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Inverse Estimation of the Unsaturated Soil Hydraulic Properties from Column Outflow Experiments Using Free-Form Parameterizations

^a Institute of Applied Mathematics, Univ. of Erlangen-Nuremberg, Martensstr. 3, 91058 Erlangen, Germany
^b Institute of Geoecology, Braunschweig Technical Univ., Langer Kamp 19c, 38106 Braunschweig, Germany

View larger version (35K): [in a new window]   Fig. 1. Quadratic B-spline parameterization results. Estimated (solid line) and original (dashed line) hydraulic functions and corresponding simulated (black line) and measured (points) data with 5% Gaussian noise. From left to right: 2, 5, and 33 nodes. Corresponding residuals are magnified by a factor of two (area plots).

View larger version (14K): [in a new window]   Fig. 2. Evaluation of the objective function in the multilevel algorithm for the considered examples and values of the condition number of the sensitivity matrix for different parameterization levels.

View larger version (35K): [in a new window]   Fig. 3. Continuous outflow results for the Bayreuth soil. From top to bottom: Observed (dots, every second data point shown) and fitted cumulative outflow data, observed and fitted pressure head data at the 3.5-cm depth, and the corresponding retention and conductivity functions for quadratic B-spline parameterization. From left to right: 2, 9, and 33 nodes (solid black lines). The central plots also show results obtained by fitting the van Genuchten–Mualem model to the data (dashed lines). Residuals are magnified by a factor of two for cumulative outflow and by a factor of four for the pressure head data, respectively (area plots).

View larger version (15K): [in a new window]   Fig. 4. Values of the objective function in the multilevel algorithm for the Bayreuth continuous outflow experiment and values of the condition number of the sensitivity matrix for different parameterization levels.

View larger version (35K): [in a new window]   Fig. 5. Multistep outflow results for the Bayreuth soil. From top to bottom: Observed (red dots) and fitted cumulative outflow data, observed and fitted pressure head data at the 3.5-cm depth, and the corresponding retention and conductivity functions. From left to right: 2, 9, and 33 nodes (solid black lines). The central plot also shows results obtained by fitting the standard van Genuchten–Mualem model to the data (dashed blue lines). All residuals shown are magnified by a factor of two (area plots).

View larger version (16K): [in a new window]   Fig. 6. Values of the objective function in the multilevel algorithm for the Bayreuth multistep outflow experiment and values of the condition number of the sensitivity matrix for different parameterization levels.