Theoretical and measured evaporation rates from an exposed piche atmograph

Agricultural Meteorology, 30 (1983) 1--11

1

Elsevier Smence Pubhshers B V , Amsterdam -- Printed m The Netherlands

THEORETICAL AND MEASURED EVAPORATION RATES FROM AN EXPOSED PICHE ATMOGRAPH* KYAW THA PAW U and MASSAMBA GUEYE**

Department of Agronomy, Purdue University, West Lafayette, IN 47907 ( U S A ) (Received February 21, 1983, rewsmn accepted May 10, 1983)

ABSTRACT Paw U, K T and Gueye, M , 1983 Theoretmal and measured evaporation rates from an exposed Pmhe atmograph Agrm M e t e o r o l , 30 1--11 The Pmhe at m om e te r Is still used throughout the world, a century after its mventmn As with most evaporation instruments, the meaning and utlhty of Pmhe readings have been questioned In the present study, a hnearlzed energy budget for a leaf ~s used to predict the daily evaporation from a Piche atmograph This approach showed a one-toone relatmnshlp with observed evaporatmn, and accounted for 70--90% of the observed variance Successful predmtlons were possible even when the meteorologmal data were taken at 12-h intervals, although the most accurate predmtmns were based on data taken at 1-h intervals Sensitivity analysis predicts that Pmhe evaporation is strongly affected by mr temperature, relative humidity, wind speed and long-wave radlatmn, albedo and short-wave radmtmn had lesser effects The present study supports the idea that the Pmhe atmograph models the potentml evapotransplratmn of an ind~wdual leaf

INTRODUCTION

Evaporation and evapotransplratlon are extremely important variables in the field of agrometeorology, t h e y influence the growth and even the survival of agronomic crops and livestock, forest specms, and influence the water use strategms of h u m a n societies Many forms of models and instruments have been developed to measure and/or estimate evaporation, potential evaporation, evapotransplratlon, and potential evapotransp~ratlon The most c o m m o n instruments used to measure evaporation processes are lyslmeters, pan and tank evaporlmeters, and atmometers The Pmhe atmograph, whmh is a recording Plche evaporlmeter, measures evaporation from a saturated filter paper disc which is chpped to a feeder tube (Klauslng, 1965, Brutsaert, 1982) In the version used in this study, a plexlglass disc was located 0.10 m above the paper disc to protect the paper from damage due to rain. The Plche atmograph closely resembles a single broad leaf, it has the advantage of being symmetrical m respect to horizontal wmd direction, is approximately the same thickness as a leaf, and records evaporation with a time resolution of less than an hour For this reason, it has been postulated that the Pmhe evaponmeter and atmograph will s~mulate * Indiana Agricultural Expemment Station Journal Paper No 9845 ** Now at Meteorologm Natlonale, Dakar, Senegal

