Water Resources Research

A dynamic soil water threshold for vegetation water stress derived from stomatal conductance models

Authors


Abstract

[1] In many terrestrial ecosystems, vegetation experiences limitation by different resources at different times. These resources include, among others, light, nutrients, and water. Frequently, however, leaf-level modeling frameworks that unite these limitations rely on empirical functions to scale stomatal conductance as a function of water stress. These functions use prescribed values of soil water content to mark the transition between water-stressed and unstressed conditions without accounting for the dependence of such a water content threshold on atmospheric and hydrologic conditions and nutrient availability. To address the phenomenon of a variable threshold to water stress, we combine an existing water-limited stomatal conductance model with an existing assimilation (photosynthesis)-limited stomatal conductance model. In this manner, we simulate variable controls on stomatal conductance and use a combination of the two models to define the threshold at which soil water content becomes limiting to transpiration. Modeled plant processes are used to define this water stress threshold as functionally dependent upon local environmental conditions (light, temperature, and atmospheric vapor pressure), parameters representing different vegetation types, and nutrient status. Simulations demonstrate that as environmental conditions become more favorable for assimilation, the likelihood of water stress increases. Specifically, there exist ranges of leaf temperature, light, and atmospheric humidity for which water stress is maximized.

1. Introduction

[2] The complex dynamics resulting from the interactions between physical and biological processes make the understanding of ecosystem response to changes in environmental conditions (e.g., water, light, nutrients) extremely difficult. This is particularly true in the case of ecosystems that are limited by different resources at different times. For example terrestrial ecosystems in the eastern U.S. may undergo severe water stress during dry years (e.g., the first years of this century), while nutrients are likely to limit productivity during wet years. In the context of this study, we define water stress as water-limited CO2 assimilation and transpiration. Understanding ecosystems such as these using models based only on one limiting factor can lead to partially correct or to misleading conclusions. As one case in particular, our current understanding of the mechanisms controlling stomatal conductance is hindered by models that do not consider explicitly limitation by different factors at different times. A comprehensive understanding of the controls on stomatal conductance requires a modeling strategy that has the ability to discriminate between individual limiting factors.

[3] Plants represent an important coupling point between terrestrial cycles of carbon and water. This coupling is ubiquitous among terrestrial ecosystems, with much research historically focusing on agricultural systems in which water availability is linked directly to crop production [Begg and Turner, 1976]. A number of studies have approached this issue from the perspective of direct inhibition of plant physiological activities by water stress [e.g., Jarvis, 1976; Jones and Turner, 1978; Morgan, 1984; Pelleschi et al., 1997] whereas others have considered regulation of plant activity by water stress through chemical feedback mechanisms [e.g., Zelitch and Waggoner, 1962; Gollan et al., 1986; Passioura, 1988; Saab et al., 1990]. All of these studies share a common reliance upon stomatal conductance as a regulator of plant water content, and many of them demonstrate functional dependence of stomatal conductance on water availability.

[4] Stomatal conductance is also controlled by the biochemical and physiological processes associated with carbon dioxide assimilation (Figure 1, right-hand side). Generally, assimilation (photosynthesis) rates are limited physically by diffusion rates through stomata and biochemically by enzymatic activity, the conversion of light energy to chemical energy, and respiration associated with physiological activity [Cowan and Farquhar, 1977; Farquhar et al., 1980; Harley et al., 1985; Collatz et al., 1991; Bonan, 2002]. It is through these biochemical processes that stomatal conductance, via assimilation, is regulated by leaf temperature, sunlight and carbon dioxide availability. Additionally, foliar nitrogen content (and thus nitrogen availability) has been linked to photosynthetic capacity [Field and Mooney, 1986; Dang et al., 1997; Meir et al., 2002], due to the high nitrogen content of the carbon-fixing enzyme, Rubisco [Evans, 1989].

Figure 1.

Conceptual model for the hydrologic and physiological controls on stomatal conductance within the soil-plant-atmosphere continuum.

[5] Attempts to address water limitation in the context of photosynthesis-limited stomatal conductance primarily involve scaling a photosynthesis-limited model by some factor representing water stress. Thornthwaite and Mather [1955], Budyko [1958], Eagleson [1982], Jacquemin and Noilhan [1990], and Avissar and Pielke [1991] have defined a piecewise linear function that scales transpiration or stomatal conductance between the threshold of water stress (i.e., the soil moisture status at which water becomes limiting to stomatal conductance and transpiration), and the wilting point soil moisture; however, this technique does not address environmental dependencies of such a water stress threshold or of the scaling function itself. Rather, this scheme makes an a priori assumption of the soil water content at which water limitation commences. Later studies [e.g., Rodríguez-Iturbe et al., 1999; Albertson and Kiely, 2001; Fernandez-Illescas et al., 2001; Porporato et al., 2001; Daly et al., 2004] established critical links between soil texture, soil hydraulic properties and water-limited transpiration, but they treat the water stress threshold as an intrinsic property of soils and vegetation. These studies have, however, discussed water stress as a dynamic parameter whose variability has the potential to affect processes such as transpiration.

