Stochastic modeling of large‐scale transient unsaturated flow systems

A new framework for modeling large‐scale transient unsaturated flow systems in spatially variable soils is proposed in order to overcome the problem of limited information about the local details of spatial soil variability. A stochastic approach, which assumes that local soil properties are realizations of three‐dimensional random fields, is followed for derivation of a large‐scale model representation (structure). The three dimensionality of the local flow and the nonlinear dependence of the local flow output on the local soil properties are considered. The large‐scale model structure is derived by averaging the local governing flow equation over the ensemble of realizations of the underlying soil property random fields. The resulting mean model representation is in the form of a partial differential equation in which averaged or effective model parameters occur. These effective model parameters (i.e., effective hydraulic conductivity and effective specific moisture capacity) are evaluated using a quasi‐linearized fluctuation equation and a spectral representation of stationary processes. The large‐scale model representation considers the large‐scale effects of soil property variability and has relatively few parameters. The general conclusions of this study are that soil property variability produces large‐scale hysteresis and anisotropy of the effective parameters. The potential theoretical and practical ramifications of these results in the area of unsaturated flow modeling need to be investigated. The general stochastic modeling framework developed here is applicable not only to unsaturated flow but also to other distributed parameter systems (e.g., saturated flow and transport, geothermal and oil reservoir modeling).