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Does transpiration limit the growth of vegetation or vice versa?
Journal of Hydrology, 100 (1988) 5748
57
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
[3] D O E S T R A N S P I R A T I O N LIMIT THE GROWTH OF V E G E T A T I O N OR VICE VERSA?*
J.L. MONTEITH
Resource Management Program, International Crops Research Institute for the Semi-Arid Tropics, Patancheru, A.P. 502 324 (India) (Received January, 1988; revised and accepted March, 1988)
ABSTRACT Monteith, J.L., 1988. Does transpiration limit the growth of vegetation or vice versa? J. Hydrol., 100: 5748. For hydrological or agronomic purposes, the potential rate of transpiration from vegetation is often calculated as a function of climatological variables, sometimes with the inclusion of a canopy resistance to water vapour diffusion. If, within leaves, the intercellular concentration of CO 2 is conservative, the canopy resistance must depend on the photosynthesis rate implying that potential transpiration depends on potential growth. The relevant form of the Penman-Monteith equation is developed to link water use efficiency with the conversion coefficient for solar radiation. When water is limiting, the maximum rate at which transpiration can occur depends mainly on the rate of extension of the root system and on the w a t e r " available" per unit soil volume. It follows that both potential and subpotential rates of transpiration are consequences of the assimilation of carbon by vegetation and its subsequent redistribution to form shoots and roots. THE QUESTION
Seminal papers published by Penman (1948) and Thorntwaite (1948) led to the definition o f " p o t e n t i a l " transpiration as the rate at which a stand of short, green vegetation loses water to the atmosphere when the supply to the root system is unrestricted. Although this definition is firmly entrenched in the literature of hydrology, micrometeorology and crop ecology, it is somewhat circular because it is difficult to define what ~'unrestricted" means in this context without introducing the concept of a maximum transpiration rate. Notwithstanding this small logical difficulty, it is clearly helpful to distinguish between potential and " a c t u a l " rates of transpiration, the former being determined mainly by the way in which foliage responds to a demand from the atmosphere and the latter by the way in which the soil matrix provides a supply to the root system.
Both potential and actual rates of transpiration have been used to estimate rates of dry matter production by crop stands. A common practice (Doorenbos Submitted as JA No. 773 by the International Crops Research Institute for the Semi-Arid Tropics.
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© 1988 Elsevier Science Publishers B.V.
58 and Kassam, 1979; Hanks, 1983) is to calculate potential transpiration rate (PT) from some version of the Penman formula and to estimate a corresponding maximum rate of dry matter production (PM) using a photosynthesis model. The amount of dry matter produced per unit of water transpired (q) can then be calculated as P M / P T . It is further assumed that, when water supply is limiting, the relation between actual dry matter production (AM) and actual transpiration is given by: 1
PM
n 1-~
-
(1)
where n is an index, justifiable dimensionally but often close to unity and rarely interpreted in terms of physiological mechanisms. This type of analysis is based on the assumption, usually implicit, that the rate at which a stand of vegetation accumulates dry matter depends on the rate at which it transpires water, whether the supply is limiting or not. It is beyond argument t h a t stomatal dimensions limit, but do not necessarily govern, rates at which both water vapour and C02 can reach the wet surfaces of cell walls from the atmosphere and vice versa. However, this identity of pathways does not imply that the carbon flux is necessarily controlled by the vapour flux. The purpose of this note is to argue t h a t it is usually the carbon flux that determines the vapour flux rather than the converse. A caveat is needed before this deliberately controversial paper continues. It deals with the loss of water vapour from the earth's surface solely in terms of transpiration and it is not concerned with the evaporation of water from the soil surface or from rain intercepted by foliage. However, this restriction does not invalidate general conclusions at the end of the paper or their relevance to the hydrological cycle in catchments where most of the ground is covered by vegetation during seasons when most solar energy is received. POTENTIALTRANSPIRATION Equations for the water vapour and carbon dioxide exchange of a single leaf will be considered first as a basis for deriving an expression for the potential rate of transpiration of a stand of vegetation. Suppose t h a t the mean mixing ratio of water vapour in the intercellular spaces of a leaf is ci (g vapour per g of air) and that the mixing ratio in ambient air is ca. The decrease in vapour c o n c e n t r a t i o n between leaf and air is p(c~ - c a) where p is the mean density of (moist) air in the system and the outward flux of vapour associated with this gradient is: E
=
p(cl
-
Ca)/(rs + rb)
(2)
where r s and rb are diffusion resistances for stomata and for the leaf boundary layer respectively.
59 The corresponding inward flux of CO2 can be written: P
=
p(Ca -- C~)/(r~ + r~)
=
pXCa/(r~ + rE)
(3)
where primes denote concentrations and resistances for CO2 transfer and x = 1 -
c;/c'~.
Because the air in substomatal cavities is effectively saturated, ci can be identified as the saturated vapour concentration at the mean temperature (T) of mesophyll tissue, i.e. cl(T) which is approximately an exponential function of T. The value of c~ is much less dependent on temperature and is determined mainly by the relative resistances to CO2 diffusion as a gas through the boundary layer and stomatal pores and in solution from the surfaces of cells surrounding the substomatal cavity to the sites of photosynthesis within the mesophyll cell complex (Jones, 1983). Laboratory evidence suggests that the ratio c~/c~ is '~somewhat conservative" (Farquhar and Wong, 1984) and that it may be treated as constant when the liquid phase component of resistance is changed experimentally, e.g., by altering the illumination of a leaf or by comparing the CO2 exchange of leaves from plants with different levels of nutrition. This behaviour implies that the liquid and gaseous components of resistance change in about the same proportion as a consequence of changes in stomatal aperture. The ratio y = rs/r' ~ is inversely proportional to the corresponding ratio of diffusion coefficients for water vapour and CO2 and has a value of 0.61. From eqns. (2) and (3), the stomatal resistance for water vapour diffusion can be written: r~
=
yr~
=
y{p(c'~x/P)-
rE}
(4)
so that: E
p(c~(T)
-
Ca)
(5)
+ (rb -- y r ~ )
(pxyc'a/P)
Commonly, the second bracketed term in the denominator is small compared with the first term so that the ratio of transpiration to photosynthesis can be expressed as a function of five dimensionless quantities: E/P
-
(ci(T)
-
ca)/(xyc'~)
(6)
The denominator can usually be treated as constant so t h a t E / P changes with the numerator alone. In the special case where the leaf and air temperature are identical, the numerator is proportional to the saturation vapour pressure deficit of the ambient air. In general, however, the system is not isothermal and the relation between E and P must then be obtained by taking account of the heat balance of the leaf and by eliminating surface temperature to obtain an expression of the Penman-Monteith type (Monteith, 1981), e.g.:
6O E
=
ARn/)~ + ? p [ c i ( T a )
-
A + 7*
ca]/rb
(7)
where: A = r a t e of c h a n g e of c~ (T) with t e m p e r a t u r e (K-l); R , = net flux of r a d i a t i o n absorbed by leaf ( J m 2s 1); ~ = l a t e n t h e a t of v a p o r i s a t i o n ( J g 1); Ta = t e m p e r a t u r e of a m b i e n t air; ~, = cp/). (K 1); cp = specific h e a t of air at c o n s t a n t pressure (J g-1 K - l ) ; and ~,* = 7(1 + rs/rh) = 7{1 + XyCa/(Prt~) - y r ~ / rb)/ from eqn. (4). 7 = cp/~(K-1); and 7* = 7( 1 + r J r b ) = 7{1 + x y c ' ~ / ( P r b ) - y r ~ / r a } from eqn.
