black sphere
+
10.4. Net Radiation and Its Components in a Free Atmosphere
699
and the air and also of the silver sphere and the air at the corresponding heights. There is found a similarity between the curves of the vertical distribution of the radiation temperature variations (radiative heat inflow) and the temperature difference of the black sphere and the air.
3. Special Instruments for Balloon and Aircraft Measurements. Since the standard pyranometers and actinometers have proved to be sufficiently reliable in measuring the shortwave radiation in the free atmosphere, up to now there was no great need to construct their special aircraft or balloon modifications. It is otherwise with net radiometers. We know that the errors of ground measurements of the net radiation by means of the standard Yanishevsky net radiometers are quite large. Their use for measuring the net radiation in the free atmosphere is made particularly difficult because in processing the obtained results it is necessary to introduce a correction for wind speed, which demands knowledge of this quantity (because wind currents are inevitably present in horizontal attitudes). For aircraft and balloon measurements (up to now realized during the night only) special net radiometers were constructed whose readings are free of the wind effect. Some of them, applied with actinometric radiosondes, have already been described. We shall now speak of other models used by aircraft or free balloon investigators on board the vehicles. Shliakhov [65] used a compensational Yanishevsky net radiometer to measure the effective radiation (the net radiation at night) from free balloons. The instrument imitates the double pyrgeometer, whose upper receiving lamina is electrically heated to the temperature at which the zero balance takes place. In the first approximation the measured net radiation is simply determined by the quantity of the joule heat generated in the lamina (that is, by strength of current passing through the plate). Investigations of the compensating net radiometer showed that its readings are much dependent on the regime of ventilation. In particular, the vertical ventilation can be greatly effective. If, however, the vertical speed of ascension is low (not more than 1 m/sec), the transfer factor of the instrument varies by not more than f 7 percent. In order to eliminate the varying effect of natural ventilation on the readings of the compensating net radiometer, in a number of flights Shliakhov used artificial ventilation with speed of 4 m/sec. When measuring the longwave radiation fluxes Shliakhov [65] also used his own design of a compensating pyrgeometer with higher sensitivity, resembling the “black shining” Angstrom type (see [l, 21). Depending on the sign of the net radiation the electric current is passed through the black
700
Net Radiation
or shiny (polished constantan) stripes for the purpose of equalizing their temperature by generating the joule heat. The rough theory of the instrument shows that the measured net radiation of the black stripes is directly proportional to the emitted joule heat (to the square of the strength of current). Since the readings of the compensating pyrgeometer depend on the regime of ventilation, a forced ventilation was used to “stabilize” its effect. Investigations showed that with the artificial horizontal ventilation of 3.8 m/sec speed and the vertical speeds of ascension not above 1.5 m/sec, the latter do not affect the results of measurements. It was found experimentally that in ventilating the pyrgeometer, the strength of compensation current must be increased. This means that the temperature of the shining stripes is higher than that of the black stripes. In this connection, to eliminate the wind effect in certain models of the pyrgeometer, Shliakhov also used a method of increasing the thermal resistance between the shining stripes and the connected thermojunctions. The empirical selection of thermal insulation practically allows complete avoidance of the influence of vertical ventilation. The evaluation of errors in the measurement of longwave radiation by means of the compensating net radiometer and pyrgeometer showed that they are never in excess of a few percent. The works of Gayevsky [45-48] described aircraft measurements of longwave radiation fluxes in daytime made with a radiation detector consisting of a linear thermopile assembled in a thick brass casing and supplied with fluoric calcium or KRS-5 filters. The main features of the thermopile are [44] : sensitivity 0.7 V/W; inertia, 3 sec; diameter of the receiving surface, 10 mm; resistance, 22 Q; sighting angle (aperture) 90’ (a later model [45] had an almost hemispherical sighting angle and slightly different parameters). The field and laboratory experiments showed that in this case the measurement errors were not above 0.01 cal/cm2 min. The instruments are fixed in the cockpit against the outlets in the ceiling and floor of the cabin. Since the filter transmits some shortwave radiation, special corrections were introduced to eliminate its “parasitic” effect. For this purpose the daytime measurements employed an auxiliary glass filter. The filter completely excluded the wind effect. The numerous calibrations of the instrument after the blackbody resealed the linearity of its scale in a wide temperature range. Houghton and Brewer [101, 1021, for aircraft measurements of thermal radiation fluxes, constructed a vacuum bolometer with a KRS-5 filter. Investigations showed that its readings were strongly dependent on the filter temperature. At small elevations this source of error is not influential.
10.4. Net Radiation and Its Components in a Free Atmosphere
70 1
The total measurement error varies from a few to 10 percent. The description of their aircraft investigations of the radiant fluxes can be found in [103-1071. The first complex actinometric observations from helicopter were realized by Malevsky-Malevich et al. [108-1101. The preceding discussion shows that only the technique of measuring the shortwave radiation and thermal radiant fluxes may be considered sufficiently refined. As to the net radiation measurement, up to now there have been no daytime attempts in the free atmosphere. The matter stands almost the same with respect to the direct solar radiation. In this connection recently there were first steps made in preparation of the complex automatic instruments for daytime balloon measurements of the net radiation and its components [67-721. The primary stage of such investigations was based on the standard actinometric instruments. 4. The Set of Automatic Instruments for Balloon Measurements of Net
Radiation and Its Components: General Features. These instruments enable continuous measurement and recording of the global, direct solar, and reflected radiation of the net radiation, the full upward and downward radiant fluxes, and also of the air temperature, humidity, and pressure of the temperature of the actinometric and recording instruments and the total ozone content. For measuring the global and reflected radiation two standard Yanishevsky pyranometers are used. The direct solar radiation is measured by means of a thermoelectrical actinometer automatically sighted on the sun with the help of a photoelectric system [I 111. The full upward and downward fluxes and the net radiation are measured by means of Yanishevsky and double net radiometers supplied with special windshields. The air temperature is taken by a platinum resistance thermometer, as is the temperature of the instruments. For measuring the pressure and humidity the respective sensors of the standard radiosonde are used. The ozone content is determined according to the spectroscopic method from the ozone absorption bands, in the ultraviolet spectrum.
Construction of the Instruments. The measurement of the direct solar radiation in a free atmosphere is made possible solely by continuous observation of the sun. The main features of the photoelectric watching system are the following: There is a sun-seeker with an all-round survey and three degrees of accuracy in targeting. The accuracy of the continuous watch is
702
Net Radiation
5 angular minutes. The weight of the installation without the power supply is 8 kg, the consumed capacity 20 W, the range of the working temperatures from -70' to +40°C. There are alternating-current amplifiers with transistors. The use of the standard net radiometer for balloon measurements was made possible only after providing special wind protection. The construction of the windshield is shown in Fig. 10.14. The receiving surfaces, 4
2
FIG. 10.14
The windshield of net radiometers.
10.4. Net Radiation and Its Components in a Free Atmosphere
703
and 5 , of the net radiometer are covered with two polyethylene hemispheres, 2, resting on the wire frames, 3. The rings, 1, press the hemispheres to the base of the framework. The testing of the instrument showed that this protection excludes almost completely the wind effect on the readings, and that the system receiving surface protection satisfies the Lambert law. The upward and downward radiant fluxes are measured by a double net radiometer consisting of two net radiometers positioned in parallel. The space between them is divided into three cavities. The middle one is meant for radiative separation of the upper and lower net radiometers. The side cavities are blackened inside, while the bottom temperature is taken with a platinum resistance thermometer. The net radiometers serve as covers for the intermediate cavities. The other receiving surfaces of the net radiometers are protected by polyethylene filters. The construction of the protection is similar to that of Fig. 10.14. Recording of Measurement Data. As has already been mentioned, the measurement of the radiant fluxes is continuous throughout the flight. The zero is fixed for each sensor regularly (every 36 sec) by disconnecting its circuit. The surrounding air temperature is also measured continuously. The platinum resistance thermometer intended for this measurement contacts the bridge scheme of the self-recorder. The other parameters are measured periodically at 36-sec intervals. All the data, except air temperature, are put on record at the tape of a 13-train oscillograph. The time marks are spaced at I-min intervals. The pressure and humidity are ciphered. Also taped are the train readings taken in the check up of their standard tension and sensitivity. Location of Actinometric Instruments of the Recording and Auxiliary Devices. The instruments are fixed to a frame made of duralumin tubes, and suspended by steel ropes and a strap, which increases the distance from the balloon casing to the center of the frame up to 100 m, thus practically eliminating the shading effect of the balloon. The length of the frame is 8 m (Fig. 10.15). The pyranometers, the net radiometer, and pyrgeometer are placed at the ends of the frame, as far as possible from the container with the recording instruments. The pyranometers are situated at the ends of a short-period pendulum fixed at the gimbals. The receiving surface of one is directed downward; of the other, upward. The pendulum period is about 0.3 sec. Such swings of low amplitude are insignificant for the pyranometers, whose time constant is about 20 sec. The net radiometer and pyrgeometer are stiffly fixed to the frame before the flight.
704
Net Radiation
The watching system with an actinometer and ozonometer is fixed at the cover of the thermoinsulating container positioned at the center of the frame (Fig. 10.15).
/-
FIG. 10.15 Arrangement of instruments on the suspension frame. (1) upper pyranometer; (2) lower pyranometer; (3) cloud photorecorder; (4) ozonometer; (5) actinometer; (6) orienting device; (7) radiosonde; (8) air temperature sensor; (9) net radiometers; (10) ozonometer; (1 1) tracking system.
Outside the container are placed the temperature, pressure, and air humidity sensors, and also an instrument for checking the horizontal plane of the frame and the angular height and position of the sun relative to the longitudinal frame axis. The latter instrument was found to be necessary when examining the actinometric recordings on the tape of the oscillograph. The slowly varying (in dependence on height) values of the global and net radiation were affected by periodical disturbances, with an alternating amplitude and periods of about 10 and 72 sec. The readings of this instrument not only enable determination of the cause for such disturbances but also permit introducing corrections to the readings of the upper pyranometer and net radiometer. Inside the thermoinsulating containter there are the recording devices, the program and order block, the amplifiers of the watching system, and the power source (anode batteries, accumulators).
5. Vertical Projile of Radiant Fluxes in the Free Atmosphere. Let us now give a short review of the results of measurement of the radiant fluxes in the free atmosphere. Consider first the more numerous data on the thermal radiation.
10.4. Net Radiation and Its Components in a Free Atmosphere
705
Thermal Radiation. In 1952-1954 Shliakhov [65] conducted a long series of nighttime balloon flights for the purpose of studying the vertical profile of the net radiation during the night. These measurements were realized by means of a special thermoelectric net radiometer and a pyrgeometer constructed by Shliakhov for balloon flights (the main features of the instruments have been given above). The observations were conducted at “platforms.” During the night the balloon managed from 4 to 6 “platforms” at 1-, 2-, 4-,6-, and 8-km elevations. Along with the actinometric measurements, meteorological observations were made and the measurement of the dust content by means of an impactor. According to Shliakhov, the net radiation F = F f - I;+ increases with height and at the highest elevation (8 km) reaches 0.346 cal/cm2 min. The effective radiation of the blackened receiving surface of the pyrgeometer (F‘ = oT4 - I;+, where T is the temperature of the receiving surface of the pyrgeometer) increases up to a certain level ( 5 to 6 km) and then begins to decrease. The comparison of the observed effective radiation with the values calculated from the Shekhter chart reveals a satisfactory agreement in the case where the effective water vapor mass necessary for the calculation of the radiant fluxes with the chart is made after the formula
dpz,
eZcand p is the absolute humidity and atmospheric where f ( p ) = pressure at the level z; and p o = 1000 mb. Observations show that the introduction of the effective water vapor mass, intended to account for the dependence of the absorption upon pressure, is quite important in the conditions of a free atmosphere. It should be noted, however, that the aircraft measurements by Gayevsky [45] showed that above 1 to 2 km the observed longwave radiation fluxes appeared to be by 15 percent more, on the average, than those computed with the help and that of the Shekhter chart (the correction for pressure f ( p ) = the departure of the computed values from the observed values increases with height. This conclusion was justified by the results of the actinometric radiosonde measurements obtained by Kostianoy [76]. It is therefore possible that Shliakhov’s data can be accounted for by the compensation of systematic errors in the calculation of the upward and downward thermal fluxes. Thus the problem of the actually justified form of the correction for the pressure cannot be considered clarified. Gayevsky’s data clearly show that the cause for the increase of the effective radiation with height is a
G),
706
Net Radiation
more rapid vertical decrease of the downward long-wave radiation flux rather than of the upward. Similar results are revealed in Lopukhin’s work [57]. Given in Table 10.13 are the ratios of the downward to upward fluxes with clear skies according to Lopukhin [57]. TABLE 10.13 Ratios of Downward to Upward FIuxes Pressure, mb: 966 FJ/Ff :
965
950
900
814
800
748
697
600
505
422
0.82 0.87 0.81 0.75 0.59 0.69 0.64 0.60 0.53 0.41 0.38
Shliakhov’s values of the radiative air cooling were from a few hundredths to 0.25 deg/h, which means that the corresponding quantities calculated from the Shekhter chart are in a good agreement with the experimental data. The measurements of the dust content at different heights, conducted by Shliakhov [65], showed it to be insignificant over all cases. The effect of dust on the longwave radiation absorption could not therefore be traced. The theoretical calculations confirmed the conclusion that during the night observations, the dust effect cannot be notable. The above investigations refer to the conditions of a clear sky. It is natural that with cloudy skies the vertical profile of the thermal radiation fluxes undergoes considerable transformation. For instance, according to the aircraft measurements of Lopukhin [58], the nighttime vertical increase of the net radiation is not so clear with overcast skies as without clouds. Inside the dense cloud cover of the lower level, as a rule there is the state of radiative equilibrium; the net radiation is either very small or zero. The last conclusion was justified by the results of aircraft measurements of longwave radiation fluxes obtained by Gayevsky [47]. Since near the cloud boundaries the observed vertical gradients of the longwave radiation fluxes are large, the radiative temperature variations, especially above the clouds, are greater than with clear skies. With net radiation in the region of lower clouds decreasing, observations indicate radiative heating in this area. At the upper cloud boundary a strong radiative cooling takes place. For example, Lopukhin [58] observed the radiative heating under the lower stratus clouds equal to 0.06 deg/h; and above the cloud tops, the cooling of 0.28 deg/h. The above results of aircraft and balloon measurements of the longwave radiation fluxes relate to comparatively small heights. Certain recent investigations have been busy with measuring the thermal radiation fluxes
10.4. Net Radiation and Its Components in a Free Atmosphere
707
at different atmospheric heights, including the stratosphere. They were realized mainly by means of actinometric radiosondes. The data on the stratosphere give some experimental information about the outgoing radiation. Kuhn et al. [112], for example, obtained the following thermal radiation flux values at 20 km on a clear summer night: F f = 0.36 cal/cm2 min, and FC = 0.04 cal/cm2 min. On a clear winter night at 12 km, F f = 0.27 and F J = 0.08 cal/cm2 min. The authors of [112] assume that the outgoing radiation Fm = F f - FC. On this assumption the experimental data for the outgoing radiation considerably depart from the theoretical calculation of the upward thermal radiation flux at the level of the tropopause. It appears that the assumption F, FT', where FTf is the upward thermal flux at the tropopause, should be considered better substantiated than the identification of the outgoing radiation with the flux difference F f - FC. This is justified not only by theoretical calculations but also by experiments. Actually, according to Kuhn et al. [112], in all cases F f F J . This means that the upward flux is only slightly transformed by the stratosphere and the difference F, - F t is clearly less than F J . In Kagan's estimation [113] the outgoing longwave radiation may be identified with the upward flux at the level of 100 mb. As given in [112], with a clear sky the observed effective radiation increases with height up to the stratosphere. It is natural though that the vertical gradient of the effective radiation should decreases as the height increases, especially in winter. For example, the actinometric radiosonde launched on February 17, 1958, showed that already in the layer 200 to 300 mb there is a radiative equilibrium (the vertical gradient of the effective radiation is zero). Kuhn and Suomi [114] published the results of 15 simultaneous launchings of actinometric radiosondes made at different points on the territory of the central and western United States on July 29, 1959. Thus the first experimental data characterizing the geographical variability of the outgoing radiation were obtained. At a later date similar results were derived by Kostianoy and Pakhomova [77] and by Kostianoy [115, 1161. The authors of [114] used two vertical cross sections to characterize the spatial distribution of the effective radiation flux F f - F J in the layer from the earth's surface to about 30 km elevation. Figure 10.16 gives a vertical cross section of the effective radiation field (expressed in hundredths of cal/cm2 min) for 0600 h of July, 1959 from Las Vegas to the International Falls (Minnesota). Analysis of the vertical sections shows that the effective radiation distribution near the ceiling of sounding is similar to the field of radiation in the
-
>
Net Radiation
708 km
FIG. 10.16
mb
Vertical cross section of the net radiation field (lo-$ calJcrnemin) between Yegas and I n t e ~ ~ ~ Fa& ~ o n~a~~ ~ n ~ s July o f a29,) ,1959, ~6~ h.
troposphere in that it is determined first of all by the rne~eorolo~cal regime of the troposphere. For example, the minimal effective radiation i s observed in the frontal region. The radiation field is found to be greatly variable at 25 to 30 krn elevation, depending on the type of air masses. With tropical sea air the mean value of the effective radiation at 25 km is 0.35 cal/cm2 mia. With conditions of a weak front, the measurements reveal a variation in
10.4. Net Radiation and Its Components in a Free Atmosphere
709
the effective radiation of 22 percent in the passage from one air mass to another. The maximal heat influx due to the longwave radiation occurs in the lower half of the troposphere. For the layer, for example, situated between the earth’s surface and the 400-mb level, the mean difference in effective radiation at the borderline is 0.20 cal/cm2 min, whereas the corresponding value for the layer from 400 to 15 mb is only 0.07 cal/cm2 min. Thus, about three-quarters of the total heat influx takes place in the tropospheric layer below 7 km. Figure 10.17 illustrates the data characterizing the vertical section of the radiative flux divergence (in cal/cm2min for a 100-mb layer) and clearly
SOUNDING POINTS
FIG. 10.17
cal/cm2min, for a Vertical cross section of the radiative divergence 100-mb layer) under the same conditions as in Fig. 10.16.
