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Estimates of potential evaporation using alternative data in Penman's formula
Agricultural Meteorology - Elsevier Publishing Company, Amsterdam - Printed in The Netherlands
ESTIMATES OF POTENTIAL EVAPORATION U S I N G ALTERNATIVE DATA IN PENMAN'S F O R M U L A E. A. FITZPATRICK AND W. R. STERN
Division of Land Research and Regional Survey, C.S.1.R.O., Canberra, A.C.T., Australia (Received March 20, 1965)
SUMMARY
In an environment with a wide seasonal range of radiation and vapour-pressure deficit, the energy and aerodynamic components of Penman's evaporation formula were calculated daily for a year, and the potential evaporation was determined from several sources of data and by alternate modes of computation. Reference values for the energy component were obtained from measured net radiation over a wellwatered crop. Reference values for the aerodynamic component were calculated from wet- and dry-bulb temperatures and windspeed using a relationship defined by Penman. Total radiation and relative duration of sunshine were found to be effective alternative sources of data for the energy component. When calculating the effective terrestrial radiation, it was found that equally satisfactory results could be obtained from a relationship based on proposals by Swinbank as by Penman's method which includes a vapour pressure term. Daily Piche and tank evaporimeter data were found to be satisfactory alternatives to the aerodynamic component. The conclusions reached are: (1) The minimal instrumentation needed to determine potential evaporation is a net radiometer, a Piche evaporimeter, and maximum and minimum thermometers, provided a suitable relation between the Piche and aerodynamic component is available. If a solarimeter is used in place of a net radiometer or sunshine recorder, a reliable albedo coefficient is necessary. When a sunshine recorder is used, a satisfactory relation between n/N and Qt/Qe is also required. (2) The use of inappropriate constants in the Penman formula is probably a greater source of error when determining potential evaporation than the deficiencies inherent in a particular type of instrument, e.g., a sunshine recorder. The constants appropriate to the particular climatic environment must be used.
INTRODUCTION
The method of PENMAN 0948) to estimate evaporation has been used widely in Agr. Meteorol., 3 (1966) 225-239
226
E. A. FITZPATRICK AND W. R. STERN
agricultural meteorology and hydrology. By this method, the potential evaporation (E0) from a free water surface is derived from energy balance and aerodynamic considerations. This is defined according to the relationship: A
---H4-A Y Eo-- A 7
(1)
+ 1.0
where H is an energy component (i.e., net radiation expressed in evaporation units), A is an aerodynamic component determined from wind.speed and the vapour-pressure deficit, A is the slope of the saturation vapour pressure curve at the given screen temperature, and 7 is the constant of the wet- and dry-bulb psychrometric equation. The ratio A/7 is a temperature-dependent, non-dimensional ratio which, in effect, is a weighting factor to assess the relative importance of the available energy (H) and the "drying power" (A) of the atmosphere (PENMAN, 1956). The principles underlying the method have been reviewed and discussed many times in recent years (e.g., SLATYERand MCILROY, 1961; PENMAN, 1963) and are not elaborated here. Instead, emphasis is on aspects of practical interest which have received less attention, namely, the relative magnitude of errors in the estimates of H, A, and E0 when alternative data and formulae are used. Although net radiation can now be measured directly with reasonable accuracy (FUNK, 1959; FRITSCHEN, 1963), it seems that in many situations it will still be necessary to call upon less specific but more generally available data from either total radiation or sunshine recorders. This is, in fact, normally the case where broad, regional assessments of potential evaporation are required for areas having only limited networks of wellinstrumented stations. In this paper estimates of the energy and aerodynamic components and the potential evaporation are examined using measurements from a locality which is characterized by a wide range in total and net radiation and in the vapour-pressure deficit throughout the year.
METEOROLOGICAL PROCEDURES
The data were recorded at the Kimberley Research Station, Kununurra, Western Australia (longitude 128o36' E latitude 15042' S) between October 17, 1961 and October 11, 1962, in a field study to determine water usage by irrigated cotton (STERN, 1965). The crops were irrigated at intervals of 8-10 days depending on accumulated tank evaporation except during periods with adequate rainfall. Daily observations of the following elements are used in this paper: --- Net radiation over an irrigated crop - - Total (global) radiation Duration of bright sunshine -
-
/lgr. Meteorol.,
3 (1966) 225-239
ESTIMATES OF POTENTIAL EVAPORATION
227
Tank evaporation (Australian Standard) Piche evaporation Total run of wind Maximum temperature - - Minimum temperature - - Dry-bulb temperature - - Wet-bulb temperature -
-
-
-
-
-
-
-
Net radiation was measured with a C.S.I.R.O. net radiometer (FUNK, 1959). Six instruments were exposed horizontally at 1.5 m over irrigated cotton at different stages of development. Values from the instruments for any one day differed little between crops at varying stages of development, and the mean of these has therefore been used here. Total incoming radiation was measured with a Kipp solarimeter (RADIATION COMM. I.A.M., 1958, p.415). The instrument was sited on the roof of the main laboratory. Duration of bright sunshine was recorded with a Campbell-Stokes Sunshine Instruments (METEREOL.OFFICE, 1956) situated in a standard meteorological enclosure. Tank evaporation was observed daily from a standard, sunken Australian tank (COMMWEALTH BUR. METEREOL., 1954; HOUNAM, 1961) installed within the meteorological enclosure. The tank is made of galvanized iron and is a cylinder 3 ft. diameter and 3 ft. deep, immersed in a larger tank 4 ft. diameter and 2 ft. 10 inches deep, the unit being sunken into the ground so that the rim of the outer tank is just above ground level. Care was taken to maintain the level of the water in the inner tank between 2 inches and 3 inches below the level of the rim. The tank was emptied, cleaned, and checked for leaks before the experiment began and again tested for leaks once during the course of the experiment. Evaporation from a Piche evaporimeter hung in a Stevenson screen (PRESCOTT and STIRK, 1951) was also observed daily. The new disk was perforated with a pin-hole before replacing the previous disk at 09h00 local time each day. The daily run of total wind was recorded with a cup contact anemometer M K II (METEREOL. OFFICE, 1956) mounted at a height of 2 m at the site of the experiment. The instrument was checked against a similar anemometer exposed in the meteorological enclosure at a height of 1.6 m. Maximum, minimum, wet-bulb, and dry-bulb temperatures were observed daily at 09h00 local time from standard thermometers in Stevenson screens at the site of the experiment and also at the meteorological enclosure. The observations made at the experimental area are used here, but in practice there was little difference between the readings at the two sites.
