Use of simulation methods for determining critical leaf water potential for stomatal closure in field conditions

Ecological Modelling, 50 (1990) 133-144

133

Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

USE OF SIMULATION METHODS FOR DETERMINING LEAF WATER POTENTIAL FOR STOMATAL CLOSURE IN FIELD CONDITIONS

CRITICAL

NADER KATERJI Station de Bioclimatologie, Institut National de la Recherche Agronomique, 78850 Thiverval Grignon (France)

(Accepted 6 July 1989) ABSTRACT Katerji, N., 1990. Use of simulation methods for determining critical leaf water potential for stomatal closure in field conditions. Ecol. Modelling, 50: 133-144. We propose here a method, applicable to the whole canopy, for determining the critical value of leaf water potential ~bFC at which stomata begin to close. This method combines the simulation of leaf water potential by means of a model of transfer in the soil-plant system with the simulation of stomatal resistance by means of Bowen's ratio. These simulations necessitate, for the most part, physical measures which can be recorded. After experimental verification, we observed that the simulated ~bFC values correspond well to those obtained by conventional methods, and then that 6FC values observed throughout the growth cycle of the potato crop remain practically stable (~bFC = --0.95 MPa).

INTRODUCTION T h e r e s p o n s e o f s t o m a t a l resistance rs to leaf w a t e r p o t e n t i a l +F, a n d m o r e precisely the value of the critical p o t e n t i a l ~ FC at which s t o m a t a begin to close, is of special interest to researchers; k n o w i n g +FC s h o u l d allow geneticists to classify species or varieties a c c o r d i n g to their ability to w i t h s t a n d d r o u g h t (Ackerson, 1983; A d j a h o s s o u et al., 1984; A b o u s s o u a n S e r o p i a n a n d P l a n c h o n , 1985). F r o m an ecological p o i n t of view, a possible m o d i f i c a t i o n of the p a r t i c u l a r ~ FC value deserves analysis, b e c a u s e it reflects the ability of plants to a d a p t to new water-stress c o n d i t i o n s ( M a c C r e e , 1974; Sullivan a n d Eastin, 1974). In s o m e cases, this m o d i f i c a t i o n i n d u c e s a l o w e r s t o m a t a l 'sensitivity', leading to s t o m a t a l closare at increasingly l o w e r ~bF values (see B r o w n et al., 1976; Ponce, 1978), or o n the c o n t r a r y it c a n i n d u c e a higher s t o m a t a l sensitivity (Schulze et al., 1974; H a l l et al., 1975; C l e m e n s a n d Jones, 1978). 0304-3800/90/$03.50

© 1990 Elsevier Science Publishers B.V.

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The present paper aims at demonstrating that two different methods for determining critical leaf water-potential ~FC lead to the same results: the first method, a conventional one, requires punctual and manual measures of rs and ~kF, whereas the second one, which will be presented here, consists of: replacing stomatal resistance measurements by Bowen's ratio (ratio of sensible heat flux to latent heat flux). Indeed, in keeping with the theoretical (Monteith, 1965; Perrier et al., 1975) and experimental (Ritchie and Jordan, 1972; Perrier et al., 1975; Baldocchi et al., 1985; Itier and Riou, 1985) works which demonstrated the relationship between Bowen's ratio and stomatal resistance, both Bowen's ratio and stomatal resistance will be verified as evolving similarly as functions of ~bF. - replacing the measured values of leaf water potential ~ F by the calculated values derived from a model of water transfer in the soil-plant system incorporating the dehydration and rehydration of the whole plant (Katerji et al., 1983a, b, 1986). Both methods will be verified to yield analogous results, our method having of course a twofold advantage being both characteristic of the whole canopy and mostly derived from recordable parameters. -

METHODS AND TECHNIQUES The present study was performed at the Station of Bioclimatology (Versailles, Paris region) on a 1-ha potato (cv. Bintje) plot during the period 20 July-30 August 1983. At the beginning of the experiment, the crop had attained the maximum aerial growth (LgI = 4). 1. Determination of stomatal res&tance Hourly measurements of stomatal resistance were carried out in the uppermost plant layer (25-50 cm) for 8 days (distributed between 7 / 2 6 and 8/30) without any light regulation. The values obtained showed a markedly lower heterogeneity than for the other crop layers (Katerji et al., 1983c). At each hourly measuring, 20 punctual measurements of rs were made on the upper and lower leaf surfaces with a diffusion porometer (Automatic porometer MKII). Hourly equivalent resistance rse is defined as:

rse [ l] -1

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2. Determination of Bowen's ratio Let us recall that the energy balance (usually expressed in (W/m2)) of the plant canopy can be written as follows:

R,,+G+H+Lw=O Bowen's ratio has been defined (Bowen, 1926) as the ratio of sensible heat flux to latent heat flux, that is, H/LE. Fluxes H and LE were determined every hour by means of the combined aerodynamic method (Itier, 1981). Calculations were made from the measurements of net radiation of the heat flux within the soil and from temperature and windspeed gradients measured at two different levels above the crop. The reliability of this device as compared to the other flux-measuring methods has been analysed by Itier (1981); results show that the error in hourly measured flux values is of approximately 15%.

3. Determination of leaf water potential Leaf water potential was measured using a pressure chamber (Scholander et al., 1965). Measurements were made each hour from 1 h before sunrise until the time at which the water potential reached an equilibrium (generally 2-3 h after sunset). Every hour, twelve measurements were made, i.e. six replications in both upper and lower vegetation layers, each 15-25 cm thick; ~PF was then calculated by means of a method derived from that of Van Bavel and Ahmed (1976), which consists of correcting the relative mean for each layer by use of a coefficient corresponding to the ratio of stomatal resistance in each layer to total plant resistance. An average 0.07% error on the ~kr measurements can be observed (Katerji et al., 1986), to which errors related to the very principle of calculating the mean ~ z must be added. The total error on ~bv could be estimated at 10%.

4. Calculation of leaf water potential The method used for calculating IpF on the basis of a dynamic model for water transfer in the soil-plant system is given in detail elsewhere (Katerji et al., 1983a, b, 1984, 1986); we will recall briefly its principle and the different steps in the calculation of this model.

a. Diagram of water transfer from soil to leaf The proposed diagram is presented in Fig. 1A. It includes a main circuit from soil to leaf presenting a resistance, R, and a reservoir connected to this circuit via a resistance.

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vlV iT °I

R

(Jrlpc

--

(A) ~p

Fig. 1. (A) Diagram of the types of water transfer in plants, showing in particular: potentials in: the soil 0ks), reservoir (ffp), leaf (~kF) resistances R and r - fluxes: transpiration (T), root absorption (a) and internal flow (q). (B) Relationship between the potential ~kp and relative water content v / V of the reservoir (v = actual water volume; V= maximum v) showing in particular: - the angular coefficient p of the linear branch - the critical potential ffpC above which p is assimilated to infinity in the model. The three potentials i n t r o d u c e d into the m o d e l are leaf potential (~kF), plant reservoir potential (+p), a n d average soil potential (~ks) in the root area. The three flows are transpiration ( T ) , root a b s o r p t i o n ( a ) a n d reservoir contribution (q) (positive during drying, negative d u r i n g rehydration).

b. Transfer equations The three flows are linked by the relation T=a+q

(1)

The drops in potential on the paths of resistances R a n d r are given b y

~bs - ~kF = Ra

(2)

and ~ p -- ~ F =

rq

(3)

If v represents the v o l u m e of water at time t in the reservoir, V the highest value of v, a n d p the slope of the curve giving ~kp as a f u n c t i o n of the relative h u m i d i t y v / V (P = V d ~ k p / d v f u n c t i o n of v / V ) , the flow q equal to - d v / d t m a y be written as follows: q=

V dhbp p dt

CRITICAL LEAF WATER POTENTIAL

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The two parameters V and p characteristic of the model are involved only through their V/p ratio.'

c. Determination of the parameters of the model The parameters introduced into the model are: the resistance R of the principal soil-leaf circuit (Fig. 1A) the resistance r linking the reservoir to the principal circuit (Fig. 1A) - the critical value +pc for the reservoir potential, value above which O is assimilated to zero (Fig. 1B, the vertical part of the curve) the value V/O when ~bp is less than ~pc (Fig. 1B). The methods for determining the parameters are described in other references (Katerji et al., 1986). Briefly, this determination is based on the determination of 4's and of T and +F values at regular time intervals (here every hour) from dawn (T = 0) to the time of night at which equilibrium is reached again. -