710
Net Radiation
shows the complexity of the spatial structure of the radiative heat inflow field. Here the regions of radiative cooling are marked C and those of heating are W . Staley and Kuhn [90] carried out two launchings of actinometric sondes in the area of intensive baroclynic zones in the middle troposphere. One of the ascents (April 5, 1958, southwestern United States) revealed an anomalous vertical profile of the effective radiation and the upward longwave radiant flux. Beginning from the upper boundary of the temperature inversion in the baroclynic zone to the ceiling of sounding (near 125 mb), the upward flux increases with height in spite of the monotonic decrease of the air temperature. Analysis of the possible causes for this abnormality shows that the most probable of them is the transfer of the radiosonde from the area obliterated by clouds to the cloudless atmosphere with a warm underlying surface. This justifies the importance of taking into account the horizontal nonhomogeneity of the atmosphere and underlying surface in the interpretation of the measurement data on the radiant fluxes in the free atmosphere. This also makes it possible to expect, in particular, that the results of measurements of the radiant fluxes from satellites and from balloons will be different. The calculation of the vertical profiles of the radiative temperature variations in both cases yielded quantitatively similar results. The obtained vertical dependences of the radiative temperature variations were sharply nonmonotonic with a transition from radiative cooling to heating in the baroclynic zones. The radiative cooling above and below these zones very from 0 to 4-5 deg/day. The radiative heating in the baroclynic zones is slightly less, but with a maximum of 4 deg/day. The curves of the vertical distribution of the radiative temperature variations at maximal height enables us to suppose that radiative heating occurs in the tropopause. The qualitative comparison of the experimental data with the results of theoretical calculations reveals a satisfactory agreement (except that the measurements do not show the radiative cooling at the upper inversion layer boundary predicted by theory). This may be explained by the low “resolving power” of the instruments, which does not allow detection of the radiative temperature variations in relatively thin atmospheric layers. According to 50 actinometric radiosoundings (with a Pohl net radiometer) performed by Ronicke [I171 at San Salvador (Central America) in different seasons, the mean vaules of the upward longwave radiation flux in the lower stratosphere is 0.35 cal/cm2 min in the dry season, 0.32 cal/cm2 min in the transitional period, and 0.29 cal/cm2 min during the rainy season. In all cases the observed effective radiation increased up to
10.4. Net Radiation and Its Components in a Free Atmosphere
71 1
about the tropopause and then slightly decreased with height in the lower stratosphere. According to the measurements of Fenn and Weickmann [97] in the Thule area (Greenland), made on February 14, 1959, the effective radiant flux at about 30-km height was approximately 0.16 cal/cm2 min. The vertical profile of the effective radiation is characterized by its increase with height from 0.05 cal/cm2 rnin at ground level to 0.20 cal/cm2 rnin within 15 to 20 km. Above 20 km the effective radiation was observed to decrease with height. Comparison of the results of these measurements with the above data for the intermediate latitudes shows that the Arctic values of the effective radiation are much smaller. It is obviously explained, in the main, by the low temperature of the underlying surface during the polar night. The actinometric radiosounding carried out by Muller [93], mostly in the cloudless conditions, showed, that on May 4, 1959 (18.21 to 20.20 GMT), the net longwave radiation increased from 0.075 cal/cm2 rnin at ground level to 0.315 cal/cm2 rnin at the height of 10.2 km (this level does not coincide with the minimal temperature level in the tropopause), then decreased to 0.195 cal/cm2 min at 13.75 km, and finally increased to 0.210 cal/cm2 rnin near 24 km. Comparison with the calculations from the Moller chart shows that the agreement in the troposphere is good but that the calculations do not reveal the inversion in the variation of the net longwave radiation in the stratosphere. The mean (over 46 launchings) vertical profile of the net radiation clearly demonstrates the above-mentioned inversion in the net radiation variation in the stratosphere. Analysis of the averaged profiles of the net longwave radiation relating to different circulation types showed that the minimal values of the outgoing radiation are observed with the zonal circulation ; the maximal, with the meridional. Mantis [118] studied the regularities in the variation of the outgoing radiation from measurement data on the temperature T R of a black sphere. The sounding with the black-sphere method showed that above 60 mb, the temperature TR had no vertical variation (the decrease with height of the downward longwave radiation flux in the stratosphere appears to be compensated by the increase of the upward flux). For the determination of the outgoing radiation it was therefore possible to use the following empirical formula F, = 2.12aTR4(50 mb) (10.22) where a is the Stefan-Boltzmann constant, and T R (50 mb) is the temperature of the black sphere at 50-mb level. Using this formula for the calcula-
712
Net Radiation
tion of F,, Mantis found out a strong decrease of the outgoing radiation connected with the increase in the upper cloud amount. Since the cirrus cloud has little effect on the incoming shortwave radiation, the net radiation of the system earth-atmosphere should therefore be expected to increase with the upper level clouds. With clear skies the outgoing radiation showed little variation, although the total water vapor content in a vertical column of atmosphere was greatly varying. The temperature dependence of the outgoing radiation was likewise weakly expressed. Three nighttime soundings at different places were used to plot charts of the isolines of the outgoing radiation over the eastern United States. These charts clearly show that cloudiness is the main factor that determines the variability of radiation. The latitudinal dependence of the outgoing radiation is characterized by a decrease northward. The obtained values of the outgoing radiation are in satisfactory agreement with the results of theoretical calculations. The averaging of all observational data gave a value of 0.345 cal/cm2 min. The mean effective radiation of the earth’s surface is 0.064 cal/cm2 min. Thus the heat loss due to the radiative cooling of the entire atmospheric thickness is 0.281 cal/cm2 min. The accuracy of these determinations is about 5 percent. Shortwave Radiation. Although the measurements of shortwave radiation fluxes in the free atmosphere are fairly numerous, all relate to relatively low heights. Since 1946-1947 the Central Aerological Observatory and then the Geophysical Observatory of Tashkent as well as some other local geophysical observatories (in Kiev, Minsk, Odessa) have been undertaking investigations of various elements of the net radiation in the free atmosphere, of the shortwave radiant fluxes above all. A great contribution to the development and direction of these studies was made by an outstanding Soviet specialists in actinometry and atmospheric optics, V. G. Kastrov, whose work dealt with the methods for measurements and with a number of important actinometric problems concerning the free atmosphere. The above research employed free balloons, automatic stratostats, and aircraft. The first stage of the investigations was devoted mainly to the vertical profiles of shortwave (global and reflected) radiation. Observations were usually conducted only during clear or almost clear days. The purpose of this research was to study the factors of the shortwave radiation attenuation in the atmosphere and to obtain information on the radiant heat inflow due to shortwave radiation at different atmospheric levels.
10.4. Net Radiation and Its Components in a Free Atmosphere
713
The applied instruments were standard actinometers used with surface measurements (pyranometers, actinometers, pyrheliometers). In the measurements from free balloons the pyranometers were fixed on gimbals and dropped from a cord at 50 to 70 m below the balloon cabin. The balloon ceiling was usually 7 to 9 km. The heights reached by aircraft varied from 3 to 6 km. In all cases along with the actinometric measurements recorded were the temperature, pressure, and humidity of the air. In 1953-1954 Piatovskaya [60, 61 ] conducted aircraft measurements of shortwave radiation fluxes up to 3 km, over various homogeneous surfaces with clear skies and with clouds of force 2, not more (Leningrad region). In the observation of the global radiation a standard Yanishevksy pyranometer was used. To measure the reflected radiation a special high sensitivity pyranometer was applied. The readings were taken at 200,500,1000,1500,2000,2500, and 3000 m. The technique of processing the readings was usually in combination with Kastrov’s method, which takes into account the peculiarities of aircraft actinometric measurements. According to [60], the global radiation almost always increases with height. Its decrease occurred only in the cases where the sun was obscured by cirrus clouds invisible to the eye. The gradient of the increase was in all cases decreasing with height, especially above 2 km. For example, in the layer 0 to 1 km it averaged 0.076 cal/cm2 min km, while for 2 to 3 km it decreased to 0.034 cal/cm2 min km. The dependence of the global radiation fluxes upon the altitude of the sun is in all cases nonlinear, The attenuation of the global radiation in the 0- to 3-km layer has an annual mean of 0.18 cal/cm2 min. The measurements of the reflected radiation (upward flux) were made above Lake Ladoga (Leningrad region) over all seasons and above a homogeneous area with crop planting (in winter a smooth snow field). The reflected radiation almost always increased with height, and its vertical profile depended upon the underlying surface type. As did global radiation, the reflected radiation showed a notable vertical increase only in the layer 1.5 to 2 km thick, above which it either rapidly slowed down or completely stopped. The vertical gradient of the reflected radiation was greatly variable. The maximal gradients were observed in the layer 1 to 2 km. For example, averaged over a year, the vertical gradient in this layer is 0.018 cal/cm2 min km, while in the underlying layer 0 to 1 km, it is 0.009 kal/cm2 min km and 0.008 kal/cm2 min km for the 2- to 3-km level. Calculations of the net shortwave radiation as a difference between the global and reflected radiation give, as a rule, an increase of the net radiation with height. The net radiation difference between two levels was used to
714
Net Radiation
calculate the shortwave radiation absorption by l-km layers. The absorbed radiation greatly varies in dependence upon season and decreases with height. For a year the absorbed radiation in the entire 0- to 3-km layer was, on the average, 0.135 cal/cm2 min. Calculations of the shortwave radiation absorption by water vapor from the Moller and Kastrov formulas showed that it decreased with height, and had a summer maximum and a winter minimum, averaging 0.042 cal/cm2 min for a year in the 0- to 3-km layer. The ratio of the measured absorbed radiation to that calculated by taking account of the absorption by water vapor only decreases with height. In the 0- to 3-km layer, its mean shows little seasonal variation, and the above ratio is, on the average, 3.2 for a year. The absorbed radiation values were used to calculate the radiative heating. Individual values of the radiative heating vary within a wide range from hundredths to 0.3 deg/h. Averaged over a year, the radiative heating is 0.1 deg/h in the 0- to 3-km layer. When calculated, taking into account the absorption by water vapor only, it was 0.03 deg/h. Interesting aircraft measurements of the shortwave radiation fluxes up to relatively high elevations (13 km) were carried out by Roach [119]. The data of these observations were processed to obtain the albedo and radiative heat inflow due to the absorption of shortwave radiation. Similarly to the above mentioned Soviet results, Roach found a considerable residual absorption of the shortwave radiation caused by aerosols. In atmospheric layers strongly polluted with aerosols, the radiative air heating can exceed 10 deg/day. Brewer and Wilson [120] have carried out measurements of solar ultraviolet radiation in a free atmosphere.
The Net Radiation and Its Components. Above has been described a set of automatic balloon instruments intended for daytime measurements of the net radiation and its components. Let us now consider some results of the balloon measurements, as given in [67-771. The daytime sounding with actionometric balloons up to 25 to 32 km was started in 1961. The data on the radiant flux profiles, obtained in 19611962 are summarized in [55, 681. We shall treat the results of 1963-1964 [71]. Knowledge of the radiant flux profiles makes it possible to study the energy transformation in the atmosphere, to find the seasonal peculiarities in the variation of the radiant fluxes, and to estimate the outgoing radiation. The gradients of the radiant fluxes enable calculation of the radiative flux divergence over each atmospheric component in the thermal regime. One of the soundings with a set of actinometric instruments was perfor-
715
10.4. Net Radiation and Its Components in a Free Atmosphere
med on October 23, 1964. The ascension took 2 h 30 min. The variation in the solar height during this period was 4' (from 26'21' to 22'36'). The area was exposed to the influence of a high-pressure ridge expanding over the eastern European territory of the U.S.S.R. in the zone of the washed out polar front that separated the continental temperature air from the continental tropical air. The branch of the Arctic front was near the polar. For this reason at some elevation there was observed a zone of close pressure isolines. It represented the stream flow passing from Tselinograd (North Kazakh, S.S.R.) to the southern Urals-Kuibyshev (on theVo1ga)Syktyvkar (on the N. Dvina). The launching was carried out in the outer anticyclonic area of the stream flow. Radiant Fluxes. Direct Solar Radiation S (Fig. 10.18). After the instruments were removed from the cloud at 1.9-km altitude, the actionometer was automatically targeted on the sun. The value S at this altitude was 1.22 cal/cm2 min. In the layer from 2 to 5 km, the solar radiation increased by a quantity AS = 0.35 cal/cm2 min. The increase of S then slowed down, but continued up to a height of 22 km, where S = 1.94 cal/cm2 min. Above 22 km, the flux of direct solar radiation was practically constant.
The Reflected Radiation Rk (Fig. 10.18). The ground value of the reflected radiation flux was 0.035 cal/cm2 min. It was the same up to the level of the continuous cloudiness (1 km).
Q
------ --___-__
-- _-__
6 18 20 22 24 26 28 H, km
FIG. 10.18
30
Q-R -R
B
32
Vertical profiles of net radiation and its components measured in the ascent on October 23, 1964.
716
Net Radiation
In the cloud layer, Rk increased with a gradient 0.086 cal/cm2 rnin km in the lower part, with 0.187 cal/cm2 rnin km in the middle, and with 0.16 cal/cm2 rnin km in the upper layer. The maximal value during the given flight was 0.5 cal/cm2 min. With increasing balloon elevation above the cloud the reflected radiation decreased of 0.3 cal/cm2 rnin at the heights over 24 km (h, = 23'). The fall of 0.05 cal/cm2 rnin at the very end of the ascension related to the discontinuity in the cloud underlying the balloon.
The Net Radiation B (Fig. 10.18). Two types of net radiometer with a polyethylene wind protection were used for measuring B with the usual Yanishevsky and a double net radiometers. The vertical profiles of the net radiation obtained by means of both instruments fully coincide, but the range of fluctuations of B as shown by the double net radiometer was probably due to the use of gimbals. The systematic deviation between the respective net radiation readings was 15 to 20 percent. Those of the usual net radiometer were taken to be the principal readings because it was calibrated in the wind channel, whereas the double net radiometer was calibrated with respect to the sun at the horizontal position of its receiving surface. The ground value of the net radiation was 0.125 cal/cm2 min and did not vary in the space below the cloud nor even up to the middle cloud level. At about 7 km there was a small minimum of 0.1 cal/cm2 min, while above this altitude the observed B gradually increased to 0.24 cal/cm2 rnin at 28.5 km, which can be explained mainly by the changing properties of the underliyng surface. The Albedo A (Fig. 10.19, curve 3). In the layer under the cloud the albedo varied from 18 to 20 percent. The " peak " albedo inside the cloud reached 85 percent, after which it showed a monotonic decrease. At 20 km its value was already 42 percent, remaining at that up to 27 km and then decreasing slowly (with a decrease in R k ) down to 35 percent at the level of 31.5 km. The decrease of the albedo over 27 km resulted from the change in the nature of the underlying surface (cloud conditions). The Global Radiation Q (Fig. 10.18). The global radiation value at ground level equaled 0.2 cal/cm2 min. In the layer below the cloud and in the lower cloud, Q was practically constant. It increased to 0.66 cal/cm2 min. closer to the upper cloud boundary and was equal to 0.65 cal/cm2 rnin above the cloud top. The variation of the global radiation flux in the layer from 2 to 6 km was by about 0.12 cal/cm2 min. From 8 to 20 km it increased only by 0.03 cal/cm2 min, which is explained by the increase of S and the vertical decrease of the diffuse radiation. Above 26 km, Q was slowly increasing.
10.4. Net Radiation and Its Components in a Free Atmosphere
717
The value of the global radiation at the level of the sounding ceiling (31.5 km) was fully determined by S' = S sin h, , that is, the contribution of the diffuse radiation was insignificant. A 100
90
80 70 60
$. 50 a 40
O'
2
4
6 8 10 I2 14 16 18 20 22 24 26 28 30 32H, km
FIG. 10.19 Vertical albedo profiles. (1,2) for clear weather; (3) for cloudiness.
