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The radiation balance of a tropical pasture, II. Net all-wave radiation
Agricultural Meteorology Elsevier Publishing Company, Amsterdam-Printed in The Netherlands
THE RADIATION BALANCE OF A TROPICAL PASTURE, H. NET ALL-WAVE RADIATION
J. D. KALMA
Division o f Land Research, Commonwealth Scientific and Industrial Research Organization, Canberra, .4. C. T. (Australia/ (Received September 8, 1971)
ABSTRACT Kalma, J. D., 1972. The radiation balance of a tropical pasture, II. Net all-wave radiation. Agric. Meteorol., 10: 261-275. Seasonal changes in net all-wave and long-wave radiation are discussed, as measured over three surfaces, one dominated by Townsville stylo, another by two annual grasses and a third consisting of bare soil. The short-wave reflection coefficient of these three surfaces has been discussed in Kalma and Badham (1972). Net long-wave loss during night-time varied between 3 and 12% and net long-wave loss over 24 h between 19 and 47% of total incident short-wave radiation. In general, wetting and rapid growth caused net long-wave loss, as a fraction of incident solar radiation, to decrease. Drought, maturing, lodging and senescence had the opposite effect. Differences between the three surfaces were related to cover, stand height, drought resistance and growth phase. A unique relationship was observed between daily atmospheric transmissivity and the ratio between daily totals of diffuse and total radiation. It is shown how daffy net long-wave radiation, under all conditions, may be predicted from known daily values of atmospheric transmissivity and air temperature. Effective surface radiative temperatures, indirectly obtained from measurements with single-sided pyrradiometers, have been presented for the two vegetative surfaces for three representative days. Semi-empirical relations for estimating net ail-wave radiation during daylight from incident total radiation were obtained from linear regressions computed, using hourly totals, for net ali-wave radiation on incident total radiation for all three surfaces and six successive periods covering the experimental season. Three seasonal regressions for the individual surfaces are given, and are considered to have practical applicability in further studies. Finally, long-wave and short-wave components of the radiation balance are given as percentages of monthly and seasonal mean daffy short-wave radiation income.
INTRODUCTION Townsville stylo (Stylosanthes humilis H.B.K.) is a self-seeding annual n o w well established in tropical n o r t h e r n Australia. Measurements o f c o m p o n e n t s o f the radiation balance were analysed for three surfaces, one d o m i n a t e d by a pure stand o f TownsviUe stylo, a n o t h e r by the annual grasses Digitaria ascendens and Brachiatia ramosa and the third, consisting o f bare soil.
262
J.D. KALMA
In the first paper in this series (Kalma and Badham, 1972, hereafter referred to as Part I) seasonal and diurnal aspects of the reflection of short-wave radiation have been studied. In the present paper net all-wave and long-wave radiation will be discussed and semi-empirical relationships presented enabling the radiation balance to be estimated from global radiation. The present work is intended to be a contribution to the integrated study of the Townsville stylo-grass ecosystem in northern Au'stralia, currently in progress. MATERIALS AND METHODS Measurements were made over a sown pasture of Townsville stylo (Stylosanthes hurnilis H.B.K.) at Katherine Research Station (14°28'S 132 ° 19'E; 108 m above M.S.L.) in the Northern Territory, Australia, between December 18, 1969 and March 28, 1970. In Part I full details have been given of experimental site, seasonal weather conditions and seasonal growth. Radiation measurements were made over three plots. Plot I, 800 m 2 in area, was dominated by Townsville stylo; Plot II, also 800 m 2 in area, was dominated by two naturally occurring annual grasses, Brachiaria ramosa and Digitaria ascendens; Plot III, 80 m 2 in area, was permanently kept bare by hand weeding. Incident short-wave radiation on a horizontal surface (K J,) has been monitored at Katherine Research Station with a Moll Gorczynski pyranometer* and a Rustrak recorder from 1960 till 1968 and daily totals (~K¢) have been obtained thereafter with a WhillierYellott type integrating pyranometer based on silicon solar cells**. During the experiment incident short-wave radiation was also measured with a Kipp pyranometer. The diffuse component of incoming solar radiation (D~t) was monitored with a Kipp pyranometer provided with a semicircular shade-ring (Drummond, 1956). Drummond's shade-ring corrections were used. In addition to measurements of reflected short-wave radiation, net all-wave radiation was measured with pyrradiometers*** described by Funk (1959), mounted at 2 m above the ground in the centres of plots I and II and at 1 m above the ground in the centre of plot III. Thus 95% of the upward fluxes measured over plots I and II was received from an area of 254 m 2, as compared to 64 m 2 for plot III (Reifsnyder, 1967). The pyrradiometers were internally ventilated with dry nitrogen till February 1, 1970 and with dry air thereafter. All polythene domes were ventilated externally with ambient air at a rate of 5 l/min, thus preventing the condensation of dew and assisting in the removal of raindrops and dust from the hemispheres (Fig.lA). Two other calibrated Funk pyrradiometers of similar manufacture were converted into single-sided instruments to measure upward all-wave radiation over plots I and II, at 2 m above the ground, close to the net all-wave pyrradiometers. This was done by means of an * Manufactured by Kipp en Zonen, Delft, Netherlands. ** Manufactured by Rimco Pty. Ltd., Melbourne, Australia. *** Manufactured by Swissteeo Pty. Ltd., Melbourne, Australia.
RADIATION BALANCEOF A TROPICALPASTURE
263
internally blackened aluminium cavity, with good internal surface temperature equalization attached to the upper side of the radiometers in place of the upper hemispheres (Funk, 1962). The mass of this adapter minimized rapid temperature fluctuations under nonsteady conditions, whereas its polished outer surface, protected from direct solar radiation by a special heat shield (Fig. 1B), prevented excessive solar heating. The c0ne-shaped heat shield, constructed from tin plate, was polished on the outside and blackened on the inside. An air gap existed between adapter and shield.
Heat shield~ Vents for air curtain
Sensor
ventilation
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A
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.I
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Fig.1. Schematic arrangements of a pyrradiometer showing (A) vents for external ventilation and (B) a single-sided pyrradiometer with adapter and heat shield.
If the true value of upward all-wave radiation is Qt and if Qo is the converted radiometer reading, then: Qt =aTc 4 - Qo mW cm-'z where Te = cavity surface temperature (°K) and o = Stefan-Boltzmann constant (5.67 •10-9 mW cm-~ °K-4). Tc was measured with a copper-constantan thermocouple with its "cold" junction in a thermally well-insulated kerosene bath, the temperature of which was monitored by resistance thermometry. The thermocouple was calibrated in a waterbath. No additional laboratory calibration of the converted radiometers was carried out. Measurements were made for about 70 complete days, at 10-rain intervals, of incoming solar radiation (K J,), reflected short-wave radiation (Kt) and net all-wave radiation (Q*), while complete diurnal records of upward all-wave radiation (Q'0 were available for about 20 days. The sensitivity of all field instruments was compared in December 1969 and in April 1970, with that of substandards which are regularly recalibrated by the Division of Meteorological Physics, C.S.I.R.O., Aspendale, Australia. The sensitivity of the integrating Rimco pyranometer was determined from a comparison with 70 daily totals (Y.K~) obtained with the Kipp pyranometer during the experimental season.