-

-

d. Application of the model to the calculation of hourly ~/f values Equations (1), (2), (3) and (4) lead to the following differential equations:

+ s - q~V= RT + V / p [ ( R + r) d~bF/dt + Rr(dT/dt)] The values for calculating +F, and which therefore must be measured, are the following: transpiration, T; the mean soil potential within the soil, ~ps; and the four parameters characteristic of the canopy (R, r, V/O, +pc). The mean potential within the soil +~ was assimilated to the predawn leaf potential (Tinklin and Weatherley, 1960). The hourly values of T were obtained by means of the combined aerodynamic method. Actually, this method leads to the measurement of latent heat flux LE (or actual evapotranspiration AET) but in this case, the crop canopy was dense enough (LAI > 2.5) to allow us to consider soil evaporation as negligible and to assimilate actual evapotranspiration to transpiration T. (Katerji and Perrier, 1985). The four parameters characteristic of the model (R, r, V/O, +pc) were determined approximately every ten days, then applied to the calculation of +F for other days of measurement, that is: - 7/20, 21 and 29 using the parameters determined on 7/21 - 8 / 8 and 8 / 9 using the parameters determined on 8 / 8 - 8/18, 19, 26 and 30 using the parameters determined on 8/19. EXPERIMENTAL RESULTS

Plotting equivalent stomatal resistance and H/LE ratio against measured ~F The values of equivalent stomatal resistance rse (Fig. 2) and of the H/LE ratio H/Lr (Fig. 3), obtained for the same hour, are plotted against +~.

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rse ( S m -I) 800_

0 0 0

600_

400_ o

o

0

o ° °

o

200_ 0

O0 0

0 0.5

i

07f

0

o co

0

I

0.9

o

I

i

I.I

- ~F

I

1.3

(Mpo)

Fig. 2. Variation of r~ (hourly equivalent stomatal resistance of the upper 20-50 cm stratum) as a function of ~kF (hourly mean leaf water potential of the canopy). Vertical and horizontal lines are 97.5% confidence intervals on the mean.

In general, we find that equivalent stomatal resistance rse and the Bowen ratio H/gE evolve similarly in relation to + e. The rse resistance is generally low (rse = 150 s m -1) when g'F values are high. Starting at a critical value of 4'v (q'FC = --0.95 M P a + 0 . 0 6 ) , rse becomes significantly higher and increases rapidly as qJF decreases. The H/gE ratio varies between 0 and 0.15 for +F values greater than - 0 . 9 5 MPa, then increases rapidly with decreasing ~kv- We can thus consider that the threshold for stomatal closure for the crop under study corresponds to Bowen-ratio values greater than 0.15.

Daily evolution of measured and calculated leaf water potential and of the H / LE ratio Figure 4 provides a survey of all the measurements carried out during the nine sunny days selected between late July and late August. Upper graphs

CRITICAL

LEAF

WATER

POTENTIAL

FOR

STOMATAL

139

CLOSURE

NILE 1.2 0 0 0

1.0

O, 8

0

m 0

0

0

0°6

--

O

O o

o

o

o

0.4 o

o o o

0.2

o

o

o o

0 0.5

,

,

0.6

0.7

o

o

o

o

~,

0.8

o o

Og

I

I

0.9

I

I

I.I

1~2

- t0 F (u Po) Fig. 3. Variation of the Bowen ratio (H/LE) as a function of ~PF (hourly mean leaf water potential of the canopy).