Net Shortwave Radiation Q - Rk (Fig. 10.18). This flux was calculated from the profiles Q and R k and was characteristic of the shortwave radiation transfer. The values Q - Rk within the cloud and below fluctuate near 0.15 cal/cm2 min. Their minimum in the middle cloud was 0.08 cal/cm2 min. In the upper layer Q - Rk reached 0.18 cal/cm2 min, while closer to the upper cloud boundary it decreased to 0.14 cal/cm2 min. Above the cloud the variation of the net shortwave radiation is caused by the increase of Q (up to 10 km) and decrease of Rk (within 10 to 20 km). Analysis of the results of a number of soundings reveals some general regularities in the transformation of the radiant fluxes and the fields of the meteorological elements during the summer and fall periods. Let us consider the profiles of the net radiation and its main components typical of these seasons, obtained in the soundings of 1963-1964.
The Net Radiation with a summer homogeneous underlying surface is transformed chiefly in the troposphere (Fig. 10.20). A state close to radiative equilibrium was observed in the morning hours at the solar height h, = = 25 to 30' (curves 1,2). Here the dashes indicate a probable variation of the net radiation for a homogeneous underlying surface. In fall the profile of the net radiation is likewise little variable (curve 3). With solar heights
718
Net Radiation
25 to 30°, the change in the net radiation usually occurred only within the lower 5-km layer. The exceptions are the data corresponding to the curve 3. The increase of the net radiation in the 8- to 21-km layer from 0.1 to 0.24
0
2
FIG. 10.20 (1,2) summer, h,
4
6
8
-
10 12 14 16 18 20 22 24 26 28 30 32 H,km
Vertical profiles of net radiation for summer and autumn. (3) autumn, h, = 26'; (4) summer, h, = 58'.
= 26-30';
cal/cm2 min was related to the decrease of the global radiation (see Fig. 10.18). It should be noted that the profiles 1 to 3 are reduced to the fixed solar altitudes. The profile 3, for example, is reduced to 26'32'. The minimal net radiation was obtained at low altitudes of the sun and with snow cover in November ( B = 0.07 cal/cm2 min). The Direct Solar Radiation (Fig. 10.21) undergoes changes up to about 15 to 22 km. Its vertical profile depends on the content and vertical distribution of the attenuating components : water vapor and aerosol particles.
0.8 0.6
/ *
Figure 10.21 gives four profiles of the direct solar radiation plotted from the data for the summer (curves 1, 2, 3) and fall (curve 4) periods. The air masses whose attenuating properties are characterized by the considered profiles are essentially different with respect to the content of water vapor and aerosol particles. Curve 1 was plotted with a mean atmospheric mois-
10.4. Net Radiation and Its Components in a Free Atmosphere
719
ture content equal to 2.4 " cm " of precipitated water. Profile 2 refers to the air mass of the type " warm sea," with the moisture content of 4.7 cm of precipitated water. The profiles 3 and 4 correspond to 3.5 and 1.78 cm, respectively. The considerable turbidity of the troposphere was an almost constant peculiarity of the zone of sounding. The exception was the case where there was an air mass of high transparency (profile 1) above the layer of the continuous lower cloud. The aerosol layers in the lower atmosphere are usually situated at 1 to 2 and 3 to 5 km, which is indicated by the change in the inclination of the direct solar radiation profiles of these obtained at different solar altitudes in July (1963-1964). It should be noted that differences between individual profiles disappeared above 21 km. The difference between the fluxes of solar radiation near the ceiling of sounding for the summer and fall measurements is determined by the variation in the sun-earth distance. The solar radiation profiles obtained at the heights of the sun 55' to 60' were characterized by variation of S only within the troposphere (curves 1,2). A notable increase of the direct solar radiation at h, = 25' to 30' continued up to 21 km. Above that height the increase of S continued by about 0.007 cal/cm2 min km. The measured S at the peak point of sounding was 1.87 cal/cm2 min in summer and 1.97 cal/cm2 min in fall. Reducing these values to the mean sun-earth distance, we have 1.93 and 1.94 cal/cm2 min, respectively. The given S profiles were obtained with the use of new corrections for the effect of surrounding temperature on the readings of the actinometer. Laboratory investigations revealed that the temperature correction is very important and that the correction for the joint effect of temperature and pressure cannot be determined with sufficient accuracy. The value of the mean temperature correction to the sensitivity of the actinometer is 0.0875 percent per degree.
Global Radiation Q (Fig. 10.22). The global radiation fluxes obtained at the altitudes of the sun close to 30' (curves 2,3,4) undergo transformation practically only in the lower 10-km layer. In the 10- to 15-km layer the decrease in the diffuse radiation is compensated by an increase of the direct solar radiation, and in this layer Q remains constant. Above 15 km the global radiation slowly increases with a decreasing attenuating air mass. The contribution of the diffuse radiation above 16 km can be ignored. The vertical global radiation profiles 2, 3, 4 are reduced to the fixed solar altitudes. Profile 2, for example, is reduced to h, = 30°, the other two to h, = 26'10'. The difference of the global radiation fluxes in the stratosphere results from the inequality of the solar altitudes during the measurements.
720
Net Radiation
Profiles 1 and 4 were obtained with complete cloud at the heights 2 to 3 and 1 to 2 km, respectively.
L
,
.
0
2
4
8
6
10 12
14
16
18 20 22 24 26 28 3032-
Y km
FIG. 10.22 Vertical profiles of global radiation for summer and fall. (1) summer, h, = 60°; (2, 3) summer, h, = 26-30'; (4) fall, h, = 2 6 O .
Reflected Radiation Rk (Fig. 10.23). The reflected radiation fluxes with clear skies depend more on solar altitude than on cloud. For example, the close profiles 2, 4, and 5 were obtained at a clear sky, but the profile 2
0
2
4
6
8
10 12
14
16 18 20 22 2 4 26 28 30 32 H, km
FIG. 10.23 Vertical profiles of reflected shortwave radiation. (1) summer, h, = 5 8 O , Sc force 10; (2) summer, h, = 5 5 O , clear; (3) summer, h, = 53O, cloud of three layers; (4) summer, h, = 30°, clear; (5) summer, h, = 2S0, clear; (6) autumn, h, = 2 6 O , Sc force 10.
corresponds to h, = 56' to 60°, while the profiles 4, 5 correspond to h, = 30' to 35'. The profiles 1, 3, and 6, relating to the conditions of a cloudy sky, are notably different because the profiles 1 and 3 correspond to greater solar heights than does profile 6. With an increasing height the value Rk in the sounding zone for a clear sky increased by 20 to 25 percent, and
10.4. Net Radiation and Its Components in a Free Atmosphere
72 1
for an overcast sky increased by 30 to 40 percent above the cloud level. Near the upper cloud boundary, Rk reached 0.9 cal/cm2 min. This value appears to be the highest possible for the temperate latitudes. At ground level, Rk varied from 0.04 to 0.2 cal/cm2 min. Profile 3 characterizes the variation of Rkwith three level clouds. The decrease of Rk above 10 km resulted from the variation in the underlying clouds. The same factor influenced the variation of Rk near the ceiling of sounding in the case of curves 5 and 6. The Albedo (Fig. 10.19). The variation of albedo with height is represented by only three profiles, all obtained at h, = 25' to 35'. Profile 1 is typical of the summer season, although its values are slightly higher than the usual summer means. As to the strong variability of the albedo represented by curve 3, this, as has already been mentioned, is caused by the cloud effect. Radiative Flux Divergence. The set of measurements compiled for net radiation and its components made it possible to obtain detailed profiles of the shortwave and longwave radiant fluxes. The vertical profiles of the total shortwave and longwave net radiation were used to calculate the radiative flux divergence and also the radiation temperature variations for 50-mb layers.t At this point certain details of the profiles of the radiant fluxes related to the effect of the horizontal nonhomogeneity of the underlying surface were corrected. Figure 10.24 displays the vertical profiles of the
t
1
408
V
H. km
FIG. 10.24 Radiation temperature variations for 50-mb layers from measurements of the integral net radiation. (1,2) summer; (3) autumn. t Kostianoy has discussed possibilities of direct measurements of the radiative flux divergence in his work [121].
722
Net Radiation
radiation temperature variations calculated from the total net radiation. Profiles 1 and 2 determine (ar/at),&d for the morning hours (h, = 25' to 35') on a clear July day. Profile 3 refers to the noon (h, = 25') of October 23, 1964. As is evident, the profiles of the radiation temperature variations in the considered cases are very different, although there are some common features expressed in the transition from the zones of radiative heating to the zones of cooling. Since the vertical net radiation profile varies only slightly, the values (aT/at),&dare small (except profile 3, obtained with an anomalous variation of the net radiation) and fluctuate near zero (radiative equilibrium). In the 3- to E-km layer there occurred insignificant cooling of about 0.02 deg/h, while in the 8- to 28-km layer a tendency to heating was observed. Figures 10.25 and 10.26 present the vertical profiles of the 3
0.30
0.14 0.12 0.10 0.0 0.6 0.4 0.2
0.0 -0.02 -0,06t -0.10
I
0
1,II I$II
IIII
4 6
6
I0
12
I4
16
I6
20 22 24 26 28 30 32
H , km
-0.14
- 0 26
-0.30
FIG. 10.25 Radiative heating for 50-mb layers due to absorption of shortwave radiation. (1,2) summer; (3) autumn.
radiation temperature variations, calculated from the shortwave and longwave net radiation. Here the sharp variations of (aT/at),,, for profile 3 relating to a cloud layer should be noted. It should also be noted that the great variations of (ar/at),,d calculated from Q - Rk correspond to a notable variation of the opposite sign for (aT/at),&d,calculated from Blw. Thus, in the majority of cases, the marked radiative cooling due to the
10.4. Net Radiation and Its Components in a Free Atmosphere
723
longwave radiation relate to the atmospheric layers that strongly absorb shortwave radiation.
c 0 24 0 20 0 16 0 12
0 08 0.l -34
0 02
-0.02 -006 -010 -0.14
-0.18
-0.22
FIG. 10.26 Radiation temperature variation for 50-mb layers due to longwave radiation. (1) summer; (2) autumn.
As has already been mentioned, the total net radiation in the sounding zone varied little, especially at low solar altitudes. Therefore the effect of the nonhomogeneity of the underlying surface (for instance, the underlying cloud variation) would lead to a notable exaggeration or underestimation of the radiation temperature variations. Such distortions appear to have taken place for the case described by profile 3. For the profiles (b’T/b’t)rad calculated from Q - R, negative values were at times obtained. For example, during the measurements inside a cloud layer there were obtained considerable values of -0.26 deg/h (the cloud layer is dashed). Such results can be explained by two causes: (1) by the horizontal nonhomogeneity of the shortwave radiation field inside the cloud; (2) by the precipitation of moisture on the protecting covers of the instruments during the passage through clouds. Rocket Measurements. Recent years have seen the first steps in devoloping rocket methods for investigation of outgoing radiation. Kasatkin [1221 described the construction of a high-altitude optical
724
Net Radiation
station designed for complex investigations of the radiative field at great elevations, in a wide spectral region. The station was envisaged as comprising a great number of instruments, such as telephotometers, teleradiometers, telespectrometers, spectroanalyzers, and net radiometers. Liventzov et al. [I231 made a rocket radiometer for measuring the integral longwave outgoing radiation. The radiation detector of this instrument, based on the principle of differentiation (the outgoing radiation is measured as the difference in the radiation of the earth and space), is a bismuth bolometer. Table 10.14 gives the results of the measurements carried out by Liventzov et al. [123] in 1958-1961. For comparison (which should be considered only conditional) are also given certain theoretical calculations. The outgoing radiation values are expressed in watts per square meter and also through the effective temperature TOK. Although comparison of the results of measurements and calculations is conditional (the latter are of climatological nature), it may still be noted that the measured values are in all cases less than those calculated. Since 1958 Markov et al. [124, 1251 have been carrying out systematic investigations of the outgoing infrared radiation by means of rocket- and balloon-borne instruments. The angular distribution of the outgoing radiation intensity was measured from rockets in the 0.8- to 40-p spectral region at 100 to 400 km, and simultaneously in the atmospheric thickness up to 30 km from geophysical balloons (about 50 measurements in all). The angular resolving power of the instruments was 2 x rad. The authors of [I241 have made the following conclusions of their research: (1) The observed agreement between the results of measurements and calculations is satisfactory. (2) The contribution of the upper atmospheric layers to the outgoing radiation is considerably greater than it was supposed (the height of the radiating thickness in the atmosphere can reach 150 km, and the vertical distribution of contributions to the radiation takes place over the layers, in particular, for the 2.5- to 8-p spectral region over 280, 430, and 500 km). (3) The angular distribution of the outgoing radiation does not show any small-scale nonhomogeneities. (4) There is no marked daily variation in the angular distribution of the outgoing radiation (of chief importance are the meteorological conditions of the moment).
Recently [124, 126, 1271 detailed investigations of the angular and spectral distribution of the outgoing longwave radiation have been made. Using instruments mounted on geophysical rockets that were launched to 500
TABLE 10.14 Results of Rocket Measurements and Theoretical Calculations of the Integral Longwave Outgoing Radiation. Afrer Liventzov et a!. [123 1
Theoretical Calculations
Experiments Conditions of Measurement
Clear
~
1
Kondratyev Filipovich
1.2x1O2 216
2 . 2 ~ 1 0250 ~
Moderate cloud
...
...
Complete cloud
...
...
0 . 9 ~ 1 0200 ~
...
...
2.1 x102 248
1 . 4 ~ 1 0224 ~
...
.. .
1 . 8 ~ 1 0238 ~
470
200
200
20
16
15
Date
8/27/58
7110159
6/15/60
2/15/61
Moscow time
0.8, 0.6
0.4, 12
0.5, 42
Near noon
Elevation, km Mean ground temperature, O C
100
-2
Simpson
Bauer, Philipps
1 . 9 ~ 1 0242 ~
1 . 8 ~ 1 0238 ~
726
Net Radiation
km on November 18, 1962, and June 18, 1963, Markov et al. [124, 126, 1281 realized simultaneous measurements of the spectral composition (wavelength interval 4 to 38 p ) and angular distribution (range of angles f90’ relative to the nadir) of the outgoing radiation. The measurements were made during both upward and downward flight by means of an impulse infrared rocket spectrometer. The spectral resolution of the radiation was performed with the help of modulation filters that transmitted in the region of the absorption bands of the modulating materials (quartz, lithium fluoride, fluorite, and nontransparent metallic membrane). In this case the measured value was the difference in radiation between the earth and the modulator. Since the temperature of the modulator was not fixed, in order to check its constancy and also to take account of the “parasitic” radiation of the inlets and other optical elements, the radiation of the space in the direction close to horizontal (the radiation of space is assumed to be zero) was recorded as standard. The constancy of the sensitivity of the detectingamplifying scheme was achieved by calibration to the standard incandescent lamp. The use of filters allows reaching a spectral resolving power of the order of several microns. The channels of the spectrometer embrace the following wavelength intervals : 4.5-38, 12.5-38, 4.5-8.5 p. To increase the amount of energy reaching the instrument, a slit diaphragm with the side ratios of 1:lO or 1:30 was used with the minimal resolvable angle of 2 x rad. A low inertia bolometer served as a radiation detector. All joints of the instrument with moving details were hermeticized. The spectrometer was calibrated to the black radiators with the temperatures from 77 to 350’K. The sensitivity threshold in the flying conditions was 1.5 x 10” W/cm-2, which corresponds to the resolution with respect to the effective temperature of 2.7’K. The measurement data showed that in the range of 200 to 500 km heights, the shape of the angular distribution curves are little dependent on altitude. For wide spectral regions the angular distribution was close to isotropic and almost without small-scale fluctuations. In the narrow regions the outgoing radiation intensity fluctuations were much greater (up to 50 percent). In the majority of cases the maximum in the spectral radiation distribution was observed in the 4.5- to 8.5-,u region, with the effective temperature of 270 to 280’K, whereas in the transparency window it was about 240’K (the meteorological conditions were determined by variable cloud from 1 to 2 to 7 to 8 tenths, with the lower boundary from 1 to 7 km). Comparison of the effective temperatures with the real values at various
10.4. Net Radiation and Its Components in a Free Atmosphere
727
levels revealed that in the case of the integral radiation, the effective temperature corresponded to air temperature at the 6-km level. For the region of the water vapor absorption band (4.5 to 8 . 5 ~ this ) level was 20 km. However, the high effective temperatures should in this case be attributed to the fact that the source of radiation lay in the upper atmospheric layers. In this connection the intensive infrared radiation of the atmosphere, as observed by the authors of [124, 1261, is of greatest importance. With different conditions of investigation the intensive infrared radiation of the atmospheric layers was observed at 250 to 300, 420 to 450, and about 500 km. This radiation was concentrated mainly in the wavelength range of 2.5 to 8 p and in the part of the atmosphere illuminated by the sun. The radiant flux in the sighting along the tangent, when the ray’s path through the atmosphere extended over 1000 km, reached (3 to 7) x lo2 W m-’. The radiant intensity was increasing during the maximal solar activity. Careful analysis of the conditions of instrument functioning showed that the above conclusions are not affected by any measurement errors but are quite objective. Concerning the nature of the emission it is assumed in [I261 that it was due to the excitation by the corpuscular solar radiation of certain gas molecules contained in the ionosphere. One of these gases appears to be NO (in any case with respect to 280 km). Calculations showed that with the observed radiant intensity the effected temperature must be about 2000OK. In the given case, however, it is impossible to compare the effective and the kinetic temperatures in view of the absence of the state of thermodynamic equilibrium. Lebedinsky et al. [129] carried out measurements of the spectral composition of the outgoing thermal radiation in the wavelength range of 7 to 38 p by means of a diffraction scanning spectrometer mounted on the satellite “Cosmos 45” (206-km perigee, 327-km apogee, 65’ orbital angle of inclination). The terrestrial radiation in the direction of the nadir was measured as the difference with respect to the space radiation at the satellite level in the horizontal direction. The type of cloud underlying the satellite was determined photometrically by measuring the nadir radiance in the spectral region of 0.6 to 0.8 p (the spatial resolving power of the photometer was about 30 km). The infrared spectrophotometer consisted of two monochromators with plane reflecting diffraction gratings of 24 lines/mm (of 7- to 20-p wavelength) and 12 lines/mm (14 to 38 p). In the first wavelength range the spectral resolution was increasing with an increase in wavelength from 1.4 to 1.1 p ; in the second, it varied from 2.8 to 2.1 p. The instrument angle of
728
Net Radiation
sighting field was 1'46' x 2'20', which corresponds to a ground area of 75 km2 with a mean orbital altitude of 250 km. Radiation was detected by a bolometer with a 1 x 1 mm2 surface. The instrument was calibrated to blackbody characteristics. The duration of a complete measurement cycle was 81 sec. The readings were recorded on a 35-mm tape of the sixtrain oscillograph (container with the tape was landed). The operation of the instruments produced 2880 recordings. Typical curves of outgoing radiation spectral distribution with cloudy and clear skies clearly indicated the 9.6-,u ozone band and the 15-,u carbon dioxide band. The observed correlation between photometric readings and measurement data for the 8-7 to 12-,u transparency window was markedly negative, which reflects the opposite effect of clouds on the shortwave and the longwave outgoing radiation. A similar negative correlation was observed with the outgoing radiation of 18.5-,u wavelength. The effect of clouds was found to be considerable in all the studied intervals of the spectrum. This is due to the fact that the main contribution to the outgoing radiation of the considered wavelength range is made by the lower troposphere. The temporal variability of the radiation in the region of the 9.6-,u ozone absorption band was observed to be very great, which resulted from the variations of the ozone content in the atmosphere. It is supposed that the radiation in the 14.1-,u ozone band may greatly contribute to the outgoing radiation corresponding to this wavelength. Interesting spectral measurements of the infrared outgoing radiation were made by Band and Block [129a]. Many investigations (for example, [130-1321) were devoted measurements of the ultraviolet (solar and diffuse) radiation. Important information on the outgoing radiation in the 3.4- to 4.2-,u transparency window was obtained by means of a high-resolution infrared radiometer during the operation of the Nimbus I meteorological satellite (see [133]).
