Inverse Modeling for Variably Saturated Water Flow Coupled with Heat Transport in Field Soil

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An inverse modeling to reproduce a variably saturated water flow in non-isothermal soil based on field observation is proposed. Since the water movement in the surface soil is significantly affected by the soil temperature, the governing equations system is composed of the mixed form Richards equation for the water movement and heat conduction equation for the thermal transport. To complete the water flow model of interest, unknown model parameters are determined with inverse technique. The major unknown parameter is the relative hydraulic conductivity (RHC) described as a free-form parameterized function which is a sequential piecewise cubic spline function and therefore can express the flexible functional form of the parameter. The inverse problem is defined as the minimization of errors between the observed and computed pressure heads to determine the coefficient values of the free-form function, and solved through a simulation-optimization method. To validate the water flow model developed, its practical application to in-situ soil is implemented. The results show that the functional form of RHC is successfully identified, and that both water movement and thermal transport models can produce the forward solutions which are good agreement with observed data for desorption period.

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