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A New Approach to Estimate Soil Hydraulic Parameters Using Only Soil Water Retention Data

Navin K. C. Twarakavi^a,*, Hirotaka Saito^b, Jirka imunek^a and M. Th. van Genuchten^c

^a Dep. of Environmental Sciences, Univ. of California, Riverside, CA 92521
^b Tokyo University of Agriculture and Technology, Dep. of Ecoregion Science, Fuchu, Tokyo, Japan 183-8509
^c U.S. Salinity Laboratory, 450 W. Big Springs Rd., Riverside CA 92507

View larger version (10K): [in this window] [in a new window]   Fig. 1. Schematic of the location of the Pareto optimal solution of a multiobjective problem in the objective space. Circles represent various nonoptimal parameter sets that do not provide the best solution. Points A and B represent parameter sets that provide the best solution for individual objectives F1 and F2, respectively. The line connecting Points A and B is the nondominated "Pareto optimal" set of solutions. Point C corresponds to the Pareto solution that may be regarded as the "best" possible solution.

View larger version (19K): [in this window] [in a new window]   Fig. 2. A flowchart for calculating the multiobjective vector for a given parameter set in the Multiobjective Retention Curve Estimator (MORE) approach.

View larger version (22K): [in this window] [in a new window]   Fig. 3. Tradeoffs in the objective space of the Multiobjective Retention Curve Estimator (MORE) algorithm for the silt soil (UNSODA code no. 4670). Gray points represent different parameter sets considered by the MORE approach. Circles represent the final nondominated Pareto set after 10,000 function evaluations. The star symbol represents the parameter set estimated using RETC and the solid square symbol corresponds to the "best" possible parameter set estimated using the MORE approach; k is the relative hydraulic conductivity and is the volumetric water content.

View larger version (12K): [in this window] [in a new window]   Fig. 4. Fitted (a) water content–pressure head and (b) relative unsaturated hydraulic conductivity–pressure head relationships obtained using parameter estimates from the Multiobjective Retention Curve Estimator (MORE) (solid line) for the silt soil (UNSODA code no. 4670). The points represent the experimental data. The dotted line is the solution based on RETC. Gray lines represent the several parameter sets corresponding to the nondominated Pareto set. Only retention data were used in parameter optimization by both RETC and MORE.

View larger version (23K): [in this window] [in a new window]   Fig. 5. Contour plots of the RMSE between the observed and fitted (a) water contents and (b) log of relative hydraulic conductivities as a function of shape parameters (cm–1) and n for the silt soil (UNSODA code no. 4670). The star symbol represents the parameter set estimated using RETC and the solid square symbol corresponds to the "best" possible parameter set estimated using the Multiobjective Retention Curve Estimator (MORE) approach. Gray points are the final nondominated Pareto set estimated by the MORE approach. Only retention data were used in parameter optimization by both RETC and MORE.

View larger version (20K): [in this window] [in a new window]   Fig. 6. Tradeoffs in the objective space of the Multiobjective Retention Curve Estimator (MORE) algorithm for selected soils. Gray points represent different parameter sets considered by the MORE approach. Circles represent the final nondominated Pareto set after 10,000 function evaluations. The star symbol represents the parameter set estimated using RETC and the solid square symbol corresponds to the "best" possible parameter set estimated using the MORE approach; k is the relative hydraulic conductivity and is the volumetric water content.

View larger version (16K): [in this window] [in a new window]   Fig. 7. Evolution of the tradeoff curve in the objective space of the Multiobjective Retention Curve Estimator (MORE) algorithm for the Las Cruces trench experiment. Gray points represent different parameter sets considered by the MORE approach. Circles represent the final nondominated Pareto set after 10,000 function evaluations. The solid square symbol corresponds to the "best" possible parameter set estimated using the MORE approach; k is the relative hydraulic conductivity and is the volumetric water content. The solution set estimated by RETC is less optimal than the MORE solution and is beyond the limits of the plot.

View larger version (12K): [in this window] [in a new window]   Fig. 8. Water content measured and predicted using HYDRUS-1D with the soil hydraulic parameters optimized by the RETC and Multiobjective Retention Curve Estimator (MORE) approaches for (a) Day 19 and (b) Day 35 for the Las Cruces trench experiment.

View larger version (14K): [in this window] [in a new window]   Fig. 9. Cumulative distribution functions for absolute errors in predicted water contents for (a) Day 19 and (b) Day 35 for the Las Cruces trench experiment.