Comparison of evaporation from barley with Penman estimates

Agricultural Meteorology, 15(1975) 49--60 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

COMPARISON

OF EVAPORATION

FROM BARLEY WITH PENMAN

ESTIMATES

D. R. GRANT

Meteorological Office, Bracknell (Great Britain) (Received December 15, 1974; accepted February 5, 1975)

ABSTRACT Grant, D. R., 1975. Comparison of evaporation from barley with Penman estimates. Agrie. Meteorol., 15: 49--60. Measurements of evaporation from barley using a neutron moisture meter are compared with estimates from the Penman formula. Values of aerodynamic resistance (r a) in 1971 are calculated from profile measurements of wind and temperature and empirical relationships are derived between ra, crop height and wind speed. The surface diffusive resistance (rs) is calculated throughout the 1971 season (using the generalised Penman formula derived by Monteith, 1965) from measurements of net radiation, soil heat flux, temperature, vapour pressure (ra, assumed to be equal to the resistance to transfer of water vapour) and evaporation either obtained by the Bowen ratio method or from a weighing lysimeter. A relationship is then derived between r s and leaf area index and a function of soil moisture deficit. The same formula is used in conjunction with the empirical values of r a and r s to derive estimates of evaporation in 1970. These show good agreement with the measured values. The aim is to obtain results of practical use and the empirical relationships are therefore kept as simple as possible, using only easily measured or estimated quantities. INTRODUCTION Penman's (1948) equation for evaporation:

s ( R - G) + 7.53' (1 + 0 . 0 0 5 3 7 u ) { e s ( T ) - e} XE =

W m -2

(1)

s+ T can strictly be applied o n l y to a short grass surface with a plentiful supply of w a t e r . As it u s e s o n l y e a s i l y m e a s u r e d q u a n t i t i e s , it is, h o w e v e r , o f t e n u s e d t o o b t a i n e s t i m a t e s o f e v a p o r a t i o n f r o m c r o p s o t h e r t h a n grass in c o n d i t i o n s o f i n c o m p l e t e p l a n t c o v e r a n d w i t h c o n s i d e r a b l e soil m o i s t u r e d e f i c i t s . The generalised Penman formula derived by Monteith (lot.cir.) (eq.2) can b e u s e d f o r a n y t y p e o f c r o p e v e n if w a t e r s u p p l y is r e s t r i c t e d , b u t a k n o w l e d g e

50 NOTATION List o f s y m b o l s

c~ d d e es(T ) h

= s p e c i f i c h e a t o f air = z e r o p l a n e d i s p l a c e m e n t t a k e n as 0.6 h ( G r a n t , 1 9 7 5 ) = no. o f d a y s since the p r e v i o u s 24-h rainfall g r e a t e r t h a n 2 m m = vapour pressure (mbar) = S.V.P. at t e m p e r a t u r e T ( m b a r ) = c r o p h e i g h t ( m e a s u r e d by o b s e r v i n g f r o m a d i s t a n c e m a r k s o n a p o l e in t h e crop) = V o n K a r m a n ' s c o n s t a n t (= 0 . 4 1 ) = g r e e n leaf area i n d e x ( i n c l u d i n g a w n s a n d ears) = a e r o d y n a m i c r e s i s t a n c e to t r a n s f e r o f m o m e n t u m = r e s i s t a n c e to t r a n s f e r o f w a t e r v a p o u r = s u r f a c e diffusive r e s i s t a n c e ( d e f i n i t i o n s of r s w i t h o t h e r s u f f i x e s are given in the text) = s l o p e o f S.V.P. a g a i n s t t e m p e r a t u r e g r a p h (at m e a n o f air a n d s u r f a c e t e m p e r a t u r e ) ( m b a r K -I ) = f r a c t i o n o f r a d i a t i o n at t o p o f c r o p r e a c h i n g g r o u n d ( o r t i m e ) = w i n d s p e e d (in c m sec ' in e q . 1 ) = friction velocity = c o n s t a n t f a c t o r giving r e d u c t i o n in r a d i a t i o n i n t e n s i t y in c r o p = a d j u s t e d soil m o i s t u r e deficit (see p. 57) = height above ground = roughness parameter = drag c o e f f i c i e n t at a b o u t 1 m a b o v e the t o p o f t h e c r o p = d r a g c o e f f i c i e n t derived f r o m eq.4 = drag c o e f f i c i e n t derived f r o m e q . 8 = soil h e a t f l u x = h e a t f l u x i n t o air = r a d i a t i o n p e n e t r a t i n g to b o t t o m o f n t h l a y e r = net radiation = temperature = p s y c h r o m e t r i c c o n s t a n t (= 0 . 6 5 5 m b a r K -~ ) = e v a p o r a t i o n rate = air d e n s i t y stability correction factor for m o m e n t u m transfer

