A parameterisation of soil water stress based on the A

J.-C. Calvet Agricultural and Forest Meteorology 103 2000 229–247 239 Fig. 7. The response to soil water stress of plants following a defensive strategy, using the T s -based Jarvis approach. The leaf sensitivity to leaf-to-air saturation deficit α H , left, and the minimum stomatal resistance r smin , right are plotted vs. the extractable soil moisture θ Eq. 9. Jarvis approach in Figs. 6 and 7. This result indicates that using T a as a factor of the stomatal aperture is not fundamentally different from using T s , but that T s seems to be a better descriptor of the temperature de- pendence of the g s parameters.

6. A parameterisation of soil water stress based on the A

A A–g g g s approach In Section 5.1, it was shown that the parameters of the A–g s model vary along with soil moisture and that the way this adaptation occurs differs from moderate to strong water stress and from one plant type to another. 6.1. Similarity of stressed and unstressed relationships The negative correlation found in Section 4 between lng ∗ m and lnD ∗ max for C 4 and C 3 herbaceous plants may denote a functional adaptation to the environment. Very high values of D ∗ max , as obtained for a number of species, correspond to little stomatal sensitivity to air humidity. The lack of response of g s to air humidity may restrict plant survival in dry conditions. In that situation, Fig. 3 attests that g ∗ m , and hence the gen- eral level of stomatal conductance and photosynthesis whatever, air humidity are generally lower. On the other hand, plants showing a high sensitivity to air humidity that is, closing their stomata rapidly with increasing saturation deficits, consistent with low val- ues of D ∗ max , may compensate for the resulting deficit of photosynthesis through higher values of g ∗ m . In this respect, the C 4 and C 3 lines of Fig. 3 may correspond to viable parameters of the photosynthesis in differing environmental conditions. Rather than proposing a full mechanistic model, the goal of this study is to bring out possible mechanisms of the plant response to drought from available data. The C 3 -line of Fig. 3 is valid for unstressed conditions θ 90, and is given by lng ∗ m = 2.381 − 0.6103 lnD ∗ max n = 31, r 2 = 0.40 10 The results obtained in this study for C 3 herbaceous plants suggest that: 1 as shown by Table 5, the correlated variability of the g ∗ m and D ∗ max parameters represented by the regression equation 10 is also observed for well watered plants of the same species grown under different soil substrate, or ‘pot-size’ con- ditions; 2 for extractable soil water content higher than 40, the plant response to drought is similar to the ‘pot-size’ rooting effect. Indeed, an equation similar to the unstressed g m –D max relationship of Eq. 10 is observed with moderately stressed plants 90θ 40 lng m = 1.130 − 0.4594 lnD max n = 9, r 2 = 0.38 11 Moreover, pooling these moderately stressed plants with the unstressed ones i.e. considering soil condi- tions for which 100θ 40 hardly modifies Eq. 10 240 J.-C. Calvet Agricultural and Forest Meteorology 103 2000 229–247 lng m = 2.215 − 0.5944 lnD max n = 40, r 2 = 0.40 12 while a different result is obtained if only stressed data are considered i.e. 90θ 0 lng m = −0.291 − 0.2238 lnD max n = 22, r 2 = 0.11 13 The similarity of the g m –D max relationships ob- tained under unstressed, moderately stressed, and divers ‘pot-size’ conditions may not be fortuitous and the plant response to the early stage of soil desicca- tion may be related to the soil resistance to rooting which varies according to soil water content. As already mentioned Section 5.1, increasing, moder- ate soil water stress induces two radically different effects: the plant may react either as it were grown into a ‘smaller pot’, or on the contrary into a ‘larger pot’. In other words, depending on the plant-type and maybe on the soil type, moderate soil water stress may either trigger root compaction or, on the contrary, stimulate root growth. In the first situation, the stom- atal response to vapour pressure deficit is increased, while the sensitivity to air dryness decreases in the second case. Given the limited number of studies, it is difficult to draw definite conclusions about the effect of the mechanical limitation of rooting on the value of g ∗ m and D ∗ max . However, the effect presented in Table 5 is in agreement with other results showing that various well watered pot-grown plants respond to D s , while the same plants grown in well watered natural soils do