Stochastic coupling of rainfall and biomass dynamics

A modeling scheme is presented to derive the probabilistic structure of plant biomass when subjected to stochastic precipitation conditions. Using the fact that soil moisture varies on a much shorter scale than plant biomass, analytical expressions are derived for the steady state probability distribution of the average plant biomass over a period T, which is expected to be of the order of 2 or 3 months. Analytical expressions are also given for the time-dependent mean and variance of the biomass over a period T. The analysis is based on a simple model linking the daily dynamics of plant growth and soil moisture. The derived analytical expressions reproduce the results obtained from a full simulation of the underlying model very well. The results allow the study of the impact of different climatic scenarios regarding changes in frequency and intensity of rainfall, as well as changes in the mean seasonal temperature, on the expected value and variance of plant biomass throughout time.