k n ra rv rs s t u u, x y z z0 CD

CD4 CD8 G

It I~ R T XE p @n

is r e q u i r e d diffusive

of the resistance resistance

(rv) to transfer

(r s) of the evaporating

of water

vapour

and the surface

surfaces:

s ( R - G ) + p C p / r v { e s ( T ) - e} XE =

s + 7(I + rs/r~)

(2)

To obtain the values of rv it can be assumed that r~ = ra and the latter can be obtained from profiles of wind and temperature. For rs, measurements of humidity gradient and evaporation rate are also necessary. The evaporation rate is not usually known (in fact the measurement of evaporation is the objective), and profile measurements require elaborate instrumentation. If

51

empirical relationships could be derived for rv and rs in terms of relatively simple measurements, it might be possible to use eq.2 to obtain good estimates of the evaporation from a crop throughout the season. COMPARISON

OF ACTUAL

EVAPORATION

WITH PENMAN'S

FORMULA

Figs.1 and 2 show, for 1970 and 1971 respectively, the accumulated evaporation as measured by the neutron probe (using the method described by E

100

80 •"~ u.s

60

T

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NEUTRON PROBE PENMAN MONTEITH

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Fig. 1. A c c u m u l a t e d

MAY

JUNE

JULY

I B 18 AUGUST 1970

e v a p o r a t i o n in 1 9 7 0 as m e a s u r e d b y t h e n e u t r o n p r o b e ( x ) , as calcu-

lated from the Penman

f o r m u l a ( e ) a n d as o b t a i n e d

from eq.12 (circled dots). The crop

h e i g h t is a l s o s h o w n .

Grant, 1 9 7 0 ) and as obtained from eq.1. The crop height is also plotted. There are considerable differences in the results obtained in the two seasons, but there are some c o m m o n features which were also found in similar comparisons made in earlier years. It is seen that using Penman's formula there is: (1) an over-estimation of evaporation early in the season; (2) a period, after a good crop cover is established, when the Penman and actual evaporation are nearly equal; in some years the actual evaporation can exceed the Penman value during this stage; (3) a very considerable over-estimation of the evaporation when the crop is ripe.