[6] Other models of stomatal conductance base soil water limitation on a steady state assumption balancing soil water uptake and transpiration (Figure 1, left-hand side) [e.g., Dewar, 2002; Gao et al., 2002; Buckley et al., 2003; Katul et al., 2003]. These models provide a process-based link between rates of stomatal conductance and soil moisture status, and, by assuming a continuous functional dependence of conductance upon soil moisture, they eliminate altogether the need to scale transpiration between the limiting and wilting points. However, a continuous dependence of stomatal conductance on soil moisture seems to contradict earlier conclusions that there exists a range of soil moistures to which stomatal conductance (and thereby transpiration) is insensitive [see Leuning, 1995].

[7] The main objective of this paper is to situate two common types of stomatal conductance models (moisture-limited hydraulic and the moisture-independent biochemical models), within the framework of observed plant behavior. Instead of using a priori assumptions of soil water limitations to stomatal conductance, we outline a different method for using characteristic parameters of an ecosystem (namely plant physiological properties and soil properties) to determine how environmental state variables (particularly light, temperature and vapor pressure deficit) interact to define quantitatively the threshold at which stomatal conductance becomes water limited. By relating a semiempirical model of stomatal response to light, temperature, and nutrients (Leuning's [1995] adaptation of Ball et al.'s [1987] model coupled with Farquhar et al.'s [1980] physiological model) to a hydraulic model of water-limited stomatal conductance [Gao et al., 2002], we present a framework for exploring the interplay between plant biochemical and hydraulic controls (i.e., the availability of light, nutrients and water) on the movement of water through the soil-plant-atmosphere continuum. We believe that this framework could be used to investigate dynamic water stress in terms of other biochemical or hydraulic submodels Although each submodel provides a simplified representation of the actual physiological processes controlling stomatal conductance, the analysis presented in this paper provides a basis for further study of the complex relationship between vegetation and the physical environment.

2. Methods

2.1. Model Framework

[8] The modeling framework utilizes two separate leaf-level submodels of stomatal conductance to water vapor transfer, one estimating conductance using a CO2 assimilation model that is independent of soil moisture and another estimating water-limited conductance. Other models exist, particularly for water-limited conductance, that could be adopted as submodels in the context of this framework depending on modeling objectives and timescales. For the moisture-independent submodel, we chose Leuning's [1995] adaptation of Ball et al.'s [1987] stomatal conductance (gsA) model

equation image

where b is an empirical parameter representing residual stomatal conductance in the absence of photosynthesis due to light limitation, m is an empirical coefficient, An is the rate of net photosynthesis, Cs is the CO2 concentration outside the leaf, Γ* is the CO2 compensation point (a function of ambient O2, the dual affinity of Rubisco for O2 and CO2, and leaf temperature), Dv is the difference between saturation vapor pressure at the leaf surface (es) and actual vapor pressure of the surrounding atmosphere (ea), and f(Dv) = Dv−0.5. When coupled with Farquhar et al.'s [1980] model of photosynthesis, gsA from equation (1) is a function of the biochemical processes associated with carbon assimilation, namely the enzymatic activity of Rubisco and light-dependent regeneration of the assimilatory substrate Ribulose-bisphosphate (RuBP). An and gsA modeled in this fashion are independent of soil water availability. Specifically, An is calculated as

equation image

where JE, light-limited carbon assimilation, and JC, Rubisco-limited carbon assimilation, are defined by Collatz et al. [1991] as

equation image

where Q is photosynthetically active radiation (PAR) at the leaf surface, α and a are the quantum efficiency and leaf absorpance to PAR, respectively, Ci is internal CO2 concentration, VCmax is maximum carboxylation rate, [O2] is oxygen concentration and KC and KO are the Michaelis-Menten reaction-rate parameters. Vcmax, Γ*, KC and KO are evaluated as exponential functions of leaf temperature and parameter values at 25°C [Collatz et al., 1991]. RD, daytime respiration, is also evaluated as an exponential function of temperature and RD25, the parameter value at 25°C. Equations (1)(3) make the simplifying assumption that PAR, leaf temperature and atmospheric vapor pressure are independent variables. However, the partitioning of net radiation (of which PAR is a major component) at the leaf surface is itself a function of stomatal conductance, and causes changes both in temperature and vapor pressure [Jones, 1999]. The present analysis assumes that PAR, surface temperature and surface vapor pressure are measured independently, and therefore does not consider the effect of stomatal conductance on leaf energy balance. Equation (1) is most successful at estimating stomatal conductances for well watered systems [Leuning, 1995]. In fact, the model in this form does not account for water limitation. Thus equation (1) is here used as a moisture-independent submodel.