264
J.D. KALMA
The data logging system used in this study and the procedures followed in data storage and data conversion, have been described in detail by Byrne et al. (1971). RESULTS AND DISCUSSION lncident global radiation - seasonal changes Mean monthly values of daily total solar radiation (Y.K¢, mWh cm -2) calculated for 1960-1970 and monthly means of total daily extra-terrestrial radiation (~--E, mWh cm -2) are given in Fig.2. 1200
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Fig.2. Mean monthly values of incoming solar radiation (~K-'i), extra-terrestrial radiation (-~-'~and atmospheric transmissivity (7) for Katherine, Australia (1960-70). Monthly values for December 1969-March 1970 are shown by open circles. Mean monthly ratios of ~_,K~ to 2~E (= Y, the mean atmospheric transmissivity (Huschke, 1959, p.590)) are also given, showing a maximum of 0.69 in June and a minimum of 0.54 in February. Values of 2~K$, measured with the Kipp pyranometer, were available for about 70 days during the experiment. Missing days in the Kipp records were obtained from records obtained concurrently with the integrating Rimco pyranometer. Monthly mean values of ~_,K$ for December 1969 and January, February and March 1970 are given in Fig.2 as well, with the corresponding r values for these months. Agreement with long-term averages is satisfactory. In Fig.3A observed values of ~--K~ are given, together with daily totals of extra-terrestrial radiation (~E) and estimated clear-day values. In Fig.4 daily ratios of diffuse to total incident short-wave radiation (ZD~/Y~K~) have been plotted against corresponding ~"values and an eye-fitted curve has been drawn. Fig.4 indicates that a minimum value of ED~/Y_,K~ is reached at r ~ 0.77, whereas more than
RADIATION BALANCE OF A TROPICAL PASTURE
~1200 u
265
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Fig.3. Katherine, December 1969-March 1970. Daily totals of (A) extra-terrestrial radiation (~E) and global radiation (I~K¢); (B) diffuse radiation (lODe,) relative to I;K¢; (C) rainfall. 1.0
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Fig.4. The relation between atmospheric transmissivity (r) and diffuse radiation as fraction of global radiation (~,D¢/~,K~.)for daily totals at Katherine, December 1969-March 1970. 95% o f incident radiation is diffuse when r is less than 0.3. Fig.4 has been used to estimate T_d)¢ as a fraction o f T_,K¢, when D e was not measured. In Fig.3B all values o f ~,D¢/Y-,K$ have been plotted against date. A correlation with daily rainfall, plotted in Fig.3C, is evident, both for EK$ and T-,D¢/ZK¢.
266
J.D. KALMA
Seasonal changes in net short-wave, net long-wave radiation and net all-wave radiation Measured totals of net short-wave radiation (ZK*), net long-wave radiation during night-time (EL*n0, net long-wave radiation for 24 h (EL*) and net all-wave radiation for 24 h (YQ*) have been plotted as fractions of ZK$ for all three plots in Fig.5.* Seasonal changes in short-wave reflection (Fig.5) have been discussed in Part I. 1.0
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Fig.5. Daily totals of net short-wave radiation (ZK*), daily totals of net all-wave radiation (~Q*), night-time totals of long-wave radiation (XL*nt) and daily totals of net long-wave radiation (ZL*) relative to daffy totals of global radiation (XK*). Plot 1, Townsville stylo, is shown by a solid line; plot II, grasses, by a dashed and dotted line; plot III, bare soil, by a short dashed line. Katherine, December 1969-March 1970. With the exception of December 23, 1969 and March 1, 1970, Y,L*nt/~,KJ, (Fig.5) varied only between - 0 . 0 3 and - 0 . 1 2 . Till February 13, 1970, all three plots were very similar. Thereafter rapid growth occurred in plots I and II (see Part I), resulting in comparable ratios for plots I and II, while ZL*nt/~KJ, was consistently 0 . 0 3 - 0 . 0 5 less over the bare soil surface o f plot III. This difference was undoubtedly a consequence of the greater diurnal temperature amplitude of the bare soil surface. Relatively, Y'L*nt was smallest for December 1 8 - 2 3 , 1969 and February 6 - 2 7 , 1970; both these periods were marked b y increased cloudiness and greater water availability. * A day covers the 24 h between sunrise on one calendar day and sunrise on the following calendar day and has been dated according to day-time date.
RADIATION BALANCEOF A TROPICALPASTURE
267
Seasonal variability in ZL*/ZK~ (i.e. on a 24-h basis; Fig.5) was much greater, ranging from -0.19 to -0.47. Plots I and III showed a similar trend till January 29, 1970, with differences not exceeding 0.05. Plot I was severely water stressed during most of January and it appears that L* over plot I, as with the reflection coefficient (Part I) was strongly influenced by the radiative characteristics of the underlying soil, because of its incomplete cover. ZL*/~,K~ for plot II during this period was 0.05-0.10 less. Wetting caused the three plots to be very similar (e.g., December 20, January 12, January 29 and February 11). The relative drop in net long-wave loss during these days (especially over plot III) was associated with a decrease in L t resulting from lower surface temperatures and/or an increase in L ~ through greater cloudiness. From January 29 onwards plots I and II were reasonably similar. Both reached maximum cover and stand height around February 20. Supply of water to the vegetative surfaces appears to have been adequate till February 26, while the bare soil of plot III dried out about February 15. The values ZL*/ZK~ for plots I and II reached a maximum o f - 0 . 2 between February 14 and 27, when dry matter production was at a maximum, and decreased thereafter to reach a value of -0.42 at the end of the experiment (March 27, 1970). In summary, wetting caused the short-wave reflection coefficient and net long-wave loss relative to ZK~, for all plots to decrease, while for plots I and II rapid growth (associated with active transpiration and hence lower surface temperatures) resulted in an increase in short-wave reflection and a relative decrease in net long-wave loss. The seasonal trend in ZQ*/ZK~ (Fig.5) integrates the seasonal trends illustrated in other curves in Fig.5. This ratio varied between 0.62 and 0.32. With the exception of March 6 - 9 , 1970, plots I and II were very similar, never differing more than 0.05. ~,Q*/ZK~ for bare soil varied between 0.3 and 0.4 when the surface was dry and increased to 0.5-0.6 when adequately wetted, as for plots I and II (December 18-24, January 12-14, January 29 and February 10-12). It can be seen from Fig.5 that ~Q*dt (i.e., on a day-time basis) varied between 69 and 43% of ZK4,. Periods of increased cloudiness and greater water availability give rise to an even more pronounced increase in ZQ*dt/ZK~ than in ZQ*/Y_Jf~.
Estimating net long-wave radiation from air temperature and atmospheric transmissivity Swinbank (1963) showed that under clear skies long-wave radiation downward (L ~ear) could be predicted satisfactorily from air temperature alone. In the present study daily mean air temperature (Ta, °K), calculated from ½ (max. temp. + min. temp.) was used to obtain average flux intensities of L~clear from L~tclear = 5.31 • 10-14 x (Ta)6 mW cm-2 It was assumed that for periods of a day, mean air temperature equals mean temperature of the vegetative surface (Ts, °K), although net loss of sensible heat probably occurred on the majority of days studied, making the above assumption somewhat unrealistic (see Van
268
J.D. KALMA
Wijk, 1963). Long-wave radiation upward (L t) was calculated using Stefan-Boltzmann's law, assuming a long-wave emissivity of 1.0. Increasing cloudiness and decreasing atmospheric transmissivity r will cause an increase in L ~,. A factor C was introduced to account for this effect, giving for L* under all conditions:
L* = CL ~dear - L t mW cm -z where:
C = (L* + Lt)/L~clear Plot II was considered to be most representative for the pastures surrounding the experimental area. For that reason measured values of L* expressed in mW cm -2 for plot II were used together with calculated values of L t and L$clear to study the relationship between C and r for about 60 days (Fig.6).
