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A first-order autoregressive Markovian model AR(1) is formulated on the basis of the hydrologic budget and soil water transport equation. The model predictions compared well with neutron probe measurements of soil moisture content, and the statistical moments were conserved. The applied water events were white noise in structure, and the random shocks generated from the flow dynamics simplifications have a statistical mean of zero and were uncorrelated for all time lags. The derived AR(1) model parameter is used to compute the mean diffusivity of the soil, which is in agreement with reported lab measurements and field estimates obtained from cumulative evaporation measurements made with two large lysimeters.

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A two‐level point stochastic model for the rainfall occurrences at a given rainfall station is constructed in the time dimension. The model is a cluster process of the Neyman‐Scott type. The model has the rainfall‐generating mechanisms as its primary level and the rainfalls that are generated by these mechanisms as the secondary level. It uses infinite superposition of rainfalls and has a very flexible dependence structure. The model is fitted to daily rainfall sequences in Indiana after these are stationarized by a transformation. The fit of the model is then tested in terms of its correlation and marginal probability characteristics. The present form of the Neyman‐Scott cluster model is time homogeneous. Therefore the Neyman‐Scott process, as presented in this paper, may be of practical use only for modeling the stationary rainfall occurrences.

Unsaturated flows within subsurface regions control many large‐scale hydrological and environmental processes. This study addresses the issue of spatial averaging of unsaturated flow equations at field scales. Two models for horizontally averaged unsaturated flow have been developed from two different approaches in this study. The spatially horizontally averaged Richards equation (SHARE) model is represented by a system of two coupled partial differential equations for the mean water saturation in each horizontal soil layer and the cross‐covariance of the saturated hydraulic conductivity and the water saturation in each horizontal soil layer in a heterogeneous field. As an alternative to the spatial averaging/perturbation approach which was used for SHARE, a spatially horizontally averaged form of Green‐Ampt model is obtained by field scale spatial horizontal averaging of the local soil water dynamics which are represented approximately by rectangular profiles. This strategy leads to analytical solutions for average water content and the results can be upscaled to large spatial areas. The computational effort required to evaluate such analytic expressions is trivial in comparison with that of the numerical solution of Richards equation. The averaged Green‐Ampt model, though approximate, yields good results when large variations exist in the soil properties in the horizontal directions.