not Tardieu and Simonneau, 1998. Specific experiments on the effect of pot size on transpiration showed that there is a reduction of plant transpiration with decreasing pot size Ray and Sinclair, 1998. Moreover, physiological experiments showed that the resistance that soil exerts to penetration by plant roots may have an influence on the photosynthesis rate Masle et al., 1990. A consequence of these observations is that the location of the unstressed g ∗ m and D ∗ max parameters of a given plant on the C 4 - or C 3 -line of Fig. 1 may depend on soil depth, texture, density, structure, and presence of stones. Since soil hardness also depends on soil water content, there might be an interaction between the soil water stress and the soil hardness effects on the plant functioning. This observation may explain reported dissimilarities between past studies Turner et al., 1984. Finally, the two responses to stress illustrated by Figs. 4 and 5 may be interpreted as two distinct strate- gies: 1. The growth of the root-system of the plants fol- lowing the first strategy sunflower, hazel tree, and the MUREX fallow may be stimulated under mod- erate soil water stress, consistent with a displace- ment towards higher values of D max on the C 3 -line. This somewhat ‘offensive’ way to respond to water stress may be related to the ability of these plants to develop a deep root-system Cabelguenne and De- baeke, 1998. Such a behaviour was described by Reid and Renquist 1997 in the case of field-grown tomatoes. Exploring deeper soil layers may be a way to compensate for the lack of stomatal regu- lation associated with high values of D max Manes et al., 1997. Also, short-cycled plants may follow such a strategy. In this case, the lack of stomatal control is compensated by a phenological ability to survive drought, either through a rapid reproductive cycle or through underground vegetative elements able to survive water shortage. 2. On the contrary, the ‘defensive’ strategy of cowpea and soybean may be explained by an increased stomatal regulation in response to higher soil hard- ness appearing in relation to lower soil moisture. Following the C 3 -line for moderate soil water stress, that is, improving the assimilation capacity by increasing g m , while saving water by reduc- ing D max , enables the plant to survive drought in spite of limited water supply and a relatively long growing cycle. 6.2. An empirical response function A representation of both offensive and defensive strategies based on the A–g s approach is given by Figs. 8–10 for C 3 plants having the same unstressed pa- rameters. Schematically, the first phase of soil water stress is represented by a linear response of D max to values of extractable soil water θ comprised between 100 and a given critical value θ C an arbitrary value of 50 is taken in Fig. 8. During this phase, g m is related to D max by the C 3 -line logarithmic equation. For values of θ below θ C , g m and D max are alternately constant and proportional to the θ θ C ratio, for the J.-C. Calvet Agricultural and Forest Meteorology 103 2000 229–247 241 Fig. 8. Schematic representation of two strategies of C 3 plants to adapt the values of mesophyll conductance g m and maximum leaf-to-air saturation deficit D max in response to soil water stress. In the offensive strategy solid line, dia- monds D max deviates from its unstressed value D ∗ max through D max = D X max + D ∗ max − D X max θ − θ C 1 − θ C , where D X max is the maximum value of D max , for values of θ lower than the crit- ical extractable soil moisture θ C that is, for moderate soil water stress. Meanwhile, g m decreases according to D max , following the C 3 logarithmic regression equation of Fig. 3. In the defensive strategy dashed line, boxes, the same equations are used, where D X max is replaced by D N max , the minimum value of D max . Below θ C , i.e. for more pronounced water stress g m remains constant, and D max = D N max + D X max − D N max θθ C in the offensive strategy, while g m = g X m θ θ C and D max remains constant in the defensive strategy g X m is the value of g m corresponding to D N max through the C 3 regression line. As an example, the values of D N max , D ∗ max , and D X max , are 55, 148, and 403 g kg − 1 , respectively, and θ C = 50. offensive and the defensive responses, respectively. The leaf stomatal conductance, transpiration, net as- similation A n , and water use efficiency W UE , as calculated by the modified A–g s model as a function of θ and D s , are given in Figs. 9 and 10 for the same offensive and defensive