•Z*
o.9
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"
0,8
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Fig.6. The relation between correction factor C and atmospheric transmissivity ,. Daily totals, Katherine, December 1969-March 1970. Although C decreases with increasing z (indicating an increase in L~,) a minimum value of about 1.0 would have been expected at a maximum r value of 0.8, if the above assumed equality between Ta and ~ had been correct. Fig.6 indicates that the true surface temperature, and hence L t , are increasingly underestimated with increasing r. It is virtually impossible to separate the two effects illustrated in Fig.6. The effect of differences between ground and air temperatures on the net radiation flux through L*, has been discussed by various authors (e.g., Fitzpatrick and Stern, 1965; Sellers, 1965; Linacre, 1968) who emphasized macro- and micro-advection and dryness of the surface as major causes. Clear day values of L*, calculated from the Stefan-Boltzmann law and Swinbank's equation have been corrected for presence of clouds by several authors (e.g., Fitzpatrick and Stern, 1965; Rijks, 1968) using: L* = L'clear (a + (l - a)n/N) where n and N are actual and possible hours of bright sunshine and a is a constant, ranging between 0.1 and 0.3. A close relationship between n/N and r is commonly accepted (e.g., Fitzpatrick and Stern, 1965). It is shown in Fig.7 that a curvilinear relationship exists between (L *observed/L *clear) and r, which has the form:
(L *observed/L*lear) = 0.394/(0.98 -- r) ~-- 0.4/(1 -- r) given in Fig. 7 by a solid curve.
RADIATION BALANCE OF A TROPICAL PASTURE
269
/
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0.5
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0.4
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0.6
0.8
Fig.7. The relation between atmospheric transmissivity r and the ratio between observed and calculated daily net 1ong-wave loss. Katherine, December 1969-March 1970. The above function is tentatively proposed as a means of estimating for the Katherine region mean daily net long-wave loss for an extended area under all conditions from mean daily screen temperature and the ratio between daily totals of incident short-wave and extra-terrestrial radiation.
Temperature of the experimental surfaces and atmospheric emissivity Upward long-wave radiation ( L t ) from a surface with long-wave emissivity e may be written as: L t = eaTs' + (1 - e)L~. = o(Ts*)4 where L,t = long-wave downward radiation; Ts = true surface temperature; Ts* = apparent surface temperature, assuming e = 1; o = 5.67 - 10 -9 mW cm -~ (°10"4. Sellers (1965), reviewing data from various sources, states that most soils and vegetative surfaces have emissivities of between 0.90 and 0.95. In the present study emissivities of the surface were not known precisely and e = 1 has been assumed subsequently. Another source of error is flux divergence between radiometer and surface. Estimated maximum errors, resulting from instrumental errors, the assumption e = 1 and the neglect of flux divergence, are an underestimate by about 3 - 4 ° C during the day and an overestimate by 1 - 2 ° C at night (cf. Rose and Thomas, 1968; Monteith and Szeicz, 1962). Using singlesided pyrradiometers and inverted pyranometers to obtain K t , complete records were obtained by difference f o r L t and hence for Ts* on about 20 days for plots I and II. In Fig.8 air temperatures, as measured in the screen at 2 m above the ground, and apparent surface temperatures of plots I and II have been plotted against local standard time for two rainless days and one rainy day, separated in time by 37 and 49 days, respectively. Surface temperature of the two plots exceeded screen temperature on all three days during a major part of day-time hours but was lower than screen temperature during all night-time hours. The rapid drop o f air and surface temperatures after 5 p.m. on February 6 (Fig.8) was caused by rain as indicated by arrows. Differences between the surface temperatures of plot I (Townsville stylo) and plot II (grasses) decreased as the
270
J. D. K A L M A December :30-31
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Local stondord time Fig.8. Air temperature (shown by a short dashed line) and effective radiative surface temperatures(Ts*) on three days for plot I, Townsville stylo, shown by a solid line and plot 1I, grasses, shown by a.dashed and dotted line. Arrows indicate occurrence of rain. Katherine, 1 9 6 9 - 7 0 .
season progressed. These differences, especially earlier in the season, are probably caused by the sparser cover in plot I making the underlying soil surface an important contributor to L t. Differences in surface roughness and in availability of water may also be important factors at various stages in the season, especially under water stress, when TownsviUe stylo leaves show a non-random leaf distribution, which reduces the effective surface cover significantly. Although the present method of indirect estimation is not considered sufficiently
RADIATION BALANCEOF A TROPICAL PASTURE
271
accurate for calculating long-wave radiation from the sky (L,t), and studying its diurnal distribution in great detail, preliminary results indicate that the diurnal variation of L,t as observed on clear days was much smaller than when calculated from Swinbank's (1963) formula, which is based on night-time data. Night-time values agreed closely, but a clear day-time trend existed in the deviation of measured values from estimated values. Calculated values were as much as 8 mW cm "a greater than measured values at mid-afternoon. Paltridge (1970) reported maximum deviations of 4 mW cm a. Estimating net radiation
Measurements of net radiation Q* over agricultural surfaces are very seldom made on a routine basis, but many attempts have been made recently to relate Q* to incident solar radiation K,L, which is more generally measured. Various (semi-)empirical expressions have been proposed (see Linacre, 1968 for a review). Monteith and Szeicz ( 196 I) established a linear relation of Q* on K*. Their heating coefficient concept, based on the assumption that L* is linearly dependent on Q*, appeared to be very useful (Rijks, 1968), although it was developed originally for clear days only. Monteith (1965), however, states that the method may only be valid in temperate regions. It has since been shown by various authors (Stanhill et al., 1966; Idso, 1968; Idso et al., 1969; Kalma and Stanhill, 1969) that unpredictable changes in atmospheric emissivity limit the general validity of the concept. The equation of Monteith and Szeicz (1961) is: Q* =a(1 - o~)K~ + b where ¢x= short-wave reflection coefficient and a, b are constants. This equation has been used for instantaneous fluxes, half-hourly and hourly totals. Fritschen (1967) showed experimentally, using hourly totals, that this method did not have any advantage over the more general expression: Q* = a'K~. + b'
where a', b' are constants. Davies (1967) used a similar expression for relating day-time totals of Q* to daily totals of incident short-wave radiation. However, a general lack of data near the origin may yield unrealistic intercepts, as Fritschen (1967) points out, and may therefore limit the general applicability of such equations. In what follows, linear regression of hourly totals of net all-wave radiation on hourly totals of incident short-wave radiation have been computed using: Q* = a'K.[ + b',
whereas for calculation of day-time totals of net all-wave radiation Fritschen's method of computing the average hourly rate of Q* from the average hourly rate of K~ has been used. This was shown by Idso et al. (1969), to be more realistic than linear regression of total day-time net radiation on total incoming solar radiation.