10.5. Climatology of Net Radiation of the Earth The first measurements of the net radiation of the atmosphere and the system earth-atmosphere (to be considered in the next section) are quite recent. For this reason various methods of their theoretical calculation are used in the determination of these quantities, particularly when the investigation is concerned with the climatology of the net radiation. We shall consider later some results of such theoretical calculations, mainly following the works [134-1411.
10.5. Climatology of Net Radiation of the Earth
729
1. Net Radiation of the Atmosphere. Equation (10.2), which determines the atmospheric net radiation, contains three components : the effective radiation F,, the outgoing radiation F,, and the solar radiation absorbed by the atmosphere, 4'. Calculations and observations show that the latter value. is much smaller than the other components. The atmospheric net radiation is therefore determined mainly by the thermal radiative influx I;, - F,. It is easy to see that, on the average, F,, < Fm , and consequently the atmospheric net radiation is negative. This is due to the fact that the atmosphere absorbs only the earth's thermal radiation (and considerably less so the solar radiation), while its emission is directed toward the earth's surface and toward space. Kondratyev and Dyachenko [1351 calculated the longwave net radiation of the atmosphere as Fa = F,, - F,, which made possible the plotting of charts to show its geographical distribution (the given longwave radiation values are absolute throughout the section). For these charts the data of 260 points (165 continental and 95 maritime) equally spaced over the earth's surface were used. The polar latitudes (over 80" N and 70" S ) and high altitudes were not considered because of the lack of a necessary amount of data. The total area of the investigated surface is 460.1 million km2 out of the earth's 510 million km2. The isolines of the chart of the distribution of the annual longwave net radiation totals are plotted at 20 kcal/cm2. The monthly isolines have a 2 kcal/cm2 spacing. The work [135] gives a map of the distribution of the annual totals of the atmospheric longwave net radiation (Fig. 10.27) and 12 monthly charts. It follows from considerations of the charts that the field of the atmospheric longwave net radiation is farly homogeneous, with a small range of the monthly and even the annual totals variation. The considered values show a monotonic increase from the poles equatorward in all the charts. Analysis of the chart of the annual longwave net radiation totals (Fig. 10.27) reveals that these totals vary from less than 100 kcal/cm2 yr in the polar latitudes to 160 kcal/cm2 yr at the equator. The isolines are mostly in the latitudinal direction. At the sea-continent border, discontinuities of the isolines result from the horizontal nonhomogeneity of the temperature field. A certain break of zonality in the variation of the isolines is observed over cold and warm ocean currents. With the cold currents the longwave net radiation of the atmosphere Fa decreases. This occurs, for example, over the cold Peruvian current or above the currents caused by the westerlies near the southwestern coasts of Australia. The warm currents are connected
730
Net Radiation
10.5. Climatology of Net Radiation of the Earth
731
with an increase in the longwave net radiation totals. Such an increase is observed over the warm Gulf Stream, over a branch of the northern Pacific ocean current, and over the warm currents in the Indian ocean. These data reveal a possibility of satellite detection of ocean currents, since the fields of the outgoing radiation and radiative flux divergence in the atmosphere indicate their presence. The great ocean area of the Southern hemisphere and the position of the thermal equator north of the geographical borderline causes the mean heat inflow to the atmosphere of the Southern hemisphere to be larger than that of the Northern hemisphere. The maximal longwave net radiation of 140 to 160 kcal/cm2 yr takes place over the warm equatorial currents with a frequent recurrence of clouds. The absolute maximum in the longwave radiative heat influx to the atmosphere was observed over the Pacific Ocean and equaled 163 kcal/cm2 yr. Comparison of the geographical distribution charts for the longwave net radiation of the atmosphere, F,, with analogous charts for the outgoing radiation F, and for the effective radiation of the underlying surface, Fo ,shows that the distribution of the longwave net radiation over the ocean is largely determined by the influence of the outgoing radiation. On continents the longwave radiation is determined by the effective radiation of the earth’s surface. In this connection it should be noted that the minimal F, values are related to deserts, where the observed effective radiation of the surface, Fo ,is at its highest (due to the high temperatures, low atmospheric moisture content, and insignificant cloud). For example, in the Northern hemisphere a notable decrease of the annual totals, F, , was observed in the deserts of North Africa and Arabia, where F, was less than 120 kcal/cm2 yr. In the Southern hemisphere the longwave net radiation was observed to decrease considerably over the Great Sandy Desert of Australia and over the deserts of South Africa. The absolute minimum was noted over the Kalahari desert (South Africa), with F, less than 100 kcal/cm2 yr. The mean atmospheric longwave net radiation for the globe is 131.5 kcal/cm2 yr (Table 10.15). The mean continental value is 119.0 kcal/cm2 yr, and the maritime is 136.0 kcal/cm2 yr. These values were calculated with account taken of the fact that the land and the sea areas are 29 and 71 percent of the globe, respectively. The authors of [I351 also obtained the annual totals of the atmospheric longwave net radiation for different latitudinal zones (Table 10.15). In their determination the sea-land proportionality for each latitudinal belt was taken into account. The mean annual total for a zone was calculated
732
Net Radiation
from the formula
where S is the total zonal area, S, and S, are the respective area of land and sea, and (Fa)L and (Fa)sare the atmospheric longwave net radiation over land and sea, respectively. The analysis of Table 10.15 shows that the longwave radiative heat inflow for the whole atmospheric thickness increases from the poles equatorwards. Note here that the mean net radiation for the Southern hemisphere is slightly larger than for the Northern hemisphere. This is due to the great ocean area of the former. Let us now characterize the results of the analysis of the monthly distribution charts of the atmospheric longwave net radiation (Figs. 10.28 and 10.29 give the January and July maps). The monthly maps of the longwave net radiation distribution are to some degree similar to the annual charts. In winter the Northern hemisphere has a clear minimum of F, in the area of the Siberian anticyclone, while the Gulf Stream somewhat increases the heat inflow to the atmosphere of the North Atlantic region. The tropical maxima slightly displace from season to season. In summer they are observed near the tropics; in winter, closer to the equator. From the consideration of these maps it is possible to state that the maximal absolute values of the monthly totals Fa occur over the equatorial ocean. In July the maximum of the heat inflow displaces north of the equator and is more than 12 kcal/cm2 mo(in the Pacificocean more than 13 kcal/cm2 mo). A reverse picture is observed in January. The F, maxima displace from the equator southward and exceed 12 kcal/cm2 mo (13 kcal/cm2 mo in the Pacific Ocean). Further analysis of the monthly charts shows that the maxima in the longwave radiative heat inflow to the atmosphere in this case are also connected with the maximal outgoing radiation (F, N 16 kcal/cm2 mo) observed over ocean. This is evident from the comparison of the above charts and also from a graph of the dependence of the atmospheric longwave net radiation on the outgoing radiation plotted for oceans (Fig. 10.30). The relationship is farly close and linear. The correlation coefficient r = 0.94. The effective radiation of the surface appears to have little influence on the radiative heat inflow to the atmosphere over the ocean. This is explained by the fact that the maritime Fa values are little variable and relatively small (3 to 4 kcal/cm2 mo) as compared with F,.
TABLE 10.15 Mean Latitudinal Values Fa (kcal/cm2yr). Afrer Kondratyev and Dyachenko [135]
Latitude, deg
90-80 80-70 70-60 60-50 5040 40-30 30-20 20-10 10-0 0-10 10-20 20-30 3040 40-50 50-60 60-70 70-80 80-90 From 80' N lat. to 70" S lat.
Land Area,
Sea Area,
Total Zonal Area, mln (lo6) km2
%
%
10 29 72 57 52 43 38 26 23 24 22 23 12 3 1 10 78
90 71 28 43 48 57 62 74 77 76 78 77 88 97 99 90 22
3.9 11.6 18.9 25.6 31.5 36.4 40.2 42.8 44.1 44.1 42.8 40.2 36.4 31.5 25.6 18.9 11.6 3.9
71
460.1
119.0
Mean Zonal
Mean
Mean
Fa
Fo
over Land, kcal/cm2 yr
over Sca, kcal/cm2 yr
kcal/cm2 yr
115 114 112 110 119 126 132 131 131 113 111 114 118
118 121 120 129 139 150 150 151 147 135 127 125 120
116 117 116 121 131 144 146 146 144 130 125 124 120
136.0
131.5
Fa
C Fa Zonal, kcal/cm2 yr
L
0 01
111 21.9 x 1OI8 30.0 x 1OI8 36.6 x los8 44.1 x 10'8 52.7 x 1Ol8 61.7 x 1OI8 64.5 x 10'8 64.5 x los8 61.7 X 1Ol8 52.3 x lor8 45.6 x 39.1 x 1Ol8 30.8 x 1Ol8
s z z
s
w
4
w w
FIG. 10.28 Geographical distribution of monthly totals of the atmospheric longwave budget, January.
10.5. Climatology of Net Radiation of the Earth
736
Net Radiation
..
.... . ..... ... .... .
.. . . :.: .
.. ... ...:....... .... .. .
. ...
i
*
e
1301~~
120
110
130
140
150
160
FIG. 10.30 Dependence between the longwave budget and the outgoing radiation.
The continental Fa values are strongly affected by the effective radiation of the earth's surface, whose influence becomes less only with a complete low cloud cover. In this case the temperatures of the earth's surface and the lower cloud boundary are equalized, which leads to almost zero values of the effective radiation. The relationship between the atmospheric longwave net radiation, Fa, and the continental outgoing radiation F, is not simple. Let us consider the graphs of Fig. 10.31 for the purpose of analyzing the annual variation in the atmospheric longwave net radiation. The presented
(0)
Fig. 10.31
737
I............ I I U P r n I x x I
-
MONTH (d 1
7
I
mnnrrIxxI month
(e 1
t
13
7 1 . . . . . . . - - . . -
r m s ! m l x s I
&
MONTH (9)
FIG. 10.31 Annual variation of the longwave net radiation in different landscape and climatic zones.
(a) tundra [(l) Amderma, Siberian Arctic; (2) Cape Barrow]; (b) forest of the temperate latitudes [(l) Sverdlovsk, (2) Forth Nelson]; (c) wooded steppe and forest of the temperate latitudes [(l) Rostov-on-Don, (2) El Passo]; (d) arid zones of the subtropical latitudes and the Mediterranean area [(l) Tashkent, (2) Rome]; (e) region of subequatorial monsoons [(l) Fort Larni, (2) Calcutta]; (f) tropical deserts [(I) Vadi Halfa, (2) Alice Springs]; (g) equatorial climate of the tropical forests [(l) Sao Gabriel, (2) Batavia, (3) Singapore].
738
Net Radiation
curves depict the annual variation of Fa with different climatological and local features. To secure direct comparison of Fa and F, throughout the year, the selected points were coincident or close climatologically to those used in the work of Yefimova and Strokina [37]. It is evident from the consideration of Fig. 10.31 that the annual variation of the atmospheric longwave net radiation in tundra has a May and September maxima of 10.5 kcal/cm2 mo at Amderma (Siberian Arctic) and 9.5 kcal/cm2 mo at Point Barrow (N. Alaska). These maxima are due to a considerable cloud amount and the resulting low F, values. During the warm period the observed minimum is fairly deep (9.0 to 9.2 kcal/ cm2 mo) and is due to the maximal F,. Figure 10.31(b) presents the annual variation of the longwave net radiation for the wooded area of the temperature latitudes. The curves are rather smooth, with a summer maximum of 10.2 to 10.5 and a winter minimum of 8.7 to 9.0 kcal/cm2 mo. In the zone of wooded steppe, and the steppe presented in Fig. 10.31(c), the quantity considered has a deep spring minimum (at Rostov-on-Don, 9.1 kcal/cm2 mo; at El Paso, 8.0 kcal/cm2 mo). This period is characterized by large effective radiation values. In early summer (June and July) a maximum Fa is observed (9.7 to 10.2 kcal/cm2 mo). The atmospheric longwave net radiation decreases notably closer toward fall. Figure 10.31(d) gives the curves of the annual Fa variation for the dry areas of the temperate latitudes (Tashkent) and for the Mediterranean (Rome). The annual variation of Fa is here quite great, with a range of about 2 kcal/cm2 mo. The minimum Fa occurs in summer and is due to the high values of the effective radiation of the earth’s surface, resulting from hot and cloudless weather. The great monthly F, totals in the dry temperate zones are caused by the high temperatures and the presence of cloud. A similar increase of Fa in the Mediterranean follows the considarable cloud amount and increased humidity during winter. In the dry temperate zone (Tashkent) the maximal Fa is observed in spring, with low F, and high F, values. In summer there is a minimum of Fa due to the maximal F,, though in this period the outgoing radiation F, exceeds 16 kcal/cm2 mo. Returning to the analysis of the charts of the longwave net radiation geographical distribution, we note that in deserts (Sahara, Kalahari, Arabian) the January Fa values are fairly large (6 to 8 kcal/cm2 mo), which can be accounted for by the high temperatures and little cloud. The F, values here are small, with minima less than 10 kcal/cm2 mo (less than 8 kcal/cm2 mo in Australia).