0002-1571/83/$03 00

© 1983 Elsevmr Scmnce Pubhshers B V

potential leaf evapotransplratlon well (Stanhfll, 1962; Klausmg, 1965, World Meteorologmal Orgamsatlon, 1969) Varmus workers have examined the relationship between the Pmhe evaponmeter, pan evaponmeters, and potential evapotransp~ratmn as calculated by various models (Prescott and Stlrk, 1951, De Vnes and Venema, 1954, Stanhlll, 1962, Thom et al, 1981). The exposure of the Pmhe vaned from study to study, some had the Pmhe fully exposed to the weather elements (De Vnes and Venema, 1954, Lmvfll et al, 1978), while others have studmd the Plche reside some form of shelter (Prescott and Stlrk, 1951, Stanhfll, 1962, Fitzpatrick and Stern, 1966, Brochet and Gerbmr, 1972. Heme, 1981, Thom et al, 1981), or a wind tunnel (Roth, 1961). For a Pmhe reside a shelter, the vapor deficit has been considered the mam term controlhng evaporation, with the ventilation of the shelter also bemg a factor (Prescott and Stlrk, 1951, Stanhfll, 1962; Brochet and Gerbmr, 1972, Thom et al, 1981) Stanhlll (1962) concluded that the Pmhe m a shelter was not a reliable predictor of average weekly and monthly evapotransplratmn, although it was very econommal For fully exposed Pmhes, all of the terms of the standard energy budget for surfaces are relevant Prescott and St~rk (1951) used equations for heat and mass transfer that have smce been modified, and they could not measure long-wave radlatmn so they had to estimate it In our model, standard heat and mass flux equations were used along with radiation budget measurements including Eppley pyrgeometer data. As the coeffmmnts for current leaf-heat and mass-flux equations were derived from filter paper leaf-analogs m wind tunnel flux (Gates, 1968), it was expected that some success would be achieved m modeling the exposed Pmhe In the present work, ewdence is presented showing that an exposed Pmhe atmograph can be modeled quite accurately with a semi-theoretical hneamzed leaf energy budget similar to those of Penman (1948), Prescott and St~rk (1951), De Vnes and Venema (1954), Raschke (1956, 1960), Roth (1961), Montelth (1973), Gates (1962, 1980), Norman (1979) and Thom et al. (1981). This indicates that the Piche may be a better instrument than prewously thought Two hypotheses were tested (1) relatively accurate forecasts for Pmhe atmograph evaporation can be made with data collected at intervals common for typical meteorological networks, (2) certain variables are more important to potential evaporation processes than others. Hypothes~ (1) was tested by predicting the daily evaporation from the lhche based on data collected at 1, 2, 3, 6 and 12 h intervals The predicted values of evaporation for a day ending at midnight were calculated by summing up the evaporation amounts for each observation interval. The correlation between predicted and observed dmly values of evaporation was tested by regression analysis Hypothesis (2) was tested by varying the values of a synthetic data set used to estimate evaporation from the Pmhe The variables were changed by 20 or 50%, and the estimated evaporatmn changes noted. Three base

levels w e r e used, o n e f o r low, o n e f o r m o d e r a t e a n d o n e f o r high e v a p o r a t m n rates MATERIALS AND METHODS An e n e r g y b u d g e t e q u a t i o n was u s e d t o e s t i m a t e t h e e n e r g y a n d mass flux f r o m an e x p o s e d P m h e filter p a p e r disc ( o u t s i d e a w e a t h e r shelter) T h e e q u a t i o n was h n e a r l z e d so t h a t it was a f i r s t - o r d e r h n e a r f u n c t i o n o f t h e d i f f e r e n c e b e t w e e n t h e air a n d filter p a p e r t e m p e r a t u r e s , i n s t e a d o f a q u a t r m f u n c t i o n o f t h e p a p e r t e m p e r a t u r e P r e d m t l o n s b a s e d o n this m o d e l were compared with observations taken with an exposed Pmhe atmograph during the months of August and September 1975, and June 1976 Meteorologmal variables w e r e o b t a i n e d f r o m t h e P u r d u e U m v e r s l t y A g r o n o m y F a r m w e a t h e r statmn Observed Pmhe evaporatmn data were put through a simple quahty analysis screen a n d t h e sensitivity o f t h e e n e r g y b u d g e t e q u a t m n t o changes m m e t e o r o l o g m a l a n d o t h e r v a r m b l e s was e x a m i n e d . T h e e n e r g y b u d g e t o f a leaf has b e e n t r e a t e d e x t e n s i v e l y b y such a u t h o r s as R a s c h k e ( 1 9 6 0 ) a n d G a t e s ( 1 9 6 8 , 1 9 8 0 ) (KS+Kt)(1--a)+LS+Lt

= 2H + 2LE + 2eoT~

(1)

w h e r e KS is t h e s h o r t - w a v e r a d m t m n f l u x c o m i n g d o w n , K f is t h e s h o r t - w a v e r a d m t m n f l u x going up, a is t h e e f f e c t i v e a l b e d o a v e r a g e d o v e r t h e wavelengths o f t h e solar r a d m t m n flux, L$ is t h e l o n g - w a v e r a d m t m n f l u x c o m i n g d o w n f r o m t h e s k y , L t is t h e l o n g - w a v e r a d m t m n f l u x going u p f r o m t h e g r o u n d , H is t h e sensible h e a t flux, L E is t h e l a t e n t e n e r g y flux, a n d e o T ~ is t h e long-wave r a d m t m n f l u x r a d m t e d b y t h e filter p a p e r , w i t h all u m t s b e i n g W m -2 T h e sensible h e a t t e r m , b a s e d o n w i n d t u n n e l e x p e r i m e n t s , is (Gates, 1968, 1980) H

