Parameter estimation for unsaturated flow models

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Virginia Polytechnic Institute and State University

The estimation of parameters in models for soil unsaturated hydraulic properties from transient flow experiments via inversion of the governing initial-boundary value problem is examined. Emphasis is on the estimation of parameters from in-situ experiments where available data are in the form of spatially and temporally distributed water content and pressure head measurements. The inverse problem is formulated as a weighted least-squares problem. A simple but efficient Levenberg-Marquardt algorithm is developed for its solution. Sensitivity analysis is used to determine optimal sampling strategy for a one-dimensional ponded infiltration-drainage experiment. The analysis shows that sensitivities are highest, and therefore measurements should be concentrated, in zones where large moisture and pressure head gradients occur. The unsaturated flow process was found to be relatively insensitive to the saturated hydraulic conductivity. The latter parameter will therefore be difficult to estimate precisely. A numerical study on the effects of input uncertainty on estimation results indicates that complexity of the model that can be meaningfully identified from a given set of data is controlled by the level of data uncertainty. When data error from several sources was compounded, broad features of the unknown water retention and hydraulic conductivity functions were still predicted acceptably well, but it was no longer possible to distinguish more detailed features, such as hysteresis in the retention function. The parameter estimation algorithm is applied to data from two in-situ experiments. The first involves drainage from a large and uniformly packed lysimeter at Los Alamos National Laboratory. The experiment was intensively monitored, resulting in accurate input data for the inversion. Results obtained for this problem are very favorable, with excellent agreement between predicted and separately determined water retention and hydraulic conductivity functions. The second experiment is a field irrigation-drainage experiment conducted at New Mexico State University. Due to greater soil heterogeneity and less well-defined initial and boundary conditions, the apparent input uncertainty is considerably greater than was the case for the Los Alamos experiment. In agreement with results from the earlier theoretical analysis it was found that hydraulic properties could be predicted reasonably well, but it was not possible to distinguish layering in the soil profile or hysteresis in the water retention function, although the data show evidence of both phenomena.