Does the empirical Ball-Berry law of stomatal conductance emerge from maximization of productivity?

The stomatal conductance of vegetation canopies links the exchange fluxes of energy, water, and carbon at the interface of the land surface and the atmospheric boundary layer. The Ball-Berry empirical law describes the behavior of stomatal conductance as a function of environmental conditions and net photosynthetic rate. Here we test whether the Ball-Berry law of stomatal functioning can be understood as the emergent result of optimized vegetation behavior that maximizes productivity. We conducted a range of sensitivity simulations with PlaSim, an Earth system model of intermediate complexity, in which we varied maximum surface conductance, which is strongly affected by stomatal functioning. We then evaluated how the emergent relationship between simulated productivity, relative humidity, surface conductance, and optimal functioning compares to the empirical Ball-Berry model. The model simulations show that the best correspondence with the Ball-Berry relationship (expressed by r2 values) corresponds roughly to the value of maximum surface conductance that maximizes productivity. This implies the Ball-Berry relationship emerges from optimized stomatal functioning. Hence, it would seem to be more appropriate to use an optimality principle for modelling stomatal functioning than to "force" land-atmosphere models with an empirical, emergent relationship.