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J.D. KALMA
The experimental season 1 9 6 9 - 7 0 was subdivided into six periods on the basis o f characteristic changes in dry m a t t e r p r o d u c t i o n , leaf area index and albedo (see Part I). Linear regressions were c o m p u t e d for Q* on KJ, for each o f the three experimental plots, for all six periods. Hourly totals in mWh cm -2 were used, for daylight periods only. Table I shows regression equations, correlation coefficients and results o f error analysis for all 18 linear regressions. In addition results are shown of linear regressions c o m p u t e d from data pooled for all three surfaces for each o f the periods. Finally, all data for each of the three plots were pooled for c o m p u t i n g linear regressions b e t w e e n Q* and K J, over the whole experimental period. TABLE I Slope (a'), intercept (b'), standard deviation from regression (Sy. x) and correlation coefficient (r) for linear regressions of net radiation on solar radiation for six periods ( A - F ) and three surfaces (I-III) for hourly totals duringday-time. Katherine, 1969-70 (mWh cm -2 ) (see text for explanation of groupings) Period (dates)
Plot
a'
b'
Sy. x
r
A (December 17December 26)
I II 111
0.642 0.635 0.629
-2.4 -2.2 -1.5
5.1 3.8 6.2
0.98 0.99 0.97
B (December 2 7 January 11)
1 II III
0.650 0.627 0.598
-8.3 -6.4 -7.2
3.0 2.2 3.4
0.99 0.99 0.98
C (January 12January 26)
I 11 III
0.640 0.617 0.556
-5.1 -4.6 -3.5
3.0 2.1 3.6
0.99 0.99 0.98
D (January 2 7 February 6)
I II III
0.655 0.632 0.568
-3.8 -3.9 -3.0
3.5 1.9 3.5
0.99 0.99 0.98
E (February 7 February 21)
I II 11I
0.684 0.633 0.583
-4.1 -2.9 -3.4
1.6 1.2 3.4
0.99 0.99 0.99
F (February 2 2 March 27)
I II III
0.649 0.580 0.557
-5.1 -3.4 -5.4
7.0 3.7 4.0
0.96 0.98 0.98
A B C D E F
I-III 1-III I-Ill I-Ill I-II1 I-III
0.635 0.625 0.604 0.618 0.633 0.595
-2.0 -7.3 -4.4 -3.6 -3.5 -4.6
5.1 3.2 3.5 3.7 3.4 5.7
0.98 0.99 0.98 0.98 0.99 0.96
A-F A-F A-F
I II II1
0.643 0.613 0.579
-4.5 -3.6 -3.9
4.9 3.4 5.2
0.99 0.98 0.97
A-F
I-III
0.612
-4.0
4.8
0.97
RADIATION BALANCE OF A TROPICAL PASTURE
273
Hourly totals o f Q* can be estimated satisfactorily from one of the 18 linear regressions in the upper half of Table I. The sample standard deviation from regression Sy.x in these regressions varies between 1.2 and 7.0 mWh cm -'z. Considerable scatter exists in intercept b'. The term b' equals Q* at zero insolation and varies between - 1.5 and - 8 . 3 mWh cm -2. It appears that, in view of the scatter in both slope and intercept, any future use of the equations depends on information on surface characteristics, as well as on meteorological factors such as rainfall. The first alternative given in Table I, pooling of all surfaces for each of the six periods still depends on knowledge of seasonal aspects of growth and weather. The second alternative, three seasonal regressions for the individual surfaces, is therefore considered to be of greatest applicability in tropical pastures o f northern Australia. Standard errors from regression vary between 3.4 and 5.2 mWh cm -~. These values are slightly greater than those given by Fritschen (1967) for six irrigated crops in arid Arizona, for generally clear days. Total day-time net radiation ~,Q*atmay be determined from Y.K~t by determining the average hourly rate of K~ from ~K~ and day length in hours, calculating the average hourly rate of Q* using the regression equations and converting into ~Q*dt using day length in hours. It was noted from the present data, that the intercept b' agrees well with observed hourly totals of Q* around sunrise and sunset, whereas fluctuation in Q* during nighttime is generally small (cf. StanhiU et al., 1966). The expression ~ Q * t can therefore satisfactorily be calculated from b' and length o f night-time in hours. Constants o f the three seasonal regressions for individual surfaces have been used to calculate the relative magnitudes of the radiation balance components from monthly and seasonal means of total daily incoming solar radiation (~KJ,), o f the short-wave reflection coefficients (a, see Part I) and monthly and seasonal mean length of day and night. They are expressed in Table II as percentages o f the monthly and seasonal mean daily total radiation. Totals o f net long-wave radiation during day-time and over 24 h as a fraction of Y.K~t can be obtained from (1 - ct - Y.Q*dt/~,K~) and ( 1 - a - ~K,t), respectively. TABLE II Components of the radiation balance as percentages of monthly and seasonal mean daily short-wave radiation income (I;K~). (~Q*dt = day-time total of net all-wave radiation: ~Q* = 24 h total of net all-wave radiation: a =albedo; I --- pasture with Townsville stylo dominance; II -- pasture with dominance of grasses; III= bare soil plot)
~.Q*dt/XK*(%) xQ*/XK*(%)
ZK~ Day (mWh cm-2) length (h)
Night length (h)
1 - a(%) I
II
III
I
II
III
I
II
III
December January February March
658 674 613 654
12.93 12.83 12.57 12.18
11.07 11.17 11.43 11.82
83 83 79 80
81 79 76 76
80 79 80 79
55 56 55 56
54 54 54 55
50 50 50 51
48 48 47 48
48 49 47 48
44 44 43 44
Season
651
12.63
11.37
81
78
79
56
54
50
48
48
44
274
J. D, KALMA
A comparison o f Table II with data f r o m various sources, listed by Stanhill et al. (1966) and Linacre (1968), shows favourable agreement with measurements over a great range of surfaces and under various climatic conditions. It should finally be n o t e d that the regression equations presented in this paper may provide sufficiently accurate estimates for various applications, but great care should be exercised w h e n using the equations elsewhere, for different surfaces. ACKNOWLEDGEMENTS I am i n d e b t e d to Mr. R. B a d h a m for his co-operation in the experimental program, to Messrs. D. E. Watson and A. G. Swan for technical assistance and to Mrs. K. Haszler for assistance in data processing and c o m p u t e r programming. Mrs. A. K o m a r o w s k i was responsible for m u c h c o m p u t a t i o n a l work. I am grateful to Mr. P. M. Fleming and Dr. C. W. Rose for their critical advice and c o m m e n t s .
REFERENCES Byrne, G. F., Rose, C. W., Begg, J. E., Torssell, B. W. R. and McPherson, H. G., 1971. Instrumentation for crop-environment measurement in a tropical savannah climate. C.S.LR.O., Australia, Div. Land Res. Tech. Pap., 32:19 pp. Davies, J. A., 1967. A note on the relationship between net radiation and solar radiation. Q. J. R. Meteorol. Soc., 93: 109-115. Drummond, A. J., 1956. On the measurement of sky radiation. Arch. Meteorol. Geophys. Bioklimatol., Set. B, 7: 413-436. Fitzpatrick, E. A. and Stern, W. R., 1965. Components of the radiation balance of irrigated plots in a dry monsoonal environment. J. Appl. Meteorol., 4: 449-460. Fritschen, L. J., 1967. Net and solar radiation relations over irrigated field crops. Agric. Meteorol., 4: 55-62. Funk, J. P., 1959. Improved polythene-shielded net radiometer. J. ScL lnstr., 36: 267-270. Funk, J. P., 1962. Improvements in polythene-shielded net radiometer. Syrup. Eng. Aspects Environmental Control Plant Growth, Melbourne, 1962, pp. 248-254. Huschke, R. E., 1959. Glossary of Meteorology. Am. Meteorol. Soc., Boston. Idso, S. B., 1968. An analysis of the heating coefficient concept. Z Appl. Meteorol., 7: 716-717. Idso, S. B., Baker, D. G. and Blad, B. L., 1969. Relations of radiation fluxes over natural surfaces. Q. J. R. Meteorol. Soc., 95: 244-257. Kalma, J. D. and Badham, R., 1972. The radiation balance of a tropical pasture, I. The reflection of short-wave radiation. Agric. Meteorol., 10, in press. Kalma, J. D. and Stardaill, G., 1969. The radiation climate of an irrigated orange plantation. Solar Energy, 12: 491-508. Linacre, E. T., 1968. Estimating the net radiation flux. Agric. Meteorol., 5: 49-63. Monteith, J. L., 1965. Radiation and crops. Exptl. Agric., 1: 241-251. Monteith, J. L. and Szeicz, G., 1961. The radiation balance of bare soil and vegetation. Q. J. R. Meteorol. Soc., 87: 159-170. Monteith, J. L. and Szeicz, G., 1962. Radiative temperature in the heat balance of natural surfaces. Q. J. R. Meteorol. Soc., 88: 496-507. Paltridge, G. W., 1970. Day-time long-wave radiation from the sky. Q. J. R. Meteorol. Soc., 96: 645-653. Reifsnyder, W. E., 1967. Radiation geometry in the measurement and interpretation of radiation balance. Agric. Meteorol., 41 : 255-265.
