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Stochastic Analysis of Transient Flow in Heterogeneous, Variably Saturated Porous Media

The van Genuchten–Mualem Constitutive Model

Hydrology, Geochemistry, and Geology Group (EES-6), MS T003, Los Alamos National Laboratory, Los Alamos, NM 87545

View larger version (17K): [in a new window]   Fig. 1. Comparisons between moment equation–based approach (ME) and Monte Carlo simulations (MC) for Case 1: CVKS = 10%, CV = 10%, CVn = 5%, CVQ = 0, and Q = -0.005 m d-1. (a) Mean pressure head; and (b) head variance.

View larger version (19K): [in a new window]   Fig. 2. Comparisons between moment equation–based approach (ME) and Monte Carlo simulations (MC) for Case 2: CVKS = 10%, CV = 10%, CVn = 5%, CVQ = 0, Q = -0.05 m d-1. (a) Mean pressure head; and (b) head variance.

View larger version (15K): [in a new window]   Fig. 3. Comparisons between moment equation–based approach (ME) and Monte Carlo simulations (MC) for the log unsaturated hydraulic conductivity Y in Case 2. (a) Mean Y; and (b) variance 2Y.

View larger version (17K): [in a new window]   Fig. 4. Comparisons between moment equation–based approach (ME) and Monte Carlo simulations (MC) for the effective water content e in Case 2. (a) Mean e; and (b) variance 2e.

View larger version (17K): [in a new window]   Fig. 5. Comparisons between moment equation–based approach (ME) and Monte Carlo simulations (MC) for Case 3: CVKS = 100%, CV = 20%, CVn = 5%, CVQ = 0, Q = -0.005 m d-1. (a) Mean pressure head; and (b) head variance.

View larger version (16K): [in a new window]   Fig. 6. Comparisons between moment equation–based approach (ME) and Monte Carlo simulations (MC) for Case 3: CVKS = 100%, CV = 20%, CVn = 5%, CVQ = 0, Q = -0.05 m d-1. (a) Mean pressure head; and (b) head variance.

View larger version (20K): [in a new window]   Fig. 7. Contributions to head variance due to variabilities on individual parameters, CVp = 10%, where p = KS, , n, or Q.

View larger version (18K): [in a new window]   Fig. 8. Contributions to head variance due to variabilities on individual parameters, CVKS = 50%, CV = 30%, CVn = 10%, or CVQ = 100%.

View larger version (21K): [in a new window]   Fig. 9. Propagation of head variance from top to bottom due to variability of infiltration rate CVQ = 200%.

View larger version (31K): [in a new window]   Fig. 10. Mean pressure head and head variance computed using moment approach for an integrated saturated–unsaturated system. (a) Mean flow field; and (b) head variance.