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Transient Flow in a Heterogeneous Vadose Zone with Uncertain Parameters

^a Geosciences Research Group, Idaho National Engineering and Environmental Laboratory, P.O. Box 1625, MS 2025, Idaho Falls, ID 83415-2025
^b Department of Mathematics, University of Arizona, Tucson, AZ 85721-0089
^c Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545

View larger version (16K): [in a new window]   Fig. 1. Mean saturation profiles, = + , normalized with the dimensionless flux Q.

View larger version (16K): [in a new window]   Fig. 2. The normalized variance of reduced saturation, 2/Q2, computed by direct MCS as a function of the number of Monte Carlo realizations. It is reported at the dimensionless depth z = 0.5 and several values of the dimensionless time t. The variance of log conductivity is 2Y = 0.4.

View larger version (19K): [in a new window]   Fig. 3. Mean reduced saturation (the Kirchhoff variable, matrix potential), /Q, on the soil surface, z = 0, computed analytically with the first-order approximation of the moment differential equations (MDE) and the mean-field approximation (MFA), and numerically with the Monte Carlo simulations (MCS).

View larger version (18K): [in a new window]   Fig. 4. The variance of reduced saturation, 2, on the soil surface, z = 0, computed analytically with the first-order approximation of the moment differential equations (MDE) and numerically with Monte Carlo simulations (MCS).