responses described in Fig. 8, respectively. The water use efficiency W UE represents the plant ability to assimilate carbon for a given loss of transpired water. W UE = A n E 14 It clearly appears that the leaf response to soil wa- ter stress sharply depends on the value of D s . Namely, there is an interaction between soil and atmospheric water stress. A remarkable difference between offen- sive and defensive responses consists in a higher W UE for intermediate soil water contents in the defensive case, for given D s conditions, whereas W UE dimin- ishes in the offensive one. Also, A n varies signifi- cantly according to θ and D s in the defensive response, while A n is much more stable in the offensive one. This is consistent with different survival mechanisms: 1 water-saving regulation in the defensive strategy implying a constant adaptation of photosynthesis; 2 weak physiological response to soil water stress, compensated by a more efficient root water-uptake or a more rapid growing cycle in the offensive strat- egy. These results may explain why so many different parameterisations of the soil water stress have been proposed for SVAT-modelling Mahfouf et al., 1996. Since the θ –D s interaction is not explicitly treated in any of them, each parameterisation may result in cor- rect simulations under given D s conditions, for given soil and plant-response strategies, but fail elsewhere. 6.3. Application to interactive vegetation modelling In order to test the suitability of these conclusions, the offensive response displayed in Fig. 8 was applied to the interactive-vegetation simulations performed by the ISBA–A–g s model on the three growing cycles of the MUREX fallow, in south-western France Calvet et al., 1998, 1999. This is to verify that the tenta- tive, simplified parameterisation of stress presented in Fig. 8 may be employed in a long-term simulation and interacts well with the other processes described in the algorithm. For these simulations, a fixed value of biomass per unit of LAI of 76 g m − 2 was employed, together with a maximum leaf life-expectancy of 40 days. The comparison between simulated and mea- sured LAI and θ as calculated over a 1.35 m soil depth is shown in Fig. 11. Soil moisture is simulated well over the 3 years. The abrupt decrease of LAI in 1995 is due to the cutting of the vegetation. This event is prescribed in the model which, in turn, is able to simulate the regrowth. The observed and simulated contrast of the vegetation cycles of 1996 and 1997 are due to very different precipitation regimes: 1996 was a rainy year, while 1997 was relatively dry, especially during the spring. It must be noted that the model underestimation of LAI during the 1997 drought is consistent with the rather large soil moisture content measured at the end of this period: if measured LAI values are imposed, soil moisture is poorly simulated 242 J.-C. Calvet Agricultural and Forest Meteorology 103 2000 229–247 Fig. 9. Simulated response of leaf-air exchange variables to soil water stress in the offensive strategy. The simulations are performed using the parameters of Fig. 8, at 30 ◦ C, a solar radiation of 800 W m − 2 , and CO 2 air concentration of 350 ppm, for leaf-to-air saturation deficits of 3, 6, 12, 24, and 48 g kg − 1 solid, dashed, dash-dotted, dash-three-dotted, and long-dashed lines, respectively. A Leaf stomatal conductance; B leaf transpiration; C CO 2 assimilation and D water use efficiency. Fig. 10. Simulated response of leaf-air exchange variables to soil water stress in the defensive strategy. The simulations are performed using the parameters of Fig. 8, at 30 ◦ C, a solar radiation of 800 W m − 2 , and CO 2 air concentration of 350 ppm, for leaf-to-air saturation deficits of 3, 6, 12, 24, and 48 g kg − 1 solid, dashed, dash-dotted, dash-three-dotted, and long-dashed lines, respectively. A Leaf stomatal conductance; B leaf transpiration; C CO 2 assimilation and D water use efficiency. J.-C. Calvet Agricultural and Forest Meteorology 103 2000 229–247 243 Fig. 11. Comparison between measurements boxes and diamonds performed over the MUREX fallow and simulations line of the ISBA–A–g s model Calvet et al., 1998, accounting for the offensive strategy described in Fig. 8 the same numerical values are used. A Leaf area index and B extractable soil water content. during this period. A possible explanation may be that the planimetric method employed to estimate LAI fails when many leaves become senescent, because of the difficulty to make the difference between ‘green’ leaf-parts and senescent ones.

7. Discussion