= 9 . 1 4 ( V / D ) ° s (T1 - - Ta) = pCp(T~ - - T a ) / r h

(2)

w h e r e V is t h e w i n d s p e e d m m s -1, D is t h e l e a f or disc d m m e t e r m m , p is t h e d e n s i t y o f mr m k g m -3 , Cp is t h e specffm h e a t o f mr m J k g -1 K, rh IS t h e a e r o d y n a m m resistance t o h e a t t r a n s f e r , T1 is t h e leaf t e m p e r a t u r e a n d Ta is t h e mr t e m p e r a t u r e m K or C T h e r e s i s t a n c e t e r m rhlS t h u s a f u n c t m n o f V a n d D (see eq 2) T h e l a t e n t e n e r g y t e r m L E was h n e a r l z e d , f o l l o w i n g P e n m a n ( 1 9 4 8 ) , M o n t e l t h ( 1 9 7 3 ) a n d T h o m et al ( 1 9 8 1 ) LE

=

[(pCp)h'l{[A(Tp

- - T a ) + (es - - e a ) ] / r a }

(3)

w h e r e L is t h e l a t e n t e n e r g y o f e v a p o r a t i o n m J k g - 1 , E is t h e e v a p o r a t i o n r a t e m kg m -2 s -1, ~ is t h e p s y c h r o m e t n c c o n s t a n t m Pa C - 1 , ra IS t h e aerod y n a m m r e s i s t a n c e t o w a t e r v a p o r f l u x m s m -1 , Tp is t h e P m h e filter p a p e r t e m p e r a t u r e m C, Ta is t h e air t e m p e r a t u r e m C, A is t h e slope o f t h e satur a t i o n v a p o r p r e s s u r e as a f u n c t i o n o f a~r t e m p e r a t u r e m Pa C -1 , e a is t h e

water vapor pressure m the atmosphere m Pa, and e, is the saturated water vapor pressure at the au temperature m Pa The equation for aerodynamic resistance to water vapor transfer is (Gates, 1968, 1980)

ra

= 200 (D/V)0 5

14)

where the constant 200 so 5 m-l was derived from wmd tunnel experiments and 1s compatible with flat-plate transfer theory (Gates, 1968). Equation 1 may be solved for the leaf temperature Z’i and evaporation flux E either by iterative processes or by lmeanzation of the long-wave term mTf , where E is the emissivity and u is the Stefan-Boltzmann constant The linearized equation estimated results similar to the iterative equation, but was more economic m terms of computer usage and was, therefore, used Tf

= T,4 + 4 T,3(T, - T,) If the amount

of absorbed

R, = (KJ + Kt)(l then the evaporation E = 0.5 & - eoTz

-a)

mcommg

radiation

(R,) is defined

as

+ LJ. + Lt

(6)

from the Piche filter paper can be shown to be + I4e@

+ E(pC,)lr,

I) He, - e,UAl

(7)

where the terms of the equation have been previously defined. This result is derived m a manner sirmlar to the Penman-Mont&h equation, with the leaf-air temperature difference term (Tl - T, ) being eliminated (Norman, 1979; Thorn et al., 1981). An emissivlty of 1 0 was assumed for the filter paper; the disc diameter was 5 cm. Spectrophotometnc data showed the wet filter paper had an average albedo of 0.86 for visible radiation and 0.57 for near-infrared radiation <1.8pm wavelength. All other data (visible, near-infrared and long-wave radiation, wmd speed, vapor pressure deficit, and arr temperature) were obtained from the computerized Purdue-National Weather Service (NWS) Agricultural Weather station located at the Purdue University Agronomy Farm, 10 km NW of West Lafayette, Indiana (40’28’N 87’OO’W); the mstrumentation was described by Dale et al. (1982). The data sets for the months of July 1976, and August and September 1975 were selected because they were the most complete Some correction was necessary to calculate the wmd speed at the Plche height because the atmograph was at 0.45 m and the anemometer at 7 m Neutral conditions above a grass surface were assumed, which resulted m a value of V at the Plche height equal to 0.7 times the measured wmd at 7 m Based on information supplied by NWS personnel responsible for the operation of the automated system, the accuracy of the mstruments was assumed to be better than. 1 0 C for temperature, 1.0 m s-* for wind speed,