RADIATION BALANCE OF A TROPICAL PASTURE
275
Rijks, D. A., 1968. Water use by irrigated cotton in Sudan. II. Net radiation and soil heat flux. J. Appl. Ecol., 5: 685-706. Rose, C. W. and Thomas, D, A., 1968. Remote sensing of land surface temperatures and some applications in land evaluation, ln: G. A. Stewart (Editor), Land Evaluation. Macmillan, Melbourne, pp. 367-375. Sellers, W. D., 1965. Physical Climatology. Univ. Chicago Press, Chicago and London, 272 pp. Stanhill, G., Hofstede, G. J. and Kalma, J. D., 1966. Radiation balance of natural and agricultural vegetation. Q. J. R. Meteorol. Soc., 92: 128-140. Swinbank, W. C., 1963. Long-wave radiation from clear skies. Q. J. R. Meteorol. Soc., 89: 339-348. Van Wijk, W. R., 1963. Physics of Hant Environment. North-Holland, Amsterdam, 382 pp.
THE RADIATION BALANCE OF A TROPICAL PASTURE, H. NET ALL-WAVE RADIATION
J. D. KALMA
Division o f Land Research, Commonwealth Scientific and Industrial Research Organization, Canberra, .4. C. T. (Australia/ (Received September 8, 1971)
ABSTRACT Kalma, J. D., 1972. The radiation balance of a tropical pasture, II. Net all-wave radiation. Agric. Meteorol., 10: 261-275. Seasonal changes in net all-wave and long-wave radiation are discussed, as measured over three surfaces, one dominated by Townsville stylo, another by two annual grasses and a third consisting of bare soil. The short-wave reflection coefficient of these three surfaces has been discussed in Kalma and Badham (1972). Net long-wave loss during night-time varied between 3 and 12% and net long-wave loss over 24 h between 19 and 47% of total incident short-wave radiation. In general, wetting and rapid growth caused net long-wave loss, as a fraction of incident solar radiation, to decrease. Drought, maturing, lodging and senescence had the opposite effect. Differences between the three surfaces were related to cover, stand height, drought resistance and growth phase. A unique relationship was observed between daily atmospheric transmissivity and the ratio between daily totals of diffuse and total radiation. It is shown how daffy net long-wave radiation, under all conditions, may be predicted from known daily values of atmospheric transmissivity and air temperature. Effective surface radiative temperatures, indirectly obtained from measurements with single-sided pyrradiometers, have been presented for the two vegetative surfaces for three representative days. Semi-empirical relations for estimating net ail-wave radiation during daylight from incident total radiation were obtained from linear regressions computed, using hourly totals, for net ali-wave radiation on incident total radiation for all three surfaces and six successive periods covering the experimental season. Three seasonal regressions for the individual surfaces are given, and are considered to have practical applicability in further studies. Finally, long-wave and short-wave components of the radiation balance are given as percentages of monthly and seasonal mean daffy short-wave radiation income.
INTRODUCTION Townsville stylo (Stylosanthes humilis H.B.K.) is a self-seeding annual n o w well established in tropical n o r t h e r n Australia. Measurements o f c o m p o n e n t s o f the radiation balance were analysed for three surfaces, one d o m i n a t e d by a pure stand o f TownsviUe stylo, a n o t h e r by the annual grasses Digitaria ascendens and Brachiatia ramosa and the third, consisting o f bare soil.
262
J.D. KALMA
In the first paper in this series (Kalma and Badham, 1972, hereafter referred to as Part I) seasonal and diurnal aspects of the reflection of short-wave radiation have been studied. In the present paper net all-wave and long-wave radiation will be discussed and semi-empirical relationships presented enabling the radiation balance to be estimated from global radiation. The present work is intended to be a contribution to the integrated study of the Townsville stylo-grass ecosystem in northern Au'stralia, currently in progress. MATERIALS AND METHODS Measurements were made over a sown pasture of Townsville stylo (Stylosanthes hurnilis H.B.K.) at Katherine Research Station (14°28'S 132 ° 19'E; 108 m above M.S.L.) in the Northern Territory, Australia, between December 18, 1969 and March 28, 1970. In Part I full details have been given of experimental site, seasonal weather conditions and seasonal growth. Radiation measurements were made over three plots. Plot I, 800 m 2 in area, was dominated by Townsville stylo; Plot II, also 800 m 2 in area, was dominated by two naturally occurring annual grasses, Brachiaria ramosa and Digitaria ascendens; Plot III, 80 m 2 in area, was permanently kept bare by hand weeding. Incident short-wave radiation on a horizontal surface (K J,) has been monitored at Katherine Research Station with a Moll Gorczynski pyranometer* and a Rustrak recorder from 1960 till 1968 and daily totals (~K¢) have been obtained thereafter with a WhillierYellott type integrating pyranometer based on silicon solar cells**. During the experiment incident short-wave radiation was also measured with a Kipp pyranometer. The diffuse component of incoming solar radiation (D~t) was monitored with a Kipp pyranometer provided with a semicircular shade-ring (Drummond, 1956). Drummond's shade-ring corrections were used. In addition to measurements of reflected short-wave radiation, net all-wave radiation was measured with pyrradiometers*** described by Funk (1959), mounted at 2 m above the ground in the centres of plots I and II and at 1 m above the ground in the centre of plot III. Thus 95% of the upward fluxes measured over plots I and II was received from an area of 254 m 2, as compared to 64 m 2 for plot III (Reifsnyder, 1967). The pyrradiometers were internally ventilated with dry nitrogen till February 1, 1970 and with dry air thereafter. All polythene domes were ventilated externally with ambient air at a rate of 5 l/min, thus preventing the condensation of dew and assisting in the removal of raindrops and dust from the hemispheres (Fig.lA). Two other calibrated Funk pyrradiometers of similar manufacture were converted into single-sided instruments to measure upward all-wave radiation over plots I and II, at 2 m above the ground, close to the net all-wave pyrradiometers. This was done by means of an * Manufactured by Kipp en Zonen, Delft, Netherlands. ** Manufactured by Rimco Pty. Ltd., Melbourne, Australia. *** Manufactured by Swissteeo Pty. Ltd., Melbourne, Australia.
RADIATION BALANCEOF A TROPICALPASTURE
263
internally blackened aluminium cavity, with good internal surface temperature equalization attached to the upper side of the radiometers in place of the upper hemispheres (Funk, 1962). The mass of this adapter minimized rapid temperature fluctuations under nonsteady conditions, whereas its polished outer surface, protected from direct solar radiation by a special heat shield (Fig. 1B), prevented excessive solar heating. The c0ne-shaped heat shield, constructed from tin plate, was polished on the outside and blackened on the inside. An air gap existed between adapter and shield.
Heat shield~ Vents for air curtain
Sensor
ventilation
l.
A
v
3.625in.
i//]
.I
B
5.25in.
Fig.1. Schematic arrangements of a pyrradiometer showing (A) vents for external ventilation and (B) a single-sided pyrradiometer with adapter and heat shield.
If the true value of upward all-wave radiation is Qt and if Qo is the converted radiometer reading, then: Qt =aTc 4 - Qo mW cm-'z where Te = cavity surface temperature (°K) and o = Stefan-Boltzmann constant (5.67 •10-9 mW cm-~ °K-4). Tc was measured with a copper-constantan thermocouple with its "cold" junction in a thermally well-insulated kerosene bath, the temperature of which was monitored by resistance thermometry. The thermocouple was calibrated in a waterbath. No additional laboratory calibration of the converted radiometers was carried out. Measurements were made for about 70 complete days, at 10-rain intervals, of incoming solar radiation (K J,), reflected short-wave radiation (Kt) and net all-wave radiation (Q*), while complete diurnal records of upward all-wave radiation (Q'0 were available for about 20 days. The sensitivity of all field instruments was compared in December 1969 and in April 1970, with that of substandards which are regularly recalibrated by the Division of Meteorological Physics, C.S.I.R.O., Aspendale, Australia. The sensitivity of the integrating Rimco pyranometer was determined from a comparison with 70 daily totals (Y.K~) obtained with the Kipp pyranometer during the experimental season.
