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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.

Channel networks with artibtrary drainage density or resolution can be extracted from digital elevation data. However, for digital elevation data derived networks to be useful they have to be extracted at the correct length scale or drainage density. Here we suggest a criterion for determining the appropriate drainage density at which to extract networks from digital elevation data. The criterion is basically to extract the highest resolution (highest drainage density) network that satisfies scaling laws that have traditionally been found to hold for channel networks. Procedures that use this criterion are presented and tested on 21 digital elevation data sets well distributed throughout the U S .