Unsaturated flow in spatially variable fields: 2. Application of water flow models to various fields

The method of modeling water flow during infiltration and redistribution formulated in part 1 of this study has been applied to compute expectations and variances of a few water flow variables and of effective hydraulic properties. Two spatially variable soils with different degrees of variation have been investigated. The expectations and variances are obtained by using the statistical averaging procedure and probability density function (pdf) of saturated hydraulic conductivity K s . The stationarity hypotheses and the requirement that the integral scale of K s is much smaller than the length scale characterizing the field in the x, y plane have been adopted. An approximate solution which assumes the concept of a wetting front and uniform water content is used for the statistical averaging procedure. A comparison of these results with data computed by a more accurate numerical solution to Richard's equation shows that the approximate simplified models lead to a quite accurate value of the expectations and variances of the flow variables when the field is sufficiently heterogeneous. It is suggested that in spatially variable fields, stochastic modeling represents the actual flow phenomena more realistically and provides the main statistical moments (mean, variances) by using simplified flow models which can be used with confidence in applications. The field effective hydraulic properties have been defined and derived by using approximate models. It is shown that effective properties may be meaningful only under very restricted and special conditions, such as steady gravitational flow. They do not exist in the general case of infiltration‐redistribution. It is concluded that the traditional deterministic approach for solving the flow equations cannot be justified for solving flow problems in spatially variable fields.