The role of plant water storage and hydraulic strategies in relation to soil moisture availability

Abstract

Background and Aims

Plants rely on water storage capacity to increase accessibility of water for transpiration, reduce competition for water with neighboring plants, and buffer water supply during dry periods. The resulting benefits, typically a decrease in plant water stress and increase in productivity, are highly climate dependent and vary with soil moisture, vapor pressure deficit, and solar radiation. This paper analyzes the effects of plant water storage capacity on the relationship between soil moisture and carbon assimilation in woody plants.

Methods

A resistance-capacitance model is used to examine the role of plant water storage at various soil moisture levels. Hydraulic traits are co-varied according to empirical relationships, and effects of sapwood volume and wood density on carbon assimilation are explored. The time scales of plant water storage and withdrawal are analyzed as a function of plant hydraulic capacitance, water storage capacity, and resistance to transport between water storage tissue and xylem.

Results

The effects of plant water storage on carbon assimilation are found to depend strongly on soil moisture levels. The theoretically optimal sapwood volume lies near naturally occurring ranges and increases with increasing soil moisture. The theoretically optimal wood density also lies within expected ranges and decreases with increasing soil moisture.

Conclusions

A large portion of sapwood volume appears to be justified by its role in buffering diurnal variability in evaporative demand. The outlined coordination between soil moisture and optimal hydraulic traits is consistent with observed increases in sapwood capacitance and decreases in wood density across increasing rainfall gradients. This coordination provides support for the drought-tolerance vs. drought-avoidance hypothesis.

Appendices

Appendix A: Conductances

Following Daly et al. (2004), the soil-root conductance, g _{s r} , is assumed to be proportional to the soil hydraulic conductivity, K(s), divided by the average distance from the soil to root surface, i.e.,

$$ g_{sr}(s) = \frac{K(s)\sqrt{RAI_{w} s^{-d}}}{\pi g\rho_{w} Z_{r}}, $$

(16)

where R A I _w is the root area index under well-watered conditions, s ^−d is a term introduced to model root growth under water-stressed conditions, and K(s) = s ^(2b+3). See Table 6.

The decrease in plant conductance under water stress is modeled by a vulnerability curve so that g _p is close to g _{p m a x} for high ψ _l and is close to 0 for low ψ _l due to xylem cavitation (Sperry et al. 1998; Daly et al. 2004), i.e.,

$$ g_{p} = g_{pmax}\left[1+\left( \frac{\psi_{x}}{\psi_{50}}\right)^{a}\right]^{-1}. $$

(17)

where a is a parameter between 1 and 10, here assumed to be equal to 4, and ψ ₅₀ is the xylem potential at 50% loss of hydraulic conductivity. Following Waring and Running (1978) and Carlson and Lynn (1991), the storage conductance, or the conductance between the water storage and transport pathways, is assumed to decrease with the fraction of stored water as

$$ g_{w} = g_{wmax} w^{m}, $$

(18)

where g _{w m a x} is the maximum storage conductance (Table 1).

Appendix B: Water potentials

The soil water potential, ψ _s , is related to the soil moisture through a strongly nonlinear function given by Rodriguez-Iturbe and Porporato (2004) and Daly et al. (2004) as

$$ \psi_{s}(s) = \overline{\psi}_{s} s^{-b}. $$

(19)

The relationship between the stored water potential, ψ _w , and the stored water volume is most commonly represented by a logarithmic or sigmoidal curve (e.g. Chuang et al. 2006) and the specific plant water capacitance c, is defined as the change in relative stored water volume per unit change in water potential (c = d w/d ψ _w ). In this study we have chosen to approximate the stored water potential as a linear function of the relative water storage volume following Hunt et al. (1991), i.e.,

$$ \psi_{w}(w) = \frac{w - 1}{c}. $$

(20)

While a simplification, this linear relationship is a good approximation in the physically relevant regime examined here, where the relative stored water volume remains above 40%. In this range, it compares very well to data (see Fig. 2, data from Waring and Running 1978 and Domec and Gartner 2001). Moreover, this approximation allows us to more clearly tease out the effects of plant hydraulic capacitance on the dynamics of water storage.