5

20% of the reading for radiation mstruments, and lo-20% for the relative humidity. The Plche atmograph data included apparent spurious readings Some of these were eliminated by using the followmg criteria, which resulted m the omlsslon of 40% of the days (1) Readings for any day on which data were mlssmg and could not be estimated (2) Any data for a day on which the observer had recorded problems with the instrument (3) Any data for a day on which the evaporation was zero, this usually indicated preclpltatlon (4) Any data for a day on which the atmograph trace showed breaks > 4 mm These breaks represented sticking due to friction m the mechanism and were usually followed by periods of a flat atmograph trace, or they represented large condensation or preclpltatlon events RESULTS

AND

DISCUSSION

The observed dally Plche evaporation values for each of the months of August and September 1975, June 1976, and all months pooled together were regressed on the dally predicted Plche evaporation values (based on 1, 2, 3, 6 and 12 h observation intervals) The regressions were of the form Y = blX + bo, where b1 1s the slope, b,, 1s the Y intercept, X 1s the predicted Plche evaporation and Y 1s the observed Plche evaporation. The statistical parameters, their standard errors and the coefflclents of determmatlon R2 are summarized m Tables I and II Scattergrams of selected cases for June 1976, and the hourly observation intervals for August and September 1975 and all months combined, are shown m Figs 1 and 2. For the sake of brevity, the figures for the other cases for August and September 1975 and for all months combined have been omitted, as they follow the same pattern as the June 1976 cases The values of R2 for each month and for all months combined mdlcate that the model 1s a good predictor of the observed Plche evaporation As expected, the R2 values generally show some decrease as the observation mterval mcreases. However, it 1s mterestmg that the decrease 1s small m all cases except for August 1975 The values of R2 (0.904.93) for June 1976 were higher than for the other months, implying higher quality meteorologlcal and Plche data. The R2 for all of the months combined ranged from 0.83 to 0.88, which demonstrates the ability of this model to predict dally Plche evaporation The slopes for all cases, shown m Tables I and II, were not significantly different from bl = 1, at the 0 10 level of significance, except for 1, 2 and 3 h observations for September, 1975 The Y intercepts for the individual months were not slgmflcantly different from zero, except for the 6 and 12 h

TABLE I L i n e a r regreaslon c o e f f m m n t s b 1 a n d b0, w i t h s t a n d a r d errors a n d c o e f f m m n t of d e t e r m i n a t i o n R 2 for t h e e q u a t i o n Y -- bl X + b0, w h e r e Y m t h e o b s e r v e d a n d X is t h e p r e d m t e d P m h e dally e v a p o r a t m n m 10 -3 m, for J u n e 1 9 7 6 , A u g u s t 1 9 7 5 a n d S e p t e m b e r 1 9 7 5 Observation interval ( h o u r s )

b 1 ~ s(b I )

b0 + s(b0)

R2

Standard error (ram)

0 0 0 0 0

1 1 1 1 1

June 1976 1 2 3 6 12

1 1 1 1 1

06 06 04 09 09

0 0 0 0 0

07 07 08 09 09

0.61 0 56 0 61 - - 0 34 - - 1 34

0 0 0 0 0

71 72 81 77 99

93 92 90 93 90

37 38 56 37 61

August 1975 1 2 3 6 12

1 24 123 113 0 91 0 65

024 028 024 0 22 0 20

130 137 1 66 2 40 a 2 84 a

098 095 100 0 94 1 04

068 069 064 0 59 0 48

135 134 144 1 54 1 74

131 b 1305 1 25 b 1 13 0.92

013 013 0.13 0 14 0.13

036 039 0 65 0 96 1 01

059 061 0 60 0 64 0 74

085 084 0 83 0 80 0 74

1 30 133 1 37 1.50 1 69

September 1975 1 2 3 6 12

a S i g n i f i c a n t l y d i f f e r e n t f r o m 0 0 a t t h e 0 1 0 level b S l g m f m a n t l y d i f f e r e n t f r o m o n e a t t h e 0 10 level

