Use of inverse methods for estimating unsaturated flow parameters

Abstract

Transient laboratory experiments are evaluated for their use in inverse methods to estimate soil-water parameters for unsaturated flow. The experiments are upward infiltration, One-Step outflow, stepwise inflow and evaporation. The experiments are simulated numerically for three inch standard size cores. A theoretical sandy and a clayey soil are used and are described by the closed-form van Genuchten soil-water relations. During each numerical experiment, for each soil, measurements of different auxiliary variables are simulated. These auxiliary variables are the inflow or outflow at the boundary, and the water content and matric potential within the soil core at three different locations. For each auxiliary variable the sensitivity to estimate the parameters α, n and the saturated hydraulic conductivity is studied by plotting the objective function surface in the parameter planes defined by these parameters. The objective function is calculated for 900 points in each parameter plane and describes the error between the measured and generated auxiliary variable. The shape of these surfaces indicates how well an inverse procedure can find a unique and accurate solution. From these surfaces auxiliary variables, or combinations thereof, are selected which provide sensitive parameter estimates. The surfaces indicate that the contours are nonconvex and that confidence regions for parameters are not symmetric. The hydraulic conductivity is the least sensitive parameter to estimate. For a wetting experiment the parameter sensitivity will increase when the measurement of the auxiliary variable is taken further away from the inflow boundary. To obtain sensitive parameter estimates the auxiliary variable used in the inverse procedure needs to be least similar to the known and changed boundary variable. The shape of the objective function surface for the degenerate case, where an auxiliary variable would be measured at the changed boundary, can provide prior information regarding the sensitivity of estimating parameters from an auxiliary variable and regarding the start values of the parameters for the parameter search. The difference in parameter sensitivity between the sandy and clayey soil is small.