Appendix C: Leaf temperature and specific humidity

The leaf temperature and specific humidity, which influence plant transpiration and carbon assimilation, are are obtained by coupling the plant model to a boundary layer model as in Daly et al. (2004). The leaf temperature, T _l , can be obtained through the plant energy balance as

$$ \phi-H-\lambda_{w}\rho_{w}E = 0, $$

(21)

where ϕ is the net flux of radiation per unit leaf area, λ _w is the latent heat of water, ρ _w is the density of water, and H is the sensible heat flux.

$$ H = c_{p}\rho g_{a}(T_{l}-T_{a}), $$

(22)

where c _p is the specific heat of air at constant pressure and g _a is the atmospheric conductance. Substituting (22) into (21) and rearranging leads to an explicit formula for T _l as

$$ T_{l} = T_{a} + \frac{\phi-\rho_{w} \lambda_{w} E}{c_{p} \rho g_{a}}. $$

(23)

The specific humidity of the leaf mesophyll can be calculated as

$$ q_{l}(T_{l},\psi_{l}) = q_{l,sat}(T_{l})\exp\left[\frac{V_{w}\psi_{l}}{R T_{l}}\right], $$

(24)

where V _w is the partial molar volume of water, and the specific humidity at saturation, q _{l,s a t} is related to T _l as

$$ q_{l,sat}(T_{l}) = \frac{0.622}{p_{a}}a_{sat}\exp\left[\frac{b_{sat}(T_{l}-273)}{c_{sat}+T_{l}-273}\right], $$

(25)

where p _a is the atmospheric pressure (Pa) and a _{s a t} , b _{s a t} and c _{s a t} are constants (Jones 1992). See Table 4.

Table 4 Atmospheric parameters

Appendix D: Boundary layer model

The boundary layer is modeled according to McNaughton and Spriggs (1986), Daly et al. (2004) as a well-mixed slab of air with height h, specific humidity q, and potential temperature 𝜃. Within the boundary layer, the equations for heat and water balance, respectively, are

$$ \rho c_{p} h \frac{d\theta}{dt} = H + \rho c_{p}(\theta_{s} - \theta)\frac{dh}{dt}, $$

(26)

$$ \rho h \frac{dq}{dt} = \rho_{w} E + \rho(q_{s}-q)\frac{dh}{dt}, $$

(27)

where 𝜃 _s and q _s are the potential temperature and humidity, respectively, at height h. The growth rate of the boundary layer is given by

$$ \frac{dh}{dt} = \frac{H}{\rho c_{p} h \gamma_{\theta}}, $$

(28)

where γ _𝜃 is the gradient of the potential temperature at height h. The linear profiles of temperature and humidity in the atmosphere above the boundary layer respectively are expressed as

$$ \theta_{s} = \gamma_{\theta}z + \theta_{s0}, $$

(29)

and

$$ q_{s} = \gamma_{q}z + q_{s0}. $$

(30)

The solar radiation, ϕ, is modeled as

$$ \phi(t) = \frac{4\phi_{max}}{\delta^{2}}[-t^{2} + (\delta + 2t_{0})t - t_{0}(t_{0} + \delta)], $$

(31)

where ϕ _{m a x} is the maximum solar radiation, δ is the day length, and t ₀ is the time of sunrise (Lhomme et al. 1998). See Table 4.

Appendix E: Details of the carbon assimilation and stomatal conductance models

R, the ratio of mesophyll to atmospheric CO ₂ concentration and can be related to the vapor pressure deficit, D, is given by

$$ R = 1 -\frac{1}{a_{1}}\left( 1+\frac{D}{D_{x}}\right), $$

(32)

where a ₁ and D _x are empirical constants (Leuning 1995).