(4). The same e q u a t i o n can be used to r e l a t e t r a n s p i r a t i o n and p h o t o s y n t h e s i s for a stand of v e g e t a t i o n if several symbols are redefined. The c o n c e n t r a t i o n s ca and c'~ must be m e a s u r e d at a specified r e f e r e n c e h e i g h t and b o t h rb and r~ must be replaced by r~, an a e r o d y n a m i c r e s i s t a n c e for h e a t or v a p o u r t r a n s f e r b e t w e e n the r e f e r e n c e h e i g h t and the effective s o u r c e of sensible h e a t in the canopy. The leaf resistances r~ and r~ are replaced by the c o r r e s p o n d i n g resist a n c e s for the c a n o p y t r e a t e d as a "big l e a f " , viz. r~ and r~. It follows that, for a canopy: ~'* j
[1 + X y C a / ( P r ~ ) - y]
(8)
Two assumptions implicit in m a k i n g the step from leaf to c a n o p y are: (1) t h a t x and c~ are the same for all leaves; and (2) t h a t the r a t i o of c a n o p y resistances for w a t e r v a p o u r and CO2, rJr'~ is the same as the r a t i o for single leaves, rs/r~ = 0.61. F r o m i n s p e c t i o n of eqn. (7), E increases as P increases implying t h a t E will r e a c h a " p o t e n t i a l " r a t e of t r a n s p i r a t i o n w h e n c a n o p y p h o t o s y n t h e s i s also r e a c h e s a m a x i m u m r a t e for a given e n v i r o n m e n t . To o b t a i n daily rates of p o t e n t i a l t r a n s p i r a t i o n it r e m a i n s to establish how net daily r a t e s of photosynthesis (g CO2m 2d 1) can be related to a more readily available q u a n t i t y - - a crop g r o w t h r a t e C (g dry m a t t e r m Z d 1). After i n t r o d u c i n g the gross assimilation per day (A) and the c o r r e s p o n d i n g r e s p i r a t i o n o v e r 24 h (Q) as i n t e r m e d i a t e variables, t h r e e f r a c t i o n s can be defined: (1) r e s p i r a t i o n as a f r a c t i o n of assimilation ( m = Q / A ) ; (2) the f r a c t i o n (n) of r e s p i r a t i o n which o c c u r s d u r i n g the period of assimilation (daylight); and (3) dry m a t t e r p r o d u c t i o n as a f r a c t i o n of net CO2 assimilation (z). Crop g r o w t h r a t e can now be expressed as a p r o p o r t i o n of the difference b e t w e e n net d a y t i m e CO2 uptake, P, and r e s p i r a t i o n at night, i.e.: C
=
z[P-
(1 - n ) Q ]
(9)
w h e r e a s the net d a y t i m e CO2 u p t a k e is given by the difference between gross assimilation A and d a y t i m e r e s p i r a t i o n n Q , i.e.: P
=
A-nQ
=
Q(1/m
-
n)
(10)
61
E l i m i n a t i n g Q f r o m eqns. (9) a n d (10) t h e n gives: C
=
zP(1 -
m)/(1 - m n )
(11)
As an e x a m p l e , if z :: 0.5, m = 0.45, a n d n = 0.7, t h e n C = 0.4 P. T h e m a x i m u m v a l u e of c r o p g r o w t h r a t e in a g i v e n e n v i r o n m e n t does n o t a p p e a r to differ m u c h b e t w e e n species w h e n t h e y a r e divided into a few m a j o r groups, two of w h i c h p h y s i o l o g i s t s r e f e r to as C3 a n d C4 ( d e p e n d i n g on the n u m b e r of c a r b o n a t o m s in the first p r o d u c t of p h o t o s y n t h e s i s ) . M o s t t e m p e r a t e v e g e t a t i o n b e l o n g s to the C3 c a t e g o r y ; the C4 class c o n t a i n s t r o p i c a l grasses a n d c e r e a l s (e.g. s u g a r cane, s o r g h u m ) a n d a n u m b e r of d e s e r t species (Jones, 1983). T h e m a x i m u m g r o w t h r a t e of C3 c r o p species in W e s t e r n E u r o p e is a b o u t 2 0 g m 2d 1 d u r i n g spells of w e a t h e r w i t h a v e r a g e cloudiness (Sibma, 1968), i n c r e a s i n g to a b o u t 3 0 g m 2d 1 on d a y s w i t h little cloud ( M o n t e i t h , 1978). C o r r e s p o n d i n g v a l u e s of P a r e 50 and 75 g m ~d 1 or 1.0-1.5 mg m ~s 1 as m e a n r a t e s of a s s i m i l a t i o n o v e r a 14 h day. T h e s e figures c a n n o w be used in eqn. (4) to give s t o m a t a l r e s i s t a n c e s for w a t e r v a p o u r t r a n s f e r . A s s u m i n g pC'aX = 0.18 for C3 species a n d a t y p i c a l a e r o d y n a m i c r e s i s t a n c e of ra 30 s m 1, the r a n g e of r c is from 90 to 54 s m c o n s i s t e n t w i t h field experience. In c l i m a t e s w h e r e C4 species are grown, m a x i m u m v a l u e s of C, a n d t h e r e f o r e of P, a p p e a r to be a b o u t 50% l a r g e r t h a n for C~ species ( M o n t e i t h , 1978); b u t w i t h x -- 0.7, t h e v a l u e of C'aX/P is a l m o s t t w i c e the v a l u e for C3 species. V a l u e s of rc p r e d i c t e d from eqn. (4) are t h e r e f o r e a b o u t 30% l a r g e r t h a n for C3 species in the s a m e e n v i r o n m e n t . It is possible to t a k e the a n a l y s i s one s t a g e f u r t h e r w i t h t h e o b j e c t i v e of e x p r e s s i n g p o t e n t i a l t r a n s p i r a t i o n as a f u n c t i o n of c l i m a t i c v a r i a b l e s only. It would be possible to use a model to p r e d i c t the d e p e n d e n c e of P on r a d i a t i o n , t e m p e r a t u r e , etc., b u t a m o r e direct a n d m o r e useful r o u t e is t h r o u g h the e v i d e n c e t h a t C is u s u a l l y an a l m o s t l i n e a r f u n c t i o n of r a d i a t i o n i n t e r c e p t e d by a c a n o p y , at l e a s t d u r i n g v e g e t a t i v e g r o w t h w h e n p o t e n t i a l r a t e s of t r a n s p i r a tion are likely to be achieved. T h e r e l a t i o n b e t w e e n C (g m 2d 1) and t o t a l s o l a r r a d i a t i o n S ( M J m 2d 1) c a n be w r i t t e n ( M o n t e i t h , 1977) as: C
=
(12)
feS
w h e r e ~ = f r a c t i o n of i n c i d e n t r a d i a t i o n i n t e r c e p t e d by a c a n o p y , a n d e = c o n v e r s i o n coefficient (g dry m a t t e r per M J of i n t e r c e p t e d radiation). B e c a u s e the p h o t o s y n t h e s i s r a t e of leaves u s u a l l y t e n d s to a m a x i m u m v a l u e as i r r a d i a n c e i n c r e a s e s (especially in C3 species), e is e x p e c t e d to d e c r e a s e s o m e w h a t as daily i n s o l a t i o n i n c r e a s e s . To find p o t e n t i a l t r a n s p i r a t i o n from a s t a n d c o m p l e t e l y c o v e r i n g the ground, f c a n be set at u n i t y a n d for C3 species g r o w i n g in t e m p e r a t e climates, t h e v a l u e of e, d e t e r m i n e d from field e x p e r i m e n t s w i t h a r a n g e of species, lies b e t w e e n 1.3 and 1.6 g M J i (Russell et al., 1988). F o r a n u m e r i c a l e x a m p l e , if e = 1.5 g M J ~ a n d C = 0.4 P as before, t h e n P = 3.8 C. (To k e e p u n i t s c o n s i s t e n t , S m u s t be e x p r e s s e d in M J m 2s 1 i m p l y i n g t h a t i n s o l a t i o n , as u s u a l l y r e p o r t e d in M J m 2 d 1, m u s t be divided by the d u r a t i o n of d a y l i g h t in seconds.) T h e n f r o m eqn. (4) w i t h pc'~ x = 0.18 g m 3 y = 0.6 a n d r a = 3 0 s m i: r,. = 0.610.18/(3.8 S) - 30]
=
1432/S - 18
62 A c c o r d i n g to this relation, the m e a n daily v a l u e of rc should d e c r e a s e from 1.3 to 0.65 s m 1 as the i n s o l a t i o n (for a 14 h day) i n c r e a s e s from 10 to 20 M J m "~ E q u a t i o n (8) can now be r e w r i t t e n as: ~'*~ =
t'{1 + j / ( S r a ) - y}
(13)
where: j
pc'axyz(1 -
=
m)
(14)
e(1 - rim)
E q u a t i o n (14) is c u m b e r s o m e but is p r e s e n t e d h e r e to show explicitly the set of p a r a m e t e r s , m o s t l y n o n d i m e n s i o n a l , on which j depends. In practice, j could be derived e x p e r i m e n t a l l y by using eqns. (7) and (13) to give: j
S r a { ( A / 7 ) ( R n / ~ E ) + p[ci(Ta) - Ca]/(raE) - (A/~' + 1
=
y)}
(15)
All the q u a n t i t i e s on the r i g h t - h a n d side of this e q u a t i o n are available directly from climatological records or can be e s t i m a t e d from them. F i g u r e 1 shows the d e p e n d e n c e of daily t r a n s p i r a t i o n r a t e on i n s o l a t i o n c a l c u l a t e d from eqn. (7). (The Appendix gives details of the way in which r a d i a t i o n , t e m p e r a t u r e and s a t u r a t i o n deficit were assumed to c h a n g e diurnally.) The d e p e n d e n c e of E on r a d i a t i o n is almost l i n e a r because trans p i r a t i o n r a t e is d o m i n a t e d by the supply of r a d i a n t e n e r g y b o t h d i r e c t l y and t h r o u g h the c a n o p y resistance. A f u r t h e r p o t e n t i a l source of n o n l i n e a r i t y is the d e p e n d e n c e of e on S w h i c h would emerge if the r e l a t i o n b e t w e e n P and r a d i a t i o n were e s t i m a t e d from a model in which the p h o t o s y n t h e s i s of
12
8
c
4
I0
20
Solar radiation (MJ m-2 d -I)
Fig. 1. Daily t r a n s p i r a t i o n from a s t a n d of v e g e t a t i o n c o m p l e t e l y c o v e r i n g t h e g r o u n d as a f u n c t i o n of d a i l y s o l a r r a d i a t i o n , c a l c u l a t e d from eqns. (7), (9) a n d (12) w i t h c o n s t a n t s as g i v e n in t h e text
and diurnal change of weather estimated from algorithms given in the Appendix. Air temperature at sunrise is given.