53 ~oo ~-

~

~

SO --

~O 60

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20 0

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l

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NEUTRON

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MONTEITH

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•

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MARCH

31

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310

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~0

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I

2o

f

30

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9

19 JUNE

I

29

i

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9

19 JULY

I9

2

AUGUST 1971

Fig.2. Accumulated evaporation in 1971 as measured by the neutron probe ( x ) , as calculated from the Penman formula (-) and as obtained from eq.12 (circled dots). The crop height is also shown. T h e reasons f o r these d i f f e r e n c e s are easy to explain qualitatively. Early in the season m o s t of the e v a p o r a t i o n is f r o m bare soil. A f t e r rain the soil surface dries q u i c k l y and the e v a p o r a t i o n rate f r o m d r y soil is low. T h e result is t h a t o n the average the P e n m a n f o r m u l a gives an o v e r - e s t i m a t e e x c e p t in cont i n u o u s l y w e t periods. As the p l a n t c o v e r increases, the e v a p o r a t i o n f r o m the p l a n t b e c o m e s m o r e i m p o r t a n t and w h e n there is nearly c o m p l e t e c o v e r the P e n m a n rate can be e x c e e d e d (if t h e r e is a plentiful s u p p l y of water) because the value o f rv is l o w e r for a tall c r o p t h a n f o r a s h o r t grass surface. F o r long p e r i o d s in 1971 there was r e m a r k a b l e a g r e e m e n t b e t w e e n the actual evaporation and the P e n m a n e s t i m a t e s despite quite high soil m o i s t u r e deficits. T h e e f f e c t on the e v a p o r a t i o n rate o f the l o w e r values of rv m u s t , t h e r e f o r e , have been a l m o s t e x a c t l y c o m p e n s a t e d by the higher value of r s due to t h e high soil m o i s t u r e deficits. Finally the r e d u c t i o n in the e v a p o r a t i o n rate late in the season can be e x p l a i n e d by t h r e e factors: (1) the small a m o u n t o f green leaf area; (2) the shading of the g r o u n d b y the c r o p which reduces the e v a p o r a t i o n f r o m the soil w h e n it is wet; (3) the inefficient t r a n s f e r m e c h a n i s m within the c r o p c a n o p y resulting in a low rate of r e m o v a l o f w a t e r v a p o u r into the free a t m o s p h e r e . An a t t e m p t is n o w m a d e to explain all these d i f f e r e n c e s in t e r m s of variations in rv and rs t h r o u g h o u t the season and to use eq.2 to o b t a i n b e t t e r e s t i m a t e s o f e v a p o r a t i o n t h a n can be o b t a i n e d f r o m the P e n m a n f o r m u l a .

53 THE RESISTANCE (rv) TO TRANSFER OF WATER VAPOUR It will be a s s u m e d t h a t in eq.2 r a Fv. This a s s u m p t i o n m e a n s t h a t the " b l u f f b o d y e f f e c t " discussed b y T h o r n ( 1 9 7 2 ) has b e e n neglected. It can easily be s h o w n t h a t XE derived f r o m eq.2 is n o t very sensitive to e r r o r s in r~. In fact, p u t t i n g H = R - G - XE, XE is i n d e p e n d e n t of r v w h e n H / X E = 7 / S . By definition: =

rv ~- ra = u / u ~

(3)

and CD = U2,/U 2

(4)

rv ~- ra = 1 / u C D

(5)

M e a s u r e m e n t s w e r e m a d e in 1970 and 1971 of wind, t e m p e r a t u r e and h u m i d i t y profiles o v e r the barley crop. Details of these and the m e t h o d used to d e t e r m i n e u, f r o m the e q u a t i o n : du u, = k(z - d) d z ~ 1

(6)

are described b y G r a n t (1975). Using t h e s e values of u. and eq.4, CD at the m i d d l e o f t h e five levels of m e a s u r e m e n t ( k e p t at a b o u t 1 m a b o v e the t o p o f t h e c r o p as it grew) was calculated and d e n o t e d b y CD4. In n e u t r a l c o n d i t i o n s Cm -- 1 and eq.6 can be solved to give: u,

u = -

k

z-d

ln--z0

(7)

F r o m eqs.4 a n d 7: k2

Values o f CD d e n o t e d b y CDS have b e e n o b t a i n e d f r o m an empirical equation derived b y p u t t i n g d -- 0.6h and z0 = ah + 0.1 (where z0 and h are in c m ) in eq.8. T h e value o f a was varied f r o m 0.10 to 0.16. T h e 0.1 was a d d e d to ah to allow values o f h = 0 to be used. T h e values o f CDS were p l o t t e d against daily m e a n values of CD4 t h r o u g h o u t t h e entire season and an e x a m p l e o f t h e t y p e o f result o b t a i n e d is given in Fig.3. This is the graph o b t a i n e d f o r z0 = 0 . 1 4 h + 0.1. A very n o n - l i n e a r r e l a t i o n s h i p is shown. T h e n o n - l i n e a r i t y is less w h e n a = 0.16 b u t the s c a t t e r a b o u t the best fit straight line is greater. T h e p r o b a b l e e x p l a n a t i o n of t h e non-linearity is t h a t either z0 or d or b o t h are