739
10.5. Climatology of Net Radiation of the Earth
In the Northern hemisphere, in America as well as in Eurasia, the longwave net radiation of the atmosphere in January is little variable, with a range from 9 to 10 kcal/cm2 mo, lowering to about 8 kcal/cm2 mo only in the area of the Siberian anticyclone. This Fa minimum is the result of the great cooling of the underlying surface, which causes the outgoing radiation to fall to 10 kcal/cm2 mo. In July in Eurasia there is a washed-out field of the atmospheric longwave net radiation. In the high latitudes (behind the Artic Circle), Fais of the order of 9 kcal/cm2 mo. The rest of the continent has Fa less than 10 kcal/cm2 mo. In North America at the same latitudes, Fa has the same values. The exception is the Arctic regions, where Fa is about 8 to 9 kcal/cm2 mo. In the zone of deserts and semideserts the minimal F, of less than 10 kcal/ cm2 mo are observed in July, which is caused by the high effective radiation. The areas of the equatorial monsoons are presented in Fig. 10.31(e). We see a considerable range of the annual F, variation. The maxima of Fa are observed in fall (11.8 to 12.6 kcal/cm2) and the minima in winter (9.2 to 9.6 kcal/cm2 mo). A small-range annual variation of Fa takes place in the tropical deserts (see Fig. 10.31(f)). In African deserts Fa is 9.0 to 10.5 kcal/cm2, while in Australian deserts, it is somewhat lower (8.5 to 9.0 kcal/cm2 mo). Figure 10.31 (g) displays the curves of the annual variation of the quantity considered for areas with the climate of the equatorial tropical woods, where the cloud amount is significant and humidity high. The range of Fa here is smooth throughout the year, with large values of the order of 11.0 kcal/cm2 mo (San Gabriel, California). On the islands of the same climatic zone (Batavia and Singapore) the variation of F, has a large amplitude of the order of 1.0 to 1.5 kcal/cm2 mo. Calculations of the shortwave (incoming) component of the atmospheric net radiation are rather few, which results in limited information for the total net radiation of the atmosphere. This subject has been given most detailed treatment by Vinnikov [142]. According to Budyko (137), the latitudinal distribution of the annual atmospheric net radiation totals in the Northern hemisphere is characterized by the following values: Latitude, deg:
0-10
R, , kcal/cm2yr :
-56
10-20 20-30
-54
-50
30-40 40-50 50-60 60-90 0-90
-59
-69
-76
-73
-60
As seen, the atmospheric net radiation slightly decreases in absolute value within the latitudinal belt from the equator to about 25' and then increases
740
Net Radiation
again up to about 60' latitude. To the north of 60' the absolute value is again observed to decrease. The mean annual net radiation in the Northern Hemisphere is -60 kcal/cm2 yr. Its components are Fa = 50, F, = 145, q' = 35 kcal/cm2 yr. Later, these components were calculated for the Southern hemisphere. The calculation of the atmospheric net radiation components for the earth as a whole gives the following values: F, = 150, Fa = 43, q' = 39, R, = 68 kcal/cm2 yr. In Budyko's estimation the negative pet radiation of the atmosphere is by about three-quarters compensated by the heat gain due to condensation, and by one-quarter by that due to the turbulent heat loss of the underlying surface. Moller [143] studied the regularities in the annual variation of the atmospheric net radiation in various climatic zones to find that the maximal absolute value always occurred in November and was equal to 250 to 300 cal/cm2 day. The minima were observed from May to July and varied from 140 to 190 cal/cm2 day. Table 10.16, compiled by Moller, compares the results of the calculation of the annual means of the atmospheric net radiation and its components for various latitudinal zones performed by different authors. TABLE 10.16 Comparison of the Calculations of the Aimospheric Nei Radiaiion and Its Components (cal/cm2day). After Moller [143] Calculation
30-50'N
40-60'N
60-90'N
90 217 127
82 233 151
81 227 146
121 359 238
99 333 234
59 287 228
96 305 209
83 280 197
65 230 165
92 300 208
79 29 1 212
55 262 207
1. Baur and Philipps (1934) q'
Fo
- Fa
I Ra I
2. Houghton (1954)
d Fo - Fm I Ra I
3. London (1957) q'
Fo - Fa
IRa I 4. Moller (1959)
d Fo - Fa
I Ra I
741
10.5. Climatology of Net Radiation of the Earth
This comparison shows that the data of the recent calculations are in fairly good agreement, whereas those obtained earlier are either underestimated (Baur and Philipps) or exaggerated (Houghton). Vinnikov’s calculations of the components of the net and thermal atmospheric radiation [144-1461 are, as was already mentioned, the most detailed. Table 10.17, borrowed from Vinnikov [146], gives the mean latitudinal distribution of the annual totals of the thermal balance components for various latitudinal belts. Here P denotes the turbulent heat loss of the underlying surface toward the atmosphere, L, is the heat income due to condensation, C is the advective heat transfer caused by the horizontal movement in the atmosphere. We see that the data of this table reveal a low latitudinal variability of the atmospheric net radiation. TABLE 10.17 Components of the Atmospheric Thermal Balance (kcal/cm2yr). After Vinnikov [I461
I Ra I
P
Lr
C
9 13 17 23 24 15 9 8 11 15
11 9 8
29 45 46 45 44 72 119 94 71 53 57 63 61
-32
40-50 50-60
70 60 60 69 82 83 76 74 16 74 71 64 57
Earth as a whole
72
13
59
0
Latitude
70-60’ N 60-50 50-40
40-30 30-20 20-10 10-0
O-loo s
10-20 20-30 30-40
-2 3 -1 - 14 4 52 28 12 -6 -3 8 12
Berland [138] plotted the annual and monthly (for the four seasons) maps of the geographical distribution of the atmospheric net radiation for the Northern hemisphere. Analysis of these maps likewise reveals a comparatively low spatial variation of the net radiation. The field of the net radiation is particularly “washed out” in summer in view of the small latitudinal variations of the absorbed solar and outgoing radiation (the net radiation is about 4 to 6 kcal/cm2 mo). In December the variation of the net radiation is from - 10 kcal/cm2 mo in the high latitudes and to 4 kcal/cm2 mo in the
742
Net Radiation
low latitudes. The annual net radiation also has a notable geographical variation. Similar results are obtained by Vinnikov [146] for the entire globe. The annual totals on the global scale vary approximately from -40 to - 100 kcal/ cm2yr. The smallest (in absolute value) totals are observed in the intermediate and high latitudes in summer, where the atmosphere absorbs the largest amount of solar radiation.
2. The Outgoing Radiation. The investigations of the outgoing radiation have a long history (see [l, 21). We shall consider here only the more complete and recent results of Vinnikov’s study [ 1441. Vinnikov proposed an approximate method for calculating the outgoing longwave radiation, and plotted monthly and annual charts of the planetary distribution of the outgoing radiation. Figure 10.32 gives one of his charts, the global distribution of the annual totals of the outgoing radiation. Analyzing these monthly and annual maps we see that the field of the outgoing radiation is fairly homogeneous. The outgoing radiation varies within a relatively small range of monthly and annual total. In all maps, F, is seen to increase from the poles toward the tropics. This is explained first by the increasing mean temperature of the troposphere, and second by the decrease in cloud in the high-pressure belts. At the equator there is a minimum of the outgoing radiation, due to the increasing cloud amount. The monthly 10, totals in January vary from 10 kcal/cm2 mo in the high latitudes to 16 kcal/cm2 mo in the tropics, while in July this variation is from 12 to 18 kcal/cm2 mo, respectively. The annual totals vary from less than 140 kcal/cm2 in the polar latitudes to over 200 kcal/cm2yr in North Africa and Arabia. The maxima in the outgoing radiation are observed over the low-latitude deserts with high air temperatures and insignificant moisture content and cloud. At places where the cloud amount and air humidity are high (equator) the outgoing radiation has considerably smaller values, but there is no continuance of small F., The variation of F, is dependent on atmospheric moisture and cloudiness. The zonal distribution of the outgoing radiation is seen to be broken by the effect of cold and warm ocean currents. With powerful currents the isolines are strongly fractured. The warm ocean currents cause an increase, whereas the cold currents effect a decrease of both monthly and annual totals of the outgoing radiation. This is evident from the effect of the warm Gulf Stream and the cold Peruvian current. Also effective with respect to the outgoing radiation field distribution are
10.5. Climatology of Net Radiation of the Earth
744
Net Radiation
the displacement of the thermal equator north of the geographical and the great ocean area of the Southern Hemisphere. As a result the thermal radiation of the Southern Hemisphere is less, on the average, than that of the Northern Hemisphere.
3. The Net Radiation of the Earth-Atmosphere System. As seen from (10.3), the net incoming radiation of this system is determined by the direct solar and diffuse radiation absorbed by the atmosphere and of the losses from the outgoing radiation. Calculations show that the quantity considered can be both positive and negative. In its annual range net radiation of the system in the intermediate latitudes is positive in summer and negative throughout the remainder of the year. Table 10.18 gives Vinnikov's calculations [1461, which are characteristic of the latitudinal and seasonal variability of the net radiation. (One can also consult Shneerov's work [147].) TABLE 10.18 Mean Latitudinal Distribution of the Net Radiation of the Earth-Atmosphere System (kcaI/cm2).After Vinnikov [146J
Latitude
January
July
Year
70-60' N 60-50
-10 -8.7 -6.8 -4.7 -2.6 -0.5 1.5 3.4 4.9 6.1 6.8 6.7
3.9 4.4 4.9 4.8 4 3.2 2.4 1
-49 -30 -12 4 14 23 29
50-40
40-30 30-20 20-10 10-0 &loo 10-20 20-30 3 0 40-50 50-60
s
-1 -3 -5.3 -7.3
-
31 28 20 9 -8 -29
It is evident from Table 10.18 that the transition from positive to negative values (northward) takes place near 40'. An interesting conclusion reached from consideration of the above data is that the net radiation of the Southern Hemisphere exceeds that of the Northern Hemisphere. Since there are no marked variations in the thermal regime of the earth
id
>
0
TABLE 10.19 Mean Annual Latitudinal Distributionof the Net Radiation and Its Components of the Earth-Atmosphere System (wlfcmamin). Afrer London 11391 N Latitudes, deg
Net Radiation Component 0-10
10-20
20-30
30-40
40-50
5060
60-70
70-80
80-90
Mean
Absorbed solar radiation
0.403
0.409
0.387
0.341
0.276
0.224
0.169
0.122
0.160
0.324
Outgoing radiation
0.347
0.354
0.353
0.327
0.306
0.287
0.270
0.253
0.245
0.324
Net radiation
0.056
0.055
0.034
0.014 -0.030
0.139
0.OOO
-0.063
-0.101
-0.131
746
Net Radiation
as a whole, it follows that the mean annual net radiation (identical with the thermal balance) of the earth-atmosphere system must be zero. The same conclusion is reached by London [I391 in particular, whose data are given in Table 10.19. At the same time Table 10.19 gives an idea of the relationship among the components of the net radiation of the earth-atmosphere system. Berland’s data on the mean latitudinal range of the monthly net radiation and its componets for the same system are presented in Table 10.20. Comparison with Vinnikov’s data (Table 10.18) reveals a satisfactory agreement between these results. TABLE 10.20 Mean Latitudinal Variation of the Monthly Net Radiation and Its Components for the Earth-Atmosphere System (kcaI/cm2).After Berland [138]
December
June N Lat., deg
70 60 50
40 30 20 10 0
15.4 17.2 18.3 19 19.1 18.5 17.2 15.5
12.9 13.4 13.6 14.1 14.6 14.2 13.3 12.7
2.5 3.8 4.7 4.9 4.5 4.3 3.9 2.8
0.0 0.7 2.6 5.7 9.6 12.8 15.5 16.9
11.4 11.7 12.3 13.1 14.3 14.8 14.1 13.1
-11.4 -11 - 9.7 - 7.4 - 4.7 - 2 1.4 3.8
London [I391 has also calculated the seasonal and annual net radiation and its components of the system averaged for the entire Northern hemisphere (Table 10.21). The data of Table 10.21 make it possible to analyze the relation between the net radiation components. As seen, the main contribution to the income of the net radiation is made by the absorption of shortwave radiation by the earth’s surface. A significantly smaller portion of the radiation is absorbed by the atmosphere and even less by clouds. Accordingly, the greatest losses of the shortwave radiation are due to its scattering spaceward by the atmosphere and clouds. All absorbed (reflected) radiation components have an annual variation. For example, a radiant flux scattered by the atmosphere and clouds is maximal in summer, which is caused by the maximum of isolation outside the earth and an increasing cloud amount during this period. As to the reflection of radion by the earth’s
747
10.5. Climatology of Net Radiation of the Earth
TABLE 10.21 Seasonal Distribution of the Mean Net Radiation and Its Components for the Northern Hemisphere in the Average Cloud Conditions (cal/cmzmin). After London [139]
Net Radiation Components
Winter
Spring
0.348
0.580
Summer Autumn
Year
I. Incoming shortwave radiation Insolation at the upper boundary of the atmosphere
0.645
0.424
0.500
Radiation absorption in the atmosphere: (a) by ozone (b) by water vapor and dust (c) by clouds
0.011 0.044
0.016
0.019
0.010
0.014
0.067
0.092
0.057
0.065
0.005
0.010
0.011
0.007
0.008
Total absorption
0.060
0.093
0.122
0.074
0.087
0.023 0.078
0.037 0.141
0.015
0.029
0.048 0.162 0.024
0.028 0.103 0.018
0.034 0.121 0.021
0.116
0.207
0.234
0.149
0.176
0.085
0.142
0.129
0.045 0.043
0.091 0.050
0.090 0.070
0.091 0.064 0.048
0.112 0.072 0.053
0.173
0.283
0.289
0.203
0.237
0.530
0.564
0.614
0.581
0.572
0.439 0.091
0.473 0.091
0.523 0.091
0.494 0.087
0.482 0.090
Reflection and scattering of radiation spaceward: (a) by atmosphere (b) by clouds (c) by earth’s surface Total reflection Absorption of radiation by the earth’s surface : (a) of direct solar (b) of transmitted by clouds (c) of diffuse Total absorption by earths’ surface 11. Longwave radiation
Effective radiation of earth’s surface: (a) thermal terrestrial radiation (b) downward atmospheric radiation (c) effective radiation
748
Net Radiation
TABLE 10.21 (continued) Net Radiation Components
Winter
Spring Summer Autumn
Year
Thermal radiation of troposphere: (a) thermal radiation absorbed by troposphere (b) tropospheric thermal radiation
0.501
0.535
0.588
0.555
0.545
0.716
0.749
0.817
0.778
0.765
Longwave net radiation of troposphere
0.215
0.214
0.229
0.223
0.220
0.029 0.277 0.011
0.029 0.276 0.016
0.026 0.294 0.019
0.026 0.283 0.010
0.027 0.283 0.014
0.317
0.321
0.339
0.319
0.324
Thermal radiation spaceward: (a) of earth’s surface (in transparency windows) (b) of troposphere (c) of stratosphere Total outgoing radiation
surface, it has a spring maximum. Although the albedo is maximal in winter, the lowest insolation value at this time causes the reflected radiation to reach maximum only in the spring, with greater insolation values and the snow cover remaining on the major part of the hemisphere. The heat losses of the earth-atmosphere system are determined first of all by the thermal radiation of the troposphere, which makes the largest contribution to the outgoing radiation. The radiation of the earth’s surface (in the transparency windows) is less than 10 percent of the outgoing radiation, while the stratospheric contribution is still less, not exceeding 3 to 6 percent. The seasonal variability of the outgoing radiation and its components is seen to be very low. In the Northern Hemisphere the mean outgoing radiation is 0.324 cal/cm2 min, which corresponds to the effective temperature of -22’. The seasonal values of the outgoing radiation depart from the mean by not more than 2 to 5 percent. The low variability of the radiation of the earth’s surface is explained by the mutually compensating effects of its temperature increase from winter to summer, on the one hand, and by the increasing cloud amount and decreasing atmospheric transparency due to the increase of the total water vapor content, on the other. It is important to note, however, that the conclusion about the low variability of the out-
10.5. Climatology of Net Radiation of the Earth
749
going radiation holds good only with respect to the outgoing radiation values averaged over the whole Northern Hemisphere. As is evident from Table 10.21, the net radiation of the earth-atmosphere system for the Northern Hemisphere is positive in spring and summer, and negative in autumn and winter. The maximum summer value is 0.072 cal/ cm2 min, while the winter minimum is 0.084 cal/cm2 min. Vinnikov [ 1461 plotted monthly (for all months) and annual charts of the geographical distribution of the net radiation of the considered system. The most characteristic feature of this geographical distribution is its closeness to the zonal, which gives evidence of the leading role of the astronomical factors in the radiation regime. The zonality is seen to be broken in the desert areas. Also evident in the net radiation field is the nonhomogeneity of the underlying surface at the ocean-land division, which is indicated by the discontinuity of isolines. The net radiation of the earth-atmosphere system is positive throughout the year only in a narrow equatorial zone of f 10’ latitudes. At all other places the net radiation changes sign twice a year. For about three months (in summer) the net radiation is positive over the entire hemisphere (souhern and northern). The zone of negative values appears at the poles in summer and then gradually expands southwards, occupying the territory south of 30’ for five months. In spring the zero isoline begins to recede toward the north. The maximal positive values reach 40 kcal/cm2 yr, while the negative become 60 kcai/cm2 yr. Making use of the charts given in the “Atlas of the heat balance of the globe” [141], it is possible to determine all components of the thermal and water balances for the land, ocean, and the earth as a whole. Calculations show that the earth as a planet absorbs 168 kcal/cm2 yearly. Of this, 112 kcal/cm2 yr, or two-thirds, is absorbed at the earth’s surface and 56 kcal/ cm2 yr, or one-third, in the atmosphere. The earth‘s surface loses yearly, on the average, 40 kcal/cm2, owing to the long-wave effective radiation, which results in its mean net radiation being 72 kcal/cm2 yr. Of this, 59 kcal/cm2 yr is spent in evaporation and 13 kcal/cm2 yr is given to the atmosphere in the turbulent heat loss. It should be noted that the heat expenditure in evaporation is 82 percent of the net radiation for the whole earth, this expenditure constitutes 90 percent for the ocean and almost 50 percent for land. In accordance with the amount of heat lost in evaporation the mean annual total of evaporation from the earth’s surfaces appears to equal 100 cm. This is, at the same time, the annual total of precipitation at the earth’s surface. The numerical values of the main components of the thermal and water
750
Net Radiation
balances of the earth’s surface obtained in the recent investigations somewhat exceed the formerly found values. In particular, the majority of the earlier studies would give the annual precipitation and evaporation for the whole earth equal to 80 to 90 cm. Their increase to 100 cm/yr is explained mainly by the greater accuracy in determining the normal precipitation on oceans, where it was not sufficient in the former years. As is known, the solar radiation is the chief climate-forming factor. It is of interest, however, that even now the amount of energy used by man is comparable with the net radiation value (see Budyko’s work [140]. According to latest data, the mean net radiation of the total continental surface is 49 kcal/cm2 yr, while the energy consumed by mankind is about 0.02 kcal/cm2 yr, with almost 1 kcal/cm2 for large areas in individual countries. Assuming that the annual increase of the energy generation be 10 percent we may expect that the total amount of energy due to man’s efforts will exceed the net radiation in less than a hundred years. In such conditions the role of the main climate-forming factor will pass to the energy generated by mankind. It is natural to expect, then, considerable changes in the regularities of the radiation regime and climate. The above-considered calculations performed by different authors show certain discrepancies, which stresses the necessity of experimental investigations of the quantity considered. An important step in this direction has been made by using data on the outgoing radiation obtained from meteorological satellites. Let us now discuss these data. 10.6. Investigations of the Earth’s Net Radiation by Means of Satellites The instruments used with the TIROS and NIMBUS meteorological satellites to measure the outgoing radiation in various spectral regions and the first results of these measurements are described by this author (see [148]). This author’s other work [149] is devoted to the practical application of such data. In the present section we shall reduce the subject to consideration of the recent satellite data on the componentes of the net radiation of the earth-atmosphere system (the significance of degradation errors in satellite radiometers must be mentioned, as for example, in [150, 1511). In accordance with the theoretical calculations discussed in the preceding paragraph the satellite data show that the outgoing longwave radiation has an equatorial minimum, almost symmetrical maxima in the subtropics, and a monotonic decrease polewards. Such results were obtained, for example, by Winston and Rao [152, 1531 (five-channel radiometer of Tiros 11; see Fig. 10.33), House [I541 (hemispheric sensors of the outgoing radiation in Tiros
10.6. Investigations of the Earth’s Net Radiation by Means of Satellites
751
550 I
Y.
