Abstract
An alternative approach to the inverse problems encountered prior to the computations of saturated-unsaturated groundwater flow is addressed. The soil hydraulic properties (i.e., the relative hydraulic conductivity K_r and the volumetric water content θ) which are the a priori unknown parameters in the Richards equation governing the flow are interpolated by an assembly of the piecewise cubic spline functions expressed in terms of the pressure head. This free-form parameterization approach provides high flexibility and degrees of freedom in identifying the functional form of the parameters, compared with the conventional approaches in that the functions are of specific shape as in the van Genuchten model of a fixed functional form. In addition, the approach is field-oriented in a point that the solution of the inverse problem can be achieved having only recourse to the observed time-series data of pressure head which are relatively easily in situ available. To find the shapes of such spline functions best expressing head-dependency of the soil hydraulic properties, a simulation-optimization algorithm with the aid of the Levenberg-Marquardt method is developed which serves to iteratively solve an optimization problem of minimizing errors between the observed (or measured) and computed values of the pressure head, in combination with the embedded simulation module for solving forward problems. Validity of the approach is examined with its application to different two soil types which are characterized by less and more sensitive changes of the relative hydraulic conductivity near saturation, respectively. The results show that the approach developed could be a viable alternative to the conventional fixed functional form approaches.
