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Upscaling Schemes and Relationships for the Gardner and van Genuchten Hydraulic Functions for Heterogeneous Soils

^a Desert Research Institute, Division of Hydrologic Sciences, 755 East Flamingo Rd., Las Vegas, NV 89119
^b U.S. Salinity Lab., 450 West Big Springs Rd., Riverside, CA 92507-4617

View larger version (68K): [in this window] [in a new window]   Fig. 1. Location map of the Corn Creek Fan where the field hydraulic properties were measured.

View larger version (18K): [in this window] [in a new window]   Fig. 2 Scatter plot of relative differences in effective values of the saturated hydraulic conductivity, Ks, and shape parameter vs. corresponding p-norms for two variance levels (one and four times those observed for the field data). G: Gardner model, vG: van Genuchten model. The numbers in parentheses indicate the dimensionless water table depth, z0* = z0, where is the mean of the field-measured van Genuchten vG values and z0 is the water table depth.

View larger version (28K): [in this window] [in a new window]   Fig. 3 Plots showing p-norms of (a) the saturated hydraulic conductivity, Ks, and (b) the shape parameter for the Gardner (G) and van Genuchten (vG) models when the dimensionless water table depth z0* = 5: (1) 10 000 regenerated points, correlation length divided by grid length (CL) = 5, correlation coefficient between and Ks (CC)(G) >0.9, CC(vG) >0.9; (2) 10 000 regenerated points, CL = 50, CC(G) >0.9, CC(vG) >0.9; (3) 84 measured points, CC(G) = 0.24, CC(vG) = 0.74; (4) 10 000 regenerated points, CL = 5, CC(G) = 0.24, CC(vG) = 0.75; (5) 10 000 regenerated points, CL = 5, CC(G) >0.9, CC(vG) >0.9, variance four times measured value.

View larger version (23K): [in this window] [in a new window]   Fig. 4 The p-norm relationships between the Gardner (G) and van Genuchten (vG) models for (a) saturated hydraulic conductivity, Ks, and (b) the shape parameter when the dimensionless water table depth z0* = 10. CL is correlation length divided by grid length and CC is the correlation coefficient between and Ks.

View larger version (20K): [in this window] [in a new window]   Fig. 5 The p-norm relationships between the Gardner (G) and van Genuchten (vG) models for (a) saturated hydraulic conductivity, Ks, and (b) the shape parameter when the dimensionless water table depth z0* = 5. CL is correlation length divided by grid length and CC is the correlation coefficient between and Ks.

View larger version (19K): [in this window] [in a new window]   Fig. 6 The p-norm relationships between the Gardner (G) and van Genuchten (vG) models for (a) saturated hydraulic conductivity, Ks, and (b) the shape parameter when the dimensionless water table depth z0* = 2.5. CL is correlation length divided by grid length and CC is the correlation coefficient between and Ks