264
J.D. KALMA
The data logging system used in this study and the procedures followed in data storage and data conversion, have been described in detail by Byrne et al. (1971). RESULTS AND DISCUSSION lncident global radiation - seasonal changes Mean monthly values of daily total solar radiation (Y.K¢, mWh cm -2) calculated for 1960-1970 and monthly means of total daily extra-terrestrial radiation (~--E, mWh cm -2) are given in Fig.2. 1200
"~'~
/~,~ ""'-"
% \.
1000
800
/
j
F ..~ 6 0 0 I.O
I~
0.8 ¥
,oo ~ °~°
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0.6
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i
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~
M
i
A
i
M
i
d
i
J
i
A
i
S
i
O
,
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0.(3
Fig.2. Mean monthly values of incoming solar radiation (~K-'i), extra-terrestrial radiation (-~-'~and atmospheric transmissivity (7) for Katherine, Australia (1960-70). Monthly values for December 1969-March 1970 are shown by open circles. Mean monthly ratios of ~_,K~ to 2~E (= Y, the mean atmospheric transmissivity (Huschke, 1959, p.590)) are also given, showing a maximum of 0.69 in June and a minimum of 0.54 in February. Values of 2~K$, measured with the Kipp pyranometer, were available for about 70 days during the experiment. Missing days in the Kipp records were obtained from records obtained concurrently with the integrating Rimco pyranometer. Monthly mean values of ~_,K$ for December 1969 and January, February and March 1970 are given in Fig.2 as well, with the corresponding r values for these months. Agreement with long-term averages is satisfactory. In Fig.3A observed values of ~--K~ are given, together with daily totals of extra-terrestrial radiation (~E) and estimated clear-day values. In Fig.4 daily ratios of diffuse to total incident short-wave radiation (ZD~/Y~K~) have been plotted against corresponding ~"values and an eye-fitted curve has been drawn. Fig.4 indicates that a minimum value of ED~/Y_,K~ is reached at r ~ 0.77, whereas more than
RADIATION BALANCE OF A TROPICAL PASTURE
~1200 u
265
Z E
days)
EKI, (clear
Ixl
400 kl 0 ~"B)
'
'
'
'
'
'
'
.
.
.
.
0.8
o12 0.01 . / (C)
.
oI, llo
o
,I
.
D~.18 oec.~s
.
.
.
.
.
.
.
.
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.
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I,.
.I.
,
t
~h.3 J,,.11 ~ . ~ j~.~ Feb.4 Fe~.12 ~eb.m r~M~'.S ~dr.~ ~r. 24
196g 11970
Fig.3. Katherine, December 1969-March 1970. Daily totals of (A) extra-terrestrial radiation (~E) and global radiation (I~K¢); (B) diffuse radiation (lODe,) relative to I;K¢; (C) rainfall. 1.0
0.8
0.6
"-~ 0.4 kl
0.2
o.,
o'.2'
o:,
'
"t'
o'.6
'
o'.8
'
~.o
Fig.4. The relation between atmospheric transmissivity (r) and diffuse radiation as fraction of global radiation (~,D¢/~,K~.)for daily totals at Katherine, December 1969-March 1970. 95% o f incident radiation is diffuse when r is less than 0.3. Fig.4 has been used to estimate T_d)¢ as a fraction o f T_,K¢, when D e was not measured. In Fig.3B all values o f ~,D¢/Y-,K$ have been plotted against date. A correlation with daily rainfall, plotted in Fig.3C, is evident, both for EK$ and T-,D¢/ZK¢.
266
J.D. KALMA
Seasonal changes in net short-wave, net long-wave radiation and net all-wave radiation Measured totals of net short-wave radiation (ZK*), net long-wave radiation during night-time (EL*n0, net long-wave radiation for 24 h (EL*) and net all-wave radiation for 24 h (YQ*) have been plotted as fractions of ZK$ for all three plots in Fig.5.* Seasonal changes in short-wave reflection (Fig.5) have been discussed in Part I. 1.0
ZK~/EKt (26
;"
,_. . . . :~. . . . .
=O.6 ~'
~
....
-
.
-
~
"'EQ"~ I I Z K'~
-
:
A
:
:
~
~..-..~:.-.-.:.-::.:~
~
A
0.4
i
ZI:
f
-0 4
.EKe,
i
.
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""'"°'"~
~\ "~''' ~ "". . .'. . . . . . ,
Dec. 26 Jan. 3 1969 1970
i
-..
Jan. 11
""" ...... " ' ' Jan.19
Jon. 27
.
.
Feb. 4
.
.
Feb.12
.
Feb. 20
"
Feb.28
,
,
Mar. 8
".......
Mar. 16
i"c:~1
Mar'. 24
Fig.5. Daily totals of net short-wave radiation (ZK*), daily totals of net all-wave radiation (~Q*), night-time totals of long-wave radiation (XL*nt) and daily totals of net long-wave radiation (ZL*) relative to daffy totals of global radiation (XK*). Plot 1, Townsville stylo, is shown by a solid line; plot II, grasses, by a dashed and dotted line; plot III, bare soil, by a short dashed line. Katherine, December 1969-March 1970. With the exception of December 23, 1969 and March 1, 1970, Y,L*nt/~,KJ, (Fig.5) varied only between - 0 . 0 3 and - 0 . 1 2 . Till February 13, 1970, all three plots were very similar. Thereafter rapid growth occurred in plots I and II (see Part I), resulting in comparable ratios for plots I and II, while ZL*nt/~KJ, was consistently 0 . 0 3 - 0 . 0 5 less over the bare soil surface o f plot III. This difference was undoubtedly a consequence of the greater diurnal temperature amplitude of the bare soil surface. Relatively, Y'L*nt was smallest for December 1 8 - 2 3 , 1969 and February 6 - 2 7 , 1970; both these periods were marked b y increased cloudiness and greater water availability. * A day covers the 24 h between sunrise on one calendar day and sunrise on the following calendar day and has been dated according to day-time date.
RADIATION BALANCEOF A TROPICALPASTURE
267
Seasonal variability in ZL*/ZK~ (i.e. on a 24-h basis; Fig.5) was much greater, ranging from -0.19 to -0.47. Plots I and III showed a similar trend till January 29, 1970, with differences not exceeding 0.05. Plot I was severely water stressed during most of January and it appears that L* over plot I, as with the reflection coefficient (Part I) was strongly influenced by the radiative characteristics of the underlying soil, because of its incomplete cover. ZL*/~,K~ for plot II during this period was 0.05-0.10 less. Wetting caused the three plots to be very similar (e.g., December 20, January 12, January 29 and February 11). The relative drop in net long-wave loss during these days (especially over plot III) was associated with a decrease in L t resulting from lower surface temperatures and/or an increase in L ~ through greater cloudiness. From January 29 onwards plots I and II were reasonably similar. Both reached maximum cover and stand height around February 20. Supply of water to the vegetative surfaces appears to have been adequate till February 26, while the bare soil of plot III dried out about February 15. The values ZL*/ZK~ for plots I and II reached a maximum o f - 0 . 2 between February 14 and 27, when dry matter production was at a maximum, and decreased thereafter to reach a value of -0.42 at the end of the experiment (March 27, 1970). In summary, wetting caused the short-wave reflection coefficient and net long-wave loss relative to ZK~, for all plots to decrease, while for plots I and II rapid growth (associated with active transpiration and hence lower surface temperatures) resulted in an increase in short-wave reflection and a relative decrease in net long-wave loss. The seasonal trend in ZQ*/ZK~ (Fig.5) integrates the seasonal trends illustrated in other curves in Fig.5. This ratio varied between 0.62 and 0.32. With the exception of March 6 - 9 , 1970, plots I and II were very similar, never differing more than 0.05. ~,Q*/ZK~ for bare soil varied between 0.3 and 0.4 when the surface was dry and increased to 0.5-0.6 when adequately wetted, as for plots I and II (December 18-24, January 12-14, January 29 and February 10-12). It can be seen from Fig.5 that ~Q*dt (i.e., on a day-time basis) varied between 69 and 43% of ZK4,. Periods of increased cloudiness and greater water availability give rise to an even more pronounced increase in ZQ*dt/ZK~ than in ZQ*/Y_Jf~.
