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 maximizingthe photosynthetic production during the expected duration ofdrought. The expected duration of drought is calculated fromthe probability that rain occurs during a certain period, whichis assumed constant. The underlying plant model describes photosyntheticproduction and the consumption of water from the soil, witha given initial soil water content. Water is consumed throughtranspiration at a rate dependent on water vapour deficit, temperatureand stomatal conductance and carbon is assimilated at a ratedependent on light intensity and stomatal conductance. The optimizationproblem is solved with driving variables and the probabilityof rain corresponding to a Fenno-Scandian climate. The resultingoptimal stomatal control consists of two processes with differenttime constants: (1) daily variation depending on the drivingvariables, and (2) a declining trend as a function of the initialsoil water content and the probability of rain. The result allowsfor a physical interpretation of the so-called ‘cost ofwater’ used in similar optimization studies. An approximatemodel is derived from the optimal solution, such that the ‘costof water’ is a function of the soil water content. Photosynthesis; transpiration; stomatal conductance; soil water content; probability of rain; optimal control; drought; model