54 CDB

x X

X

.04

x

d = 0.6h

x x

x

Zo = 0.14h + 0,1

x

X x

;x x

~x x X X

Xx ~

X

~x

•0 3

X

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X

X

~(x

X

x X

xW

Xx

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X

x

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x

x

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x

x

x

Xx

x

X

× X xxX

X

~ x-Y.,,X x )I(xX'~x'"

•01

x x

x

×

x× ~ ~

×X

0

Fig.3. Comparison

1

I

I

I

.01

02

03

04

C~a

o f d r a g c o e f f i c i e n t s c a l c u l a t e d f r o m e q s . 4 a n d 8.

d e p e n d e n t on t h e drag c o e f f i c i e n t and are n o t simple f u n c t i o n s o f t h e crop height. Despite the non-linearity, CDS with d = 0.6h and z0 = 0.14h + 0.1 gives an a p p r o x i m a t i o n to CD4 which is within +.005 on 74% o f occasions. The biggest p r o p o r t i o n a l error is w h e n C D = 0.01 ( c r o p height = 20 cm) w h e n CD8 overestimates CD4 by a b o u t 50%. As CDvaries by a f a c t o r o f 10 over the season a 50% error m i g h t n o t be i m p o r t a n t . In the calculations to follow, the values o f d = 0.6h and z0 = 0.14h + 0.1 are used. It was f o u n d t h a t a b e t t e r fit to the data c o u l d be o b t a i n e d f r o m a second o r d e r p o l y n o m i a l in h viz. : CD = 0.003 + 2.4"10--4 h + 1 . 9 " 1 0 - 6 h 2

(9)

There is no physical e x p l a n a t i o n for this e q u a t i o n and it c a n n o t be used for o t h e r crops.

55 THE SURFACE DIFFUSIVE RESISTANCE (rs) Eq.2 can be r e - w r i t t e n as:

Fs

=

r7 /sH l 7Ec°I es' ' I ~7

- -

--

- e

2a,

w h e r e H = R - G - ~.E. Daily m e a n values of r s can be o b t a i n e d b y averaging, over the daylight hours, the h o u r l y m e a n values o f rs derived f r o m e q . 2 a using h o u r l y m e a n values of CD, u, R, G, T and e at a height of a b o u t l m a b o v e the t o p o f the crop, in c o n j u n c t i o n with eq.5 and m e a s u r e m e n t s of e v a p o r a t i o n b y either the l y s i m e t e r o f the B o w e n ratio m e t h o d . In using eq.5 f o r rv it is again a s s u m e d t h a t rv = ra b u t r~ derived f r o m e q . 2 a is n o t sensitive to errors in rv. In f a c t w h e n H / X E = ~//s, r~ is i n d e p e n d e n t of r v and during m o s t o f t h e season the value of H / X E is n o t m u c h d i f f e r e n t f r o m 7/s. T h e e r r o r in r~ derived h o u r l y is u n a c c e p t a b l y high in the early m o r n i n g and late a f t e r n o o n w h e n the evaporation rates are low. As a result, daily m e a n values o f r~ c a l c u l a t e d f r o m h o u r l y values can have large errors. In this p a p e r the daily m e a n values of r~ are o b t a i n e d f r o m m e a n values of all the variables b e t w e e n 0 4 h 0 0 a n d 2 0 h 0 0 . If t h e r e were an in-phase r e l a t i o n s h i p b e t w e e n a n y t w o t e r m s f o r m i n g a p r o d u c t in e q . 2 a the values of rs o b t a i n e d b y this m e t h o d w o u l d differ f r o m the m e a n of the values of r~ c a l c u l a t e d e v e r y hour. A c o m p a r i s o n with the h o u r l y m e a s u r e m e n t s o f r~, h o w e v e r , shows t h a t the errors in the values of r~ calculated f r o m the daily m e a n values of the variables are u n i m p o r t a n t c o m p a r e d with the range of v a r i a t i o n of r~ f o u n d to o c c u r during the season. T h e v a r i a t i o n of r~ t h r o u g h o u t the season is s h o w n in Fig.4. The values of r s on d a y s f o l l o w i n g rain (r~w) (i.e., o n days w h e n w a t e r s u p p l y is n o t restricted) are circled a n d t h e dashed line indicates the variation of these values t h r o u g h o u t the season. As e x p e c t e d rsw is high early in the season a n d decreases to a m i n i m u m w h e n the c r o p c o v e r is at a m a x i m u m in May. It t h e n increases again a n d b e c o m e s v e r y high at t h e end o f the season f o r the reasons a l r e a d y discussed. The f o l l o w i n g d e r i v a t i o n o f an e x p r e s s i o n for r s is n o t i n t e n d e d to be rigorous, b u t it is given t o s h o w t h a t t h e r e is s o m e physical r e a s o n i n g b e h i n d the e m p i r i c a l r e l a t i o n s h i p suggested. T h e e v a p o r a t i o n f r o m the soil will d e p e n d t o a large e x t e n t on t h e a m o u n t of r a d i a t i o n falling o n it. When o n l y a f r a c t i o n (t) of the r a d i a t i o n at the t o p of the c r o p reaches the g r o u n d t h e e v a p o r a t i o n will be r e d u c e d . I t is a s s u m e d t h a t the full r a d i a t i o n reaches the g r o u n d a n d t h e resistance t o d i f f u s i o n t h r o u g h the soil surface is increased b y an a m o u n t d e p e n d i n g on t. T o k e e p the m o d e l as simple as possible it is a s s u m e d t h a t : 1 r' ss