GENERAL PROCEDURES
When using Penman's method many of the assumptions and formulae normally A gr. Meteorol., 3 (1966) 225-239
228
E. A. FITZPATRICKAND W. R. STERN
called upon to evaluate separate components of the energy balance are by-passed if measurements of net radiation are available. Therefore, in comparing estimates from various types of observations it is logical to use the values determined from measured net r~diation as the control group. This has been the procedure throughout this study. The original Penman's method referred to a free water surface for which an average albedo coefficient of 0.06 can be considered appropriate at this latitude (BuDYKO, 1956). However, observations of net radiation over water were not available from the experimental site, and instead net radiation over the irrigated crop was used. The albedo coefficient of the crop was determined from time to time under a variety of incoming radiation conditions and was found within the narrow limits of 0.171 and 0.196 with a mean value of 0.18. Therefore, when evaluating H from either total radiation or sunshine data, the mean albedo coefficient was used over the entire year. With the aid of electronic computers, all of the terms in eq.1 can be readily evaluated from the basic data prepared on punch cards. A number of computer programs have recently been developed for calculating Penman's potential evaporation (e.g., LAMOREUX,1962; YOt;N~, 1963; BERRY, 1964), but to satisfy special reserach needs and to accommodate a wider range of available data, a program was specially prepared for use in our laboratories. The program can be used to obtain estimates from either net radiation, total radiation, duration of sunshine, or fractional cloudiness for periods of any specified length. In addition, there is provision for relating E0 to measured losses from evaporimeters or lysimeters. For the purposes of this study, the program provided an effective means for determining values of H, A, and E0 from a variety of meteorological observations. Penman has not advocated application of the method with daily data. However, our aim here is not to assess the intrinsic reliability of the method, but rather to examine the relative magnitude of errors as may result through the use of alternative data in Penman's formula. Thus, although there may be some reason to question the reliability of the method as such when applied with daily data, it was considered instructive from a comparative point of view to analyse our data in this way for this purpose. We recognize that for many practical purposes such as scheduling irrigation and assessing regional variation in evaporation, the evaporation rates over single daily intervals are not normally required. From such daily evaluations we have also determined mean rates over longer intervals, and have correlated these with observed evaporation and with several empirical evaporation predictors. Results of such an analysis using five-day intervals are presented elsewhere (STERNand FITZPATRICK, 1965). Our use of daily data in this study does not imply that we have evidence that changes in heat storage are always negligible on a daily time scale. Indeed, it may well be that intrinsic errors in the estimate due to the neglect of heat storage are as large as those which we have found arising from the use of different types of data. The findings we report here should be interpreted strictly in an comparative sense.
Agr. Meteorol., 3 (1966)225-239
229
ESTIMATES OF POTENTIAL EVAPORATION
ANALYSIS OF DATA
Energy component When direct measurements of net radiation are not available, the energy component is determined from the estimated net radiation using the relationship expressing the radiation balance: Qn
(1 - - a) Qt - - Qb
(2)
where Qn is the net radiation, a is the albedo coefficient, Qt is the total radiation, and Qb is the effective terrestrial radiation. H is then obtained by simple conversion of Qn to evaporation units using a conversion factor based upon the latent heat of vaporization of water. If direct measurements of Qt are not available it has been customary to estimate this from the relative duration of sunshine by an expression having the form:
Qt Qe
a ~ b-
n N
(3)
where Qe is the extra-terrestrial radiation, n is the observed duration of sunshine, N is the daylentgh, and a and b are empirical constants. However, in another study (FITZPATRICK and STERN, 1965) it was shown that a relationship of this form is unsatisfactory for estimating total radiation under overcast or nearly overcast conditions. At this site much improved estimates of Qt can be obtained from:
Qt Qe
(
n) 0.373 + 0.385 ~ -
0.0042
(4)
n + 0.0154 N
Direct measurements of the long-wave radiation flux outward from the surface, and between the atmosphere and the surface, are seldom available, and therefore Qb is generally estimated from meteorological data. Penman has proposed a single equation for Qb incorporating the Stefan-Boltzman relationship and based upon empirical expressions due to BRUNT (1932) and ANGSTROM (1924) which relate the downward long-wave radiation from the atmosphere to vapour pressure and cloudiness:
Qb=-aT4(a+ b~)(c
n
+d~-)
(5)
where a is the Stefan-Boltzman constant in appropriate units, T is the mean screen absolute temperature, ed is the vapour pressure, and n/N is the ratio of the duration of bright sunshine to day length. Penman proposes values of 0.56 and ---0.09 for a and b respectively (with ed in mm Hg) and 0.1 and 0.9 for c and d respectively. However, in this climatic environment values for a, b, c, and d equal to 0.352, --0.049, 0.3 and 0.7 respectively have been found to give much improved estimates of Qb (eq. 13 in FITZPATRICKand STERN, 1965). Agr. Meteorol., 3 (1966) 225-239
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........ Correlation c o e f f i c i e n t : Sample size, 3 0 4
------
Fig.1. The relationship between daily values of the energy component determined from measured net radiation and the estimated energy component, using Penman's formula for effective terrestrial radiation. (Centroid of regression shown by open circle.) A. Using observed total radiation data; energy component (Hest.) obtained without reference to observed duration of sunshine. B. Using estimates of total radiation; energy component (Hast.) obtained without reference to measured total radiation.
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....... + 2 . 0 x S.E. of e s t i m a t e (-+ 0.050 cm/day) /;".., "- ; I /,/--/' -~ . / , ' " C. . . . lati . . . . . f f i c i e n t : ÷ 0.947 ." / . _.~-/~', " o ~ , /
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N >
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231
ESTIMATES OF POTENTIAL EVAPORATION
We have also shown that if Qt is known, improved estimates of the effective terrestrial radiation can be obtained if, instead of using the observed n/N in eq.5, values of n/N from an inverse relationship corresponding to eq.3 is used (eq.15 in FITZPATRICK and STERN, 1965). Two sets of daily estimates of the energy component (//est.) were evaluated from eq.2 using values of Qb calculated from eq.5 with the constants, a, b, c and d given above which we have found appropriate for this climatic environment. The first set was determined using the measured Qt and using for n/N in eq.5 the values determined from the inverse relationship corresponding to eq.3. This set of estimates is shown in Fig. I A plotted against observed energy component (H) determined from the measured net radiation. The second set was determined in similar manner using eq.2 and 5, but with Qt from eq.4 instead of the actual measured values, and with n/N in eq.5 from the observed duration of sunshine instead of the calculated values from the inverse relationship corresponding to eq.3. Fig.lB shows the relationship between the second set and the observed energy component. Agreement between the regression fitted by least squares and the one-to-one relationship is remarkably good when either total radiation or sunshine data are used as described above. In both cases 96~o of all points fall within the broken lines in Fig. 1A and B which are placed at twice the standard error of estimate. The above methods were repeated using an alternative formula which has been found to give estimates of Qb of approximately the same accuracy:
Qb
(
n)
cr T 4 (1.0 - - 0.936 × 10-~ T 2) 0.155 + N -
(6)
This relationship is based in principle upon findings of SWINBANK (1963) but the constants which are linked with the n/N term have been determined by regression analysis from our data (FITZPATRICK and STERN, 1965; eq.14). Results are shown in Fig.2A and B. There is good agreement between the centroid of the fitted regression and the corresponding point on the one-to-one relationship. The slopes of the fitted regression in this case depart further from one-to-one relationship than in Fig.lA and B but, considering the extent of the scatter, this disparity is not serious. As in Fig.lA and B, only about 4G of all points fall outside of plus and minus twice the standard error of estimate.
Aerodynamic component The aerodynamic component of Penman's potential evaporation is defined by the relationship:
A
(ea -- ea) f (u)
(7)
where e, is the saturation vapour pressure at the mean screen temperature, ed is the saturation vapour pressure at the dew point (i.e., the bulk vapour pressure of the air at screen height), and f (u) is a function of wind speed. Agr. Meteorol., 3 (1966)
225-239
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L e a s t squares regression: H = a +b Has t g = -0.064 ~ O.0141~ ~ = 1 f210 _+0.0257 "
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Correlation coefficient: +0.906 Sample s i z e : 3 0 4
.........