T A B L E II L i n e a r r e ~ e s a l o n c o e f f i c i e n t s b i a n d b0, w i t h s t a n d a r d e r r o r s a n d c o e f f i c i e n t o f d e t e r m i n a t i o n R for t h e e q u a t i o n Y = b i X + b0, w h e r e Y is t h e o b s e r v e d a n d X is t h e p r e d i c t e d P l c h e daffy e v a p o r a t i o n in 1 0 " 3 m, f o r all m o n t h s c o m b i n e d

Observatlon interval (hours)

b I +--s(b i )

1 2 3 6 12

1 02 1 01 0 99 0.96 0 90

b0 -+s(b0)

0 05 0 05 0 05 0 05 0.06

1 47 a 1.50 a 1 57 a 1 56 a 1 09 a

as1gmfmantly dlfferent from 0 0 at the 0 10 level

0 0 0 0 0

35 35 37 38 46

R ~

Standard error (ram)

0.88 0 88 0.87 0 86 0 83

1.44 1 46 1 52 1 57 1 75

21

18

/x

OI

ob 0

E E 15 0

c-

•

•

f::: O

"O 12 O E}

u..l 9

/x

"O (D

0

(D LD

/x

..Q 6 O

/x

L .f o •

3

-0

o~•

3

6 9 12 Predicted Evaporation

15 in m m

18

21

F~g i Scattergram of dally values m 1 0 - 3 m of predicted and observed evaporatmn for June 1976, for I h (open circles),6 h (closed mrcles) and 12 h (open triangles) observatmn intervals

observations m August However, the b0 for all m o n t h s c o m b i n e d was different than 0 at the 0.10 level of slgmfmance Scattergrams f or the data sets, such as Figs. 1 and 2, also help m identifymg any errors of this model. The departure o f the predm t ed values from the observed ones seem to be mainly m the regnme of low and m e d m m evaporation An error analysis was c a m e d o u t to aid m i nt erpret at i on of the data Tables III and IV summarize t he percentage changes m evaporation rates given a percentage change m each variable, the ratio of the change m the evaporation rate and the change m the varmble is also gwen m these tables The tables show the mean value o f all of the vaxmbles, the sensltsvlty analysis was carried o u t by changing one variable at a time, and holding all others at their respectwe mean values The tables show that the variables whmh

/

21

1.1 18

0 O

0

E

E 15 ¢..

0

m

cO m ~-

0

0

J

12

Ib-

0 Q. 0

O0

LU 9 10

A

A

t..

¢/}

6

0 ~_ 0

0

~0~'--

•

3

~f

/^

I

3

o

1

I

J

I

6 9 12 15 Predicted Evoporotion ,n mm

i

18

21

Fig 2 Scattergrarn of daffy values m 10 -3 m of predicted and observed evaporat=on for 1 h observation intervals, for June 19~/6 (open circles), Augtmt 1975 (closed circles) and September 1975 (open triangles)

influence evaporation the m o s t are air temperature, wind speed, relative humidity and long-wave radiation, while all other variables have a lesser effect. Estimates of error for the instrumental readings, coupled with sensitivity analysis yields an approximation o f h o w much error may be caused by unstru. mental error. Estimates of L~g~unental error, along with the resultant errors m estlmated evaporation rates (h -1 ) are s h o w n m Table V. The m a x i m u m mstrumentaUy-induced error for tow evaporation rates is 1.2 (10 -3) m day -1 and for medium evaparation rates is 2.3 ( 1 0 - 3 ) m d a y - 1. This indicates that a significant percentage o f the slope and Y.mtercept errors could have been due to instrumental error. These errors would have to be biased so that they resulted m underestimates of evaporation, especmtly on days with much evaporation

+20 -+20 +-20 +-20 -+20 -+20

(%)

A variable

+-2 -+6 -+8 -+4 -+2 +-9

3 ( 1 0 -2) m m / ° C 5 ( 1 0 - 2 ) m m / m s -1 9 (10-s) mm/W m-: 2 (10 -4) m m / W m -2 7 (10 -4 ) m m / W m -2 4( 10 -3) m m / 1 %

