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The soil moisture dynamics under seasonally fixed conditions are studied at a point. The water balance is described through the representation of rainfall as a marked Poisson process, which in turn produces an infiltration into the soil dependent on the existing level of soil moisture. The losses from the soil are due to evapotranspiration and leakage, which are also considered dependent on the existing soil moisture. The steady-state probability distributions for soil moisture are then analytically obtained. The analysis of the distribution allows for the assessment of the role of climate, soil and vegetation on soil moisture dynamics. Further hydrologic insight is obtained by studying the various components of an average water balance. The realistic representation of the processes acting at a site and the analytical tractability of the model make it well suited for further analyses that consider the spatial aspect of soil moisture dynamics.
Rodriguez‐Iturbe et al. (Fri,) studied this question.