[9] For the water-limited submodel of stomatal conductance, we selected a hydromechanical model by Gao et al. [2002] that assumes a steady state balance between water uptake by roots and water loss by transpiration. The Gao et al. [2002] model was selected because it includes no a priori assumption of a threshold for soil water limitation [e.g., Dewar, 2002; Katul et al., 2003], and it contains few parameters relative to other models [e.g., Buckley et al., 2003]. This model does have several limitations, including its assumption of steady flow through the soil-plant-atmosphere continuum, its simplistic treatment of the relationship between stomatal conductance, leaf water potential and turgor pressure [see Buckley et al., 2003], and its inability to account for xylem cavitation [see Sperry, 2000]. At short timescales (subdaily), these limitations may affect model performance due to the presence of transient (i.e., nonsteady) states of plant hydraulics and the short-term effects of cavitation on plant hydraulic conductance. Nevertheless, we employed the Gao et al. [2002] model because of its simplicity and its continuous (linear) dependence of stomatal conductance upon soil water potential. This model reduces whole-plant hydrodynamics to a relation between soil water potential ψs and stomatal conductance (gsW), and takes the form

equation image

where g0m is the maximum residual stomatal conductance at saturated soil conditions, Q is PAR and kψ, kαβ, and kβg are model-specific parameters. dv is Dv normalized by atmospheric pressure. According to Gao et al. [2002], kψ relates soil water potential to stomatal conductance by assuming direct proportionality between gs and the deformation of leaf guard cells caused by changes in turgor pressure. kαβ is the sensitivity of gsW to changes in PAR as a result of the effect of PAR on K+ concentrations in the guard cells rather than direct control of photosynthesis by PAR. kβg is a parameter that describes the ease of guard cell deformation, efficiency of soil to leaf conductance, and response of gsW to changes in dv. These parameters were derived from observable plant processes; however, Gao et al. [2002, 2003] estimated parameter values both for specific plant species and broader functional types through nonlinear regression of equation (4) using corresponding leaf-level measurements of independent variables and gsW.

[10] To account for variable limitation of stomatal conductance by different factors at different times, we define stomatal conductance as gs−min, the minimum of gsA and gsW, or

equation image

Equation (5) mimics both the observed natural phenomenon and common modeling practice of limiting stomatal conductance by soil moisture below a certain threshold.

[11] This equation is the relationship necessary to describe the variable limitation of stomatal conductance by factors controlling both assimilation and transpiration. More importantly, equation (5) expresses stomatal conductance explicitly (1) as a response to the biochemistry of photosynthesis and (2) as a principal element of the soil-plant-atmosphere continuum.

2.2. Water Stress Threshold

[12] By combining equations (4) and (5), we define a threshold for water stress from the soil water potential required to balance stomatal conductances of the water-limited submodel (gsW, equation (4)) and assimilation-limited submodel (gsA, equation (1)) as

equation image

where ψ* is an explicit function of Q and dv, and implicitly dependent upon An (and its functional dependencies) and Cs through the gsA term. We limit ψ* to a maximum value of 0. The value of ψ* relative to ψsindicates whether the system is water limited or not. If ψs < ψ* a plant is water-stressed, otherwise some other factor limits stomatal conductance. This water stress threshold is defined not only by vegetation-specific submodel parameters, but also by micrometeorological variables that may change greatly through the course of a single day (specifically light, temperature, CO2 concentration and humidity). These functional dependencies result in a water stress threshold that is dynamic not only with respect to vegetation type, but also in response to micrometeorology.

2.3. Calculating Stomatal Conductance From Observed Micrometeorological Data

[13] Half-hourly micrometeorological data were collected from a crop field at Blandy Experimental Farm in Virginia, USA (39.06°N, 78.07°W, elevation 183 m) between 20 April 2001 and 29 May 2001 (days 110 through 149). The model was parameterized using a 20 day subset of data (days 110 through 129). Eddy covariance was used to measure water vapor and carbon dioxide fluxes at a height of 3.5 m above the ground surface near the center of a 10 ha field of rye. The site and measurements are described in further detail by Emanuel et al. [2006]. Leaf-level stomatal conductances were scaled from tower-based measurements of evapotranspiration (ET) using the resistance analogy

equation image

where RTot is the total ecosystem resistance to water vapor transfer, Rcan is the canopy resistance to water vapor transfer and Rav is the aerodynamic resistance to water vapor transfer (s m−1). Rav was estimated from the stability corrections to the logarithmic wind profile

equation image

where z is measurement height, do is the zero-plane displacement, zom and zov are the roughness heights for momentum and water, and k is the von Karman constant. Additionally, u is the mean horizontal wind velocity (m s−1), and Ψm and Ψv are the diabatic functions for momentum and water vapor [e.g., Brutsaert, 1982]. Rcan is commonly estimated from surface energy fluxes and atmospheric vapor pressure deficit using the Penman-Monteith equation [Monteith, 1973]; however, by measuring plant canopy skin temperature (Tc) directly using a sensor temperature-corrected infrared thermometer (IRTS-P, Campbell Scientific/Apogee Instruments, Logan UT) and assuming vapor-saturated air at the canopy (leaf) surface, we obtain a direct measurement of dv and calculate RTot as

equation image

where ET is evapotranspiration (m s−1) measured by eddy covariance. Since no rain fell during or immediately prior to the calibration period (based on records from a nearby meteorological station; Figure 2), we neglected soil evaporation and assumed that the soil was dry enough to consider ET equal to the transpiration rate during this time. We estimated saturation vapor pressure (es) from Tc using Richards' [1971] empirical formula.

Figure 2.

Precipitation near Blandy Experimental Farm for 2001. Inset shows soil moisture (θ) during the calibration period (days 110–129).