We assume that, under well-watered conditions, there is no control of carbon assimilation by the leaf water potential up to the point ψ _l,A1, at which point the assimilation decreases linearly to 0 at the point ψ _l,A0, i.e.,

$$\begin{array}{@{}rcl@{}} A_{\psi_{l}}(\psi_{l})=\left\{ \begin{array}{ll} \text{0} & \quad \psi_{l} < \psi_{lA0} \\ \frac{(\psi_{l}-\psi_{lA0})}{(\psi_{lA1}-\psi_{lA0})} & \quad \psi_{lA0} < \psi_{l} \leq \psi_{lA1} \ \\ \text{1} & \quad \psi_{l} > \psi_{l_{A1}}. \ \end{array} \right. \end{array} $$

(33)

The function $A_{\phi ,c_{i},T_{l}}(\phi , c_{i}, T_{l})$ is given by

$$ A_{\phi,c_{i},T_{l}}(\phi, c_{i}, T_{l}) = \min{(A_{c}, A_{q})}, $$

(34)

and describes the dependence of carbon assimilation on ϕ, c _i , and T _l given by the Farquhar model (Farquhar et al. 1980) for C ₃ plants. The Rubisco-limited rate of carbon assimilation, A _c , is given by

$$ A_{c}=V_{c,max}\frac{c_{i}-{\Gamma}^{*}(T_{l})}{c_{i}+K_{c}(T_{l})(1+o_{i}/K_{o}(T_{l}))}, $$

(35)

where V _{c,m a x} is the maximum carboxylation rate, K _c and K _o are the Michaelis-Menten coefficients for CO ₂ and O ₂, respectively, o _i is the oxygen concentration, and Γ^∗ is the CO ₂ compensation point. The light-limited assimilation rate, A _q , is

$$ A_{q} = \frac{J(\phi, T_{l})}{4}\frac{(c_{i}-{\Gamma}^{*}(T_{l}))}{(c_{i}+2{\Gamma}^{*}(T_{l}))}, $$

(36)

where J, the electron transport rate, is equal to min (J _{m a x} (T _l ),Q). Q is the absorbed photon irradiance (mol photons m ⁻² s ⁻¹) and is given by

$$ Q(\phi)=\frac{\phi\lambda\kappa_{2}}{2N_{a}hc}, $$

(37)

where 50 percent of the incoming radiation is considered photosynthetically active radiation (PAR) (Jones 1992), λ is the average wavelength (m) for PAR (assumed to be 550 nm), h is Planck’s constant (Js), c is the speed of light (m/s), N _a is Avogadro’s constant (mol ⁻¹), and κ ₂ is the quantum yield of photosynthesis in mol CO ₂ mol ⁻¹ photons. J _{m a x} (T _l ) is given by

$$ J_{max}(T_{l})=J_{max0}\frac{\exp[\frac{H_{vJ}}{RT_{0}}(1-\frac{T_{0}}{T_{l}})]}{1+\exp(\frac{S_{vQ}T_{l}-H_{dJ}}{RT_{l}})}. $$

(38)

The maximum carboxylation rate, V _{c,m a x} , and the CO ₂ compensation point, Γ^∗, are given by

$$ V_{c,max}(T_{l})=V_{c,max0}\frac{\exp[\frac{H_{vJ}}{RT_{0}}(1-\frac{T_{0}}{T_{l}})]}{1+\exp(\frac{S_{vC}T_{l}-H_{dJ}}{RT_{l}})} $$

(39)

and

$$ {\Gamma}^{*}(T_{l})={\Gamma}_{0}[1+{\Gamma}_{1}(T_{l}-T_{0})+{\Gamma}_{2}(T_{l}-T_{0})^{2}], $$

(40)

where the temperature dependence of the Michaelis-Menten constants K _c and K _o is described by a modified Arrhenius equation, i.e.,

$$ K_{x}(T_{l})=K_{x0}\exp\left[\frac{H_{Kx}}{RT_{0}}\left( 1-\frac{T_{0}}{T_{l}}\right)\right], $$

(41)

where x stands for either c or o. Parameter values are given in (Tables 5 and 6).

Table 5 Plant photosynthetic parameters

Table 6 Soil parameters