t rss

56

where r'~sis the apparent resistance to diffusion through the soil surface when shaded by the crop and rss is the true value when there is no shading. F o l l o w i n g M o n t e i t h ( 1 9 6 5 ) if n = green leaf area index and the s t a n d is divided into layers, each with leaf area index equal to u n i t y , we can write: I n = xnI0 where I0 is the i n c i d e n t radiation, In is the r a d i a t i o n p e n e t r a t i n g to the b o t t o m of n t h layer and x is a c o n s t a n t ( < 1 . 0 ) d e p e n d i n g primarily on the g e o m e t r y of the leaves. By an a r g u m e n t similar t o t h a t used t o o b t a i n an a p p a r e n t diffusive resistance o f the soil surface we can write: 1

1 -

! £ sc

(1-xn) rsc

where 1 - x n is the f r a c t i o n of the radiation i n t e r c e p t e d by the green leaves, r'sciS the a p p a r e n t resistance to diffusion o f water t h r o u g h the c r o p and r~c [s

190

910

I

zs 6

8

× x

5

x

4

5

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x

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3j

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0-9 0.8 0.7 I 0-6

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0.2 I

0.2 x

0.1

I 31

I 10

I 20 APRIl_

I 30

I 10

I 20 MAY

I 30

I 9

I 19 JUNE

I 29

I 9

I 19 JULY 1971

0.1 29

Fig.4. Values of r s calculated from mean values of CD, u, R, G, T, e and E from 04h00 to 20h00 (roughly hours of daylight). Circled crosses are values of r s after wet days. The squares are values calculated from eq.10. is the diffusive resistance o f the c r o p if all leaves were fully sunlit. A n u m b e r o f a s s u m p t i o n s are implied in this relationship w h i c h are barely justifiable, b u t it does give s o m e i n d i c a t i o n o f h o w r'sc m i g h t vary with n. F r o m a corn-

57 parison of t h e f r a c t i o n o f the i n c i d e n t r a d i a t i o n reaching the g r o u n d with the leaf area i n d e x b e f o r e a n y senescence o c c u r r e d , a value o f x = 0.69 was obtained. It is n o w assumed t h a t the resistances of the soil and plants are in parallel (which is n o t a rigorous a s s u m p t i o n ) and we obtain: 1