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Fig.2. The relationship between daily values of the energy component determined from measured net radiation and the estimated energy component ~- using a fornmla for effective terrestrial radiation based on relationship given by Swinbank. (Centroid of regression shown by open circle). A. Using o~ observed total radiation data; energy component (Hest.) obtained without reference to observed duration of sunshine. B. Using estimates of total radiation: energy component (Hest.) obtained without reference to measured total radiation.
o
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0.91
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233
ESTIMATES OF POTENTIAL EVAPORATION
The specific relationship proposed by PENMAN (1956, p. 16) defining the aerodynamic component is: / U2 \ A ---- 0.35 ( c a - ca) ~0.5 + 1-]O0-)
(S)
where A is in mm/day, ea and ea are in mm Hg, and (-72is the wind speed in miles/day at a height of 2 m. Daily values of the aerodynamic component were calculated from eq.8. In Fig.3 the relationship is shown between these and the measured evaporation from the Piche and sunken tank evaporimeters. Although there is a wide scatter in the points, particularly in the case of the tank evaporation, there is clearly a linear relationship in each case. The regression equations defining A in terms of these measurements are: 0.0172 + 0.621 Ep
(9)
A ---- 0.0211 + 0.747 E,
(10)
A and:
where Ep and Et are the measured evaporation in cm/day from the Piche and tank evaporimeters respectively. It is clear from Fig.lA and B that the basic methods proposed by Penman give good agreement between the estimated and observed energy component providing reliable constants appropriate for the climatic environment have been obtained. Except over the lower range of values, errors in the daily estimates of H are not appreciably larger when estimates are made from sunshine data than when measured total radiation is used. This, of course, again assumes that the relationship between total radiation and duration of sunshine is reliable and has been identified for the particular climatic environment. These findings are of interest since often data for duration of sunshine are the only data available. It is important to note here that the extrapolation of relationships between Qt/Qe and n/N to localities having distinctive cloudiness characteristics or differing greatly in latitude should be approached with caution. A comparison of Fig.l and 2 indicates that Swinbank's proposals can be used effectively to estimate the energy component without the necessity for vapour pressure data. It is clear that errors in the estimated energy component are not appreciably larger when eq.6 is used in place of eq.5. Thus, if vapour pressure data are not available, Penman's potential evaporation may still be estimated provided a suitable approximation of the aerodynamic component can be made from evaporimeter data. In general, our findings indicate that errors in the final estimation of the energy component are likely to be greater due to inappropriate constants in the empirical relationships required by the method, rather than to errors in total radiation or sunshine records from instrumental causes or other deficiencies. Throughout this study we have used the measured net radiation over a wellwatered crop as reference values for the energy component. It seems probable that Agr. Meteorol., 3 (1966)
225-239
234
E.A. FITZPATRICK
A N D W . R. S T E R N
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Correlation coefficient: _+0.656 S.E. of estimate: -+0.224 cm/day Sample size: 348 115
210
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Fig.3. Relationships between daily values of aerodynamic ved Piche evaporation (A), and observed tank evaporation
component (B).
and the corresponding
Agr. Meteorol., 3 ( 1 9 6 6 )
obser-
225-239
235
ESTIMATES OF POTENTIAL EVAPORATION
what has been found here would apply equally well had the reference data been related to a free water surface (with the correct albedo coefficient). The daily values of the aerodynamic component calculated from eq.8 ranged widely during the course of these observations, the highest being 1.75 cm/day in October and the lowest being 0.07 cm/day in January. In view of the marked seasonal contrasts in vapour-pressure deficit of this environment, it seems likely that a wider range in the aerodynamic component would rarely be experienced. The reliability of evaporation measuring devices such as the Piche instrument or tank evaporimeters for purposes of estimating evaporation from an extended water surface has often been seriously questioned on the grounds of their diverse responses to local conditions. In Israel, STANHILL (1962) using average data over 10-day periods has demonstrated a close linear relationship between the measured Piche evaporation and Penman's aerodynamic component. An empirical linear relationship between evaporation from the Standard Australian tank evaporimeter and saturation deficit has long been known (PRESCOTT, 1938) and has been used for a variety of purposes. The observed Piche and tank evaporation thus appear to offer practical alternatives to the instrumentation required for determining the aerodynamic component according to eq.8. When using daily data, we find definite evidence of seasonal variations in the relationships between the observed evaporation from both the Piche and tank evaporimeters and the calculated aerodynamic component. Since we have been unable either to associate these seasonal differences with other meteorological measurements or offer a physical explanation for' them, and since the contribution of the areodynamic term to the final estimate of potential evaporation is normally small compared with that of the energy component, we consider that the use of other than a single, generalized relationship for the entire year is not justifiable for this purpose. Nonetheless this problem merits further investigation, particularly as there is a suggestion that the seasonal variations referred to here may be related to the degree of mass advection. It is of interest that in Fig.3 the scatter of points is appreciably greater in the case of tank evaporation than with the Piche. It would seem that much of this increased scatter is attributable to the high sensitivity of this instrument to changes in the energy balance within the micro-environment of the immediate surrounds of the tank.
ALTERNATIVE MODES OF ESTIMATING POTENTIAL EVAPORATION
It has been shown that both the energy and aerodynamic components of Penman's evaporation formula can be estimated with reasonable accuracy in a variety of ways from several sources of data. The potential evaporation estimates determined from the measured net radiation and with eq.8 used for the areodynamic component were taken as reference values for purposes of comparing the errors in Eo resulting from various modes of estimation. Daily potential evaporation (Eo) was calculated using eq.1 with all combinations of the estimates of H (from eq.5) and of A. Frequency Agr. MeteoroL, 3 (1966) 225-239
236
E. A. FITZPATRICK AND W. R. STERN
TABLE I MEANS AND STANDARDDEVIATIONS(cm/day) OF ERRORS rN ESTIMATEOF POTENTIAL EVAPOTRANSPIRATION BY ALTERNATIV~MOOESOF COMPUTATION (Sample size: 260 days for all m o d e s of c o m p u t a t i o n )
Energy component from observed duration of sunshine
Energy component from observed total radiation
Energycomponent from observed net radiation
4.00711 0.0028 0.0451 0.0020
--0.0011 0.0024 0.0383 0.0017
Reference data
0.0052 0.0041 0.0645 0.0029
0.0004 0.0039 0.0604 0.0027
0.0025 0.0023 0.0371 0.0016
~0.0082 0.0043 0.0693 0.0031
---0.0026 0.0043 0.0687 0.0030
---0.0005 0.0030 0.0475 0.0021
Aerodynamic component from standard method Mean S. E. o f m e a n S.D. S. E. of S . D .
Aerodynamic component .from Piche evaporimeter Mean S. E. o f m e a n S.D. S. E. o f S . D .
Aerodynamic component from tank evaporimeter Mean S. E. o f m e a n S.D. S. E. of S . D .
1 M e a n differs significantly from zero at P < 0.05.
distributions of the errors (i.e., differences between the reference values and the daily estimates of potential evaporation by alternative modes of computation) were prepared. These distributions were compared with Gaussian distribution curves having the same means and standarct deviations as the samples (see Table 1). An application of the t test reveals that with one exception, the calculated means of the distributions shown in Table I do not differ significantly (at P < 0.05) from zero. For all modes of computation, the errors are well approximated by the "normal" curve. A distinct trend toward increasing errors with the use of data requiring an increasing number of assumptions and connecting relationships is evident from the standard deviations given in Table I. From the wide scatter of points in Fig.3 it might at first be anticipated that large errors in the estimated potential evaporation would be incurred when working from the Piche or tank data. However, from the standard deviation shown in Table I it is seen that errors in this direction are of about the same magnitude as those which result when total radiation or duration of sunshine is used in place of measured net radiation. Our experience would suggest that errors in the estimates of Eo resulting from alternative data would not be appreciably larger than those represented by the standard deviation in Table I had eq.1 been used in lieu of eq.5. Agr. Meteorol., 3 (1966) 225-239
I
1 2 3 4
x × ×
x × ×
× x x x x × × x
×
x × ×
×
x
× × ×
Sunshine 3 Total Net radiation 4 radiation
Sunshine z Total Net radiation ~ radiation x
Energy component with vapour pressure term for eff'eetive terrestrial radiation ~
Energy component with or w i t h o u t vapour pressure term for effective terrestrial radiation s
x
×
x
×
x
x
x
× ×
Sunshine 3 Total Net radiation a radiation
Energy con~onent without vapour pressure term for effective terrestrial radiation
Aerodynamic component from evaporimeter 1
Aerodynamic component from standard Penman's method
Afode of computation
Appropriate relation between measured evaporation and aerodynamic c o m p o n e n t is required. With vapour pressure term, appropriate regional constants are required for calculating effective terrestrial radiation. Suitable relation between n/N and Qt/Qe is required. Also reliable albedo coefficient (a). Reliable albedo coefficient (a) is required.
