Estimating unsaturated soil hydraulic properties from tension disc infiltrometer data by numerical inversion

Tension disc infiltrometers are becoming increasingly popular devices for in situ measurement of the unsaturated hydraulic properties of soil. Tension infiltration data are generally used to evaluate the parameters K-s and alpha in Gardner's exponential model of the unsaturated hydraulic conductivity. Either two measurements using different disc diameters or measurements with a single disc but using multiple pressure heads are then used. In this paper we describe a parameter estimation procedure which combines the Levenberg-Marquardt nonlinear parameter optimization method involving weighted least squares, with a quasi-three-dimensional numerical model which solves the variably saturated flow equation. By numerical inversion of Richards' equation the unknown parameters in van Genuchten's model of the unsaturated soil-hydraulic properties are estimated from observed cumulative infiltration data during transient water flow. Additional measurements of the pressure head or water content, as well as a penalty function for constraining the unknown parameters to remain in some feasible region (Bayesian estimation), can be optionally included into the parameter estimation procedure. The problem of optimal sampling design, that is, selecting the best points in space and time for making measurements, is addressed by studying the sensitivity of the objective function to changes in the optimized hydraulic parameters. We calculate objective functions based on available cumulative infiltration, pressure head, and water content measurements and also on several combinations of these data. The behavior of the objective function in three-dimensional parameter space is evaluated by means of a series of two-dimensional response surfaces. The utility of the parameter estimation procedure is demonstrated using numerically generated data. The sensitivity of the procedure to different initial estimates of the model parameters is also discussed.