Determining soil hydraulic functions from evaporation experiments by a parameter estimation Approach: Experimental verifications and numerical studies

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Abstract
A parameter estimation method is developed for the determination of unsaturated soil hydraulic properties from evaporation experiments under laboratory conditions. Variables used in the inversion procedure are soil water pressure heads at various positions and total soil weights, both measured as a function of time during the experiment. Unknown parameters of different analytical expressions used to describe the soil hydraulic properties are estimated by coupling a finite difference solution of the Richards equation with a nonlinear optimization problem. This problem is formulated by minimizing the deviations between the numerical solution of the transient flow process and the real system response measured during the experiment. Minimization of the objective function is performed using a version of the Levenberg‐Marquardt's method; the procedure also provides information about the uncertainty in parameter estimates. The performance of the selected parametric relationships is evaluated, and the applicability and accuracy of the proposed inverse method are shown by comparing estimated water retention and hydraulic conductivity functions with experimental results obtained via the instantaneous profile method. Parameter sensitivity analyses and stability of the inverse solutions are discussed with reference to the originally designed evaporation experiment and to an evaporation method that is developed with a view to reducing experimental efforts. Further insights into the properties of existence and uniqueness of inverse solutions are gained by examining contour plots of the objective functions under varying experimental conditions. The results confirm the reliability and flexibility of the proposed method and suggest that the evaporation flux imposed at the upper soil surface may determine the well posedness of the optimization problem.

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