NONSTATIONARY STOCHASTIC-ANALYSIS OF STEADY-STATE FLOW-THROUGH VARIABLY SATURATED, HETEROGENEOUS MEDIA

In this study we develop a first-order, nonstationary stochastic model for steady state, unsaturated flow in randomly heterogeneous media. T he model is applicable to the entire domain of a bounded vadose zone, unlike most of the existing stochastic models. Because of its nonstati onarity, we solve it by the numerical technique of finite differences, which renders the flexibility in handling different boundary conditio ns, input covariance structures, and soil constitutive relationships. We illustrate the model results in one and two dimensions for soils de scribed by the Brooks-Corey constitutive model; It is found that the f low quantities such as suction head, effective water content, unsatura ted hydraulic conductivity, and velocity are nonstationary near the wa ter table and approach stationarity as the vertical distance from the water table increases. The stationary limits and the critical vertical distance at which stationarity is attained depend on soil types and r echarge rates. The smaller the recharge rate is, the larger the critic al distance; and the coarser the soil texture is, the smaller the dist ance. One important implication of this is that the existing simpler, gravity-dominated flow models may provide good approximations for flow in vadose zones of large thickness and/or coarse-textured soils altho ugh they may not be valid for vadose zones of fine-textured soils with a shallow water table. It is also found that the vertical extent of a domain where nonstationarity is important may be estimated by solving the one-dimensional Richards equation for mean head with average soil properties and appropriate boundary conditions. On the basis of the m ean head, one may then determine whether the full, nonstationary model must be solved or whether a simpler, gavity-dominated model will suff ice. The flow quantities are also nonstationary in the horizontal dire ction near the lateral boundaries, as found for flow in saturated zone s.