-

rs

t

1

~- - - ( 1 - x n )

rss

rsc

The e f f e c t of a soil m o i s t u r e deficit m u s t n o w be considered. When there is appreciable rainfall on the previous day and the soil is w e t in the m o r n i n g a suffix " w " will be a d d e d to the n o t a t i o n for the resistances and we o b t a i n 1 --

t =

rsw rssw

1-x~ +

-

-

(10)

rscw

This e q u a t i o n should fit the " d a s h e d " line in Fig.4. Using values o f t o b t a i n e d f r o m the m e a s u r e m e n t s of radiation above and below the crop and measurem e n t s of leaf area index m a d e t h r o u g h o u t the season, a r e a s o n a b l y g o o d fit to the line is o b t a i n e d if rssw = 1.0 sec c m - ' and rsc w = 0.2 sec c m - ' . T h e squares in Fig.4 give the values o b t a i n e d f r o m eq.10. It w o u l d be e x p e c t e d t h a t rss w o u l d increase very rapidly if n o f u r t h e r rain fell and a s t u d y of the results for 1971 suggests a relationship: rss = rssw (1 + 0.5 d ' - l )

(11)

where d' is the n u m b e r of days since the previous daily rainfall o f m o r e t h a n 2 m m . T h e e x a c t f o r m of this relationship is u n i m p o r t a n t . A n y relationship ensuring t h a t rss increases rapidly in dry w e a t h e r w o u l d be equally good. A m o r e precise k n o w l e d g e o f the variation o f rscwith soil m o i s t u r e deficit is necessary. It appears f r o m the results in 1971 t h a t during active vegetative g r o w t h rsc is always r e d u c e d after rain to the a p p r o p r i a t e value of r~¢w for the time o f year, w h a t e v e r the value of the soil m o i s t u r e deficit after t h e rain. Availability o f w a t e r near the soil surface appears to be the i m p o r t a n t f a c t o r in d e t e r m i n i n g r~c which can still be low even w h e n t h e r e are large soil m o i s t u r e deficits at lower levels in the soil. Thus, it w o u l d be e x p e c t e d t h a t t h e r e would be a relationship b e t w e e n rs~ and w h a t we shall call " t h e adjusted soil m o i s t u r e d e f i c i t " in the t o p 30 cm of soil which is o b t a i n e d as follows. At all times in the season the soil m o i s t u r e deficit is p u t equal to zero after rain and increased during the following dry spell at the e v a p o r a t i o n rate until all the r e c e n t rain has evaporated; t h e r e a f t e r it reverts to the soil m o i s t u r e deficit b e f o r e the rain fell. A m a x i m u m o f 40 m m is i m p o s e d as this is a p p r o x i m a t e l y the m a x i m u m a m o u n t o f water which can be e x t r a c t e d f r o m the t o p 30 cm. (A higher limi~

58 should be used in h e a v y soil.) Using the 1971 m e a s u r e m e n t s it is f o u n d t h a t a g o o d fit to t h e d a t a can be o b t a i n e d b y p u t t i n g : rsc = Qcw (1 + 0 . 0 6 y ) w h e r e y -- t h e adjusted soil m o i s t u r e deficit in m m as d e f i n e d above. The resulting empirical value of r~ is t h e n : 1

t

1-

-

0.69 n

(12)

+

G

1.0 ( 1 + 0 . 5 d ' -

:~)

0.2 ( 1 + 0 . 0 6 y )

USE OF THE EMPIRICAL RELATIONSHIPS As an overall c h e c k on t h e empirical relationships derived f o r r a and rs, the e v a p o r a t i o n t h r o u g h o u t the 1971 season has b e e n c o m p u t e d f r o m eq.2 using eqs.5, 8, and 12 a n d daily m e a n values of R, G, T and e. As t h e 1971 d a t a were used to derive t h e e m p i r i c a l relationships this c o m p u t a t i o n o n l y serves to c h e c k t h a t the very severe a p p r o x i m a t i o n s and a s s u m p t i o n s m a d e are justifled b y the results. T h e results are p l o t t e d in Fig.2 w h e r e the i m p r o v e m e n t over t h e e v a p o r a t i o n calculated f r o m eq.1 is clearly shown. A m o r e severe test of the m e t h o d is o b t a i n e d b y a p p l y i n g it to t h e 1 9 7 0 data w h e n as seen f r o m Fig.1 t h e r e was a very c o n s i d e r a b l e d i f f e r e n c e b e t w e e n the actual e v a p o r a t i o n and t h e P e n m a n e s t i m a t e s . T h e e v a p o r a t i o n using eq.2 and the e m p i r i c a l values for r~ and r~ is seen to be a v e r y g o o d a p p r o x i m a t i o n to the actual e v a p o r a t i o n m e a s u r e d .