Sunshine recorder Solarimeter Net radiometer M a x i m u m - m i n i m u m thermometers Wet-bulb and dry-bulb thermometers Anemometer Evaporimeter
Instrumentation
I N S T R U M E N T A T I O N R E Q U I R E D FOR V A R I O U S MODES OF C O M P U T I N G P E N M A N ' S P O T E N T I A L E V A P O R A T I O N
TABLE 1I
ta~ ",--.1
z
©
,<
z
t'~
©
o
238
E. A. FITZPATRICK AND W. R. STERN
In Table II are summarized the combinations of instruments that are required for each mode of computting Eo, assuming either eq. 5 or 6 is used in estimating the effective terrestrial radiation. For experimental purposes, satisfactory determinations of daily potential evaporation can be achieved with no more extensive instrumentation than maximum and minimum thermometers, a net radiometer, and a Piche evaporimeter (or some similar instrument responding to both dryness of air and to wind). At the broader level of regional assessment of potential evaporation, it would appear that a network of stations equipped with m a x i m u m - m i n i m u m thermometers, simple sunshine recorders and instruments such as the Piche evaporimeter would appear practicable. As we have already noted, however, we have detected a degree of dissimilarity in the relationship between the Piche observations and the aerodynamic component between seasons, and it would seem that similar differences between stations having distinctive climates would also occur. Also, it would appear that this instrument, like the tank evaporimeter, is highly sensitive to peeularities of site and to the mode of installation and maintenance. Extrapolation of relationships between Piche evaporation and the aerodynamic component should thus be considered with some caution. Regardless of whatever substitute instrumentation which might be employed to extend the network of stations contributing usefal data, it remains essential that accurate measurements be made of total radiation, net radiation (preferably over several standard reference surfaces)and atmospheric moisture content at selected stations which are situated such that they can, insofar as is possible, be regarded as representative of their macroclimatic environments.
ACKNOWLEDGEMENTS
We wish to thank Mr. S. J. Rance and Mr. C. F. Massey for maintaining the equipment and carrying out the observations in the field, and Mr. K. T. Hannan, Mrs. A. Kamarowski, and Mr. S. J. Rance for assistance with the computations.
REFERENCES
ANGSTROM,A., 1924. Solar and terrestrial radiation. Quart. J. Roy. Meteorol. Soc., 50 : 121-126. BERRY, G., 1964. The evaluation of Penman's natural evaporation formula by electronic computer. Australian J. Appl. Sci., 15 : 61-64. BRUNT, D., 1932. Notes on radiation in the atmosphere. Quart. J. Roy. Meteorol. Soc., 58 : 389-418. BUDYKO, M., 1956. Teplovoi Balans Zemnoi Poverkhnosti. Gidrometeorologicheskoe Izdatel'stvo, Leningrad, 255 pp. (English translation by STEPANOVA, N. A., 1958. The Heat Balance qfthe Earth's Surface. U.S. Dept. Comm., OfficeTech. Serv., Washington, 259 pp) COMMONWEALTHBUR, METEOROL., 1954. Australian Meteorolo¢ical Observer's Handbook. Government Printer, Melbourne, 148 pp. FITZPATRICK, E. A. and STERN,W. R., 1965. Components of the radiation balance of irrigated plots in a dry monsoonal climate. J. Appl. Meteorok, in press. Agr. Meteorol., 3 (1966) 225-239
ESTIMATES OF POTENTIAL EVAPORATION
239
FRITSCHEN, L. J., 1963. Construction and evaluation of a miniature net radiometer. J. Appl. Meteorol., 2 : 165-172. FUNK, J. P., 1959. Improved polythene-shielded net radiometer. J. Sci. Instr., 36 : 267-270. HOUNAM, C. E., 1961. Evaporation in Australia. Commonwealth Bur. Meteorol., Bull., 44 : 88 pp. LAMOUREUX,W. W., 1962. Modern evaporation formulae adapted to computer use. Monthly Weather Rev., 90 : 26-28. METEOROL. OFFICE, 1956. Handbook of Meteorological Instruments, 1. Instruments for surface observations. H.M. Stationary Office, London, 458 pp. PENMAN, H. L., 1948. Natural evaporation from open water, bare soil, and grass. Proc. Roy. Soc. (London), Set. A, 193 : 120-145. PENMAN, H. L., 1956. Evaporation--An introductory survey. Neth. J. Agr. Sci., 4 : 9-29. PENMAN, H. L., 1963. Vegetation and hydrology. Commonwealth Bur. Soil Sci. ( Gt. Brit.) Tech. Commun., 53 : 124pp. PRESCOTT, J. A., 1938. Indices of agricultural climatology, d. Australian Inst. Agr. Sci., 4 : 33-40. PRESCOTT, J. A. and STIRK, G. B., 1951. Studies on the Piche evaporimeter. Australian J. Appl. Sci., 2 : 243-256. RADIATION COMM. I.A.M., 1958. Radiation instruments or measurements. Ann. Intern. Geophys. Year, 6 : 371-466. SLATYER, R. O. and MCILRO¥, I. C., 1961. Practical Microclimatology with Special Reference to the Water Factor in Soil-Plant-Atmosphere Relationships. UNESCO, Paris, 308 pp. STANH1LL,G., 1962. The use of the Piche evaporimeter in the calculation of evaporation. Quart. J. Roy. Meterorol. Soc., 88 : 80-82. STERN, W. R., 1965. The seasonal growth characteristics of irrigated cotton in a dry monsoonal environment. Australian J. Agr. Res., 16 : 347-366. STERN, W. R. and FITZPATRICK,E. A., 1965. Calculated and observed evaporation in a dry monsoonal environment. J. Hydrol., 3 : 297-311. SWINBANK, W. C., 1963. Long-wave radiation from clear skies. Quart. d. Roy. Meteorol. Sue., 89 : 339-348. YOUNG, C. P., 1963. A computer programme for the calculation of mean rates of evaporation using Penman's formula. Meteorol. Nag., 92 : 84-89.
Agr. Meteorol., 3 (1966)225-239
ESTIMATES OF POTENTIAL EVAPORATION U S I N G ALTERNATIVE DATA IN PENMAN'S F O R M U L A E. A. FITZPATRICK AND W. R. STERN
Division of Land Research and Regional Survey, C.S.1.R.O., Canberra, A.C.T., Australia (Received March 20, 1965)
SUMMARY
In an environment with a wide seasonal range of radiation and vapour-pressure deficit, the energy and aerodynamic components of Penman's evaporation formula were calculated daily for a year, and the potential evaporation was determined from several sources of data and by alternate modes of computation. Reference values for the energy component were obtained from measured net radiation over a wellwatered crop. Reference values for the aerodynamic component were calculated from wet- and dry-bulb temperatures and windspeed using a relationship defined by Penman. Total radiation and relative duration of sunshine were found to be effective alternative sources of data for the energy component. When calculating the effective terrestrial radiation, it was found that equally satisfactory results could be obtained from a relationship based on proposals by Swinbank as by Penman's method which includes a vapour pressure term. Daily Piche and tank evaporimeter data were found to be satisfactory alternatives to the aerodynamic component. The conclusions reached are: (1) The minimal instrumentation needed to determine potential evaporation is a net radiometer, a Piche evaporimeter, and maximum and minimum thermometers, provided a suitable relation between the Piche and aerodynamic component is available. If a solarimeter is used in place of a net radiometer or sunshine recorder, a reliable albedo coefficient is necessary. When a sunshine recorder is used, a satisfactory relation between n/N and Qt/Qe is also required. (2) The use of inappropriate constants in the Penman formula is probably a greater source of error when determining potential evaporation than the deficiencies inherent in a particular type of instrument, e.g., a sunshine recorder. The constants appropriate to the particular climatic environment must be used.