[14] By computing RTot and Rav, and solving equation (7) for Rcan, we estimate canopy conductance gcan (m s−1) as the reciprocal of (RTotRav), and stomatal conductance at the leaf level as

equation image

where LAI is leaf area index (m2 m−2) and gsEC is the leaf-level stomatal conductance calculated from eddy covariance measurements. Two simplifying assumptions are implied by this scaling strategy: (1) the canopy is represented by a single “big leaf” and (2) micrometeorological variables measured at or above the canopy surface (namely PAR, canopy skin temperature and atmospheric humidity) are representative of conditions at the leaf surface.

[15] Additionally, we measured volumetric soil moisture integrated through the root zone (0–30 cm) using a time domain reflectometry probe installed perpendicular to the ground surface near the base of the flux tower. PAR was measured approximately 2 m above the plant canopy using a net radiometer. These measurements are also described in greater detail by Emanuel et al. [2006]. We make additional simplifying assumptions that this soil moisture and PAR measurements are representative of conditions within the measurement footprints of the other instruments.

2.4. Model Application

[16] The case study of rye cultivation at Blandy Experimental Farm was used to parameterize and test the combined model of stomatal conductance (equations (1)(5)). Soils at the study site have been previously classified as silt loam [Soil Conservation Service, 1982], and bulk density samples collected at the site indicate a porosity n of 0.58. Using this information, volumetric soil moisture was converted to soil water potential using empirical equations given by Clapp and Hornberger [1978].

[17] Nonlinear least squares regression was used to estimate each submodel's four core parameters (Table 1) independently based on half-hourly measurements made between days 110 and 129. For the assimilation-limited submodel we estimated Vcmax25 (maximum carboxylation rate at 25°C), Rd25, m and b; and for the water-limited submodel we estimated g0m, kψ, kαβ and kβg. Other terms relating to the photosynthesis submodel and field specific conditions were held constant for this study (Table 2). Eddy covariance measurements were selected for use based on the Moving Point Test of Gu et al. [2005]. To be conservative, we chose the wettest 12.5% percent of the data to parameterize the assimilation-limited submodel as an operational means of representing “well watered conditions” stipulated by Leuning [1995]. The remaining subset, consisting of the driest 87.5% of the data, was used to parameterize the water-limited submodel. Parameters estimated from nonlinear regression were used to simulate gs−min with equation (5). The model was validated by comparing gs−min to gsEC for an additional 20-day period (days 130–149).

Table 1. Model-Specific Parameters Used in the Submodels of Water-Limited and Assimilation-Limited Stomatal Conductancea
ParameterValueUnitsDescription
  • a

    Values are shown for rye, estimated in this study. Numbers in parentheses are distances to the 95% confidence limits.

Water-Limited Submodel
gom69.0 (15.6)mmol m−2 s−1Maximum stomatal conductance in dark with saturated soil
kψ0.142 (0.145)mmol m−2 s−1 kPa−1Stomatal sensitivity to ψ
kαβ0.151 (0.046)mmol m−2 s−1 (μmol m−2 s−1)−1Stomatal sensitivity to PAR
kβg44.0 (19.4)mmol m−2 s−1 (mb mb−1)−1Stomatal sensitivity to dv
 
Assimilation-Limited Submodel
Vcmax2538.8 (10.8)μmol m−2 s−1Maximum carboxylation rate at 25°C
Rd250.46 (1.8)μmol m−2 s−1Daytime respiration rate at 25°C
m12.0 (1.8)unitlessSlope of assimilation-limited stomatal conductance
b0.015 (0.012)mol m−2 s−1Residual assimilation-limited stomatal conductance
Table 2. Constants Used for Stomatal Conductance Submodels
ConstantValueUnitsDescription
Photosynthesis Submodel Constantsa
[O2]0.209mol mol−1ambient O2 concentration
a0.86μmol CO2 (μmol Photons)−1leaf absorbtance to CO2
α0.05Unitlessquantum efficiency
τ252600UnitlessCO2/H2O specificity ratio
kc25296μmol mol−1Michaelis-Menten CO2 constant
ko25296mmol mol−1Michaelis-Menten O2 constant
Q10τ0.57unitlesstemperature sensitivity for τ
Q10kc2.1unitlesstemperature sensitivity for kc
Q10ko1.2unitlesstemperature sensitivity for ko
Q10Rd2.0unitlesstemperature sensitivity for Rd
Q10Vcmax2.4unitlesstemperature sensitivity for Vcmax
 
Field-Specific Constants
P930Mbatmospheric pressure
z3.5Mmeasurement height
h1Mcanopy height (measured)
do0.6Mzero-plane displacementb
zom0.15Mroughness height for momentumc
zov0.015Mroughness height for water vapord
u*min0.06ms−1friction velocity threshold
ψsat5.66kPasaturation water potential
bψ5.3UnitlessClapp-Hornberger power law constant
n0.58m3 m−3porosity
 
General Constants
g9.81m s−2gravitational acceleration
Cp1005J kg−1 K−1specific heat capacity of air
Lv2.45 × 106J kg−1latent heat of vaporization
R8.314J mol−1 K−1ideal gas constant
ρa1.18kg m−3air density
k0.4Unitlessvon Kármán constant

