Modeling stomatal conductance in the earth system: linking leaf water-use efficiency and water transport along the soil–plant–atmosphere continuum

Abstract. The Ball–Berry stomatal conductance model is commonly used in earth system models to simulate biotic regulation of evapotranspiration. However, the dependence of stomatal conductance (g_s) on vapor pressure deficit (D_s) and soil moisture must be empirically parameterized. We evaluated the Ball–Berry model used in the Community Land Model version 4.5 (CLM4.5) and an alternative stomatal conductance model that links leaf gas exchange, plant hydraulic constraints, and the soil–plant–atmosphere continuum (SPA). The SPA model simulates stomatal conductance numerically by (1) optimizing photosynthetic carbon gain per unit water loss while (2) constraining stomatal opening to prevent leaf water potential from dropping below a critical minimum. We evaluated two optimization algorithms: intrinsic water-use efficiency (ΔA_n /Δg_s, the marginal carbon gain of stomatal opening) and water-use efficiency (ΔA_n /ΔE_l, the marginal carbon gain of transpiration water loss). We implemented the stomatal models in a multi-layer plant canopy model to resolve profiles of gas exchange, leaf water potential, and plant hydraulics within the canopy, and evaluated the simulations using leaf analyses, eddy covariance fluxes at six forest sites, and parameter sensitivity analyses. The primary differences among stomatal models relate to soil moisture stress and vapor pressure deficit responses. Without soil moisture stress, the performance of the SPA stomatal model was comparable to or slightly better than the CLM Ball–Berry model in flux tower simulations, but was significantly better than the CLM Ball–Berry model when there was soil moisture stress. Functional dependence of g_s on soil moisture emerged from water flow along the soil-to-leaf pathway rather than being imposed a priori, as in the CLM Ball–Berry model. Similar functional dependence of g_s on D_s emerged from the ΔA_n/ΔE_l optimization, but not the ΔA_n /g_s optimization. Two parameters (stomatal efficiency and root hydraulic conductivity) minimized errors with the SPA stomatal model. The critical stomatal efficiency for optimization (ι) gave results consistent with relationships between maximum A_n and g_s seen in leaf trait data sets and is related to the slope (g₁) of the Ball–Berry model. Root hydraulic conductivity (R_r^*) was consistent with estimates from literature surveys. The two central concepts embodied in the SPA stomatal model, that plants account for both water-use efficiency and for hydraulic safety in regulating stomatal conductance, imply a notion of optimal plant strategies and provide testable model hypotheses, rather than empirical descriptions of plant behavior.