Duration and frequency of water stress in vegetation: An analytical model

In the study of the evolutionary dynamics of soil moisture at a site, it is particularly important to define some characteristic properties of the temporal structure of the periods in which the soil water content is below certain levels indicative of water stress conditions in vegetation. The analysis of such properties provides an approach to establish some hydrologic basis for the understanding and modeling of ecosystems functioning in water-limited environments. This paper deals with a stochastic point process model of soil water balance. Expressions for both the mean number and the mean duration of time intervals during which the soil moisture is below a given threshold are analytically derived as a function of climate, soil, and vegetation. The seasonal mean value of water deficit is also analytically obtained. These properties are used to characterize the state of water stress in plants and to study its dependence on the interrelated dynamics. Estimates are included for the probability distributions of the frequency and duration of the stress and soil water deficit, for different hypotheses on climate, soil, and vegetation. Both the hydrologic and the ecologic implications of the results are briefly outlined.