63 individual leaves was a hyperbolic function of irradiance. The dependence of E on temperature shown in the figure is almost entirely a consequence of the larger values of saturation deficit used at the higher temperature. ACTUALTRANSPIRATION In terms of the analysis already presented, the rate of transpiration from a stand of vegetation will be less than the potential rate when: (1) ground cover is incomplete; and/or (2) photosynthesis rates are suboptimal because of: (a) a shortage of water or nutrients; (b) ageing in a significant fraction of the foliage; and (c) attack by pests and diseases.
Incomplete ground cover To obtain an approximate estimate of transpiration rate from a stand of foliage which does not intercept all incident radiation, eqn. (7) can readily be modified by writing f S in place of f in the denominator. Little error is likely to arise if Rn is replaced by f Rn though the fractional transmission of net and of solar radiation are not generally identical. However, this procedure takes no account of the way in which the microclimate of a canopy depends on the wetness of the soil surface, a point explored by Choudhury and Monteith (1988) in a much more complex model of surface heat balance.
Shortage of water What mechanisms operate when the supply of water to a stand of vegetation cannot sustain transpiration at a potential rate? The closure of stomata is a plant's short-term response to the problem of balancing supply and demand but as soon as the transpiration rate falls below the potential value, the demand side of the balance becomes almost irrelevant it is the supply that matters. Supply is determined mainly by the rate at which roots are able to extract water and this process is usually discussed in terms of gradients of potential between water in the xylem vessels of roots and in the soil surrounding them. A more direct approach to the problem is provided by measurements of seasonal changes in soil water content as a function of depth, readily obtainable from measurements with neutron probes, for example. Measurements below stands of annual crops during periods when there is little input of water at the soil surface show that: (1) A root front moves downward through the soil at a velocity which Angus et al. (1983) reported was between 2 and 4 cm d 1 for a range of tropical species. For cereals in a temperate climate, the maximum rate appears to be about 2 c m d 1 (McGowan, 1974; Day et al., 1978). Much slower rates would be expected in soil that was compacted, very dry, or infertile but field evidence is too scanty to make generalisations.
64
(2) After t h e a r r i v a l of t h e r o o t front, the r a t e of e x t r a c t i o n of w a t e r d e c r e a s e s m o r e or less e x p o n e n t i a l l y w i t h t i m e ( P a s s i o u r a , 1983). This b e h a v i o u r c a n be m o d e l l e d in a simple way. S u p p o s e t h a t the w a t e r a v a i l a b l e at d e p t h z a n d t i m e t, e x p r e s s e d in cm 3 cm a, is: O(z, t) =
0(0) (exp - t/v)
(16)
where: t = t i m e m e a s u r e d f r o m the a r r i v a l of the r o o t f r o n t (d); 0 (0) = w a t e r a v a i l a b l e a t t = 0, a s s u m e d i n d e p e n d e n t of depth; a n d r - t i m e c o n s t a n t of e x t r a c t i o n process, also a s s u m e d i n d e p e n d e n t of d e p t h b u t e x p e c t e d to d e p e n d on r o o t l e n g t h per u n i t v o l u m e ( P a s s i o u r a , 1983). I f t' is t i m e m e a s u r e d f r o m the d a y w h e n the r o o t f r o n t s t a r t s to descend, t h e n t = t' - z / u w h e n z < ut. T h e r a t e of e x t r a c t i o n at d e p t h z a n d time t' is t h e r e f o r e g i v e n by: ~O(z, t)/~t
=
(1/~)0(0)[exp -
(t' - z/u)/~]
(17)
I n t e g r a t i o n w i t h r e s p e c t to z f r o m 0 to ut" gives the r a t e of w a t e r s u p p l y and t h e r e f o r e the t r a n s p i r a t i o n r a t e as: E
=
u0(0)[1 - e x p ( - t ' / z ) ]
(18)
It follows t h a t the r a t e of e v a p o r a t i o n a p p r o a c h e s a m a x i m u m v a l u e of uO(O), i n d e p e n d e n t of z w h e n t' is m u c h l a r g e r t h a n ~. T h e t o t a l a m o u n t of w a t e r e x t r a c t e d a f t e r a t i m e t' w h e n the r o o t s h a v e r e a c h e d a d e p t h z = ut' is found by i n t e g r a t i n g eqn. (18) w i t h r e s p e c t to t' to give: f Edt'
=
z0(0)[1 - (z/t)(1
- exp -- t'/z)]
(19)
w h e r e zO(O) is t h e t o t a l a m o u n t of w a t e r a v a i l a b l e in d e p t h z, a n d (T/t') [1 - exp - t'/z)] is t h e u n u s e d f r a c t i o n of t h a t w a t e r . W h e n t h e r e is no i n p u t of w a t e r f r o m the soil surface, this r e s i d u a l f r a c t i o n is e s s e n t i a l for t h e s u r v i v a l of p l a n t s if t h e i r r o o t s y s t e m s stop g r o w i n g before t h e y a r e m a t u r e , as in m o s t c e r e a l s d u r i n g t h e period of g r a i n filling. E v e n a t m a t u r i t y , it a p p e a r s t h a t crop s t a n d s o f t e n fail to a b s t r a c t all t h e w a t e r held in t h e r o o t zone and " a v a i l a b l e " in t e r m s of s o m e s t a n d a r d r a n g e of p o t e n t i a l s (e.g. 0.03-1.5 MPa). R i t c h i e (1981) a n d o t h e r s h a v e t h e r e f o r e s u g g e s t e d t h a t " a v a i l a b i l i t y " s h o u l d be r e p l a c e d by " e x t r a c t a b i l i t y " defined as t h e t o t a l a m o u n t of w a t e r e x t r a c t e d by c r o p r o o t s up to t h e d a y it is h a r v e s t e d ; b u t this p r o c e d u r e m a y n o t be logical if the f r a c t i o n is a f u n c t i o n of t i m e as eqn. (19) suggests. T h e m a x i m u m r a t e of e x t r a c t i o n uP(O) will be small w h e n a r o o t s y s t e m descends slowly in a l i g h t soil. F o r example, if u = 1 . 5 c m d ~ a n d 8(0) 0.1 cm3cm 3, the t r a n s p i r a t i o n r a t e c a n n o t exceed 1 . 5 m m d 1. In a t e m p e r a t e climate, t h e s u p p l y of w a t e r f r o m t h e r o o t s would be e n o u g h to m e e t the p o t e n t i a l t r a n s p i r a t i o n r a t e on an o v e r c a s t d a y b u t n o t on a cloudless day. T a k i n g a c r o p s t a n d in the semi-arid t r o p i c s as t h e o t h e r e x t r e m e , if u - 4 c m d 1 a n d 0(0) = 0 . 2 c m 3 c m - a, the m a x i m u m t r a n s p i r a t i o n r a t e would
65 30
E E
20
6
8
I0
12
14
16
18
Time (h)
Fig. 2. Diurnal change of canopy conductance for water vapour transfer (1/re) for conditions of potential transpiration throughout the day (upper curve) and for latent heat flux limits as specified, determined by maximum rates of soil water extraction (see text). be 8 mm d 1, enough to maintain potential transpiration during the cool season but not in the hot season. In practice, the supply of water for transpiration as determined by eqn. (18) must often be enough to sustain transpiration at a potential rate at the beginning and end of each day but not enough during the middle of the day. Figure 2 shows how the conductance (1/re) of a canopy completely covering the ground would change diurnally if: (a) transpiration proceeded at a potential rate t h r o u g h o u t (outer curve); or (b) extraction of water by the root system imposed limits of 200, 300 and 400 W m -2 equivalent to 0.3, 0.45 and 0 . 6 m m h ~. If the limit is 300 W m- 9 for example, the increase of canopy conductance is enough to maintain transpiration at a potential (i.e. radiation-limited) rate for several hours after sunrise. After 10 h, however, the latent heat equivalent of the potential rate exceeds 300 W m ~ so the actual rate becomes fixed at this value. Equation (7) predicts t ha t the conductance will then change inversely with the s atu r at i on deficit of the atmosphere. During the afternoon, conductance increases as air becomes more humid till about 15h after which the potential tr an s pi r a t i on rate is again maintained. The curves for conductance when the supply is limited have a lack of symmetry about noon which is a consequence of the assumption t hat maximum temperature (and therefore maximum s atu r a t i on deficit) occurs at 14 h (Appendix). Although the p a t t e r n of stomatal closure appearing in Fig. 2 is comparable with many field observations, several processes would be expected to delay and smooth diurnal changes: diurnal changes of plant water content; water ~'saved" behind the descending root front during the night; and differences in soil conditions and plant behaviour across a field.