INTRODUCTION
The method of PENMAN 0948) to estimate evaporation has been used widely in Agr. Meteorol., 3 (1966) 225-239
226
E. A. FITZPATRICK AND W. R. STERN
agricultural meteorology and hydrology. By this method, the potential evaporation (E0) from a free water surface is derived from energy balance and aerodynamic considerations. This is defined according to the relationship: A
---H4-A Y Eo-- A 7
(1)
+ 1.0
where H is an energy component (i.e., net radiation expressed in evaporation units), A is an aerodynamic component determined from wind.speed and the vapour-pressure deficit, A is the slope of the saturation vapour pressure curve at the given screen temperature, and 7 is the constant of the wet- and dry-bulb psychrometric equation. The ratio A/7 is a temperature-dependent, non-dimensional ratio which, in effect, is a weighting factor to assess the relative importance of the available energy (H) and the "drying power" (A) of the atmosphere (PENMAN, 1956). The principles underlying the method have been reviewed and discussed many times in recent years (e.g., SLATYERand MCILROY, 1961; PENMAN, 1963) and are not elaborated here. Instead, emphasis is on aspects of practical interest which have received less attention, namely, the relative magnitude of errors in the estimates of H, A, and E0 when alternative data and formulae are used. Although net radiation can now be measured directly with reasonable accuracy (FUNK, 1959; FRITSCHEN, 1963), it seems that in many situations it will still be necessary to call upon less specific but more generally available data from either total radiation or sunshine recorders. This is, in fact, normally the case where broad, regional assessments of potential evaporation are required for areas having only limited networks of wellinstrumented stations. In this paper estimates of the energy and aerodynamic components and the potential evaporation are examined using measurements from a locality which is characterized by a wide range in total and net radiation and in the vapour-pressure deficit throughout the year.
METEOROLOGICAL PROCEDURES
The data were recorded at the Kimberley Research Station, Kununurra, Western Australia (longitude 128o36' E latitude 15042' S) between October 17, 1961 and October 11, 1962, in a field study to determine water usage by irrigated cotton (STERN, 1965). The crops were irrigated at intervals of 8-10 days depending on accumulated tank evaporation except during periods with adequate rainfall. Daily observations of the following elements are used in this paper: --- Net radiation over an irrigated crop - - Total (global) radiation Duration of bright sunshine -
-
/lgr. Meteorol.,
3 (1966) 225-239
ESTIMATES OF POTENTIAL EVAPORATION
227
Tank evaporation (Australian Standard) Piche evaporation Total run of wind Maximum temperature - - Minimum temperature - - Dry-bulb temperature - - Wet-bulb temperature -
-
-
-
-
-
-
-
Net radiation was measured with a C.S.I.R.O. net radiometer (FUNK, 1959). Six instruments were exposed horizontally at 1.5 m over irrigated cotton at different stages of development. Values from the instruments for any one day differed little between crops at varying stages of development, and the mean of these has therefore been used here. Total incoming radiation was measured with a Kipp solarimeter (RADIATION COMM. I.A.M., 1958, p.415). The instrument was sited on the roof of the main laboratory. Duration of bright sunshine was recorded with a Campbell-Stokes Sunshine Instruments (METEREOL.OFFICE, 1956) situated in a standard meteorological enclosure. Tank evaporation was observed daily from a standard, sunken Australian tank (COMMWEALTH BUR. METEREOL., 1954; HOUNAM, 1961) installed within the meteorological enclosure. The tank is made of galvanized iron and is a cylinder 3 ft. diameter and 3 ft. deep, immersed in a larger tank 4 ft. diameter and 2 ft. 10 inches deep, the unit being sunken into the ground so that the rim of the outer tank is just above ground level. Care was taken to maintain the level of the water in the inner tank between 2 inches and 3 inches below the level of the rim. The tank was emptied, cleaned, and checked for leaks before the experiment began and again tested for leaks once during the course of the experiment. Evaporation from a Piche evaporimeter hung in a Stevenson screen (PRESCOTT and STIRK, 1951) was also observed daily. The new disk was perforated with a pin-hole before replacing the previous disk at 09h00 local time each day. The daily run of total wind was recorded with a cup contact anemometer M K II (METEREOL. OFFICE, 1956) mounted at a height of 2 m at the site of the experiment. The instrument was checked against a similar anemometer exposed in the meteorological enclosure at a height of 1.6 m. Maximum, minimum, wet-bulb, and dry-bulb temperatures were observed daily at 09h00 local time from standard thermometers in Stevenson screens at the site of the experiment and also at the meteorological enclosure. The observations made at the experimental area are used here, but in practice there was little difference between the readings at the two sites.
GENERAL PROCEDURES
When using Penman's method many of the assumptions and formulae normally A gr. Meteorol., 3 (1966) 225-239
228
E. A. FITZPATRICKAND W. R. STERN
called upon to evaluate separate components of the energy balance are by-passed if measurements of net radiation are available. Therefore, in comparing estimates from various types of observations it is logical to use the values determined from measured net r~diation as the control group. This has been the procedure throughout this study. The original Penman's method referred to a free water surface for which an average albedo coefficient of 0.06 can be considered appropriate at this latitude (BuDYKO, 1956). However, observations of net radiation over water were not available from the experimental site, and instead net radiation over the irrigated crop was used. The albedo coefficient of the crop was determined from time to time under a variety of incoming radiation conditions and was found within the narrow limits of 0.171 and 0.196 with a mean value of 0.18. Therefore, when evaluating H from either total radiation or sunshine data, the mean albedo coefficient was used over the entire year. With the aid of electronic computers, all of the terms in eq.1 can be readily evaluated from the basic data prepared on punch cards. A number of computer programs have recently been developed for calculating Penman's potential evaporation (e.g., LAMOREUX,1962; YOt;N~, 1963; BERRY, 1964), but to satisfy special reserach needs and to accommodate a wider range of available data, a program was specially prepared for use in our laboratories. The program can be used to obtain estimates from either net radiation, total radiation, duration of sunshine, or fractional cloudiness for periods of any specified length. In addition, there is provision for relating E0 to measured losses from evaporimeters or lysimeters. For the purposes of this study, the program provided an effective means for determining values of H, A, and E0 from a variety of meteorological observations. Penman has not advocated application of the method with daily data. However, our aim here is not to assess the intrinsic reliability of the method, but rather to examine the relative magnitude of errors as may result through the use of alternative data in Penman's formula. Thus, although there may be some reason to question the reliability of the method as such when applied with daily data, it was considered instructive from a comparative point of view to analyse our data in this way for this purpose. We recognize that for many practical purposes such as scheduling irrigation and assessing regional variation in evaporation, the evaporation rates over single daily intervals are not normally required. From such daily evaluations we have also determined mean rates over longer intervals, and have correlated these with observed evaporation and with several empirical evaporation predictors. Results of such an analysis using five-day intervals are presented elsewhere (STERNand FITZPATRICK, 1965). Our use of daily data in this study does not imply that we have evidence that changes in heat storage are always negligible on a daily time scale. Indeed, it may well be that intrinsic errors in the estimate due to the neglect of heat storage are as large as those which we have found arising from the use of different types of data. The findings we report here should be interpreted strictly in an comparative sense.
