A Dynamic Model for Strategies and Dynamics of Plant Water-Potential Regulation Under Drought Conditions

Vegetation responds to drought through a complex interplay of plant hydraulic mechanisms, posing challenges for model development and parameterization. We present a mathematical model that describes the dynamics of leaf water-potential over time while considering different strategies by which plant species regulate their water-potentials. The model has two parameters: the parameter λ describing the adjustment of the leaf water potential to changes in soil water potential, and the parameter Δψww describing the typical ‘well-watered’ leaf water potentials at non-stressed (near-zero) levels of soil water potential. Our model was tested and calibrated on 110 time-series datasets containing the leaf- and soil water potentials of 66 species under drought and non-drought conditions. Our model successfully reproduces the measured leaf water potentials over time based on three different regulation strategies under drought. We found that three parameter sets derived from the measurement data reproduced the dynamics of 53% of an drought dataset, and 52% of a control dataset [root mean square error (RMSE) < 0.5 MPa)]. We conclude that, instead of quantifying water-potential-regulation of different plant species by complex modeling approaches, a small set of parameters may be sufficient to describe the water potential regulation behavior for large-scale modeling. Thus, our approach paves the way for a parsimonious representation of the full spectrum of plant hydraulic responses to drought in dynamic vegetation models.

Methods S1: Connection to canopy conductance
Alongside the vapour pressure deficit and leaf conductivity, Δ is a main driver of transpiration, and is thus coupled to canopy conductance. The forcing pressure Δ and canopy conductivity can be linked by Darcy's law (McDowell et al., 2016). Adopting the mathematical definitions and nomenclature of Martínez-Vilalta et al., (2014), we solve the canopy conductance as follows: where and are the sapwood and leaf areas, respectively, is the sapwood conductivity, and denotes the vapour pressure deficit (all variables and their units are listed in Table 2).
As the leaf water potential and stomatal conductance are usually mutually dependent, and g C are also interdependent. Here we simplify Eq. (S1) such that depends on alone, and is independent of . Over the time scale of the calculation (daily in this case), we assume that and are constant for a given plant canopy, meaning that depends on only through the possible induction of cavitation. Under this condition, the dynamics of Eq. (S1) is a function of , and alone. 3

Methods S2: Numerical optimization routines
We used three different heuristic minimization techniques: "random search", "simulated annealing" and "differential evolution" to ensure that minimum parameter set found by the algorithms was global across the selected parameter domain. All minimization routines were translated into / implemented in CPP. The method "random search" method was implemented based on Archetti & Schoen, (1984) with fixed step size, the "differential evolution" implementation was based on Price, We selected an implicit-midpoint-ordinary-differential-equation-solver for equation 8, because it combined system stiffness robustness with performance. Using a simple 'explicit-Euler' solver for equation 8 exhibited numerical instability for rapid changes in soil water potential.

Methods S3: Implications for photosynthesis and carbon uptake
These boundary cases are defined as follows (Roman et al., 2015).
• Case 1: Extreme isohydric behavior: the change of ( ) with respect to ( ) is zero ( = 0). In this case, is constant and Δ decreases as the soil dries. By Eq. (S1), a decrease in Δ implies a decrease in , reduced transpiration, and consequent reduction in photosynthesis and carbon uptake.
• Case 2: Perfect isohydrodynamic behavior: the change of with respect to is equal to one ( = 1). In this case, adjusts to maintain a constant Δ as the soil dehydrates.
Keeping Δ constant requires maintaining a high , ensuring that transpiration and photosynthesis continue under increasingly dry conditions. However, xylem cavitation under severe soil-moisture stress can decrease the , thus lowering the xylem conductivity .
• Case 3: Anisohydric behavior (Roman et al., 2015): the change of with respect to exceeds unity ( > 1). Under drought stress, anisohydric plants adjust their until Δ actually increases. Plants adopting this strategy maintain a high and high transpirationand photosynthesis rates, even under strong drought stress. Loss of xylem conductivity induced by cavitation is compensated by the decrease in and increase in Δ .
Note that the classical isohydricity concept assumes an interdependence between the stomatal behavior and water potential regulation. We provide a possibility to connect leaf water potential regulation to the stomatal conductivity in Eq. (S1).