66 Evidence from the laboratory (Jones, 1983) suggests t hat the stomata of many species start to close in response to an increase of saturation deficit. The same phenomenon has been reported from the field where it is less easy to distinguish the " di r ect " effect of the s a t ur at i on deficit on leaf conductance and indirect effects of the type illustrated by Fig. 2. AN ANSWER Does tr an s p ir at i on limit growth or vice versa? I have argued that if the internal CO2 c o n c e n t r a t i o n of leaves in a plant stand can be treated as a conservative quantity, then canopy conductance must depend on the carbon exchange of leaves, at least when the supply of water available to roots is enough to sustain a potential rate of transpiration. Maximum stomatal conductance is achieved when rates of photosynthesis are maximal and therefore when rates of growth are maximal. It follows t hat potential rates of transpiration can be regarded as a consequence of r a t h e r t han a cause of maximal growth rates. The same argument is valid for subpotential rates of transpiration th at obtain when ground cover is incomplete. When tr an s p irat i on rate is limited by water supply, there is a sense in which the rate of growth must also depend on t ha t supply. However, I argued that the rate at which water is extracted from soil by annual vegetation depends partly on the rate of descent of the root system (u) and partly on the proliferation of roots at a given depth (through O. So there is also a sense in which the rate of transpiration is determined by the rate at which the root system permeates the soil. Moreover, when a fraction of the water available in the root zone is left in the profile when a crop is mature, it is clear t hat the amount of water transpired by the stand over the whole growing season is limited by the size of the root system. Different arguments may apply to perennial vegetation including forests but little experimental evidence is available. The analysis could be extended to take account of the process of atmospheric '~equilibration" discussed by Shut t l ew or t h (this volume). Briefly, there are theoretical grounds (MacNaughton, 1976) for predicting t hat when air passes over an extensive uniform surface, the vertical gradient of saturation deficit will tend to zero so t hat the atmospheric saturation deficit becomes a function of surface wetness instead of behaving as an independent variable. Assuming t h at the analysis presented here remains valid when the (potential) evaporation rate reaches its theoretical limit [ARn/(A + I')], the implication is t hat the atmospheric s a t u r a t i o n deficit should be a function of canopy conductance and therefore of photosynthesis rate and solar radiation. The fact t h a t hourly and daily means of all these quantities are highly correlated does not prove that this line of argument is correct - - but makes it hard to disprove! The question posed by this paper is not an academic one. The analysis which it prompted led to a new way of linking two conservative parameters which have emerged from field measurements: the water use efficiency of a stand (q) and the conversion coefficient for intercepted radiation (e). Hydrologists might
67
be able to exploit this link to estimate the loss of water associated with biomass production as determined from satellite images. The analysis also casts doubts on the logic of attempting to use empirical relations such as eqn. (1) to estimate growth rates from transpiration rates, either for rainfed or for irrigated crops. Lastly, it draws attention to the urgent need for a much better understanding of how the uptake of water by roots depends on the fraction of assimilate which plants move below the ground, out of sight and - - in so many studies of plant water balance - - out of mind. A P P E N D I X - - A L G O R I T H M S USED TO D E F I N E W E A T H E R FOR FIGS. 1 AND 2 Solar r a d i a t i o n was assumed to c h a n g e sinusoidally with time according to the relation: S
= Smsin(ut/N)
where: S m m a x i m u m r a d i a t i o n at noon (Win 2); t = time from sunrise (h); and N daylength t a k e n as 14 h. Net r a d i a t i o n was obtained by assuming a c o n s t a n t reflection coefficient of 0.2 and a long-wave loss of 100Wm 2 in cloudless weather, t a k e n as equivalent to S~ 9 0 0 W m 2. Because the algorithm: Rn
0.8S - 100(Sin/900),
S m < 900
does not allow for t h e effect of c h a n g e s of surface t e m p e r a t u r e on R n , it was necessary to replace r.~ in eqn. (8) by the combined r e s i s t a n c e s for convective and radiative h e a t loss in parallel i.e. (r~ ~ + r~ ~) w h e r e r R = 210Sm 1 at 20°C (Monteith, 1981). T e m p e r a t u r e was assumed to c h a n g e sinusoidally with an amplitude of 20 (S m/900), i.e. 20°C on a cloudless day, with a m i n i m u m of Tin," at sunrise and with a m a x i m u m 2 h after noon, i.e.: T = Tin,n + 20 (Sin/900)sin (ut/N') with N' = 18 h. V a p o u r pressure was assumed c o n s t a n t t h r o u g h o u t the day at 0 . 8 k P a with Tin,. - 1O°C and 1.8kPa with V m l n - - 20°C. C o r r e s p o n d i n g values ofc~ are 4.9 and l l . l m g g 1. The value of A was calculated from the c u r r e n t air t e m p e r a t u r e .
REFERENCES Angus, J.F., Hasegawa, S., Hsiao, T.C., Liboon, S.P. and Zandstra, H.G., 1983. The water balance of post-monsoon dryland crops. J. Agric. Sci., 101: 699-701. Choudhury, B.J. and M o n t e i t h , J.L., 1988. A four-layer model for the h e a t budget of h o m o g e n e o u s land surfaces. Q.J.R. Meteorol. Soc., 114: 373-398. Day, W., Legg, B.J., F r e n c h , B.K., J o h n s t o n , A.E., Lawlor, D.W. and Jeffries, W. de C., 1978. A d r o u g h t e x p e r i m e n t using mobile shelters. J. Agric. Sci., 91: 599-623. Doorenbos, J. and Kassam, A.H., 1979. Yield responses to water. FAO Irrig. Drain. Pap., No. 33, FAO, Rome. F a r q u h a r , G.D. and Wong, S.C., 1984. An empirical model of s t o m a t a l conductance. Aust. J. P l a n t Physiol., 11:191 210. Hanks, R.J., 1983. Yield and water-use relationships. In: H.M. Taylor, W.R. J o r d a n and T.R. Sinclair (Editors), L i m i t a t i o n to Efficient W a t e r Use in Crop Production. Am. Soc. Agron., Madison, Wisc. Jones, H.G., 1983. P l a n t s and Microclimate. Cambridge U n i v e r s i t y Press, Cambridge. M a c N a u g h t o n , K., 1976. E v a p o r a t i o n and advection. Q. J.R. Meteorol. Soc., 102:181 191. McGowan, M., 1974. Depth of w a t e r e x t r a c t e d by roots. In: Isotopes and Radiation Techniques in Soil P h y s i c s and I r r i g a t i o n Studies. IAEA, Vienna, pp. 435-445.
68 Monteith, J,L., 1977. Climate and efficiency of crop production in Britain. Phil. Trans. R. Soc., Ser. B, 281:277 294. Monteith, J.L., 1978. Reassessment of maximum growth rates for C 3 and C 4 crops. Exp. Agric., 14: 15. Monteith, J.L., 1981. Evaporation and surface temperature. Q. J.R. Meteorol. Soc., 107:1 27. Passioura, J.B., 1983. Root and drought resistance. Agric. Water Manage., 7: 265-280. Penman, H.L., 1948. Natural evaporation from open water, bare soil and grass. Proc. R. Soc. Lond., Ser. A., 193: 12(~145. Ritchie, J.T., 1981. Water dynamics in the soil-plant-atmosphere system in soil water and nitrogen in Mediterranean ecosystems. In: J.L. Monteith and C. Webb (Editors). Nijhoff and J u n k The Hague. Russell, G., Jarvis, P.J. and Monteith, J.L., 1988. Absorption of radiation by canopies and stand growth. In: G. Russell, P.G. Jarvis and B. Marshall (Editors), Plant Canopies: Their Growth, Form and Function. Cambridge University Press, Cambridge. Mass. Shuttleworth, W.J., 1988. Macrohydrology The New challenge for process hydrology. J. Hydro]., 100:31 56 (this volume). Sibma, L., 1968. Growth of closed crop surfaces in The Netherlands. Neth. J. Agric. Sci., 16:211 216. Thornthwaite, C.W., 1949. A rational approach to the classification of climate. Geogr. Rev., 38: 55-94.