Agr. Meteorol., 3 (1966)225-239
229
ESTIMATES OF POTENTIAL EVAPORATION
ANALYSIS OF DATA
Energy component When direct measurements of net radiation are not available, the energy component is determined from the estimated net radiation using the relationship expressing the radiation balance: Qn
(1 - - a) Qt - - Qb
(2)
where Qn is the net radiation, a is the albedo coefficient, Qt is the total radiation, and Qb is the effective terrestrial radiation. H is then obtained by simple conversion of Qn to evaporation units using a conversion factor based upon the latent heat of vaporization of water. If direct measurements of Qt are not available it has been customary to estimate this from the relative duration of sunshine by an expression having the form:
Qt Qe
a ~ b-
n N
(3)
where Qe is the extra-terrestrial radiation, n is the observed duration of sunshine, N is the daylentgh, and a and b are empirical constants. However, in another study (FITZPATRICK and STERN, 1965) it was shown that a relationship of this form is unsatisfactory for estimating total radiation under overcast or nearly overcast conditions. At this site much improved estimates of Qt can be obtained from:
Qt Qe
(
n) 0.373 + 0.385 ~ -
0.0042
(4)
n + 0.0154 N
Direct measurements of the long-wave radiation flux outward from the surface, and between the atmosphere and the surface, are seldom available, and therefore Qb is generally estimated from meteorological data. Penman has proposed a single equation for Qb incorporating the Stefan-Boltzman relationship and based upon empirical expressions due to BRUNT (1932) and ANGSTROM (1924) which relate the downward long-wave radiation from the atmosphere to vapour pressure and cloudiness:
Qb=-aT4(a+ b~)(c
n
+d~-)
(5)
where a is the Stefan-Boltzman constant in appropriate units, T is the mean screen absolute temperature, ed is the vapour pressure, and n/N is the ratio of the duration of bright sunshine to day length. Penman proposes values of 0.56 and ---0.09 for a and b respectively (with ed in mm Hg) and 0.1 and 0.9 for c and d respectively. However, in this climatic environment values for a, b, c, and d equal to 0.352, --0.049, 0.3 and 0.7 respectively have been found to give much improved estimates of Qb (eq. 13 in FITZPATRICKand STERN, 1965). Agr. Meteorol., 3 (1966) 225-239
to
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.+..... y'/
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/.
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÷0.914
0'.1 0:2 0'.3 0'.4 015 Host. ( e s t i m a t e d f r o m n/N using eq.5 w i t h (cm/day)
//
/
Least squares regression: H= a + b Has t /" , a = 0.0091 _+0.0138~ b = 0.997 +_0.0254 - 1:1 re,ationship /.,'/% : ' " / + 2 . 0 x S.E. of estimate (+_ 0.063 cm/day),- , 4• •° . ' .".1' I%. )/ /%9" " "
........ Correlation c o e f f i c i e n t : Sample size, 3 0 4
------
Fig.1. The relationship between daily values of the energy component determined from measured net radiation and the estimated energy component, using Penman's formula for effective terrestrial radiation. (Centroid of regression shown by open circle.) A. Using observed total radiation data; energy component (Hest.) obtained without reference to observed duration of sunshine. B. Using estimates of total radiation; energy component (Hast.) obtained without reference to measured total radiation.
2
E
E 0.4
c ~ 0.5 L m
~u L Q6
c 0.7. o ._o
1:1 relationship
-o
Has t
....... + 2 . 0 x S.E. of e s t i m a t e (-+ 0.050 cm/day) /;".., "- ; I /,/--/' -~ . / , ' " C. . . . lati . . . . . f f i c i e n t : ÷ 0.947 ." / . _.~-/~', " o ~ , /
Least squares regression: H = a + b a = - 0 0 0 0 4 _ + 0 0 1 1 5 , b=I.0025_+ 0.0806
0.9
Z
Z
>
¢b
N >
>
b~
231
ESTIMATES OF POTENTIAL EVAPORATION
We have also shown that if Qt is known, improved estimates of the effective terrestrial radiation can be obtained if, instead of using the observed n/N in eq.5, values of n/N from an inverse relationship corresponding to eq.3 is used (eq.15 in FITZPATRICK and STERN, 1965). Two sets of daily estimates of the energy component (//est.) were evaluated from eq.2 using values of Qb calculated from eq.5 with the constants, a, b, c and d given above which we have found appropriate for this climatic environment. The first set was determined using the measured Qt and using for n/N in eq.5 the values determined from the inverse relationship corresponding to eq.3. This set of estimates is shown in Fig. I A plotted against observed energy component (H) determined from the measured net radiation. The second set was determined in similar manner using eq.2 and 5, but with Qt from eq.4 instead of the actual measured values, and with n/N in eq.5 from the observed duration of sunshine instead of the calculated values from the inverse relationship corresponding to eq.3. Fig.lB shows the relationship between the second set and the observed energy component. Agreement between the regression fitted by least squares and the one-to-one relationship is remarkably good when either total radiation or sunshine data are used as described above. In both cases 96~o of all points fall within the broken lines in Fig. 1A and B which are placed at twice the standard error of estimate. The above methods were repeated using an alternative formula which has been found to give estimates of Qb of approximately the same accuracy:
Qb
(
n)
cr T 4 (1.0 - - 0.936 × 10-~ T 2) 0.155 + N -
(6)
This relationship is based in principle upon findings of SWINBANK (1963) but the constants which are linked with the n/N term have been determined by regression analysis from our data (FITZPATRICK and STERN, 1965; eq.14). Results are shown in Fig.2A and B. There is good agreement between the centroid of the fitted regression and the corresponding point on the one-to-one relationship. The slopes of the fitted regression in this case depart further from one-to-one relationship than in Fig.lA and B but, considering the extent of the scatter, this disparity is not serious. As in Fig.lA and B, only about 4G of all points fall outside of plus and minus twice the standard error of estimate.
Aerodynamic component The aerodynamic component of Penman's potential evaporation is defined by the relationship:
A
(ea -- ea) f (u)
(7)
where e, is the saturation vapour pressure at the mean screen temperature, ed is the saturation vapour pressure at the dew point (i.e., the bulk vapour pressure of the air at screen height), and f (u) is a function of wind speed. Agr. Meteorol., 3 (1966)
225-239
0.6'
0.4.
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o.,
0.2
-
--
--
/
/
/
coefficient
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/
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°
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,
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0:4 0.5 0.6 Has t ( e s t i m a t e d from Qt " (cm/day)
/::..;
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/.,
/ ,"//,~ / /
//U:
/ z / z / / / / 1 1
/ ""
"" -• / ~ ° "
_+ 2.0 x S.E of e s t i m a t e (-+0.055 c m / d e y ) / ( •
1:1 r e l a t i o n s h i p
L e a s t squares regression: H = a +b Has t g = -0.064 ~ O.0141~ ~ = 1 f210 _+0.0257 "
Somple size: 2 6 9
Correlation
.........
-
--
,~
/
/ / ///
/ //
@
///
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•
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/
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O
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0.7-
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".
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~
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0.2 0.3 0.4 -O'.5 Nest. ( e s t i m o t e d f r o m n/N (cm/day)
/
,
/
./ / "
+_ 2.0 x S.E. of estimate (t O.66cm/doY)//'°;.
