Optimal Control of Gas Exchange during Drought: Theoretical Analysis

An optimal strategy of stomatal control during a drought period, in plants adapted to a humid climate, is derived by maximizing the photosynthetic production during the expected duration of drought. The expected duration of drought is calculated from the probability that rain occurs during a certain period, which is assumed constant. The underlying plant model describes photosynthetic production and the consumption of water from the soil, with a given initial soil water content. Water is consumed through transpiration at a rate dependent on water vapour deficit, temperature and stomatal conductance and carbon is assimilated at a rate dependent on light intensity and stomatal conductance. The optimization problem is solved with driving variables and the probability of rain corresponding to a Fenno-Scandian climate. The resulting optimal stomatal control consists of two processes with different time constants: (1) daily variation depending on the driving variables, and (2) a declining trend as a function of the initial soil water content and the probability of rain. The result allows for a physical interpretation of the so-called ‘cost of water’ used in similar optimization studies. An approximate model is derived from the optimal solution, such that the ‘cost of water’ is a function of the soil water content.