57
Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
[3] D O E S T R A N S P I R A T I O N LIMIT THE GROWTH OF V E G E T A T I O N OR VICE VERSA?*
J.L. MONTEITH
Resource Management Program, International Crops Research Institute for the Semi-Arid Tropics, Patancheru, A.P. 502 324 (India) (Received January, 1988; revised and accepted March, 1988)
ABSTRACT Monteith, J.L., 1988. Does transpiration limit the growth of vegetation or vice versa? J. Hydrol., 100: 5748. For hydrological or agronomic purposes, the potential rate of transpiration from vegetation is often calculated as a function of climatological variables, sometimes with the inclusion of a canopy resistance to water vapour diffusion. If, within leaves, the intercellular concentration of CO 2 is conservative, the canopy resistance must depend on the photosynthesis rate implying that potential transpiration depends on potential growth. The relevant form of the Penman-Monteith equation is developed to link water use efficiency with the conversion coefficient for solar radiation. When water is limiting, the maximum rate at which transpiration can occur depends mainly on the rate of extension of the root system and on the w a t e r " available" per unit soil volume. It follows that both potential and subpotential rates of transpiration are consequences of the assimilation of carbon by vegetation and its subsequent redistribution to form shoots and roots. THE QUESTION
Seminal papers published by Penman (1948) and Thorntwaite (1948) led to the definition o f " p o t e n t i a l " transpiration as the rate at which a stand of short, green vegetation loses water to the atmosphere when the supply to the root system is unrestricted. Although this definition is firmly entrenched in the literature of hydrology, micrometeorology and crop ecology, it is somewhat circular because it is difficult to define what ~'unrestricted" means in this context without introducing the concept of a maximum transpiration rate. Notwithstanding this small logical difficulty, it is clearly helpful to distinguish between potential and " a c t u a l " rates of transpiration, the former being determined mainly by the way in which foliage responds to a demand from the atmosphere and the latter by the way in which the soil matrix provides a supply to the root system.
Both potential and actual rates of transpiration have been used to estimate rates of dry matter production by crop stands. A common practice (Doorenbos Submitted as JA No. 773 by the International Crops Research Institute for the Semi-Arid Tropics.
0022-1694/88/$03.50
© 1988 Elsevier Science Publishers B.V.
58 and Kassam, 1979; Hanks, 1983) is to calculate potential transpiration rate (PT) from some version of the Penman formula and to estimate a corresponding maximum rate of dry matter production (PM) using a photosynthesis model. The amount of dry matter produced per unit of water transpired (q) can then be calculated as P M / P T . It is further assumed that, when water supply is limiting, the relation between actual dry matter production (AM) and actual transpiration is given by: 1
PM
n 1-~
-
(1)
where n is an index, justifiable dimensionally but often close to unity and rarely interpreted in terms of physiological mechanisms. This type of analysis is based on the assumption, usually implicit, that the rate at which a stand of vegetation accumulates dry matter depends on the rate at which it transpires water, whether the supply is limiting or not. It is beyond argument t h a t stomatal dimensions limit, but do not necessarily govern, rates at which both water vapour and C02 can reach the wet surfaces of cell walls from the atmosphere and vice versa. However, this identity of pathways does not imply that the carbon flux is necessarily controlled by the vapour flux. The purpose of this note is to argue t h a t it is usually the carbon flux that determines the vapour flux rather than the converse. A caveat is needed before this deliberately controversial paper continues. It deals with the loss of water vapour from the earth's surface solely in terms of transpiration and it is not concerned with the evaporation of water from the soil surface or from rain intercepted by foliage. However, this restriction does not invalidate general conclusions at the end of the paper or their relevance to the hydrological cycle in catchments where most of the ground is covered by vegetation during seasons when most solar energy is received. POTENTIALTRANSPIRATION Equations for the water vapour and carbon dioxide exchange of a single leaf will be considered first as a basis for deriving an expression for the potential rate of transpiration of a stand of vegetation. Suppose t h a t the mean mixing ratio of water vapour in the intercellular spaces of a leaf is ci (g vapour per g of air) and that the mixing ratio in ambient air is ca. The decrease in vapour c o n c e n t r a t i o n between leaf and air is p(c~ - c a) where p is the mean density of (moist) air in the system and the outward flux of vapour associated with this gradient is: E
=
p(cl
-
Ca)/(rs + rb)
(2)
where r s and rb are diffusion resistances for stomata and for the leaf boundary layer respectively.
59 The corresponding inward flux of CO2 can be written: P
=
p(Ca -- C~)/(r~ + r~)
=
pXCa/(r~ + rE)
(3)
where primes denote concentrations and resistances for CO2 transfer and x = 1 -
c;/c'~.
Because the air in substomatal cavities is effectively saturated, ci can be identified as the saturated vapour concentration at the mean temperature (T) of mesophyll tissue, i.e. cl(T) which is approximately an exponential function of T. The value of c~ is much less dependent on temperature and is determined mainly by the relative resistances to CO2 diffusion as a gas through the boundary layer and stomatal pores and in solution from the surfaces of cells surrounding the substomatal cavity to the sites of photosynthesis within the mesophyll cell complex (Jones, 1983). Laboratory evidence suggests that the ratio c~/c~ is '~somewhat conservative" (Farquhar and Wong, 1984) and that it may be treated as constant when the liquid phase component of resistance is changed experimentally, e.g., by altering the illumination of a leaf or by comparing the CO2 exchange of leaves from plants with different levels of nutrition. This behaviour implies that the liquid and gaseous components of resistance change in about the same proportion as a consequence of changes in stomatal aperture. The ratio y = rs/r' ~ is inversely proportional to the corresponding ratio of diffusion coefficients for water vapour and CO2 and has a value of 0.61. From eqns. (2) and (3), the stomatal resistance for water vapour diffusion can be written: r~
=
yr~
=
y{p(c'~x/P)-
rE}
(4)
so that: E
p(c~(T)
-
Ca)
(5)
+ (rb -- y r ~ )
(pxyc'a/P)
Commonly, the second bracketed term in the denominator is small compared with the first term so that the ratio of transpiration to photosynthesis can be expressed as a function of five dimensionless quantities: E/P
-
(ci(T)
-
ca)/(xyc'~)
(6)
The denominator can usually be treated as constant so t h a t E / P changes with the numerator alone. In the special case where the leaf and air temperature are identical, the numerator is proportional to the saturation vapour pressure deficit of the ambient air. In general, however, the system is not isothermal and the relation between E and P must then be obtained by taking account of the heat balance of the leaf and by eliminating surface temperature to obtain an expression of the Penman-Monteith type (Monteith, 1981), e.g.:
6O E
=
ARn/)~ + ? p [ c i ( T a )
-
A + 7*
ca]/rb
(7)
where: A = r a t e of c h a n g e of c~ (T) with t e m p e r a t u r e (K-l); R , = net flux of r a d i a t i o n absorbed by leaf ( J m 2s 1); ~ = l a t e n t h e a t of v a p o r i s a t i o n ( J g 1); Ta = t e m p e r a t u r e of a m b i e n t air; ~, = cp/). (K 1); cp = specific h e a t of air at c o n s t a n t pressure (J g-1 K - l ) ; and ~,* = 7(1 + rs/rh) = 7{1 + XyCa/(Prt~) - y r ~ / rb)/ from eqn. (4). 7 = cp/~(K-1); and 7* = 7( 1 + r J r b ) = 7{1 + x y c ' ~ / ( P r b ) - y r ~ / r a } from eqn.