2.5. Sensitivity Analyses

[18] We subjected the primary response variables, gs−min and ψ*, to sensitivity analyses to determine the relative effect on our results of variability or uncertainty in the model parameters. For each of the eight model parameters, values were determined from the literature (Table 3 and Gao et al. [2002]), and sensitivity was evaluated over the range of each parameter (summarized as “sensitivity range” in Table 4). Since measurements of gsEC were available for comparison with modeled gs−min, we used the behavioral mapping analysis of Hornberger and Spear [1981] to assess sensitivity of gs−min to parameter values. The behavioral mapping analysis required a Monte Carlo simulation with 10,000 realizations. For each realization, values for each submodel parameter were sampled randomly from uniform distributions (i.e., sensitivity ranges) and were used to estimate gs−min for the validation period. The correlation coefficient and regression slope between gs−min and gsEC were used to assess goodness of fit between observed and simulated conductances, and to assign each parameter set to a category of those that met correlation and slope requirements (behavior) and those that did not (nonbehavior). For each parameter, a two-sample Kolmogorov-Smirnov (K-S) test was used to compare cumulative distribution functions of behavior and nonbehavior categories. The resulting K-S statistic measured the significance of gs−min sensitivity to model parameters.

Table 3. Parameter Estimates From the Literature for Assimilation-Limited Stomatal Conductance Submodela
Vcmax25Rd25mb
Value, μmol m−2 s−1Species/DescriptionValue, μmol m−2 s−1Species/DescriptionValueSpecies/DescriptionValue, mol m−2 s−1Species/Description
Needleleaf Trees
50.4maritime pine (1)3.3P. strobus (4)5.5P. taeda (6)0.000P. taeda (6)
45.7boreal conifers (2)2.3P. massoniana (5)7.5needle forest (2)  
37.5P. sylvestris (2)1.6P. elliottii (5)    
2.3P. caribaea (5)    
2.5boreal conifer (2)    
1.0P. sylvestris (3)    
 
Broadleaf Trees
39.7temperate broadleaf (2)0.7temperate broadleaf (2)9.0nonneedleleaf (10)0.010deciduous forest (8)
47.8P. orientalis (7)2.1A. pseudoplatanus (9)9.5deciduous forest (2)0.061P. orientalis (7)
40.7L. tulipifera (7)2.2B. pendula (9)7.8deciduous forest (8)0.052L. tulipifera (7)
51.9P. xyedoensis (7)1.9F. sylvatica (9)9.8P. orientalis (7)0.094P. xyedoensis (7)
27.8C. japonicum (7)2.1F. excelsior (9)9.3L. tulipifera (7)0.058C. japonicum (7)
60.0Q. alba (8)1.9J. regia (9)6.9P. xyedoensis (7)  
63.1Q. prinus (8)2.1Q. petraea (9)5.8C. japonicum (7)  
37.6A. rubrum (8)2.2Q. robur (9)    
42.8A. saccharum (8)2.1P. orientalis (7)    
39.2N. sylvatica (8)2.1L. tulipifera (7)    
77.8A. pseudoplatanus (9)2.4P. xyedoensis (7)    
70.5B. pendula (9)2.2C. japonicum (7)    
66.3F. sylvatica (9)      
84.6F. excelsior (9)      
63.6J. regia (9)      
87.7Q. petraea (9)      
90.5Q.robur (9)      
Table 4. Parameters Used to Represent Vegetation Functional Types and Ranges for Each Parameter Used in Sensitivity Analysisa
ParameterBroadleaf TreesNeedleleaf TreesRye (This Study)Sensitivity Range
  • a

    For water-limited submodel, values for broadleaf and needleleaf trees are from Gao et al. [2002, 2003]. For the assimilation-limited submodel, values for broadleaf and needleleaf are averages from previous studies listed in Table 3. Parameters obtained from nonlinear regression on rye at Blandy Experimental Farm are used to represent grasses. For all parameters the sensitivity range is the range of values reported across all functional types.

Water-Limited Submodel
gom251.31213.4569.063.2–456
kψ0.30990.11890.1420.0145–0.534
kαβ0.22440.33380.1510.087–0.545
kβg0352.4844.00–667
 
Assimilation-Limited Submodel
Vcmax2558.344.538.827.8–90.5
Rd251.992.170.460.71–3.27
m8.36.512.05.5–12
b0.0550.0000.0150–0.094

[19] The water stress threshold varied with soil properties and vegetation type, and also with changing environmental conditions (equation (6)). A general sensitivity analysis evaluated the sensitivity of ψ* to variability of parameters and micrometeorological conditions. Parameters were increased systematically and individually over the sensitivity ranges (Table 4) while others were held constant and ψ* was calculated from equation (6) for combinations of relatively warm (25°C) and cool (15°C) leaf temperatures and relatively humid (relative humidity, RH = 0.60) and dry (RH = 0.30) atmospheric conditions. PAR was held constant at a moderate level of 1000 μmol m−2 s−1 (approximately one-half full sunlight, 520 W m−2) for the entire analysis.

[20] Additionally, we simulated ψ* across ranges of environmental conditions and plant functional types. Parameters for the two submodels were collected from the literature and assembled in sets representing three plant functional types: grasses, broadleaf trees, and needleleaf trees. For each plant functional type, we evaluated variability of ψ* over simulated ranges of environmental conditions (PAR and RH) while holding temperature and Ca constant.

