This chapter presents a probabilistic model for the temporal dynamics of soil moisture, with the goal of providing a simplified yet realistic description amenable to analytical solutions. Such an analysis is the necessary starting point for the quantitative understanding of the impacts of soil moisture on ecosystems' dynamics, such as the vegetation response to water stress, the hydrologic control on cycles of soil nutrients, and the dynamics of plant competition for water. The same approach may also be useful to obtain insights into other processes closely related to soil moisture dynamics, such as soil–atmosphere interactions, soil production, and soil gas emissions.

The probabilistic soil moisture model that we describe in this chapter was originally proposed by Rodríguez-Iturbe et al. (1999a) and improved by Laio et al. (2001a). Here all the various physical processes involved in the soil moisture dynamics, the simplifying assumptions, and their related implications are discussed in detail. Particular attention is devoted to the role of soil properties and plant transpiration characteristics.

The solution of the problem in probabilistic terms, which is made necessary by the introduction of the stochastic representation of rainfall, is carried out for statistically steady-state conditions during a growing season. The results allow assessment of the roles of climate, soil, and vegetation on the soil moisture probability density function (pdf) and on the average long-term water balance. The chapter closes with a brief discussion of possible simplifications of the soil moisture dynamics that are of interest when considering the large-scale water balance.