(4). The same e q u a t i o n can be used to r e l a t e t r a n s p i r a t i o n and p h o t o s y n t h e s i s for a stand of v e g e t a t i o n if several symbols are redefined. The c o n c e n t r a t i o n s ca and c'~ must be m e a s u r e d at a specified r e f e r e n c e h e i g h t and b o t h rb and r~ must be replaced by r~, an a e r o d y n a m i c r e s i s t a n c e for h e a t or v a p o u r t r a n s f e r b e t w e e n the r e f e r e n c e h e i g h t and the effective s o u r c e of sensible h e a t in the canopy. The leaf resistances r~ and r~ are replaced by the c o r r e s p o n d i n g resist a n c e s for the c a n o p y t r e a t e d as a "big l e a f " , viz. r~ and r~. It follows that, for a canopy: ~'* j
[1 + X y C a / ( P r ~ ) - y]
(8)
Two assumptions implicit in m a k i n g the step from leaf to c a n o p y are: (1) t h a t x and c~ are the same for all leaves; and (2) t h a t the r a t i o of c a n o p y resistances for w a t e r v a p o u r and CO2, rJr'~ is the same as the r a t i o for single leaves, rs/r~ = 0.61. F r o m i n s p e c t i o n of eqn. (7), E increases as P increases implying t h a t E will r e a c h a " p o t e n t i a l " r a t e of t r a n s p i r a t i o n w h e n c a n o p y p h o t o s y n t h e s i s also r e a c h e s a m a x i m u m r a t e for a given e n v i r o n m e n t . To o b t a i n daily rates of p o t e n t i a l t r a n s p i r a t i o n it r e m a i n s to establish how net daily r a t e s of photosynthesis (g CO2m 2d 1) can be related to a more readily available q u a n t i t y - - a crop g r o w t h r a t e C (g dry m a t t e r m Z d 1). After i n t r o d u c i n g the gross assimilation per day (A) and the c o r r e s p o n d i n g r e s p i r a t i o n o v e r 24 h (Q) as i n t e r m e d i a t e variables, t h r e e f r a c t i o n s can be defined: (1) r e s p i r a t i o n as a f r a c t i o n of assimilation ( m = Q / A ) ; (2) the f r a c t i o n (n) of r e s p i r a t i o n which o c c u r s d u r i n g the period of assimilation (daylight); and (3) dry m a t t e r p r o d u c t i o n as a f r a c t i o n of net CO2 assimilation (z). Crop g r o w t h r a t e can now be expressed as a p r o p o r t i o n of the difference b e t w e e n net d a y t i m e CO2 uptake, P, and r e s p i r a t i o n at night, i.e.: C
=
z[P-
(1 - n ) Q ]
(9)
w h e r e a s the net d a y t i m e CO2 u p t a k e is given by the difference between gross assimilation A and d a y t i m e r e s p i r a t i o n n Q , i.e.: P
=
A-nQ
=
Q(1/m
-
n)
(10)
61
E l i m i n a t i n g Q f r o m eqns. (9) a n d (10) t h e n gives: C
=
zP(1 -
m)/(1 - m n )
(11)
As an e x a m p l e , if z :: 0.5, m = 0.45, a n d n = 0.7, t h e n C = 0.4 P. T h e m a x i m u m v a l u e of c r o p g r o w t h r a t e in a g i v e n e n v i r o n m e n t does n o t a p p e a r to differ m u c h b e t w e e n species w h e n t h e y a r e divided into a few m a j o r groups, two of w h i c h p h y s i o l o g i s t s r e f e r to as C3 a n d C4 ( d e p e n d i n g on the n u m b e r of c a r b o n a t o m s in the first p r o d u c t of p h o t o s y n t h e s i s ) . M o s t t e m p e r a t e v e g e t a t i o n b e l o n g s to the C3 c a t e g o r y ; the C4 class c o n t a i n s t r o p i c a l grasses a n d c e r e a l s (e.g. s u g a r cane, s o r g h u m ) a n d a n u m b e r of d e s e r t species (Jones, 1983). T h e m a x i m u m g r o w t h r a t e of C3 c r o p species in W e s t e r n E u r o p e is a b o u t 2 0 g m 2d 1 d u r i n g spells of w e a t h e r w i t h a v e r a g e cloudiness (Sibma, 1968), i n c r e a s i n g to a b o u t 3 0 g m 2d 1 on d a y s w i t h little cloud ( M o n t e i t h , 1978). C o r r e s p o n d i n g v a l u e s of P a r e 50 and 75 g m ~d 1 or 1.0-1.5 mg m ~s 1 as m e a n r a t e s of a s s i m i l a t i o n o v e r a 14 h day. T h e s e figures c a n n o w be used in eqn. (4) to give s t o m a t a l r e s i s t a n c e s for w a t e r v a p o u r t r a n s f e r . A s s u m i n g pC'aX = 0.18 for C3 species a n d a t y p i c a l a e r o d y n a m i c r e s i s t a n c e of ra 30 s m 1, the r a n g e of r c is from 90 to 54 s m c o n s i s t e n t w i t h field experience. In c l i m a t e s w h e r e C4 species are grown, m a x i m u m v a l u e s of C, a n d t h e r e f o r e of P, a p p e a r to be a b o u t 50% l a r g e r t h a n for C~ species ( M o n t e i t h , 1978); b u t w i t h x -- 0.7, t h e v a l u e of C'aX/P is a l m o s t t w i c e the v a l u e for C3 species. V a l u e s of rc p r e d i c t e d from eqn. (4) are t h e r e f o r e a b o u t 30% l a r g e r t h a n for C3 species in the s a m e e n v i r o n m e n t . It is possible to t a k e the a n a l y s i s one s t a g e f u r t h e r w i t h t h e o b j e c t i v e of e x p r e s s i n g p o t e n t i a l t r a n s p i r a t i o n as a f u n c t i o n of c l i m a t i c v a r i a b l e s only. It would be possible to use a model to p r e d i c t the d e p e n d e n c e of P on r a d i a t i o n , t e m p e r a t u r e , etc., b u t a m o r e direct a n d m o r e useful r o u t e is t h r o u g h the e v i d e n c e t h a t C is u s u a l l y an a l m o s t l i n e a r f u n c t i o n of r a d i a t i o n i n t e r c e p t e d by a c a n o p y , at l e a s t d u r i n g v e g e t a t i v e g r o w t h w h e n p o t e n t i a l r a t e s of t r a n s p i r a tion are likely to be achieved. T h e r e l a t i o n b e t w e e n C (g m 2d 1) and t o t a l s o l a r r a d i a t i o n S ( M J m 2d 1) c a n be w r i t t e n ( M o n t e i t h , 1977) as: C
=
(12)
feS
w h e r e ~ = f r a c t i o n of i n c i d e n t r a d i a t i o n i n t e r c e p t e d by a c a n o p y , a n d e = c o n v e r s i o n coefficient (g dry m a t t e r per M J of i n t e r c e p t e d radiation). B e c a u s e the p h o t o s y n t h e s i s r a t e of leaves u s u a l l y t e n d s to a m a x i m u m v a l u e as i r r a d i a n c e i n c r e a s e s (especially in C3 species), e is e x p e c t e d to d e c r e a s e s o m e w h a t as daily i n s o l a t i o n i n c r e a s e s . To find p o t e n t i a l t r a n s p i r a t i o n from a s t a n d c o m p l e t e l y c o v e r i n g the ground, f c a n be set at u n i t y a n d for C3 species g r o w i n g in t e m p e r a t e climates, t h e v a l u e of e, d e t e r m i n e d from field e x p e r i m e n t s w i t h a r a n g e of species, lies b e t w e e n 1.3 and 1.6 g M J i (Russell et al., 1988). F o r a n u m e r i c a l e x a m p l e , if e = 1.5 g M J ~ a n d C = 0.4 P as before, t h e n P = 3.8 C. (To k e e p u n i t s c o n s i s t e n t , S m u s t be e x p r e s s e d in M J m 2s 1 i m p l y i n g t h a t i n s o l a t i o n , as u s u a l l y r e p o r t e d in M J m 2 d 1, m u s t be divided by the d u r a t i o n of d a y l i g h t in seconds.) T h e n f r o m eqn. (4) w i t h pc'~ x = 0.18 g m 3 y = 0.6 a n d r a = 3 0 s m i: r,. = 0.610.18/(3.8 S) - 30]
=
1432/S - 18
62 A c c o r d i n g to this relation, the m e a n daily v a l u e of rc should d e c r e a s e from 1.3 to 0.65 s m 1 as the i n s o l a t i o n (for a 14 h day) i n c r e a s e s from 10 to 20 M J m "~ E q u a t i o n (8) can now be r e w r i t t e n as: ~'*~ =
t'{1 + j / ( S r a ) - y}
(13)
where: j
pc'axyz(1 -
=
m)
(14)
e(1 - rim)
E q u a t i o n (14) is c u m b e r s o m e but is p r e s e n t e d h e r e to show explicitly the set of p a r a m e t e r s , m o s t l y n o n d i m e n s i o n a l , on which j depends. In practice, j could be derived e x p e r i m e n t a l l y by using eqns. (7) and (13) to give: j
S r a { ( A / 7 ) ( R n / ~ E ) + p[ci(Ta) - Ca]/(raE) - (A/~' + 1
=
y)}
(15)
All the q u a n t i t i e s on the r i g h t - h a n d side of this e q u a t i o n are available directly from climatological records or can be e s t i m a t e d from them. F i g u r e 1 shows the d e p e n d e n c e of daily t r a n s p i r a t i o n r a t e on i n s o l a t i o n c a l c u l a t e d from eqn. (7). (The Appendix gives details of the way in which r a d i a t i o n , t e m p e r a t u r e and s a t u r a t i o n deficit were assumed to c h a n g e diurnally.) The d e p e n d e n c e of E on r a d i a t i o n is almost l i n e a r because trans p i r a t i o n r a t e is d o m i n a t e d by the supply of r a d i a n t e n e r g y b o t h d i r e c t l y and t h r o u g h the c a n o p y resistance. A f u r t h e r p o t e n t i a l source of n o n l i n e a r i t y is the d e p e n d e n c e of e on S w h i c h would emerge if the r e l a t i o n b e t w e e n P and r a d i a t i o n were e s t i m a t e d from a model in which the p h o t o s y n t h e s i s of
12
8
c
4
I0
20
Solar radiation (MJ m-2 d -I)
Fig. 1. Daily t r a n s p i r a t i o n from a s t a n d of v e g e t a t i o n c o m p l e t e l y c o v e r i n g t h e g r o u n d as a f u n c t i o n of d a i l y s o l a r r a d i a t i o n , c a l c u l a t e d from eqns. (7), (9) a n d (12) w i t h c o n s t a n t s as g i v e n in t h e text
and diurnal change of weather estimated from algorithms given in the Appendix. Air temperature at sunrise is given.