[21] We also used the linear relationships between leaf nitrogen and An developed by Field and Mooney [1986] to demonstrate the effect of variable foliar nitrogen concentration on ψ* over changing environmental conditions (RH and temperature). Specifically, we varied VCmax in direct proportion to foliar nitrogen concentrations to demonstrate the potential influence of nutrient availability on the modeled water stress threshold.

3. Results and Discussion

3.1. Model Parameterization and Validation

[22] This modeling strategy yields a reasonable prediction of leaf-level stomatal conductance, gs−min, particularly when compared to individual submodel predictions (Figure 3). Differences in regression slopes between the calibration period and validation period may be due, in part, to the assumption of constant LAI for the entire experiment. In other words, if LAI increases throughout the course of the validation period, simulated stomatal conductance may underestimate expected stomatal conductance by a factor proportional to LAI. In much the same manner, assuming static values for other parameters may adversely affect model fit at timescales of vegetation growth. For example, changes in biomass and biomass distribution during the course of a growing season (i.e., plant growth and aboveground versus belowground production) will likely affect not only LAI but also plant hydraulic conductivity. In these cases, model fit may be improved by some knowledge of how these parameters vary through time, or use of a submodel with more explicit definition of the relationships between processes and evolving vegetation states may be warranted.

Figure 3.

Simulated stomatal conductances (gs−min) versus eddy covariance-derived stomatal conductances (gsEC) for (a) calibration period and (b) validation period. For the calibration period, gs−min (open circles) has ρ = 0.77 and slope of 1.01. Submodel conductances gsA (black dots, ρ = 0.48 for calibration period) and gsW (gray dots, ρ = 0.67 for calibration period) are also shown. For the validation period, gs−min has ρ = 0.70 and slope = 1.27 (for gsA, ρ = 0.59 and for gsW, ρ = 0.63). Regression slope is shown as dashed line; 1:1 is shown as solid line.

[23] Agreement between gs−min and gsEC appears to be better during drier conditions than during wetter conditions (Figure 4); however, no significant relationship exists between the residual term gsECgs−min and soil moisture. Systematic underestimation of gsEC between days 140 and 150 may result from the contribution of surface evaporation to ET following the precipitation events occurring between days 139 and 143. On the basis of equation (9), any contribution of surface evaporation to measured ET results in an artificial increase in gsEC. Unlike other periods, during which the soil was dry enough to assume that ET consisted entirely of transpiration, wet conditions on these days likely violated this assumption.

Figure 4.

(top) Predicted transpiration (gs−mindv) versus eddy-covariance-derived evapotranspiration (gsECdv) for the validation period. Open circles are eddy covariance measurements, and solid circles are predicted values of water-limited (gray circles) or assimilation-limited (black circles) transpiration. (middle and bottom) Canopy surface temperature (Tc) and volumetric soil moisture (θ) during the validation period.

3.2. Sensitivity to Environmental Variables and Model Parameters

[24] Simulated gs−min was sensitive to seven of the eight model parameters (Figure 5). Varying Rd25 across ranges of published values did not significantly affect the model fit. This parameter is often considered a residual term for net photosynthesis, and is at least several times smaller than gross photosynthesis. The parameter that exerts the most influence on gs−min is kβg, the sensitivity of stomatal conductance to dv. Because of the close relationship between stomatal conductance and dv [Leuning, 1995; Oren et al. 1999; Gao et al. 2002], kβg is expected to have a strong impact on modeled stomatal conductance. Notice how the dependence of gs−min on dv is in overall agreement with the empirical result by Oren et al. [1999] who found stomatal conductance to be proportional to [1 − η Log(dv)] with η = 0.53–0.60. In fact, for relatively high values of kβg (needle leaves or rye, see Table 4) the right-hand side of equation (4) is proportional to 1/dv (water-limited conditions), in agreement with the framework by Katul et al. [2003], whereas according to equation (1) stomatal conductance is proportional to dv−0.5 (assimilation-limited conditions). For 1 kPa < dv < 5 kPa [1 − η Log(dv)] can be approximated by dv−1 [Katul et al., 2003] and falls between the two curves dv−1 and dv−0.5.

Figure 5.

Behavior and nonbehavior cumulative distribution functions for model parameters gom (K-S = 0.18), kψ (K-S = 0.05), kαβ (K-S = 0.19), kβg (K-S = 0.78), Vcmax25 (K-S = 0.20), m (K-S = 0.23), and b (K-S = 0.16) during the study period.

[25] Because the behavior analysis is conditioned upon field observations, this analysis is only directly applicable to the range of environmental conditions observed during the field observations. It is possible and altogether likely that behavior mapping of model responses to different vegetation or under different environmental conditions of light, temperature and humidity would result in different sensitivities of gs−min. Furthermore, we note that, particularly when calibrated using ecosystem-level data, the physical significance of individual parameters is broadened to incorporate multiple factors and ecosystem processes including the potential effects of cavitation on xylem-water conductance and access to soil water based on rooting depth [e.g., Sperry et al., 2002].

[26] The second sensitivity analysis examined the sensitivity of ψ* to model parameters in different regimes of temperature and atmospheric humidity (Figure 6). Two important characteristics of ψ* are apparent from this sensitivity analysis:

Figure 6.