indicate the evolutions of H / L E , and lower graphs those of measured and calculated leaf water potential. The soil dried progressively due to a relative drought in August (only two rainfalls of more than 1 mm, the first one of 14 mm on 10 August, the second one of 8 mm on 20 August; in fact, the predawn leaf water potential was observed to decrease from - 0 . 2 4 (7/20) to - 0 . 4 2 MPa (8/30), whereas the minimum values measured around midday decrease from - 0 . 8 5 on (7/2) to - 1 . 1 MPa (8/30). The two (measured and calculated) values of + F plotted in Fig. 4 are in good agreement as their difference seldom exceeds - 0 . 1 MPa. This confirms the applicability of the model calculating +v. The upper graphs exhibit the daily evolutions of H / L E during the same nine days. H / L E remained roughly constant and low (H/LE < 0.15 during the first three days under consideration (20, 21 and 29 July)). During the six following days this ratio exceeded the above-mentioned value more or less early in the morning to attain about 5 to 10-fold higher values by midday. More precisely, let us consider the measured or calculated value of water potential corresponding to the first hour when the H / L E ratio exceeded 0.15. Table 1 shows that all mean values ranged from - 0 . 9 2 to - 0 . 9 3 + - 0 . 1 MPa; reference to Fig. 2 reveals that this is precisely the critical value of ~bF at which stomatal resistance rs decreased rapidly. This table suggests more-

0.4

~

o

2~'

. .

2i/7

. .

7/21

. .

--I~

",:5

29/7

7/29

2e~'

0.92 0.87

8/8

8/8

- 0.93 - 0.81

8/9

"o~"

9/8

- 1.0 - 1.08

8/18

it"

A

18/8

- 0.98 - 0.96

8/19 - 1.05 - 0.95

8/26

19/8

- 0.70 - 0.85

8/30

26/8

50/8

~b FM = -- 0.93 _+0.12 ~kFC = - - 0 . 9 2 _ + 0 . 1

MPa.

Fig. 4. E v o l u t i o n d u r i n g n i n e s u n n y d a y s , c h a r a c t e r i z e d b y a n i n c r e a s i n g soil d r y n e s s of: - t h e B o w e n r a t i o H/LE - c a l c u l a t e d leaf w a t e r p o t e n t i a l s ~Fc ( X ) a n d m e a s u r e d leaf w a t e r p o t e n t i a l s ~Fm (Q))" S h o w i n g , in p a r t i c u l a r , t h e critical v a l u e - 0 . 9 5

~Fm

-I,2

o-

--;o-",5

- 1.0 - - "

- O.el

- 0,6

-

-0.2

0.5

I°0

20•7

. .

~bVm ( M P a ) 4' Fc ( M P a )

H

7/20

Days

C a l c u l a t e d ~kFc or m e a s u r e d 4'vm l e a f w a t e r p o t e n t i a l at t h e t i m e at w h i c h t h e B o w e n r a t i o b e c o m e s g r e a t e r t h a n 0.15

TABLE 1

7~

CRITICAL

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FOR STOMATAL

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141

over that the critical value of ~Pv which can thus be considered as representative of the values indicated, did not vary systematically during the time period under consideration ( 7 / 2 1 - 8 / 3 0 ) . DISCUSSION AND CONCLUSION Studying water stomatal regulation usually requires the determination of both stomatal resistance rs and leaf water potential ~kF- The results presented here show that stomatal resistance can be replaced by Bowen's ratio H/LE (sensible heat flux to latent heat flux) and measured values of 4'v by the data calculated on the basis of a model. Substituting H/LE for rs provides the following advantages: H/LE characterizes the whole canopy, whereas leaf stomatal resistance measures carried out on small scale (i.e. a single leaf) must be spacially multiplied to be applicable to the whole canopy; the mean value obtained displays however a heavy error. Fluxes H and LE can be recorded by means of the combined aerodynamic method that requires only simple devices (anemometers, thermocouples . . . . fluxmeters and data gathering system). The hourly calculation of leaf water potential on the basis of the model proposed, which here too leads to values close to measured ~bF, requires but a small number of direct measurements, i.e. The predawn leaf water potential on the day considered. The complete series of hourly ~pv potentials throughout the same day, in order to determine the model's parameters; this determination must be performed approximately every 7 to 10 days. The hourly values of latent heat flux LE on the day under consideration; this value has already been mentioned, and as it can be recorded, does not imply any intervention on the part of the experimentalist. The method we propose is thus well suited to studies carded out under natural and rather simple conditions. Besides these methodological aspects, some results are worth underlining: The critical value of leaf potential ~PFC (--0.95 MPa) appeared to be stable during the whole period when it could be determined, i.e. here from 8 to 30 August. Obviously this result cannot be generalized; however, the interest of such investigations and consequently of the method proposed consists precisely in examining the possible variations of critical leaf water potential ~PFC in order to find their causes. Before any stomatal regulation, the value of the H/LE ratio varies between 0 and 0.15. These values are of the same order of magnitude as