63 individual leaves was a hyperbolic function of irradiance. The dependence of E on temperature shown in the figure is almost entirely a consequence of the larger values of saturation deficit used at the higher temperature. ACTUALTRANSPIRATION In terms of the analysis already presented, the rate of transpiration from a stand of vegetation will be less than the potential rate when: (1) ground cover is incomplete; and/or (2) photosynthesis rates are suboptimal because of: (a) a shortage of water or nutrients; (b) ageing in a significant fraction of the foliage; and (c) attack by pests and diseases.
Incomplete ground cover To obtain an approximate estimate of transpiration rate from a stand of foliage which does not intercept all incident radiation, eqn. (7) can readily be modified by writing f S in place of f in the denominator. Little error is likely to arise if Rn is replaced by f Rn though the fractional transmission of net and of solar radiation are not generally identical. However, this procedure takes no account of the way in which the microclimate of a canopy depends on the wetness of the soil surface, a point explored by Choudhury and Monteith (1988) in a much more complex model of surface heat balance.
Shortage of water What mechanisms operate when the supply of water to a stand of vegetation cannot sustain transpiration at a potential rate? The closure of stomata is a plant's short-term response to the problem of balancing supply and demand but as soon as the transpiration rate falls below the potential value, the demand side of the balance becomes almost irrelevant it is the supply that matters. Supply is determined mainly by the rate at which roots are able to extract water and this process is usually discussed in terms of gradients of potential between water in the xylem vessels of roots and in the soil surrounding them. A more direct approach to the problem is provided by measurements of seasonal changes in soil water content as a function of depth, readily obtainable from measurements with neutron probes, for example. Measurements below stands of annual crops during periods when there is little input of water at the soil surface show that: (1) A root front moves downward through the soil at a velocity which Angus et al. (1983) reported was between 2 and 4 cm d 1 for a range of tropical species. For cereals in a temperate climate, the maximum rate appears to be about 2 c m d 1 (McGowan, 1974; Day et al., 1978). Much slower rates would be expected in soil that was compacted, very dry, or infertile but field evidence is too scanty to make generalisations.
64
(2) After t h e a r r i v a l of t h e r o o t front, the r a t e of e x t r a c t i o n of w a t e r d e c r e a s e s m o r e or less e x p o n e n t i a l l y w i t h t i m e ( P a s s i o u r a , 1983). This b e h a v i o u r c a n be m o d e l l e d in a simple way. S u p p o s e t h a t the w a t e r a v a i l a b l e at d e p t h z a n d t i m e t, e x p r e s s e d in cm 3 cm a, is: O(z, t) =
0(0) (exp - t/v)
(16)
where: t = t i m e m e a s u r e d f r o m the a r r i v a l of the r o o t f r o n t (d); 0 (0) = w a t e r a v a i l a b l e a t t = 0, a s s u m e d i n d e p e n d e n t of depth; a n d r - t i m e c o n s t a n t of e x t r a c t i o n process, also a s s u m e d i n d e p e n d e n t of d e p t h b u t e x p e c t e d to d e p e n d on r o o t l e n g t h per u n i t v o l u m e ( P a s s i o u r a , 1983). I f t' is t i m e m e a s u r e d f r o m the d a y w h e n the r o o t f r o n t s t a r t s to descend, t h e n t = t' - z / u w h e n z < ut. T h e r a t e of e x t r a c t i o n at d e p t h z a n d time t' is t h e r e f o r e g i v e n by: ~O(z, t)/~t
=
(1/~)0(0)[exp -
(t' - z/u)/~]
(17)
I n t e g r a t i o n w i t h r e s p e c t to z f r o m 0 to ut" gives the r a t e of w a t e r s u p p l y and t h e r e f o r e the t r a n s p i r a t i o n r a t e as: E
=
u0(0)[1 - e x p ( - t ' / z ) ]
(18)
It follows t h a t the r a t e of e v a p o r a t i o n a p p r o a c h e s a m a x i m u m v a l u e of uO(O), i n d e p e n d e n t of z w h e n t' is m u c h l a r g e r t h a n ~. T h e t o t a l a m o u n t of w a t e r e x t r a c t e d a f t e r a t i m e t' w h e n the r o o t s h a v e r e a c h e d a d e p t h z = ut' is found by i n t e g r a t i n g eqn. (18) w i t h r e s p e c t to t' to give: f Edt'
=
z0(0)[1 - (z/t)(1
- exp -- t'/z)]
(19)
w h e r e zO(O) is t h e t o t a l a m o u n t of w a t e r a v a i l a b l e in d e p t h z, a n d (T/t') [1 - exp - t'/z)] is t h e u n u s e d f r a c t i o n of t h a t w a t e r . W h e n t h e r e is no i n p u t of w a t e r f r o m the soil surface, this r e s i d u a l f r a c t i o n is e s s e n t i a l for t h e s u r v i v a l of p l a n t s if t h e i r r o o t s y s t e m s stop g r o w i n g before t h e y a r e m a t u r e , as in m o s t c e r e a l s d u r i n g t h e period of g r a i n filling. E v e n a t m a t u r i t y , it a p p e a r s t h a t crop s t a n d s o f t e n fail to a b s t r a c t all t h e w a t e r held in t h e r o o t zone and " a v a i l a b l e " in t e r m s of s o m e s t a n d a r d r a n g e of p o t e n t i a l s (e.g. 0.03-1.5 MPa). R i t c h i e (1981) a n d o t h e r s h a v e t h e r e f o r e s u g g e s t e d t h a t " a v a i l a b i l i t y " s h o u l d be r e p l a c e d by " e x t r a c t a b i l i t y " defined as t h e t o t a l a m o u n t of w a t e r e x t r a c t e d by c r o p r o o t s up to t h e d a y it is h a r v e s t e d ; b u t this p r o c e d u r e m a y n o t be logical if the f r a c t i o n is a f u n c t i o n of t i m e as eqn. (19) suggests. T h e m a x i m u m r a t e of e x t r a c t i o n uP(O) will be small w h e n a r o o t s y s t e m descends slowly in a l i g h t soil. F o r example, if u = 1 . 5 c m d ~ a n d 8(0) 0.1 cm3cm 3, the t r a n s p i r a t i o n r a t e c a n n o t exceed 1 . 5 m m d 1. In a t e m p e r a t e climate, t h e s u p p l y of w a t e r f r o m t h e r o o t s would be e n o u g h to m e e t the p o t e n t i a l t r a n s p i r a t i o n r a t e on an o v e r c a s t d a y b u t n o t on a cloudless day. T a k i n g a c r o p s t a n d in the semi-arid t r o p i c s as t h e o t h e r e x t r e m e , if u - 4 c m d 1 a n d 0(0) = 0 . 2 c m 3 c m - a, the m a x i m u m t r a n s p i r a t i o n r a t e would
65 30
E E
20
6
8
I0
12
14
16
18
Time (h)
Fig. 2. Diurnal change of canopy conductance for water vapour transfer (1/re) for conditions of potential transpiration throughout the day (upper curve) and for latent heat flux limits as specified, determined by maximum rates of soil water extraction (see text). be 8 mm d 1, enough to maintain potential transpiration during the cool season but not in the hot season. In practice, the supply of water for transpiration as determined by eqn. (18) must often be enough to sustain transpiration at a potential rate at the beginning and end of each day but not enough during the middle of the day. Figure 2 shows how the conductance (1/re) of a canopy completely covering the ground would change diurnally if: (a) transpiration proceeded at a potential rate t h r o u g h o u t (outer curve); or (b) extraction of water by the root system imposed limits of 200, 300 and 400 W m -2 equivalent to 0.3, 0.45 and 0 . 6 m m h ~. If the limit is 300 W m- 9 for example, the increase of canopy conductance is enough to maintain transpiration at a potential (i.e. radiation-limited) rate for several hours after sunrise. After 10 h, however, the latent heat equivalent of the potential rate exceeds 300 W m ~ so the actual rate becomes fixed at this value. Equation (7) predicts t ha t the conductance will then change inversely with the s atu r at i on deficit of the atmosphere. During the afternoon, conductance increases as air becomes more humid till about 15h after which the potential tr an s pi r a t i on rate is again maintained. The curves for conductance when the supply is limited have a lack of symmetry about noon which is a consequence of the assumption t hat maximum temperature (and therefore maximum s atu r a t i on deficit) occurs at 14 h (Appendix). Although the p a t t e r n of stomatal closure appearing in Fig. 2 is comparable with many field observations, several processes would be expected to delay and smooth diurnal changes: diurnal changes of plant water content; water ~'saved" behind the descending root front during the night; and differences in soil conditions and plant behaviour across a field.