1:1
Least squores regression: H = a + b Nest. a= -0.0423 t 0.0159. b = 1.0965 -+0.0294
Correlation coefficient: +0.906 Sample s i z e : 3 0 4
.........
-
--
,, /
/
/
0.8
/
taa
Fig.2. The relationship between daily values of the energy component determined from measured net radiation and the estimated energy component ~- using a fornmla for effective terrestrial radiation based on relationship given by Swinbank. (Centroid of regression shown by open circle). A. Using o~ observed total radiation data; energy component (Hest.) obtained without reference to observed duration of sunshine. B. Using estimates of total radiation: energy component (Hest.) obtained without reference to measured total radiation.
o
E 0.3
E
i/~
-,~ 0 . 5
-
o
E vv 0.7"
"~ 0.8.
0.91
7
> Z
N > ,-.]
>
b~
233
ESTIMATES OF POTENTIAL EVAPORATION
The specific relationship proposed by PENMAN (1956, p. 16) defining the aerodynamic component is: / U2 \ A ---- 0.35 ( c a - ca) ~0.5 + 1-]O0-)
(S)
where A is in mm/day, ea and ea are in mm Hg, and (-72is the wind speed in miles/day at a height of 2 m. Daily values of the aerodynamic component were calculated from eq.8. In Fig.3 the relationship is shown between these and the measured evaporation from the Piche and sunken tank evaporimeters. Although there is a wide scatter in the points, particularly in the case of the tank evaporation, there is clearly a linear relationship in each case. The regression equations defining A in terms of these measurements are: 0.0172 + 0.621 Ep
(9)
A ---- 0.0211 + 0.747 E,
(10)
A and:
where Ep and Et are the measured evaporation in cm/day from the Piche and tank evaporimeters respectively. It is clear from Fig.lA and B that the basic methods proposed by Penman give good agreement between the estimated and observed energy component providing reliable constants appropriate for the climatic environment have been obtained. Except over the lower range of values, errors in the daily estimates of H are not appreciably larger when estimates are made from sunshine data than when measured total radiation is used. This, of course, again assumes that the relationship between total radiation and duration of sunshine is reliable and has been identified for the particular climatic environment. These findings are of interest since often data for duration of sunshine are the only data available. It is important to note here that the extrapolation of relationships between Qt/Qe and n/N to localities having distinctive cloudiness characteristics or differing greatly in latitude should be approached with caution. A comparison of Fig.l and 2 indicates that Swinbank's proposals can be used effectively to estimate the energy component without the necessity for vapour pressure data. It is clear that errors in the estimated energy component are not appreciably larger when eq.6 is used in place of eq.5. Thus, if vapour pressure data are not available, Penman's potential evaporation may still be estimated provided a suitable approximation of the aerodynamic component can be made from evaporimeter data. In general, our findings indicate that errors in the final estimation of the energy component are likely to be greater due to inappropriate constants in the empirical relationships required by the method, rather than to errors in total radiation or sunshine records from instrumental causes or other deficiencies. Throughout this study we have used the measured net radiation over a wellwatered crop as reference values for the energy component. It seems probable that Agr. Meteorol., 3 (1966)
225-239
234
E.A. FITZPATRICK
A N D W . R. S T E R N
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Fig.3. Relationships between daily values of aerodynamic ved Piche evaporation (A), and observed tank evaporation
component (B).
and the corresponding
Agr. Meteorol., 3 ( 1 9 6 6 )
obser-
225-239
235
ESTIMATES OF POTENTIAL EVAPORATION
what has been found here would apply equally well had the reference data been related to a free water surface (with the correct albedo coefficient). The daily values of the aerodynamic component calculated from eq.8 ranged widely during the course of these observations, the highest being 1.75 cm/day in October and the lowest being 0.07 cm/day in January. In view of the marked seasonal contrasts in vapour-pressure deficit of this environment, it seems likely that a wider range in the aerodynamic component would rarely be experienced. The reliability of evaporation measuring devices such as the Piche instrument or tank evaporimeters for purposes of estimating evaporation from an extended water surface has often been seriously questioned on the grounds of their diverse responses to local conditions. In Israel, STANHILL (1962) using average data over 10-day periods has demonstrated a close linear relationship between the measured Piche evaporation and Penman's aerodynamic component. An empirical linear relationship between evaporation from the Standard Australian tank evaporimeter and saturation deficit has long been known (PRESCOTT, 1938) and has been used for a variety of purposes. The observed Piche and tank evaporation thus appear to offer practical alternatives to the instrumentation required for determining the aerodynamic component according to eq.8. When using daily data, we find definite evidence of seasonal variations in the relationships between the observed evaporation from both the Piche and tank evaporimeters and the calculated aerodynamic component. Since we have been unable either to associate these seasonal differences with other meteorological measurements or offer a physical explanation for' them, and since the contribution of the areodynamic term to the final estimate of potential evaporation is normally small compared with that of the energy component, we consider that the use of other than a single, generalized relationship for the entire year is not justifiable for this purpose. Nonetheless this problem merits further investigation, particularly as there is a suggestion that the seasonal variations referred to here may be related to the degree of mass advection. It is of interest that in Fig.3 the scatter of points is appreciably greater in the case of tank evaporation than with the Piche. It would seem that much of this increased scatter is attributable to the high sensitivity of this instrument to changes in the energy balance within the micro-environment of the immediate surrounds of the tank.
ALTERNATIVE MODES OF ESTIMATING POTENTIAL EVAPORATION
It has been shown that both the energy and aerodynamic components of Penman's evaporation formula can be estimated with reasonable accuracy in a variety of ways from several sources of data. The potential evaporation estimates determined from the measured net radiation and with eq.8 used for the areodynamic component were taken as reference values for purposes of comparing the errors in Eo resulting from various modes of estimation. Daily potential evaporation (Eo) was calculated using eq.1 with all combinations of the estimates of H (from eq.5) and of A. Frequency Agr. MeteoroL, 3 (1966) 225-239
236
E. A. FITZPATRICK AND W. R. STERN
TABLE I MEANS AND STANDARDDEVIATIONS(cm/day) OF ERRORS rN ESTIMATEOF POTENTIAL EVAPOTRANSPIRATION BY ALTERNATIV~MOOESOF COMPUTATION (Sample size: 260 days for all m o d e s of c o m p u t a t i o n )
Energy component from observed duration of sunshine
Energy component from observed total radiation
Energycomponent from observed net radiation
4.00711 0.0028 0.0451 0.0020
--0.0011 0.0024 0.0383 0.0017
Reference data
0.0052 0.0041 0.0645 0.0029
0.0004 0.0039 0.0604 0.0027
0.0025 0.0023 0.0371 0.0016
~0.0082 0.0043 0.0693 0.0031
---0.0026 0.0043 0.0687 0.0030
---0.0005 0.0030 0.0475 0.0021
Aerodynamic component from standard method Mean S. E. o f m e a n S.D. S. E. of S . D .
Aerodynamic component .from Piche evaporimeter Mean S. E. o f m e a n S.D. S. E. o f S . D .
Aerodynamic component from tank evaporimeter Mean S. E. o f m e a n S.D. S. E. of S . D .
