Reconciling the optimal and empirical approaches to modelling stomatal conductance

Models of vegetation function are widely used to predict the effects of climate change on carbon, water and nutrient cycles of terrestrial ecosystems, and their feedbacks to climate. Stomatal conductance, the process that governs plant water use and carbon uptake, is fundamental to such models. In this paper, we reconcile two long-standing theories of stomatal conductance. The empirical approach, which is most commonly used in vegetation models, is phenomenological, based on experimental observations of stomatal behaviour in response to environmental conditions. The optimal approach is based on the theoretical argument that stomata should act to minimize the amount of water used per unit carbon gained. We reconcile these two approaches by showing that the theory of optimal stomatal conductance can be used to derive a model of stomatal conductance that is closely analogous to the empirical models. Consequently, we obtain a unified stomatal model which has a similar form to existing empirical models, but which now provides a theoretical interpretation for model parameter values. The key model parameter, g(1), is predicted to increase with growth temperature and with the marginal water cost of carbon gain. The new model is fitted to a range of datasets ranging from tropical to boreal trees. The parameter g(1) is shown to vary with growth temperature, as predicted, and also with plant functional type. The model is shown to correctly capture responses of stomatal conductance to changing atmospheric CO2, and thus can be used to test for stomatal acclimation to elevated CO2. The reconciliation of the optimal and empirical approaches to modelling stomatal conductance is important for global change biology because it provides a simple theoretical framework for analyzing, and simulating, the coupling between carbon and water cycles under environmental change.