500 “E
2 450 8 c
._ 5 5 400
7
.z 0
350
c
a 0
300 50
40
30
10 0 Latitude
20
S
10
20 30
40
50 N
FIG. 10.33 Mean latitudinal distribution of the outgoing Iongwave radiation measured from TIROS II over 26 days in comparison with theoretical calculations, (1) data of Houghton (annual means; (2) Retien (winter); (3) London (winter); (4) TIROS I1 (November-January); (5) Simpson (November-December); (6) Baur and Philipps (January).
IV; see Fig. 10.34),Bandeen et al. [ I S ] , and others. An interesting research in this field belongs to Hanel and Stroud [156].
.‘6
e
z
0.35
3
P
a 0.300 . 2 5 ~ 1I 1 I I 9060 30
0s
(II) 510 (I) so1 I
I
I
0
I
I
I
30
I
I
I I L
6090
ON
FIG. 10.34 Latitudinal variation of the outgoing longwave radiation measured from TIROS I V (semispherical sensors). (I) Feb. 8-Apr. 10, 1962; (11) Apr. 11-June 10, 1962.
The main factors of the mentioned peculiarities of the latitudinal distribution of the outgoing radiation are the earth’s cloud and temperature. For example, the outgoing radiation maxima in the subtropics are caused by the high temperature of the earth’s surface and the relatively small cloud amount (subtropical high-pressure zones). The equatorial minimum is con-
752
Net Radiation
nected with the area of the intertropical convergence zone. The results of measurements and calculations are seen to depart in a rather marked way (Figs. 10.33 and 10.34). Rao [157] investigated the Tiros I1 and Tiros I11 data on the outgoing thermal radiation relating to the belt 55' S to 55' N lat. (see Fig. 10.35).
LAT
FIG. 10.35 Latitudinal variation of the outgoing longwave radiation in summer and autumn. (1) from data of TIROS I1 (over 26 days, Nov.-Dec. 1960 and Jan. 1961); (2) data of TIROS I11 (9 days of July 1961).
As seen, in the intermediate latitudes of the Northern hemisphere the outgoing radiation increases from winter to summer, which can be caused by both a decrease in cloud and increase in the temperatue of the underlying surface. The inverse varibility of the outgoing radiation is observed in the southern intermediate latitudes. The two decreases of the outgoing radiation near the equator as observed by Tiros I1 can be explained by two local zones of greater cloudiness. The most detailed investigation of the variability of the net radiation components of the earth-atmosphere system has been made by Bandeen et al. [155] on the basis of 14 months of continuous Tiros VII operation. The method for processing observational data used in [155] is characterized in [149]. Table 10.22 gives seasonal totals of the net radiation components for the earth as a whole. Figures 10.36 and 10.37 present the curves of the latitudinal variation in the mean annual outgoing longwave radiation and albedo compared with London's calculations [ 1391. The seasonal variation of the outgoing long-wave radiation totals is seen to vary little (Table 10.22). The seasonal range of the latitudinal profile of the outgoing radiation as presented in [I551 shows that the tropical mini-
10.6. Investigations of the Earth's Net Radiation by Means of Satellites
753
TABLE 10.22 Seasonal and Annual Totals of the Net Radiation Components for the Earth. After Bandeen et al. 11551
Monthly Period
June-July Sept.-Nov. Dec.-Feb. Mar.-May
Outgoing Longwave Radiation 10l6 cal/min 1725.2 1725.2 1712.2 1746.5
Solar Radiation loz6cal/min
Albedo of Earth,
Reflected
Incident
%
699.0 922.2 859.7 796.0
2457.8 2574.8 2609.8 2544.2
28.4 35.8 32.9 31.3
mum occurs in the Northern hemisphere during most of the year, except from December to February. This causes the minimum in Fig. 10.36 to take place at 5' N lat., thus presenting asymmetry between the hemispheres.
FIG. 10.36 Latitudinal variation of annual means of the outgoing radiation (the scale of the axis of abscissas is proportional to the area of the latitudinal belts). (1) data of TIROS VII (region 8-12 p, June 1963-May 1964); (2) calculations of J. London.
The Northern hemisphere also contains the absolute maximum of outgoing radiation during as long a period (except from June to August), which asymmetry is clearly evident from Fig. 10.36. As a rule, the outgoing radiation in the northern latitudes outside the tropics is greater than in the southern, but the equatorial zones reveal an inverse relationship, which balances the heat losses in radiation by the two hemispheres.
754
Net Radiation
FIG. 10.37 Latitudinal variation of annual means of the planetary albedo (the scale of the axis of abscissae proportional to the income of solar radiation outside the atmosphere and corresponding latitudinal belts). (1) data of TIROS VII (spectral region 0.55-0.75 p , June 1963-May 1964); (2) calculations of J. London.
The latitudinal variation of albedo is almost directly opposite to that of the outgoing radiation and is caused by the cloud effect (see Fig. 10.37 and also Fig. 10.38, borrowed from [154]). The dashed curves of Fig. 10.38
--I
10
;i
.\
x)
20 10
011 I 9060
I
1
I
I
I
0 OS
I
I
I
30
1
1
1
1
6090
ON
FIG. 10.38 Latitudinal variation of albedo measuredfrom TIROS IV (sensing halfspheres). (I) Feb. 8-Apr. 10, 1962; (11) Apr. 11-June 10, 1962, [averaged area 48ON48OS; albedo: (I) 28.9 percent, (11) 37.2 percent; reflected radiation: (I) 598 cal/cma day, (11) 500 cal/crna day).
10.6. Investigations of the Earth's Net Radiation by Means of Satellites
755
characterize a possible measurement errors influence. The maximal albedo near the equator takes place at about 5' N lat. (Fig. 10.37)' coinciding with the minimum of the outgoing long-wave radiation. The minimal albedo is, however, observed at 16' N lat., that is, is somewhat displaced south of the outgoing radiation maximum. The albedo of the Northern Hemisphere exceeds that of the southern within the latitudinal belt from the equator to 12' and is smaller at higher latitudes. Analysis of the annual albedo variation reveals that its minima occur approximately in July, and maxima in October. This finds reflection in the variability of the seasonal means as well (Table 10.22). The average latitudinal distribution of the net radiation of the earth-atmosphere system shows asymmetry in relation to the equator, which results in the transition from positive values in the low latitudes to negative in the high, taking place in different latitudinal belts of the Northern and Southern Hemispheres. This is clearly seen in Fig. 10.39 [154]. 0.20
1
0.15 .E
0.10
; 2
0.05
0
H
0
3
-0.05
I-
-0.10
2 W
2
-0.1 5 -0.20
90 60
30 OS
0 LATITUDE
30
60 90
ON
FIG. 10.39 Latitudinal variation of net radiation measured from TIROS IV (sensing half-spheres). (1) data of Simpson (1928) for March-May; (2) London (autumn and spring of 1957); (3) Tiros IV (March-May, 1962).
Astling and Horn [ 1581 used the Tiros I1 measurement data for 27 days (November 26, 1960 to January 6, 1961) to plot the mean latitudinal distributions of the outgoing longwave radiation for the entire global surface and separately for continent and ocean. The measurements were concerned with the zone 50' S to 50' N lat., except a part of central Asia and northern South America, including the adjacent regions of the Pacific and Atlantic
756
Net Radiation
Oceans. The initial data for each 24 h were averages (over at least 10 values) with respect to squares of 2.5' equatorial side and then used in plotting charts of geographical distribution of the outgoing radiation for every day of the 27 days. All data relate to the angles with respect to nadir not less than 56'. The averaged meridional profiles of the outgoing radiation were calculated by reading the charted values (there were 7269 points) and the mean latitudinal magnitudes were calculated for zones of 5' width. The obtained meridional profile represents, as in the above-mentioned works, an equatorial minimum, maxima in the warm and relatively cloudless subtropical zones and decreasing radiation with a further increase in latitude. The absolute outgoing radiation values appeared to be less (especially in the zone from 5' N to 10' S Iat.) than the earlier data of the Explorer VII satellite and actinometric radiosondes. Such deviation should evidently be explained by the inaccurate consideration of the effect of the edgeward darkening of the planet's disk in processing the Tiros I1 data (the outgoing radiation measured at large angles relative to the nadir appears to be underestimated due to the effect of darkening as compared with the corresponding "undersatellite" values). This conclusion is confirmed by the fact that comparison of the outgoing radiation values, averaged over all the measurements with the values selected for the nadir angles less than 26', revealed the former's underestimation. Since, however, even the "undersatellite" values obtained with Tiros I1 are less than the Explorer VII data, it should be believed that one of the causes for this deviation is the different calibration of the respective instruments. According to data for nadir angles less than 26', the outgoing radiation in the subtropical minimal zone (15-25' N, 10-35" S lat.) is about 480 cal/cm2 day. Astling and Horn [158] found a notable difference between the meridional outgoing radiation profiles relating to continent and ocean. With continents there is a sharp minimum of the outgoing radiation within 5' N to 15' S lat., while with ocean this minimum is weaker and displaces to the interval 5' to 10" N lat. It appears that the continental displacement of the minimum southward is due to the effect of clouds related to the intertropical convergence zone. Another important difference is observed in the subtropics and relates to the influence of the underlying surface temperature in these relatively cloudless areas. Over ocean (low variability of temperature) the outgoing radiation in both hemispheres in the subtropics is about 500 cal/cm2 day, while the corresponding continental values are 540 cal/cm2 day (the summer hemisphere with high temperatures) and 475 cal/cm2 day (the winter hemisphere with low temperatures). The data of [158] on the variation of the outgoing radiation relative to
10.6. Investigations of the Earth’s Net Radiation by Means of Satellites
757
its mean show that this variation is most marked over the continents. Recently there have been attempts made at investigation of the diurnal range of the outgoing longwave radiation. Astling and Horn, for example, in processing the Tiros I1 data for 27 selected days (Nov. 26, 1960 to Jan. 6, 1961) found a notable daily variation over both continents and oceans. In the case of continents, the daytime values exceeded the diurnal means by 0.04 cal/ cm2 min, while the nighttime values were systematically lower by 0.02 cal/cm2 min. With oceans, the daily variation appeared to be less marked though still notable. The statement of daily variation in the outgoing radiation over the ocean whose surface temperature is stable enough was quite unexpected and required careful analysis of the measurement errors. So far the effect of errors has not been taken sufficiently into account, which does not allow acceptance of the above conclusion on the daily variation of the outgoing radiation for ocean as being reliable. It has been noted above that the main factors determining the outgoing longwave radiation are clouds and atmospheric stratification. The recent calculations and measurements reveal a considerable effect of the aerosol layers on the outgoing radiation (see [159]). The available experimental data are, however, contradictory. For example, Gupta [160] analyzed the daily totals (averaged over 5 days) of the outgoing longwave radiation for various Indian stations as given by the Tiros IV meteorological satellite in April, May, and June of 1962. The obtained values were then compared with the calculations of the outgoing radiation with a clear sky from the averaged aerological sounding data derived by means of the Elsasser chart. The deviation between the measured and calculated values was not more than 10 percent. Such good agreement gives evidence, in particular, of the insignificant effect of aerosol dust particles on the longwave radiation transfer. This, however, does not change the conclusion about the notable influence of aerosol on the radiative heat inflow, reached on the basis of measurements and calculations of the radiative temperature variations due to longwave radiation. The attempt to use the Tiros I1 data for evaluating the outgoing radiation and albedo means for the earth as a whole with calculated high-latitudes Values led to the planetary outgoing radiation of 0.31 1 cal/cm2min and albedo of 0.38 [158]. It should be noted that the albedo is usually assumed to equal 0.34, while according to the Explorer VII data, it is 0.33. This discrepancy should be attributed to the limited (with respect to the time interval) use of data and also to measurement errors. In processing the Tiros I11 data, Wexler [25] evaluated albedo at from 4 to 10 percent (with clear skies) to 30 percent with continuous cloud (in the
758
Net Radiation
Sahara region the albedo reaches 20 percent in clear weather). The albedo attained 54 percent for channel 5 and 47 percent for channel 3 only during the first five orbits. The mean value for this period was 20 percent. Considering that the mean cloud albedo as measured from aircraft is 50 percent with individual values of 80 percent, it becomes clear that the satellite data should be regarded as underestimated. Conover [I611 worked out a method for determining the albedo of the earth-atmosphere system based on the use of television data (cloud cover and terrestrial photographs) obtained from meteorological satellites. This method was applied in the processing of satellite pictures and the simultaneous photographs made from a U-2 aircraft at 20 km elevation. The spectral sensitivity of the satellite TV camera and of the aerophotographing instrument was approximately the same. The TV system (including video recording) was calibrated by successive irradiation of the screen from three tungsten incandescent lamps (the use of several sources was caused by the necessity to model a wide range of radiances). The determination of the absolute cloud radiance (in energy units) from the signals recorded at the ground-receiving video installation was carried out by comparing with the amplitude of signals recorded in the irradiation of the TV camera during the calibration before the fight. As shown in [161], in the photometric film processing it is necessary to consider the following factors : (1) picture-to-picture variation in exposition; (2) effect of temperature variations on the TV functioning; (3) nonhomogeneous distribution of blackening density even with homogeneous lighting; and (4) non homogeneity of the film. When calculating the albedo from cloud radiances it was assumed that the radiation reflection by clouds is isotropic; the atmosphere overlying the cloud was taken into account solely by computing the contribution of the Rayleigh scattering for the nadir angle 22’ (the angular dependence of multiply scattered light ignored) and of the absorption by ozone, whose total content was 0.28 “cm”. The values of cloud and of terrestrial radiance in satellite and aircraft estimation agree satisfactorily. The averaged satellite albedo values vary from 7 percent (the Pacific, cloudless) to 92 percent (dense and extensive cumulonimbus clouds). The snow albedo was found to decrease from 70 to 51 percent four days after snowfall. For the White Sands Desert (New Mexico) the albedo was recorded at 68 percent with solar altitude of 78’ and nadir angles from 17 to 28’. Comparison with albedo data known from literature shows that similar satellite and aircraft measurements yield exaggerated values. Nordberg et al. [I621 analyzed the results of the effective temperature and
10.6. Investigations of the Earth's Net Radiation by Means of Satellites
759
albedo determination from the Tiros 111measurement data on the outgoing radiation by making use of simultaneous wide-angle photographs of cloud distribution. The three typical situations considered in [162] relate to the Atlantic Ocean and North Africa (two representing a cloudless atmosphere) and also to the eastern United States (cloudy sky). All data were obtained for local noon. It is of essence that in all the three case the TV cameras and wide-angle radiometer were almost exactly oriented with respect to the nadir. The nadir sighting angle for the five-channel radiometer varied from 0 to 45'. The results obtained by the authors of El621 are discussed in [148, 1491. Rasool and Prabhakara [I631 were the first to realize the climatological processing of the Tiros data for 1962-63; their purpose was to derive information on the average planetary distribution of the net radiation components for the esrth-atmosphere system in the zone 60' S to 60' N lat. For more accuracy with respect to the five-channel radiometer data, only those readings were used which related to the solar zenith angles of less than 60' and nadir sighting angles less than 45'. The Tiros IV data from February to June of 1962 averaged for 5' lat 5' long squares were used to plot the planetary albedo chart. In this plot only such points were considered that corresponded to not less than a hundred individual albedo values (most often 500). The albedo calculation was made from the channel 3 readings (spectral region 0.2 to 5 p ) on the assumption of isotropy of the solar radiation reflection by the earth. In processing the results, the temporal variation of the radiometer's sensitivity was taken into account. The most characteristic features of the geographical albedo distribution may be summarized as follows: The ocean albedo, especially in subtropics, is about 20 percent. The continental albedo varies from 30 to 40 percent. On the average, the albedo is 26 and 34 percent, respectively. The mean albedo of the earth-atmosphere system within the investigated zone is 31 percent. The albedo isolines follow the oceanic contours. At the coastal line, large albedo gradients were observed. In the Southern Hemisphere the longitudinal variation of albedo is weak, except the subtropical zone with three minima over oceans. During the whole period of measurements the albedo for the Sahara and Arabian Deserts is about 45 percent and comparable with that of Central Africa and South America where the intensive cloud was observed (these data are justified by the Tiros I11 and Tiros IV results). Such a high albedo value leads to believe that the earlier estimations of the absorbed solar radiation for desert areas were exaggerated. Since the outgoing longwave radiation
760
Net Radiation
in this case is quite great, it turns out that in the Sahara conditions, the net radiation of the earth-atmosphere system approaches zero, which contradicts the familiar calculations that present a positive value. Figure 10.40 gives the isopleths of absorbed radiation q', plotted by Rasool and Prabhakara [123a, 1631 from the Tiros IV and Tiros VII data and considered as annual means. It is evident that the q' values in the temperate and subtropical northern latitudes in June and July are unusually high. Also notable is the zone of maximal absorbed radiation in the southern subtropical latitudes in summer. Both peculiarities in the absorbed radiation variation are due mainly to the effect of the low ocean albedo.