Estimating net long-wave radiation from air temperature and atmospheric transmissivity Swinbank (1963) showed that under clear skies long-wave radiation downward (L ~ear) could be predicted satisfactorily from air temperature alone. In the present study daily mean air temperature (Ta, °K), calculated from ½ (max. temp. + min. temp.) was used to obtain average flux intensities of L~clear from L~tclear = 5.31 • 10-14 x (Ta)6 mW cm-2 It was assumed that for periods of a day, mean air temperature equals mean temperature of the vegetative surface (Ts, °K), although net loss of sensible heat probably occurred on the majority of days studied, making the above assumption somewhat unrealistic (see Van
268
J.D. KALMA
Wijk, 1963). Long-wave radiation upward (L t) was calculated using Stefan-Boltzmann's law, assuming a long-wave emissivity of 1.0. Increasing cloudiness and decreasing atmospheric transmissivity r will cause an increase in L ~,. A factor C was introduced to account for this effect, giving for L* under all conditions:
L* = CL ~dear - L t mW cm -z where:
C = (L* + Lt)/L~clear Plot II was considered to be most representative for the pastures surrounding the experimental area. For that reason measured values of L* expressed in mW cm -2 for plot II were used together with calculated values of L t and L$clear to study the relationship between C and r for about 60 days (Fig.6).
•Z*
o.9
. :!.'~%~
O.
'
"
0,8
1"
Fig.6. The relation between correction factor C and atmospheric transmissivity ,. Daily totals, Katherine, December 1969-March 1970. Although C decreases with increasing z (indicating an increase in L~,) a minimum value of about 1.0 would have been expected at a maximum r value of 0.8, if the above assumed equality between Ta and ~ had been correct. Fig.6 indicates that the true surface temperature, and hence L t , are increasingly underestimated with increasing r. It is virtually impossible to separate the two effects illustrated in Fig.6. The effect of differences between ground and air temperatures on the net radiation flux through L*, has been discussed by various authors (e.g., Fitzpatrick and Stern, 1965; Sellers, 1965; Linacre, 1968) who emphasized macro- and micro-advection and dryness of the surface as major causes. Clear day values of L*, calculated from the Stefan-Boltzmann law and Swinbank's equation have been corrected for presence of clouds by several authors (e.g., Fitzpatrick and Stern, 1965; Rijks, 1968) using: L* = L'clear (a + (l - a)n/N) where n and N are actual and possible hours of bright sunshine and a is a constant, ranging between 0.1 and 0.3. A close relationship between n/N and r is commonly accepted (e.g., Fitzpatrick and Stern, 1965). It is shown in Fig.7 that a curvilinear relationship exists between (L *observed/L *clear) and r, which has the form:
(L *observed/L*lear) = 0.394/(0.98 -- r) ~-- 0.4/(1 -- r) given in Fig. 7 by a solid curve.
RADIATION BALANCE OF A TROPICAL PASTURE
269
/
2.O
1.5 e .J 1.0
0.5
OD O.O
0.2
0.4
l"
0.6
0.8
Fig.7. The relation between atmospheric transmissivity r and the ratio between observed and calculated daily net 1ong-wave loss. Katherine, December 1969-March 1970. The above function is tentatively proposed as a means of estimating for the Katherine region mean daily net long-wave loss for an extended area under all conditions from mean daily screen temperature and the ratio between daily totals of incident short-wave and extra-terrestrial radiation.
Temperature of the experimental surfaces and atmospheric emissivity Upward long-wave radiation ( L t ) from a surface with long-wave emissivity e may be written as: L t = eaTs' + (1 - e)L~. = o(Ts*)4 where L,t = long-wave downward radiation; Ts = true surface temperature; Ts* = apparent surface temperature, assuming e = 1; o = 5.67 - 10 -9 mW cm -~ (°10"4. Sellers (1965), reviewing data from various sources, states that most soils and vegetative surfaces have emissivities of between 0.90 and 0.95. In the present study emissivities of the surface were not known precisely and e = 1 has been assumed subsequently. Another source of error is flux divergence between radiometer and surface. Estimated maximum errors, resulting from instrumental errors, the assumption e = 1 and the neglect of flux divergence, are an underestimate by about 3 - 4 ° C during the day and an overestimate by 1 - 2 ° C at night (cf. Rose and Thomas, 1968; Monteith and Szeicz, 1962). Using singlesided pyrradiometers and inverted pyranometers to obtain K t , complete records were obtained by difference f o r L t and hence for Ts* on about 20 days for plots I and II. In Fig.8 air temperatures, as measured in the screen at 2 m above the ground, and apparent surface temperatures of plots I and II have been plotted against local standard time for two rainless days and one rainy day, separated in time by 37 and 49 days, respectively. Surface temperature of the two plots exceeded screen temperature on all three days during a major part of day-time hours but was lower than screen temperature during all night-time hours. The rapid drop o f air and surface temperatures after 5 p.m. on February 6 (Fig.8) was caused by rain as indicated by arrows. Differences between the surface temperatures of plot I (Townsville stylo) and plot II (grasses) decreased as the
270
J. D. K A L M A December :30-31
50 45 40
35
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4035 ~ ~ . , ~ . . ~ 30
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Local stondord time Fig.8. Air temperature (shown by a short dashed line) and effective radiative surface temperatures(Ts*) on three days for plot I, Townsville stylo, shown by a solid line and plot 1I, grasses, shown by a.dashed and dotted line. Arrows indicate occurrence of rain. Katherine, 1 9 6 9 - 7 0 .
season progressed. These differences, especially earlier in the season, are probably caused by the sparser cover in plot I making the underlying soil surface an important contributor to L t. Differences in surface roughness and in availability of water may also be important factors at various stages in the season, especially under water stress, when TownsviUe stylo leaves show a non-random leaf distribution, which reduces the effective surface cover significantly. Although the present method of indirect estimation is not considered sufficiently
RADIATION BALANCEOF A TROPICAL PASTURE
271
accurate for calculating long-wave radiation from the sky (L,t), and studying its diurnal distribution in great detail, preliminary results indicate that the diurnal variation of L,t as observed on clear days was much smaller than when calculated from Swinbank's (1963) formula, which is based on night-time data. Night-time values agreed closely, but a clear day-time trend existed in the deviation of measured values from estimated values. Calculated values were as much as 8 mW cm "a greater than measured values at mid-afternoon. Paltridge (1970) reported maximum deviations of 4 mW cm a. Estimating net radiation
Measurements of net radiation Q* over agricultural surfaces are very seldom made on a routine basis, but many attempts have been made recently to relate Q* to incident solar radiation K,L, which is more generally measured. Various (semi-)empirical expressions have been proposed (see Linacre, 1968 for a review). Monteith and Szeicz ( 196 I) established a linear relation of Q* on K*. Their heating coefficient concept, based on the assumption that L* is linearly dependent on Q*, appeared to be very useful (Rijks, 1968), although it was developed originally for clear days only. Monteith (1965), however, states that the method may only be valid in temperate regions. It has since been shown by various authors (Stanhill et al., 1966; Idso, 1968; Idso et al., 1969; Kalma and Stanhill, 1969) that unpredictable changes in atmospheric emissivity limit the general validity of the concept. The equation of Monteith and Szeicz (1961) is: Q* =a(1 - o~)K~ + b where ¢x= short-wave reflection coefficient and a, b are constants. This equation has been used for instantaneous fluxes, half-hourly and hourly totals. Fritschen (1967) showed experimentally, using hourly totals, that this method did not have any advantage over the more general expression: Q* = a'K~. + b'
where a', b' are constants. Davies (1967) used a similar expression for relating day-time totals of Q* to daily totals of incident short-wave radiation. However, a general lack of data near the origin may yield unrealistic intercepts, as Fritschen (1967) points out, and may therefore limit the general applicability of such equations. In what follows, linear regression of hourly totals of net all-wave radiation on hourly totals of incident short-wave radiation have been computed using: Q* = a'K.[ + b',
whereas for calculation of day-time totals of net all-wave radiation Fritschen's method of computing the average hourly rate of Q* from the average hourly rate of K~ has been used. This was shown by Idso et al. (1969), to be more realistic than linear regression of total day-time net radiation on total incoming solar radiation.