1 M e a n differs significantly from zero at P < 0.05.
distributions of the errors (i.e., differences between the reference values and the daily estimates of potential evaporation by alternative modes of computation) were prepared. These distributions were compared with Gaussian distribution curves having the same means and standarct deviations as the samples (see Table 1). An application of the t test reveals that with one exception, the calculated means of the distributions shown in Table I do not differ significantly (at P < 0.05) from zero. For all modes of computation, the errors are well approximated by the "normal" curve. A distinct trend toward increasing errors with the use of data requiring an increasing number of assumptions and connecting relationships is evident from the standard deviations given in Table I. From the wide scatter of points in Fig.3 it might at first be anticipated that large errors in the estimated potential evaporation would be incurred when working from the Piche or tank data. However, from the standard deviation shown in Table I it is seen that errors in this direction are of about the same magnitude as those which result when total radiation or duration of sunshine is used in place of measured net radiation. Our experience would suggest that errors in the estimates of Eo resulting from alternative data would not be appreciably larger than those represented by the standard deviation in Table I had eq.1 been used in lieu of eq.5. Agr. Meteorol., 3 (1966) 225-239
I
1 2 3 4
x × ×
x × ×
× x x x x × × x
×
x × ×
×
x
× × ×
Sunshine 3 Total Net radiation 4 radiation
Sunshine z Total Net radiation ~ radiation x
Energy component with vapour pressure term for eff'eetive terrestrial radiation ~
Energy component with or w i t h o u t vapour pressure term for effective terrestrial radiation s
x
×
x
×
x
x
x
× ×
Sunshine 3 Total Net radiation a radiation
Energy con~onent without vapour pressure term for effective terrestrial radiation
Aerodynamic component from evaporimeter 1
Aerodynamic component from standard Penman's method
Afode of computation
Appropriate relation between measured evaporation and aerodynamic c o m p o n e n t is required. With vapour pressure term, appropriate regional constants are required for calculating effective terrestrial radiation. Suitable relation between n/N and Qt/Qe is required. Also reliable albedo coefficient (a). Reliable albedo coefficient (a) is required.
Sunshine recorder Solarimeter Net radiometer M a x i m u m - m i n i m u m thermometers Wet-bulb and dry-bulb thermometers Anemometer Evaporimeter
Instrumentation
I N S T R U M E N T A T I O N R E Q U I R E D FOR V A R I O U S MODES OF C O M P U T I N G P E N M A N ' S P O T E N T I A L E V A P O R A T I O N
TABLE 1I
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238
E. A. FITZPATRICK AND W. R. STERN
In Table II are summarized the combinations of instruments that are required for each mode of computting Eo, assuming either eq. 5 or 6 is used in estimating the effective terrestrial radiation. For experimental purposes, satisfactory determinations of daily potential evaporation can be achieved with no more extensive instrumentation than maximum and minimum thermometers, a net radiometer, and a Piche evaporimeter (or some similar instrument responding to both dryness of air and to wind). At the broader level of regional assessment of potential evaporation, it would appear that a network of stations equipped with m a x i m u m - m i n i m u m thermometers, simple sunshine recorders and instruments such as the Piche evaporimeter would appear practicable. As we have already noted, however, we have detected a degree of dissimilarity in the relationship between the Piche observations and the aerodynamic component between seasons, and it would seem that similar differences between stations having distinctive climates would also occur. Also, it would appear that this instrument, like the tank evaporimeter, is highly sensitive to peeularities of site and to the mode of installation and maintenance. Extrapolation of relationships between Piche evaporation and the aerodynamic component should thus be considered with some caution. Regardless of whatever substitute instrumentation which might be employed to extend the network of stations contributing usefal data, it remains essential that accurate measurements be made of total radiation, net radiation (preferably over several standard reference surfaces)and atmospheric moisture content at selected stations which are situated such that they can, insofar as is possible, be regarded as representative of their macroclimatic environments.
ACKNOWLEDGEMENTS
We wish to thank Mr. S. J. Rance and Mr. C. F. Massey for maintaining the equipment and carrying out the observations in the field, and Mr. K. T. Hannan, Mrs. A. Kamarowski, and Mr. S. J. Rance for assistance with the computations.
REFERENCES
ANGSTROM,A., 1924. Solar and terrestrial radiation. Quart. J. Roy. Meteorol. Soc., 50 : 121-126. BERRY, G., 1964. The evaluation of Penman's natural evaporation formula by electronic computer. Australian J. Appl. Sci., 15 : 61-64. BRUNT, D., 1932. Notes on radiation in the atmosphere. Quart. J. Roy. Meteorol. Soc., 58 : 389-418. BUDYKO, M., 1956. Teplovoi Balans Zemnoi Poverkhnosti. Gidrometeorologicheskoe Izdatel'stvo, Leningrad, 255 pp. (English translation by STEPANOVA, N. A., 1958. The Heat Balance qfthe Earth's Surface. U.S. Dept. Comm., OfficeTech. Serv., Washington, 259 pp) COMMONWEALTHBUR, METEOROL., 1954. Australian Meteorolo¢ical Observer's Handbook. Government Printer, Melbourne, 148 pp. FITZPATRICK, E. A. and STERN,W. R., 1965. Components of the radiation balance of irrigated plots in a dry monsoonal climate. J. Appl. Meteorok, in press. Agr. Meteorol., 3 (1966) 225-239
ESTIMATES OF POTENTIAL EVAPORATION
239
FRITSCHEN, L. J., 1963. Construction and evaluation of a miniature net radiometer. J. Appl. Meteorol., 2 : 165-172. FUNK, J. P., 1959. Improved polythene-shielded net radiometer. J. Sci. Instr., 36 : 267-270. HOUNAM, C. E., 1961. Evaporation in Australia. Commonwealth Bur. Meteorol., Bull., 44 : 88 pp. LAMOUREUX,W. W., 1962. Modern evaporation formulae adapted to computer use. Monthly Weather Rev., 90 : 26-28. METEOROL. OFFICE, 1956. Handbook of Meteorological Instruments, 1. Instruments for surface observations. H.M. Stationary Office, London, 458 pp. PENMAN, H. L., 1948. Natural evaporation from open water, bare soil, and grass. Proc. Roy. Soc. (London), Set. A, 193 : 120-145. PENMAN, H. L., 1956. Evaporation--An introductory survey. Neth. J. Agr. Sci., 4 : 9-29. PENMAN, H. L., 1963. Vegetation and hydrology. Commonwealth Bur. Soil Sci. ( Gt. Brit.) Tech. Commun., 53 : 124pp. PRESCOTT, J. A., 1938. Indices of agricultural climatology, d. Australian Inst. Agr. Sci., 4 : 33-40. PRESCOTT, J. A. and STIRK, G. B., 1951. Studies on the Piche evaporimeter. Australian J. Appl. Sci., 2 : 243-256. RADIATION COMM. I.A.M., 1958. Radiation instruments or measurements. Ann. Intern. Geophys. Year, 6 : 371-466. SLATYER, R. O. and MCILRO¥, I. C., 1961. Practical Microclimatology with Special Reference to the Water Factor in Soil-Plant-Atmosphere Relationships. UNESCO, Paris, 308 pp. STANH1LL,G., 1962. The use of the Piche evaporimeter in the calculation of evaporation. Quart. J. Roy. Meterorol. Soc., 88 : 80-82. STERN, W. R., 1965. The seasonal growth characteristics of irrigated cotton in a dry monsoonal environment. Australian J. Agr. Res., 16 : 347-366. STERN, W. R. and FITZPATRICK,E. A., 1965. Calculated and observed evaporation in a dry monsoonal environment. J. Hydrol., 3 : 297-311. SWINBANK, W. C., 1963. Long-wave radiation from clear skies. Quart. d. Roy. Meteorol. Sue., 89 : 339-348. YOUNG, C. P., 1963. A computer programme for the calculation of mean rates of evaporation using Penman's formula. Meteorol. Nag., 92 : 84-89.
Agr. Meteorol., 3 (1966)225-239