FIG. 10.40 Isopleths of daily totals of absorbed solar radiation (cal/cm2day).
The data of Fig. 10.41 characterize the latitudinal and annual variation of the outgoing longwave radiation. Hence it is clear that the latitudinal range of considered means is very weak. A still weaker range is observed with the annual variation. Nevertheless these data, as well as the above considered results, confirm the presence of two weak subtropical maxima of the outgoing radiation along the equator, observed in August, September, and October (in the same months in spite of the opposite seasonal phases). The equatorial minimum indicates the intertropical convergence zone with more cloud.
10.6. Investigations of the Earth’s Net Radiation by Means of Satellites
761
FIG. 10.41 Zsopleths of daily totals of the outgoing longwave radiation (callcine day).
In Fig. 10.42 are given isopleths of the net radiation for the earth-atmosphere system. Since the outgoing longwave radiation field is very “diluted,” these isopleths are similar to those of the absorbed solar radiation of Fig. 10.40. It is evident from Fig. 10.42 that the maximal net radiation zones occupy the belts 20 to 40’ in both hemispheres in summer. Within 20’ N to 15’s lat. the net radiation is positive throughout the year. In Rasool and Prabhakara’s estimation [163] the net radiation of the earth as a whole is practically zero. In the Northern hemisphere this quantity is -77 x 10l8 and +81 x 10ls cal/day to the north and south of the 50’ parallel, respectively. In the Southern Hemisphere the analogous values are -92.5 x 10l8 and +94 x 10ls cal/day. Vowinckel and Orvig [35] used calculations of the solar and outgoing longwave radiation absorbed by the atmosphere and also the known values of the net radiation and its components for the underlying surface, to obtain the net radiation of the atmosphere and the earth-atmosphere system. Extremal evaluation of the effect of errors in the determination of the cloudless atmosphere moisture content on the calculation of the absorbed shortwave radiation showed that they were not in excess of 4 percent. The absorption by stratus clouds was taken into account with the help of corrections‘
762
Net Radiation
FIG. 10.42 Zsopleths of daily totals of the net radiation for the system earth's surface atmosphere (cal/cm8day).
determined from the familiar literature data. With respect to cirrus clouds, it was assumed that they would not affect the absorption. The outgoing longwave radiation was calculated from the Elsasser chart, considering water vapor only and assuming identity of the outgoing radiation and of the upward longwave radiation flux at the 300-mb level. The altitudes of the lower, middle, and upper clouds were taken respectively as 1.2, 4.0, and 5.5. km. Consideration of the calculations of the annual variation in the atmospheric net radiation and its components for various points with clear skies and in the real cloud conditions showed that its main difference from the net radiation of the underlying surface consists in a smaller amplitude due to the low value of the shortwave component as compared with the stable longwave. In all cases the atmospheric net radiation is negative, being lowest in late summer and autumn and highest in spring and early summer. All components are maximal in summer. The most characteristic feature is an exceptional stability of the outgoing longwave radiation during the year. As a rule, the negative net radiation of the atmosphere increases with cloud, since the radiation toward the earth's surface increases with the appearance of clouds and is not compensated by an increase in the absorped shortwave
10.6. Investigations of the Earth’s Net Radiation by Means of Satellites
763
radiation (an inverse situation may be observed only in the conditions of a very dry atmosphere). An unusual Arctic feature, compared with the temperate latitudes, is the increase in the outgoing radiation due to inversions with the appearance of clouds, and consequently the increasing radiative cooling of the entire atmospheric thickness. The amount of atmospheric net radiation consists mainly of radiation from the underlying surface. The zonal and meridional sections of the net radiation for the earthatmosphere system repeat the main features of the corresponding sections for the underlying surface. Monthly charts of its geographical distribution reveal a very low latitudinal variability in winter. The differences are greatest for land and oceans. In midwinter the maximum of net radiation occurs in the Norwegian Sea and moves toward the zone of pack ice closer to spring. The maximal cooling is observed over the pole only in late summer. In spring there is a notable increase of the meridional net radiation gradients (under the influence of the albedo nonhomogeneity). The typical winter contrast between ocean and continent disappears in summer. In midsummer and early autumn the regional and latitudinal variation of the net radiation strongly smooths out. In August and September the net radiation distribution presents a rather simple picture: its negative values decrease from the pole with increasing latitude. Along with the climatological characteristics of the net radiation and its components for the earth-atmosphere system, it is of interest to know their variability. Such information obtained in processing the Tiros I11 and Tiros IV data with its four orbits (middle July, 1961) and by using theoretical data is given by Davis [164] and Kennedy [165]. Table 10.23 summarizes the atmospheric net radiation values of the total radiative heat influx to the whole thickness of the atmosphere and its components (the longwave radiative heat influx and the absorbed solar radiation) and also the outgoing longwave radiation and the reflected solar radiation. It is evident from this table that these quantities have relatively small variations. The exception is the reflected solar radiation (outgoing shortwave radiation) whose greater variation is due to the effect of cloud nonhomogeneity . The outgoing longwave radiation was found to have a more “motley” field than given in [I641 by Gergen [166], who used actinometric radiosoundings at 25 United States locations during May 26 to 30, 1959. In his estimation the outgoing longwave radiation varied from 15.6 to 26.6 mW/ cm2, that is, almost by twice, which was mainly due to the cloud cover nonhomogeneity. An interesting example of the spatial variability of the outgoing radiation in the transparency window 8 to 12 p, from the Tiros
TABLE 10.23 Mean Values and Standard Deviations of the Components of the Radiative Heat Inflow for the Whole Atmospheric Thickness, of the Outgoing Longwave Radiations, and of the Reflected Solar Radiation. After Davis 11641 ~
~~
~~~
Orbit 3
Orbit 4
Measurement Mean
Std' Deviation
Mean
Std' Deviation
Orbit 29 Mean
Std' Deviation
Orbit 44 Mean
Std. Deviation
z
s w L Total radiative heat inflow, cal/cm2 min
0.1347
0.0277
0.1408
0.0228
0.1394
0.0262
0.1454
0.0233
Longwave radiative heat inflow, cal/cm2 min
0.2436
0.0258
0.2551
0.0219
0.2578
0.0231
0.2535
0.0327
Absorbed solar radiation, cal/cmz min
0.1090
0.0155
0.1143
0.0187
0.1183
0.0128
0.1084
0.0192
Outgoing longwave radiation, cal/cm2 min
0.3580
0.0513
0.3633
0.0481
0.3359
0.0360
0.3846
0.0494
Reflected solar radiation (channel 3, W/mZ)
94.4
46.7
29.6
62.2
E B'
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System 765
I11 data on July 16, 1961, is considered by Allison et al. [167]. According to their data, the effective temperature (measured in the transparency window) varies from 225 to 300’k and more in the belt 55’ N to 5 5 ’ s lat. The isolated character of the available data on the variation of the net radiation components in the earth-atmosphere system underlines the necessity of further investigations in this direction.
10.7. Statistical Features of the Net Radiation of the Earth-Atmosphere System At present the available satellite data on the outgoing radiation are so numerous as to make any complete “individual” analysis impossible, not even with high-speed electronic computers. Certain statistical methods of analysis are therefore needed to represent and generalize the material of observations that iiust be processed. This problem is also essentially interesting from the viewpoint of using outgoing radiation data as a field of random values. Statistical methods for analyzing satellite meteorological information are in their infancy (see [167a, 168-1721). We shall consider here some results obtained by Borisenkov et al. [167a, 1681, who in analyzing the outgoing radiation fields used the statistical theory of turbulence. The need to know the structure of the thermal terrestrial radiation field is essential because the strict solution of certain problems of the methods for observation and objective analysis of the radiation field is possible only if the structural characteristics of the field is known. Such knowledge, for example, can help to pinpoint the expedient frequency of satellite measurements of the outgoing radiation. It can also be used in objective analysis of radiation fields, in their comparison with the fields of other meteorological elements (temperature, for example), and so on. Even the first results of the outgoing radiation, as obtained by satellite measurements characterize the radiative field structure to a certain degree. In the work [167a] are considered the statistics of the outgoing radiation fields as obtained by the Tiros I1 meteorological satellite. The authors made use of the information summarized in the Tiros I1 radiation data catalog [173]. Tiros 11, launched on November 23, 1960, was supplied with two TV cameras for recording cloud, ice, and other ground objects, and was designed for measuring the earth’s outgoing radiation in different spectral regions. Two wide-angle sensors measured the integral fluxes of long- and short-
766
Net Radiation
wave radiation within the 50' sighting angle. For spectral measurements, a five-channel radiometer with a sighting angle of 5' and supplied with filters to isolate certain spectral regions was used. The five channels corresponded to the following intervals:
No. 1 to NO. 2 to NO. 3 to NO. 4 to No. 5 to
6-6.15 p : 8-12 PFC: 0.2-6 p : 8-30 p : 0.55-0.75 p :
water vapor absorption band atmospheric transparency window region of the reflected solar radiation integral thermal radiation region of the camera's spectral sensitivity
The above-mentioned catalog gives the results of radiation measurements by each channel for 52 orbits in the interpolation with a grid step of 40 miles. Besides, the channel 2 data are plotted on polar stereographic charts (scale 1 :50,000,000) with a grid step of 200 miles. Later, the catalog was followed by additional limitations to use of the given material [1741. It appeared that the geographical correspondence of the data had to be corrected in view of the errors in the determination of the scanning angle as a function of time. Besides, there were errors in the deciphering of the transmitted signals, due to radio noises. The distortion of signals was especially strong in channels 3 and 5. The supplement thus recommended that channel 5 data be ignored and those of channel 3 be used with great care. Only the results for channels 1,2, and 4 were therefore considered in [167a]. However, errors for these channels, apart from error in geographical location, were still great. According to [174], the mean error in the determination of the outgoing radiation for the 6 to 6.5 p region was f0.06 W/m2, which corresponds to the effective temperature error of f2' (at T = 240'K). With the channel 2 region, it was f 1.6 W/m2 (f2O at T = 270OK). With channel 4, it was f 1.7 W/m2 (31 2' at T = 260'K). The finite errors in the determination of radiation values by channels 1, 2, and 4 were f0.18 W/m2 (f 6' at T = 240'K), f4 W/m2 (f 5' at T = 270°K), and f5.6 W/m2 (f6' at T = 260'K), respectively. The errors in the water vapor absorption band (channel 1) may be still greater, owing to certain effects, which results in their finite value of & 0.2425 W/m2 (f8' at T = 240OK). In spite of quite a few shortcomings of the observational data given in the catalog, they are still valuable for some preliminary conclusions about the radiative field structure. The data were processed according to the following logic. Let us select rectangular surfaces with small latitudinal extension along the regular grids
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System 767
of the observational charts. Let the number of columns m and lines n that determine the selected grids be fixed for each surface. Denoting the radiation value in the grid r through F(r), we have the following mean value for a field of m bars and n lines : (10.23) In the case for determination of the spatial structural function of the element f, we can use the formula
bf(l)
1 sn
= -
z 8n
i=l
[f@i
+4 -
(10.24)
wheref(ri) = F(ri) - F and s = m/2 is rounded off with respect to the lesser side. The autocorrelational moment mf(/) and the normalized autocorrelational moment (autocorrelation factor) kf(l)for the element f were determined from the formulas :
The value I of the shift between the grid with the correlated elements varied from h to sh (h is the grid step; in this case h z 40 miles). Since, as has already been mentioned, the radiation measurements included considerable errors, we should try to evaluate the reliability of the obtained structural and correlation functions, taking into account these errors. Let f(ri) contain a random error E . In this case, f(ri
+ 1)
=f‘(ri
f(ri) = f ’ ( r i )
+ 1) + &(Ti+ I> +
&(Ti)
(10.27a) (10.27b)
where f ‘ is the true f value. If we assume that the measurement errors are in no way connected with the true ,f’ values and at various points of the field are statistically independent of each other, the following equation is easily obtained from (10.24) and (10.27): (10.28) bf(l) = bf’(Z) 2 2
+
768
Net Radiation
where
Substituting (10.27) in to (10.26) and considering the above assumptions, we have in the numerator: 1
nn.
1
an
+
The denominc’ior of (10.26) is (of)2 2, where
In this case
[ I
at
/=o
where k f fis the true value of the autocorrelation factor and (of)2is the true dispersion. Since in the given case there is the following relationship between the calculated and the true dispersion,
the expression for kf can be rewritten as
It is easy to see from (10.29) that the observational errors cause the true autocorrelation moment always to exceed the kf obtained from the data with a random error E. It also follows from (10.29) that with the error E~ small compared with the dispersion u2, the true autocorrelation factor is little different from that calculated. For example, for the pressure at sea level, E is of the order of
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System 769
0.1 mb and cr 21 10 mb. It is obvious that such an error in the determination of the autocorrelation factor is negligible. In the investigation of the correlation moments of radiative fields, however, the error cannot be ignored, since the ratio &/cr is 0.4 to 0.5 at best, while for individual fields E and cr are comparable. The derived formulas enable certain correction of the structural and autocorrelation functions. Note here that at a given &, the autocorrelation factors obtained for orbits with higher (T values are more trustworthy, since in this case the calculated kf(l) are closer to the true values. The calculated structural characteristics of radiative fields for channels 1, 2, and 4 are given below, but analysis of them should take into consideration the preceding remarks. The structural and correlation functions were calculated for 50 fields of channel l , 56 of channel 2, and 62 of channel 4. The number of cases here exceeds the number of orbits, since the radiation fields for several orbits were divided into two regions. Figures 10.43 through 10.45 give the mean, maximal and minimal structural functions, and autocorrelation factors for the mentioned fields. All calculations were made with a Ural2 electronic digital computer. Q060L
a-0.040
a020
-
xil 0
(b)
P
-04 -02
FIG. 10.43 Structural functions ( a ) and autocorrelation factors (b) of the radiation field. Channel I. (1) maximum; (2) mean; (3) minimum.
770
Net Radiation
-0.2 -0.4
-0.6 b
FIG. 10.44 Structural functions ( a ) and autocorrelation factors (b) of the radiation field. Channel 2. Numbered as in Fig. 10.43. a
100
'n
20 2
4
6
8
10
12
Ii
I6
IbL
I .ol-
' r
-0.4
-
FIG. 10.45 Structural functions ( a ) and autocorrelation factors (b) of the radiation field. Channel 4. Numbered as in Fig. 10.43.