272
J.D. KALMA
The experimental season 1 9 6 9 - 7 0 was subdivided into six periods on the basis o f characteristic changes in dry m a t t e r p r o d u c t i o n , leaf area index and albedo (see Part I). Linear regressions were c o m p u t e d for Q* on KJ, for each o f the three experimental plots, for all six periods. Hourly totals in mWh cm -2 were used, for daylight periods only. Table I shows regression equations, correlation coefficients and results o f error analysis for all 18 linear regressions. In addition results are shown of linear regressions c o m p u t e d from data pooled for all three surfaces for each o f the periods. Finally, all data for each of the three plots were pooled for c o m p u t i n g linear regressions b e t w e e n Q* and K J, over the whole experimental period. TABLE I Slope (a'), intercept (b'), standard deviation from regression (Sy. x) and correlation coefficient (r) for linear regressions of net radiation on solar radiation for six periods ( A - F ) and three surfaces (I-III) for hourly totals duringday-time. Katherine, 1969-70 (mWh cm -2 ) (see text for explanation of groupings) Period (dates)
Plot
a'
b'
Sy. x
r
A (December 17December 26)
I II 111
0.642 0.635 0.629
-2.4 -2.2 -1.5
5.1 3.8 6.2
0.98 0.99 0.97
B (December 2 7 January 11)
1 II III
0.650 0.627 0.598
-8.3 -6.4 -7.2
3.0 2.2 3.4
0.99 0.99 0.98
C (January 12January 26)
I 11 III
0.640 0.617 0.556
-5.1 -4.6 -3.5
3.0 2.1 3.6
0.99 0.99 0.98
D (January 2 7 February 6)
I II III
0.655 0.632 0.568
-3.8 -3.9 -3.0
3.5 1.9 3.5
0.99 0.99 0.98
E (February 7 February 21)
I II 11I
0.684 0.633 0.583
-4.1 -2.9 -3.4
1.6 1.2 3.4
0.99 0.99 0.99
F (February 2 2 March 27)
I II III
0.649 0.580 0.557
-5.1 -3.4 -5.4
7.0 3.7 4.0
0.96 0.98 0.98
A B C D E F
I-III 1-III I-Ill I-Ill I-II1 I-III
0.635 0.625 0.604 0.618 0.633 0.595
-2.0 -7.3 -4.4 -3.6 -3.5 -4.6
5.1 3.2 3.5 3.7 3.4 5.7
0.98 0.99 0.98 0.98 0.99 0.96
A-F A-F A-F
I II II1
0.643 0.613 0.579
-4.5 -3.6 -3.9
4.9 3.4 5.2
0.99 0.98 0.97
A-F
I-III
0.612
-4.0
4.8
0.97
RADIATION BALANCE OF A TROPICAL PASTURE
273
Hourly totals o f Q* can be estimated satisfactorily from one of the 18 linear regressions in the upper half of Table I. The sample standard deviation from regression Sy.x in these regressions varies between 1.2 and 7.0 mWh cm -'z. Considerable scatter exists in intercept b'. The term b' equals Q* at zero insolation and varies between - 1.5 and - 8 . 3 mWh cm -2. It appears that, in view of the scatter in both slope and intercept, any future use of the equations depends on information on surface characteristics, as well as on meteorological factors such as rainfall. The first alternative given in Table I, pooling of all surfaces for each of the six periods still depends on knowledge of seasonal aspects of growth and weather. The second alternative, three seasonal regressions for the individual surfaces, is therefore considered to be of greatest applicability in tropical pastures o f northern Australia. Standard errors from regression vary between 3.4 and 5.2 mWh cm -~. These values are slightly greater than those given by Fritschen (1967) for six irrigated crops in arid Arizona, for generally clear days. Total day-time net radiation ~,Q*atmay be determined from Y.K~t by determining the average hourly rate of K~ from ~K~ and day length in hours, calculating the average hourly rate of Q* using the regression equations and converting into ~Q*dt using day length in hours. It was noted from the present data, that the intercept b' agrees well with observed hourly totals of Q* around sunrise and sunset, whereas fluctuation in Q* during nighttime is generally small (cf. StanhiU et al., 1966). The expression ~ Q * t can therefore satisfactorily be calculated from b' and length o f night-time in hours. Constants o f the three seasonal regressions for individual surfaces have been used to calculate the relative magnitudes of the radiation balance components from monthly and seasonal means of total daily incoming solar radiation (~KJ,), o f the short-wave reflection coefficients (a, see Part I) and monthly and seasonal mean length of day and night. They are expressed in Table II as percentages o f the monthly and seasonal mean daily total radiation. Totals o f net long-wave radiation during day-time and over 24 h as a fraction of Y.K~t can be obtained from (1 - ct - Y.Q*dt/~,K~) and ( 1 - a - ~K,t), respectively. TABLE II Components of the radiation balance as percentages of monthly and seasonal mean daily short-wave radiation income (I;K~). (~Q*dt = day-time total of net all-wave radiation: ~Q* = 24 h total of net all-wave radiation: a =albedo; I --- pasture with Townsville stylo dominance; II -- pasture with dominance of grasses; III= bare soil plot)
~.Q*dt/XK*(%) xQ*/XK*(%)
ZK~ Day (mWh cm-2) length (h)
Night length (h)
1 - a(%) I
II
III
I
II
III
I
II
III
December January February March
658 674 613 654
12.93 12.83 12.57 12.18
11.07 11.17 11.43 11.82
83 83 79 80
81 79 76 76
80 79 80 79
55 56 55 56
54 54 54 55
50 50 50 51
48 48 47 48
48 49 47 48
44 44 43 44
Season
651
12.63
11.37
81
78
79
56
54
50
48
48
44
274
J. D, KALMA
A comparison o f Table II with data f r o m various sources, listed by Stanhill et al. (1966) and Linacre (1968), shows favourable agreement with measurements over a great range of surfaces and under various climatic conditions. It should finally be n o t e d that the regression equations presented in this paper may provide sufficiently accurate estimates for various applications, but great care should be exercised w h e n using the equations elsewhere, for different surfaces. ACKNOWLEDGEMENTS I am i n d e b t e d to Mr. R. B a d h a m for his co-operation in the experimental program, to Messrs. D. E. Watson and A. G. Swan for technical assistance and to Mrs. K. Haszler for assistance in data processing and c o m p u t e r programming. Mrs. A. K o m a r o w s k i was responsible for m u c h c o m p u t a t i o n a l work. I am grateful to Mr. P. M. Fleming and Dr. C. W. Rose for their critical advice and c o m m e n t s .
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Rijks, D. A., 1968. Water use by irrigated cotton in Sudan. II. Net radiation and soil heat flux. J. Appl. Ecol., 5: 685-706. Rose, C. W. and Thomas, D, A., 1968. Remote sensing of land surface temperatures and some applications in land evaluation, ln: G. A. Stewart (Editor), Land Evaluation. Macmillan, Melbourne, pp. 367-375. Sellers, W. D., 1965. Physical Climatology. Univ. Chicago Press, Chicago and London, 272 pp. Stanhill, G., Hofstede, G. J. and Kalma, J. D., 1966. Radiation balance of natural and agricultural vegetation. Q. J. R. Meteorol. Soc., 92: 128-140. Swinbank, W. C., 1963. Long-wave radiation from clear skies. Q. J. R. Meteorol. Soc., 89: 339-348. Van Wijk, W. R., 1963. Physics of Hant Environment. North-Holland, Amsterdam, 382 pp.