142

N. KATERJl

those r e p o r t e d b y Ritchie a n d J o r d a n (1972) o n S o r g h u m , K a t e r j i a n d Perrier (1983) o n lucern, and K a t e r j i et al. (1988) o n t o m a t o . T h e results p r e s e n t e d in Fig. 4 also suggest that w h e n p r e d a w n leaf w a t e r p o t e n t i a l d r o p p e d b e l o w - 0 . 3 M P a , the p o t a t o c r o p e x h i b i t e d w a t e r stress. T h e value is of the same o r d e r of m a g n i t u d e as these r e p o r t e d in the literature for several species: c o r n ( D r y e r a n d Stewart, 1984), eggplant (Schoch et al., 1987) a n d t o m a t o ( K a t e r j i et al., 1988). Finally, the p r e s e n t s t u d y e n a b l e d us to analyse the i n f l u e n c e of the + v p o t e n t i a l o n c r o p w a t e r supply. This r e p r e s e n t s b u t o n e of the possible applications of the d e t e r m i n a t i o n o f the ~bv p o t e n t i a l d u r i n g the day. I n d e e d similar studies could b e applied to o t h e r biological f u n c t i o n s such as p h o t o s y n t h e s i s or growth, as these f u n c t i o n s h a v e also b e e n related to the p o t e n t i a l ~bF (cf. the literature review b y L u d l o w , 1976; H s i a o et al., 1976; Boyer, 1976; C o w a n , 1977). REFERENCES Aboussouan-Seropian, C. and Planchon, C., 1985. Rrponse de la photosynthrse de deux vari&rs de bl6 h un drficit hydrique foliaire. Agronomie, 5: 639-644. Ackerson, R.C., 1983. Comparative physiology and water relation of two corn hybrids during water stress. Crop Sci., 23: 278-283. Adjahossou, D.F., Louguet, P. and Vieira da Silva, J., 1984. Corrrlations entre les rrsistances stomatiques de divers croisements de palmier ~t huile (Elaeis guineensis Jacq.) et la tolrrance h la srcheresse. Acta Oecol. Oecol. Plant., 2: 119-131. Baldocchi, D.D., Verna, S.B. and Rosenberg, N.J., 1985. Water use efficiency in a soybean field: influence of plant water stress. Agric. For. Meteorol., 34: 53-65. Boyer, J.S., 1976. Water deficits and photosynthesis. In: T.T. Kozlowski (Editor), Water Deficits and Plant Growth. Vol. 4, Soil and Water Measurements, Plant Response, and Breeding for Drought Resistance. Academic Press, New York, pp. 153-190. Bowen, J.S., 1926. The ratio of heat losses by conduction and by evaporation from anywater surface. Phys. Rev., 27: 779-787. Brown, K.W., Jordan, W.R. and Thomas, J.C., 1976. Water stress induced alteration of the stomatal response to decreases in leaf potential. Physiol. Plant., 37: 1-5. Clemens, J. and Jones, P.G., 1978. Modification of drought resistance by water stress conditioning in Acacia and Eucalyptus. J. Exp. Bot., 29: 895-904. Cowan, I.R., 1977. Stomatal behaviour and environment. Adv. Bot. Res., 4: 117-225. Dwyer, L.M. and Stewart, D.W., 1985. Indicators of water stress in corn (Zea mays L.). Can. J. Plant Sci., 64: 537-546. Hall, A.E., Carnacho, S.E. and Kaufmann, M.R., 1975. Regulation of water loss by citrus leaves. Physiol. Plant., 33: 62-65. Hsiao, T.C., Acevedo, E., Fereres, E. and Henderson, D.W., 1976. Stress metabolism, water stress, growth and osmotic adjustment. Phil. Trans. R. Soc. London Ser. B, 273: 479-500. Itier, B., 1981. Une mrthode simple pour la mesure de l'rvapotranspiration rrelle ~t l'rchelle de la parcelle. Agronomie, 1: 869-876.

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