Free-Form estimation of soil hydraulic properties using Wind's method

Transient evaporation experiments offer the potential to determine simultaneously the soil hydraulic properties necessary to simulate water flow in unsaturated soils. We present a new algorithm for determining the retention and conductivity curve from evaporation experiments which uses Wind's method with a free-form soil water retention function. Our algorithm estimates nodal values of volumetric water content and derives a smooth and monotone retention curve by cubic Hermite interpolation. A multilevel routine increases the number of nodes and their adequate number is identified by a performance criterion which balances goodness of fit, the cross correlation between the estimated water contents and the number of degrees of freedom. We calculate point values of unsaturated hydraulic conductivity by the instantaneous profile method and discard unreliable conductivity estimates by a statistical filter criterion. Results for three synthetic data sets including an uncertainty analysis of the estimated retention curves show that the algorithm is suitable to identify, both correctly and precisely, the soil hydraulic properties. An application to a real data set confirms these results. In order to enable the free-form functions to be used in numerical flow simulations, we extrapolate the retention function to the dry range and compute a coupled conductivity function based on the Mualem model. Major advantages of the proposed method are the enormous flexibility provided by the free-form functions, the low level of parameter cross-correlation in comparison with classic parametric functions, and the possibility of assessing the uncertainty of the retention curve individually in different ranges of pressure head.