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System 771
To obtain the structural and correlation functions, the values of all functions for each Z were plotted on the graphs, the means were calculated, and the average b(1) and k(Z) lines were drawn. The maxima and minima with b(Z) and k(Z) were simply drawn by a smooth curve around the field of points obtained, and isolated large departures were ignored. In order to check the function isotropy, analogous calculations were made, with selections taken from the radiation values in the grids perpendicular to the initial direction. The first calculations were concerned with the linear grids but now they included the vertical columns. The linear values are plotted in solid lines and the vertical in dashes. Since the columns contain less grids than lines, the latter calculations ended with smaller 1. It is evident from the figures that, on the average, isotropy is best fulfilled for the integral radiation and is worse, for the radiation in the water vapor absorption band. It will be shown further that for individually selected radiation fields, there may be no isotropy, even in the 8- to 30-p region. We see that the variation of the structural functions first shows a rapid increase and then a practical stability with certain 1. Let us designate the distance at which b, reaches “saturation” by d. On the average, for the radiation fields of each channel, d w 16 h. The radiant flux in the 6- to 6.5-p region is practically determined by the atmospheric water vapor radiation, with a maximum at about the 400-mb area level. The structural functions of the radiant flux in this region will thus characterize the spatial structure of the water vapor distribution and its temperature. The Tiros I1 data on the channel 1 range, as was already metioned, contain far greater relative errors than on the radiation of channels 2 and 4. For this reason the channel 1 information should be considered very rough. It is possible that the considerable dispersion of points for the field k,(Z) and relatively large deviations from the conditions of isotropy may be partly explained by the low accuracy of these data. The obtained nonstandard values of the structural function for each Z are naturally less in the given case than b,(Z) and b,(l) because the absolute value of radiation for the 6- to 6.5-p region is small compared with the radiation in the 8- to 12 and 8 to 30 p regions. The field of points b,(Z) is, however, more compact than with b,(Z) and b4(Z). Thus, since the ratio of the maximal structural function to the minimal (from the rounding lines) at distances close to finite is of the order of 7 to 8, it is about 20 for b,(d) and b,(d). This fact may be explained by the more uniform spatial distribution of water vapor in comparison with that of cloudiness, which strongly affects the value and nature of the structural functions b,(Z) and b4(Z). Considering the variation of the autocorrelation factor k,(l) with distance, it is
772
Net Radiation
evident that it shows a slower decrease than in the other two channels. In the initial interval (for Z < 3h), however, the decrease of k,(Z) is more rapid than that of k2(Z)and k4(I). Besides, the difference between the maximal and minimal lines of the k,(l) field is considerably larger than for channels 2 and 4. This appears to be caused by the low accuracy of the obtained values of radiation in this spectral region. From the determination of the structural function it follows that b’, 0 = 0. Therefore we have, on the basis of (10.28),
b,(O)
= 2&2
Extrapolating the mean b,(l) value (Fig. 10.43(a)) up to I = 0, we have 2 2 N 0.006 W2/m4. As seen, the average error determined by zero extrapolation equals the average error in the radiation measurement given by the supplement to the Tiros I1 catalog [174]. At present the greatest attention is drawn to the 8- to 12-,u atmospheric window (of all the five spectral regions). The radiation detected from the satellite in this interval is by 75 percent due to the radiation of the earth’s underlying surface or clouds. It can thus be used to determine their temperature. Since the cloud surface temperature is usually much lower than that of the underlying surface, the radiation field in the 8- to 12-,u region can be used to estimate the cloud distribution and the pressure systems involving considerable cloud amount. The structural radiation functions for this part of the spectrum will therefore be strongly dependent upon the character of cloud fields. The same dependence must take place for channel 4. Comparing the structural and correlations functions of radiation of channels 2 and 4, we see that they have a close resemblance. Especially close are the mean b,(Z) and b4(Z), although the isotropy of the average radiative field for the 8- to 12-,u window is considerably more than for the 8- to 30-,u region. Comparison of the autocorrelation factors shows that the connection between radiation over different points of channels 2 and 4 undergoes approximately the same extinction. Such agreement between the structural and correlation funtions of radiation for channels 2 and 4 enables attempting transition from b(I) and k(Z) of the one channel to those of the other. Figure 10.46 is a graph of the relation between the structural functions of these radiative fields for a selected value I = 1Oh. The relationship is linear and is represented by the equation of regression : b4(II0)= o.71b2(Il,,)
+ 4.67
(10.30)
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System 773
with a relatively high correlation coefficient of 0.89. This justifies the great closeness of the connection. 80 I-
70 60
50
-*
40
-
30 20 10
0
I
10
I
I
l
20 30 40
I
I
50
60 70 80
1
1
b2
FIG. 10.46 Relationship between structural functions of the radiation fields (Channels 2 and 4, I = 10 h).
Since the radiative fields can, on the average, be considered isotropic, the following simple relationship is established between the structural function and the autocorrelation factor on the basis of (10.24)and (10.25),provided the condition for homogeneity is fulfilled : bf(l) = 20; [l - kf(Z)]
(10.31)
It follows from the expression (10.31)that closer relations between the investigated characteristics lead to a decrease of the structural function, while their separation makes it increase. In particular, if such distances L are selected for which k f ( L ) = 0, then b f ( L )= 2aP.To check the fulfillment of this relation, the data of Figs. 10.43 to 10.45 were used to determine L, for which kf = 0, and the values bf(L) = 2a2 were taken from the mean curve. The f-value dispersion was directly determined for each field and later averaged. The obtained E~ values are given in Table 10.24. It is evident from Table 10.24 that the coincidence of the obtained c2 is quite satisfactory, which justifies the validity of the statement about the isotropy and homogeneity of the mean radiative field in the above spectral intervals. Let us further consider some applications of the derived structural characteristics. Since in plotting charts the observational data are interpolated in
774
Net Radiation TABLE 10.24 Dispersion of the Radiative Field. After published data [174]
Spectral Region, p
az (from Figs. 10.43-10.44)
6-6.5 8-12 8-30
0.0118 20.0 17.5
a2 Averaged with Respect to Isolated Fields 0.0126 21.90 16.85
the grids of the regular net, it is natural to inquire about the optimal frequency of radiation measurements made from the satellite, which would have an interpolation error not exceeding the given one. The scheme for analyzing the meteorological fields in general and radiative fields in particular (adopted in the United States) did not until recently consider the structure of the analyzed fields. The interpolated value of the element f at every regular grid interesection was determined as a mean weight among several values ; the weight factor taken to be inversely proportional (without sufficient justification) to the square distance between the grid intersection and the initial point of interpolation. Such was the logic of radiation data processing as presented in the catalog [173]. If the structural and correlation functions had been taken into account, this interpolation would have been more accurate. According to Drozdov and Shepelevsky, the mean square error in the linear interpolation can be determined from the formula given in Gandin's work [175]:
Substituting the expression (10.3 1) into this formula, we have &I2 - - 6 = 2-
a '
r
I
[l - kf(f - r ) ]
+2 (10.33)
At the ends of the segment I, the error 6 is defined by the error kf.If the interpolation is performed with respect to the middle of the segment f (r = (l/2)), then (10.34)
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System
775
If we know the radiative field structure, it is obviously easy to state the finite distai-cu at which 6 will become larger than the given error. Gandin [I751 proposed a formula for interpolation which considered the minimal error condition. The interpolated fo value is thus sought in the form of a linear combination: n
fo =
c Pifi
(i = 1 , 2
- . a
n)
(10.35)
i=l
in which the weights Piare so selected that they have the minimal mean square error for interpolation with (10.35): n
E~~
=
[fo
-
x Pifil2
= min
(10.36)
i=1
In the transition from thefvalue to the autocorrelation factors, equations for determining the coefficients Pi by way of the structural characteristics of the field f are derived. The interpolation error here is defined from the formula n
6=1-
x koiPi
(10.37)
i=1
where the koi are the autocorrelation factors between the element foand the knownfi element at points i. In the case of interpolation over two points with respect to the middle of the 1 segment,
6
=
I -2Pkf(f)
(10.38)
where
The error calculated with (10.38)is slightly less, all other conditions being equal, than the error of the linear interpolation. The admissible measurement frequency in the second case therefore appears to be somewhat lower than in the first. However, for small distances, both formulas yield close results. For example, to secure an error in the integral radiation interpolation not exceeding the mean of 1.7 W/m2, the distances between the measurement points must not be larger than 60 to 70 miles. The same evolution is obtained with (10.34).It is evident that the radiation measurement errors as well as the interpolation error will affect the autocorrelation factor. More accurate estimates of the admissible I can therefore be obtained by
776
Net Radiation
taking into account the errors in the determination of k,. Depending on the position of basic points, the interpolation error can be evaluated prior to the derivation of the weight factors Pii by making use of the normalized correlation functions k,(Z). Let us present the following analogy with (10.35):
where the subscript 1 indicates the number of points at which the interpolated f value is calculated. Let us have the following system of normal equations to find the weight factors Pij by the least squares method:
(10.40)
---
where u is the dispersion with el = u2 = = on for homogeneous fields, and kii are the correlation funtions (conjugate correlation factors) dependent on the reciprocal position of the basic points only. The mean quadratic error of such a representation will be defined by the formula (10.41) where k12
kl?l
1 ... k2n ............... ...............
k21
D=
k13
kn1
k23
kna
kn3
*.'
(10.42)
1
is the determinant composed of conjugate correlation factors and D is the corresponding minor. The correlation functions can be used with (10.41) foi, the evaluation of the interpolation error and the expedient measurement frequency without preliminary knowledge of the weight factors P,. The values of the correlation function should first be corrected as noted above.
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System 777
The spatial radiation structure must be known for the calculation of radiation means in a certain satellite-orbit interval and also for the evaluation of the accuracy of such calculations. Lichtman and Kagan [I761 derived formuls for the determination of the accuracy in defining the mean for the infinitely great distance on the basis of measurement data in its final section Z : E~~ =
bAm,
+ 22 lorb,(r) dr 1
2
1
1:'
b,(r) dr
(10.43)
In addition, if a limited number of measurements n is performed in this section at points ri (i = 1, 2 n), according to the work cited, there will appear an additional error due to the limitation of the number of measurements :
If there are several parallel itineraries spaced at d or greater distance it is possible to consider that the measurements at one route are independent of those at others, and that their total length will be equal to the summed itineraries. If the distance between the routes is less than d, the second and subsequent routes must obviously be summarized with the weights proportional to b(r)/b(d),where in the given case r is the distance between the successive itineraries. Making use of the above structural functions and taking account of the admissible errors in the determination of the mean, it is easy to find with (10.43) and (10.44) the expedient dimensions of the area with respect to which the averaging should be performed. Presenting, for example, the structural function of the radiation in the 8- to 30-p region in the form b4(r) b4(d)(1 - [exp(- 0.0758r4'3)]}
-
and substituting it in (10.43), we find that for a rectangular area of 20h length and 1% width, the error in the determination of the mean radiation is approximately equal to a single measurement error. The above examples made use of the mean structural characteristics of radiative fields. However, those of individual fields can also be useful in certain investigations. When analyzing the structural functions of radiative fields, their variability in time and from region to region was noted. The authors of [I681 made an attempt at qualitative analysis of the dependence
778
Net Radiation
of the variability of b4Q upon the state of the atmospheric thermobaric field. It was assumed that, on the average, the type and character of cloud and humidi-y d i s ~ b u t i o nwould be reffected by the nature of the thermoba~c field. To perform this analysis the areas employed in the calculation of the structural radiation functions were plotted on charts of absolute topography of the 500-mb isobaric surface. The baric features were then compared with the structural radiation function of the given region. Figures 10.41 and
FIG. 10.47 Absolute topography chart of a 500-mb isobaric surface, Dec. 13, 1960.
10.48 give an exemplary baric field at the level of 500 mb (December 13, 1960) and the structural radiation functions for three regions of this field. It appears that the greater the field's horizonta~homogeneity, the smal~erthe value b,(d), and the best is the fulfillment of radiation isotropy. In region 3 the therrnobaric field is at its calmest, with corresponding and relatively small b4(d)=S 10. The fulfillment of isotropy of the radiation field is satisfactory here. In regions 2 and I the thermal field and baric features are not horizontally homogeneous. This possibly accounts for the great values and
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System
779
anisotropy of the structural characteristics of the radiative field. The anisotropy is especially marked in region 2. Apart from the physical causes it may be due to the great difference in the number of intersections along the columns and lines of the area considered. Analogous comparison of the
L
FIG. 10.48 Structural functions of the integral radiation fields. (1) 0554 hr, orbit 290; (2) 0739 hr, orbit 291 ; (3) 1240 hr, orbit 294.
structural radiation functions with thermobaric fields was made for five days. The general picture is similar to the one described above, with respect to analysis of the structural and correlation functions. Thus, even the magnitude and nature of the spatial variation of the structural (correlation) functions and the fulfillment of the isotropy conditions can, to a certain degree, be indicators of the state of the thermobaric field. Further researh in this direction will enable further verification and provide more detail to this statement. Of considerable interest is the determination of the spectral density of the most energetically important perturbations. The spectral density S(o) calculated in [168] from the formula
Irn
S(w) = k ( t ) cos W T d t n o
(10.45)
where k ( t ) is the correlation function, is presented in Fig. 10.49. The calculation was based on the Tiros I1 and Tiros I11 data and performed with the Ural 2 electronic digital computer by making use of the correlation functions of radiative fields for various spectral intervals. The spectral func-
780
(a 1
0.41
400
1200
2000
2000
3600
krn
-cn
0.3
1
3 0.2
km
km
0.41
(e 1
400
1200
2000 km
2000
3600
FIG. 10.49 Spectral density of the radiation field with using radiation data selected from intersections of the 40 miles grid step (2), of 1.25’ (2) and of 2 . F (3). (a) Channel 1 ; (b) Channel 2 ; (c) Channel 3; (d) Channel 4; (e) Channel 5.
10.7. Statistical Features of Net Radiation of the Earth-Atmosphere System 781
-.
tions were obtained for w corresponding to I = h, 2h -,with h different for each satellite. It should be noted that since the correlation function at I > 10h is not realiably determined, the values S(1) at I > 10 must not be much trusted. Figure 10.49 presents three curves characterizing the spectral density of the integral outgoing radiation field for three types of correlation function, computed with a grid step of 40 miles and 1.25' and 2.5' of the meridional arc. It follows from this figure that the most probable scales of the integral outgoing radiation perturbations at h = 40 miles are 350 and 800 km. Taking into account the limits of the correlation function fluctuations, the minimal scale of perturbations is placed at 200 to 500 km, and the maximal scale at 600 to 800 km. Perturbations on such scales are observed in the fields of other meteorological elements-of pressure and geopotential, in particular. If the radiation data are selected at a grid step h = 1.25', the calculated spectral functions (curve 2) also reveal two scales of perturbations of 400 and 700 km. Taking account of possible departures of the correlation function from the means, the scale of lesser perturbations varies within 250 to 700 km; for greater perturbations it is within 700 to 900 km. In addition, still greater perturbations are revealed whose scale is of the order of 1100 to 1700 km. It is easy to see that, in spite of the notable discrepancy between the channel 4 data with the Tiros I1 and Tiros 111, the spectral characteristics of perturbations turned out to be fairly close. The same figure gives a curve of the spectral density for the outgoing radiation field as observed at channel 4 of the Tiros I11 satellite with a grid step of 2.5'. It is obvious that in the given case the authors could not isolate the spectrum of perturbations on the 200 to 500-km scale, but then revealed in more detail perturbations on the 800-1000 km scale and even greater perturbations on the planetary scale whose dimesions were from 1600-2000 to 2500-3500 km. The radiant flux in the 6- to 6.5-p region is practically determined by the atmospheric water vapor radiation, with a maximum at 7 to 8 km. The spectral density of these radiative field (Fig. 10.49) therefore makes it possible to evaluate the scales of the energetically significant perturbations at about 400,700, and also 1100 to 1700 km (curve 2). However, curve 3 of the spectral radiation density from the Tiros I11 data at h = 2.5' has only one maximum at I 21 800 km, coinciding with a similar curve of Fig. 10.45. The two curves are then almost specular. The absence of any perturbations as shown by the Tiros I1 curve of spectral density is strange. Curve 1, however
782
Net Radiation
(Fig. 10.45), has exceptionally clear maxima at distances of the order of 350 and 800 km. Also perturbations of the radiative field appear in the atmospheric window, with a scale of about 1500 km. In calculating from the radiation data with h = 1.25', though, the spectral density has but a weak perturbation only for I 800 km. According to the curve 3, there are notable perturbations on the 1200 to 1600-km scale in this spectral interval. These perturbations are generally less marked than for the fields of the integral and water vapor radiation. It is possible that cloud fields are the important factor causing the perturbations in the atmospheric window region. The large perturbations on the plantary scale are most pronounced with radiative fields formed mainly by the whole tropospheric thickness, that is, in the spectral region isolated by channels 1 and 4. In the region of the integral shortwave radiation (Fig. 10.49) curve 2 shows two scales of perturbations, of 500 to 1000 and 1200 to 1500 km. The same order of values is revealed in the perturbation of radiative fields when channel 5 uses the selections from the intersections with a grid step 2.5' (curve 3 of Fig. 10.45). The same curve shows another maximum at I 2400 km. Two other curves, curve 3 in Fig. 10.49 and curve 2 in Fig. 10.49, have least notable perturbations. The first, curve 3, shows them only with I = 500 to 1300 and 1500 to 2100 km, while with curve 2 it is practically impossible to trace any perturbations. Since the initial measurement data on the radiation with these two channels are particularly erratic, it is natural to expect great errors in the calculated spectral density. For example, the spectral density curves for channel 3 at h = 2.5' and for channel 5 at h = 1.25', calculated from the maximal and minimal surrounding lines of the autocorrelation factors field, are almost specular. The spectral density calculated from the mean k is thus very smooth. Similar spectral analysis may appear to be very useful in comparing the radiative fields plotted from satellite data with the fields of the basic meteorological elements of pressure and temperature in particular.
-
-
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790
Net Radiation
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