General sensitivity of ψ* to relative humidity (RH) and photosynthetically active radiation (PAR) across ranges of gom, kψ, kαβ, kβg, Vcmax25, Rd25, m, and b (units shown in Table 1). WH represents warm, humid conditions (Tc = 25°C, RH = 0.60), CH represents cool, humid conditions (Tc = 15°C, RH = 0.60), WD represents warm, dry conditions (Tc = 25°C, RH = 0.30), and CD represents cool, dry conditions (Tc = 15°C, RH = 0.30). PAR is held constant at 1000 μmol m−2 s−1.

[27] First, the general effect of increasing temperature or humidity is to increase ψ*. Because temperature and humidity act on assimilation (temperature through equation (3) and humidity through the iterative solution for gsA and An [see Collatz et al., 1991]) increasing either of these variables creates conditions favorable for plant photosynthetic activity. As conditions become more favorable for carbon assimilation, stomatal conductance required to maintain optimal rates of assimilation also increases. Consequently soil water potential required to support the stomatal conductance also increases; ψ* increases to reflect this requirement (i.e., more water is required to sustain high rates of assimilation). The relationship between temperature, humidity and ψ* is complicated by the effect of temperature on dv and subsequent interactions between dv, ET and stomatal conductance (see equations (9) and (10) and also Oren et al. [1999]). Increasing temperature but not humidity causes dv to increase. On one hand, increasing dv decreases gsA (through Dv in equation (1)), and thereby decreases water stress indirectly by promoting stomatal closure. On the other hand, increasing dv directly increases ψ* by raising atmospheric demand for water (equation (6)). For the combination of parameters representing vegetation at Blandy Experimental Farm and used in the sensitivity analysis, the indirect effect of high dv to decrease ψ* through stomatal closure is masked by the direct influence of dv on ψ*.

[28] We note that ψ* is not the wilting point; in other words plant activities do not cease at soil water potentials below ψ*. Rather, ψ* indicates the point at which soil water availability can no longer support carbon assimilation at the optimal rate otherwise prescribed by environmental conditions. In this context ψ* may be interpreted as a measure of the likelihood of vegetation to experience water stress. If ψ* is very low relative to the distribution of soil moisture at a particular site, vegetation may rarely experience water stress [Ridolfi et al., 2000].

[29] The second important characteristic of ψ*, apparent from the sensitivity analysis is that soil moisture may always limit stomatal conductance and transpiration (Figure 6). In other words, for each parameter there exists some combination of environmental conditions and parameter values for which ψ* approaches or reaches its maximum value, 0. Under these conditions, ψs < ψ*, meaning soil moisture limits stomatal conductance.

[30] We also note that ψ* exhibits a positive response to some parameters and negative response to others. Parameters causing a positive response in ψ* (kψ, kβg, VCmax, m and b) are those that reduce the sensitivity of water-limited stomatal conductance to changes in soil moisture (kψ) or atmospheric humidity (kβg), or those that cause an increase in assimilation-limited stomatal conductance (VCmax, m and b). Parameters causing a negative response in ψ* (gom, kαβ and Rd25) increase water-limited stomatal conductance relative to assimilation-limited stomatal conductance, or in the case of Rd25 decrease assimilation-limited stomatal conductance by decreasing An.

3.3. Dependence of Water Stress Threshold on Environmental Conditions

[31] Transpiration derived from modeled stomatal conductance at Blandy Experimental Farm experienced periodic water stress because of changes in soil moisture and changes in other state variables used to calculate ψ*. Beginning around day 130, peak daily values of transpiration declined with falling soil moisture until by day 136, transpiration was constantly limited by soil moisture (Figure 4). On days 140 and 141, soil moisture increased in response to precipitation. On these days, transpiration was limited by assimilation (i.e., not limited by soil moisture). It is also likely that decreasing temperature and PAR suppressed An, resulting in assimilation-limited stomatal conductance and transpiration. The shift from water-stressed to unstressed conditions following precipitation is expected; however, this modeling strategy explains the shift in terms of a combination of environmental factors and not soil moisture alone.

[32] Another new aspect of this modeling framework is its ability to emulate the piecewise-linear function commonly used to scale stomatal conductance in response to water stress. Using parameters derived from Blandy Experimental Farm we simulated stomatal conductance at constant temperature and PAR with varying RH across a range of soil water potentials (Figure 7). The wilting point (gs−min = 0 mmol m−2 s−1) and the water-limited section of the function are defined by gsW whereas the water-independent section of the function is defined by gsA. ψ* is the point of intersection between these two segments, and varies as a function of atmospheric humidity.

Figure 7.

Simulated stomatal conductance (gs−min) over a range of soil water potentials at different relative humidities (RH). Photosynthetically active radiation (PAR) is held constant at 1000 μmol m−2 s−1 and temperature is held constant at 15°C.

[33] As the atmosphere becomes more humid, the slope of the water-limited range of stomatal conductance increases. The equilibrium between root water uptake and transpiration in the Gao et al. [2002] model necessitates this changing slope. Additionally, assimilation-limited stomatal conductance increases with increasing atmospheric humidity as a result of the semi-empirical sensitivity of stomatal conductance to Dv (equation (1)). Because of the independent responses of these two submodels to atmospheric humidity ψ* varies nonlinearly with atmospheric humidity. Submodels also vary independently with respect to light and temperature (directly for gsA through temperature-dependent An and indirectly for gsW through the temperature-saturation vapor pressure relationship).