TIME OF BiAERGENCE 1971

1969

1970

, ~o r'L.-.-~:~+_ q,,,× \

\ ~x

6

\

\

~

\~+,

i

•

"\

1969 Idrilled 25/3/69/

•

1971 '~drilled 2612/71)

._x..~__x_x.- x- --

~+

r--X._x~~

./"

~+~+__+__+~J+

"~°-o--o~-o-,-._o_o~

•1,

21

-I-

i 31

I

I

iO

20

APRIL

30

i I IO 20 MAY

i 30

[ i 9 19 JUNE

J 29

i i 9 19 JULY

i 29

J 8

Fig.5. Variation of t during seasons 1969, 1970 and 1971.

59 In applying the m e t h o d to 1970 and 1971, m e a s u r e m e n t s o f t h e f r a c t i o n of incident r a d i a t i o n reaching the g r o u n d (t) and leaf area i n d e x (n) were available. If t h e y were n o t available a very rough m e a s u r e m e n t of t c o u l d be o b t a i n e d b y estimating by e y e the p r o p o r t i o n o f the field in which the soil is visible and an estimate o f 1 - x n c o u l d be o b t a i n e d b y an estimate o f the f r a c t i o n of the field c o v e r e d by green crop. A r o u g h guidance can also be o b t a i n e d if the c r o p is barley f r o m the variation of t and 1 - x , t h r o u g h o u t the season in 1969, 1 9 7 0 and 1971 s h o w n in Figs.5 and 6. A high degree of precision in the estimates o f t and n is n o t necessary. 10 -69 n 9 8

÷ x •

1969 197(i 1971

,

APRIL

MAY

JUNE

JULY

Fig.6. Variation of (1--0.69 n) during seasons 1969, 1970 and 1971.

CONCLUSIONS F r o m m e a s u r e m e n t s o f daily m e a n values of net radiation, soil h e a t flux, rainfall, t e m p e r a t u r e , v a p o u r pressure and wind at a b o u t 1 m above the t o p o f a crop, and estimates o f the crop height, p e r c e n t a g e of field covered b y green c r o p and p e r c e n t a g e o f soil visible it is possible to o b t a i n a considerable improvem e n t on the P e n m a n estimates o f e v a p o r a t i o n by using the generalised e q u a t i o n and empirical relationships for r a and rs. If net radiation and soil heat flux m e a s u r e m e n t s are n o t available, the latter can be neglected w i t h o u t serious error and estimates of net r a d i a t i o n can be m a d e by one of the well k n o w n m e t h o d s (e.g., P e n m a n , 1948). ACKN OWLEDGEMENTS All m e m b e r s o f the staff o f the Meteorological Office Research Unit at Cambridge c o n t r i b u t e d to this w o r k and I am grateful to t h e m , Dr. O. R a c k h a m , Dr. E. J. M. K i r b y and the Director o f the Plant Breeding Institute for all the help t h e y have given.

60 REFERENCES Grant, D. R., 1970. Some measurements Of evaporation in a field of barley. J. Agric. Sci. Camb., 75: 433--443. Grant, D. R., 1975. Comparison of evaporation measurements using different methods. Q. J. R. Meteorol. Soc. In press. Monteith, J. L., 1965. Evaporation and Environment. Syrup. Soc. Exp. Biol., 19: 205--34. Penman, H. L., 1948. Natural evaporation from open water, bare soil and grass. Proc. R. Soc. Lond., Ser. A, 193: 120--145. Thorn, A. S., 1972. Momentum, mass and heat exchange of vegetation. Q. J. R. Meteorol. Soc., 98: 124--134.