AET/A variable

21 3 480 800 280 0

1°C 1 m s -1 W m -2 W m -2 W m -2 50

0 57

Albedo, near-infrared

Temperature Wind speed Short-wave (up and d o w n ) Long-wave (up and d o w n ) Near-infrared (up and d o w n ) Relatwe h u m i d i t y

0 86

Mean value

Albedo, vlmble

Vamable

+50 +50 + 50 + 50 +-50 +-50

--40 +40 --65

(%)

A variable

+2 +7 -+9 -+4 -+2 +9

3 ( 1 0 -2) 3 ( 1 0 -2) 0(10 -s) 2 (10 -4) 7 (10 -4) 4 ( 1 0 -3)

mm/°C m m / m s -1 m m / W m -2 m m / W m -2 m m / W m -2 mm/l%

+ 8 3 ( 1 0 -4) m m / 0 1 --1 7 ( 1 0 - 3 ) m m / 0 1 +1 2(10-3) mm/0 1

AET/A variable

Changes m evaporation per u m t change m varmble, m e d m m evaporation rates and a p p r o x i m a t e l y 50% variation

T A B L E IV

21 3 480 800 280 0

Temperature Wind speed Short-wave (up and d o w n ) Long-wave (up and d o w n ) Near-infrared (up and d o w n ) ' Relative h u m i d i t y

I°C 1 m s -1 W m-2 W m -2 W m- 2 50

Mean value

Varmble

Changes m e v a p o r a t m n per u m t change m varmble, m e d m m evaporation rates and 20% v a r m t m n

T A B L E III

T 2 13 T 0 63 T 0 08 T 0 50 + 0 07 --11

- - 0 18 - - 0 13

- - 0 14

{AETt /IA varlablet

+21 + 0 57 + 0 08 + 0 41 -I-0 07 --11

IA__ETI/I A_varmble 1

¢D

10 TABLE V E s t i m a t e d e v a p o r a t m n h -1 e r r o r d u e t o n o m i n a l i n s t r u m e n t e r r o r , m e d m m e v a p o r a t m n rates

Temperature Wind speed Short-wave radmtmn Long-wave radmtlon Near-infrared radlatlon Relatlve humldlty Total possible error

Nominal instrument error

Estimated evaporatmn error (10-3 m h -1 )

I°C 10% 20% 20% 20% 20%

0 0 0 0 0 0

021 020 008 067 015 094

0 225

CONCLUSIONS

Relatively accurate forecasts of exposed Piche atmograph evaporatmn can be made using a seml-theoretmal energy budget equation through the growing season. The equation was tested for the months of August and September 1975, and June 1976 m West Lafayette, Indiana. It accounted for 80% or more of the variance of observed dmly evaporation, based on meteorologmal data taken at 1, 2, 3, 6 and 1 2 h intervals. Error analysis mdmated most of the model error could have been caused by errors m the meteorological data. The error analysm also showed that the most important variables affectm_g Pmhe evaporation and, therefore, potentml leaf evapotransptratmn are mr temperature, wind speed, relative humidity and long-wave radmtmn. It is suggested that the Pmhe evaponmeters and atmographs are good analogs for potentml leaf evapotranspiration, because the equatmns used for modehng the Pmhe were origm~lly developed for leaves. The defmltmn used here for 'potentml leaf evapotranspimtion' m the evapotransptrataon from a leaf when water is not hmited, and when the physiological (mainly stomatal) resmtance is effectively zero. ACKNOWLEDGMENTS

Portlons of thls work were carned out by Massamba Gueye as part of a Masters Degree. M. Gueye was supported by the World Meteorological Orgamzatlon ( W M O ) and the National Oceamc and Atmospheric A d m m m tratlon ( N O A A ) during a leave of absence from the Senegalese Government. J Patrick McGarraban, who was supported under National Scmnce Foundation Atmospheric Scmnces Section grant number ATM-8021075 prowded some programming help. The authors thank Walter Stirm of the Nataonal Weather Servme (NWS), Kenneth Scheeringa, James Darnels, Jeffery Andresen and Professors Robert F Dale, James E. N e w m a n and John Snow

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