2D variably saturated flows: Physical scaling and bayesian estimation

A novel dimensionless formulation for water flow in two-dimensional variably saturated media is presented. It shows that scaling physical systems requires conservation of the ratio between capillary forces and gravity forces. A direct result of this finding is that for two physical systems to be hydraulically similar, the soil in the smaller system has to be coarser than the soil in the larger system. The new formulation is implemented in a finite-element model that compared favorably with published numerical results with a minimal mass balance error. Bayesian estimation using prior physical information was used to fit the model to experimental data that simulated tidal action in a laboratory beach. Results show that the model is not sensitive to the residual soil moisture or the parameter n in the van Genuchten model, but is sensitive to variation in the saturated hydraulic conductivity and the parameter α in the van Genuchten model. Nomographs based on the dimensionless formulation were used to scale the results of the laboratory beach to the range of natural beaches.