66 Evidence from the laboratory (Jones, 1983) suggests t hat the stomata of many species start to close in response to an increase of saturation deficit. The same phenomenon has been reported from the field where it is less easy to distinguish the " di r ect " effect of the s a t ur at i on deficit on leaf conductance and indirect effects of the type illustrated by Fig. 2. AN ANSWER Does tr an s p ir at i on limit growth or vice versa? I have argued that if the internal CO2 c o n c e n t r a t i o n of leaves in a plant stand can be treated as a conservative quantity, then canopy conductance must depend on the carbon exchange of leaves, at least when the supply of water available to roots is enough to sustain a potential rate of transpiration. Maximum stomatal conductance is achieved when rates of photosynthesis are maximal and therefore when rates of growth are maximal. It follows t hat potential rates of transpiration can be regarded as a consequence of r a t h e r t han a cause of maximal growth rates. The same argument is valid for subpotential rates of transpiration th at obtain when ground cover is incomplete. When tr an s p irat i on rate is limited by water supply, there is a sense in which the rate of growth must also depend on t ha t supply. However, I argued that the rate at which water is extracted from soil by annual vegetation depends partly on the rate of descent of the root system (u) and partly on the proliferation of roots at a given depth (through O. So there is also a sense in which the rate of transpiration is determined by the rate at which the root system permeates the soil. Moreover, when a fraction of the water available in the root zone is left in the profile when a crop is mature, it is clear t hat the amount of water transpired by the stand over the whole growing season is limited by the size of the root system. Different arguments may apply to perennial vegetation including forests but little experimental evidence is available. The analysis could be extended to take account of the process of atmospheric '~equilibration" discussed by Shut t l ew or t h (this volume). Briefly, there are theoretical grounds (MacNaughton, 1976) for predicting t hat when air passes over an extensive uniform surface, the vertical gradient of saturation deficit will tend to zero so t hat the atmospheric saturation deficit becomes a function of surface wetness instead of behaving as an independent variable. Assuming t h at the analysis presented here remains valid when the (potential) evaporation rate reaches its theoretical limit [ARn/(A + I')], the implication is t hat the atmospheric s a t u r a t i o n deficit should be a function of canopy conductance and therefore of photosynthesis rate and solar radiation. The fact t h a t hourly and daily means of all these quantities are highly correlated does not prove that this line of argument is correct - - but makes it hard to disprove! The question posed by this paper is not an academic one. The analysis which it prompted led to a new way of linking two conservative parameters which have emerged from field measurements: the water use efficiency of a stand (q) and the conversion coefficient for intercepted radiation (e). Hydrologists might
67
be able to exploit this link to estimate the loss of water associated with biomass production as determined from satellite images. The analysis also casts doubts on the logic of attempting to use empirical relations such as eqn. (1) to estimate growth rates from transpiration rates, either for rainfed or for irrigated crops. Lastly, it draws attention to the urgent need for a much better understanding of how the uptake of water by roots depends on the fraction of assimilate which plants move below the ground, out of sight and - - in so many studies of plant water balance - - out of mind. A P P E N D I X - - A L G O R I T H M S USED TO D E F I N E W E A T H E R FOR FIGS. 1 AND 2 Solar r a d i a t i o n was assumed to c h a n g e sinusoidally with time according to the relation: S
= Smsin(ut/N)
where: S m m a x i m u m r a d i a t i o n at noon (Win 2); t = time from sunrise (h); and N daylength t a k e n as 14 h. Net r a d i a t i o n was obtained by assuming a c o n s t a n t reflection coefficient of 0.2 and a long-wave loss of 100Wm 2 in cloudless weather, t a k e n as equivalent to S~ 9 0 0 W m 2. Because the algorithm: Rn
0.8S - 100(Sin/900),
S m < 900
does not allow for t h e effect of c h a n g e s of surface t e m p e r a t u r e on R n , it was necessary to replace r.~ in eqn. (8) by the combined r e s i s t a n c e s for convective and radiative h e a t loss in parallel i.e. (r~ ~ + r~ ~) w h e r e r R = 210Sm 1 at 20°C (Monteith, 1981). T e m p e r a t u r e was assumed to c h a n g e sinusoidally with an amplitude of 20 (S m/900), i.e. 20°C on a cloudless day, with a m i n i m u m of Tin," at sunrise and with a m a x i m u m 2 h after noon, i.e.: T = Tin,n + 20 (Sin/900)sin (ut/N') with N' = 18 h. V a p o u r pressure was assumed c o n s t a n t t h r o u g h o u t the day at 0 . 8 k P a with Tin,. - 1O°C and 1.8kPa with V m l n - - 20°C. C o r r e s p o n d i n g values ofc~ are 4.9 and l l . l m g g 1. The value of A was calculated from the c u r r e n t air t e m p e r a t u r e .
REFERENCES Angus, J.F., Hasegawa, S., Hsiao, T.C., Liboon, S.P. and Zandstra, H.G., 1983. The water balance of post-monsoon dryland crops. J. Agric. Sci., 101: 699-701. Choudhury, B.J. and M o n t e i t h , J.L., 1988. A four-layer model for the h e a t budget of h o m o g e n e o u s land surfaces. Q.J.R. Meteorol. Soc., 114: 373-398. Day, W., Legg, B.J., F r e n c h , B.K., J o h n s t o n , A.E., Lawlor, D.W. and Jeffries, W. de C., 1978. A d r o u g h t e x p e r i m e n t using mobile shelters. J. Agric. Sci., 91: 599-623. Doorenbos, J. and Kassam, A.H., 1979. Yield responses to water. FAO Irrig. Drain. Pap., No. 33, FAO, Rome. F a r q u h a r , G.D. and Wong, S.C., 1984. An empirical model of s t o m a t a l conductance. Aust. J. P l a n t Physiol., 11:191 210. Hanks, R.J., 1983. Yield and water-use relationships. In: H.M. Taylor, W.R. J o r d a n and T.R. Sinclair (Editors), L i m i t a t i o n to Efficient W a t e r Use in Crop Production. Am. Soc. Agron., Madison, Wisc. Jones, H.G., 1983. P l a n t s and Microclimate. Cambridge U n i v e r s i t y Press, Cambridge. M a c N a u g h t o n , K., 1976. E v a p o r a t i o n and advection. Q. J.R. Meteorol. Soc., 102:181 191. McGowan, M., 1974. Depth of w a t e r e x t r a c t e d by roots. In: Isotopes and Radiation Techniques in Soil P h y s i c s and I r r i g a t i o n Studies. IAEA, Vienna, pp. 435-445.
68 Monteith, J,L., 1977. Climate and efficiency of crop production in Britain. Phil. Trans. R. Soc., Ser. B, 281:277 294. Monteith, J.L., 1978. Reassessment of maximum growth rates for C 3 and C 4 crops. Exp. Agric., 14: 15. Monteith, J.L., 1981. Evaporation and surface temperature. Q. J.R. Meteorol. Soc., 107:1 27. Passioura, J.B., 1983. Root and drought resistance. Agric. Water Manage., 7: 265-280. Penman, H.L., 1948. Natural evaporation from open water, bare soil and grass. Proc. R. Soc. Lond., Ser. A., 193: 12(~145. Ritchie, J.T., 1981. Water dynamics in the soil-plant-atmosphere system in soil water and nitrogen in Mediterranean ecosystems. In: J.L. Monteith and C. Webb (Editors). Nijhoff and J u n k The Hague. Russell, G., Jarvis, P.J. and Monteith, J.L., 1988. Absorption of radiation by canopies and stand growth. In: G. Russell, P.G. Jarvis and B. Marshall (Editors), Plant Canopies: Their Growth, Form and Function. Cambridge University Press, Cambridge. Mass. Shuttleworth, W.J., 1988. Macrohydrology The New challenge for process hydrology. J. Hydro]., 100:31 56 (this volume). Sibma, L., 1968. Growth of closed crop surfaces in The Netherlands. Neth. J. Agric. Sci., 16:211 216. Thornthwaite, C.W., 1949. A rational approach to the classification of climate. Geogr. Rev., 38: 55-94.