3.4. Comparing Water Stress Threshold Among Plant Functional Types

[34] Representative plant functional types included broadleaf and needleleaf trees (Table 3) and grasses (represented by ryegrass at Blandy Experimental Farm). The ψ* response to PAR and RH (at a constant temperature) differed, not surprisingly, among the three plant functional types (Figure 8).

Figure 8.

Water stress threshold (ψ*) for three plant functional types as a function of photosynthetically active radiation (PAR) and relative humidity (RH). Temperature is held constant at 15°C.

[35] On the basis of the parameter sets used to represent each plant functional type, grasses have the highest ψ* values, or the greatest tendency to experience water stress (Figure 8). Across the PAR-RH variable space, ψ* is frequently 0 kPa for grasses, meaning that water is always limiting. Broadleaf trees have lower ψ* values than grasses throughout most of the variable space, and needle leaves are only water-limited over a small range of PAR and RH. These differences in ψ* among functional types suggest that grasses are most likely of the three functional types to experience water stress for wide ranges of PAR and RH, broadleaf trees are less likely to experiences water stress than grasses, and needleleaf trees are least likely to experience water stress. Interestingly, Maherali et al. [2004] found a similar relationship between the vulnerabilities of broadleaf and needleleaf trees to water stress when comparing resistances to cavitation among plant types.

[36] In general, grasses are always water-stressed except for periods of low RH and high PAR. Stomatal closure at low RH (high dv) is expected, but reduced ψ* at high PAR is counterintuitive considering the important role of PAR in assimilation (equation (3)). Reduced ψ* despite increasing PAR may result from the light sensitivity of water-limited stomatal conductance superseding the light sensitivity of An for small values of gsA at low RH. Alternatively, ψ* may decrease with increasing PAR because gsA is already in the Rubisco-limited (PAR-independent) range of assimilation, whereas gsW is still dependent on PAR. The ridge of ψ* (between 300 and 500 μmol m−2 s−1 PAR) may correspond to the transition between light-limited An and Rubisco-limited An and the resulting effect on the PAR dependence of gsA.

[37] We also examined the effect of nutrient availability on ψ* through the photosynthesis parameter Vcmax25. Field and Mooney [1986] quantified, using linear regression, the positive relationship between Rubisco-limited assimilation (Vcmax) and foliar nitrogen concentration. Using their regression equation for needleleaf trees, we examined the effect of leaf nitrogen content on ψ* across a range of temperatures in needleleaf trees at constant PAR (Figure 9). At low temperatures and leaf nitrogen levels, An is low, resulting in reduced assimilation-limited stomatal conductance and thus a low likelihood of water stress. In general, ψ* increases with increasing leaf nitrogen, resulting in a higher likelihood of water stress as photosynthetic capacity increases and requires greater stomatal conductance to meet demands for CO2.

Figure 9.

Water stress threshold (ψ*) as a function of temperature (Tc) and foliar N concentration in needleleaf plants. Relative humidity (RH) varies from (left) 0.25 to (middle) 0.50 to (right) 0.75.

[38] Areas of maximized ψ* (Figure 9) are likely areas of maximized An where temperature and foliar nitrogen are optimized for photosynthesis. Even though atmospheric demand for plant water decreases with increasing RH, ψ* increases with RH because ψ* is calculated based on the competing requirement of water-limited stomatal conductance to maintain an adequate supply of CO2 for assimilation. Thus, as conditions become increasingly favorable for CO2 assimilation water-limited stomatal conductance required to maintain the CO2 supply increases, resulting in an increase in ψ*. Because the pathway of assimilation and transpiration is shared, maintaining an optimal stomatal conductance for assimilation based on atmospheric conditions demands an adequate supply of water from the soil.

4. Conclusion

[39] Vegetation water stress is a dynamic phenomenon, varying with soil, vegetation and atmospheric conditions, and is an important control on terrestrial cycles of carbon and water. By combining two existing models of leaf-level stomatal conductance (assimilation-limited and water-limited), we have been able to (1) predict stomatal conductance (and transpiration) in the presence of alternating limitations by light, photosynthetic enzymes (through nitrogen) and soil moisture, (2) determine the critical soil water potential, ψ*, marking the threshold between water-stressed and unstressed conditions, (3) assess the variability of this threshold with respect to dynamic environmental variables and different vegetation functional types, and (4) evaluate the sensitivity of ψ* to the environment across vegetation functional types represented by vegetation-specific model parameters.

[40] We determined that ψ* varied substantially among vegetation functional types and also under various environmental conditions, suggesting that a constant value for the water stress threshold may not accurately represent stomatal response to water stress through time or between plant functional types. As an alternative, we offer a quantitative framework for addressing the preexisting notion that many factors converge to influence vegetation water stress.

Acknowledgments

[41] This research was funded by NSF (grants EAR-0236621 and EAR-0403924) and DOE-NIGEC (Great Plains Regional Center, grant DE-FC-02-03ER63613; Southeastern Regional Center, grant DE-FC-02-03ER63613). The authors also thank the faculty and staff of Blandy Experimental Farm and also Marc Parlange (Ecole Polytechnique Fédérale de Lausanne), Gabriel Katul (Duke University), and three anonymous reviewers for their helpful comments.

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