Modeling and stochastic analysis of coupled overland and vadose zone flow

In this study, a model was developed to couple overland flow with vadose zone flow. The 1-D Richards' equation was used to model unsaturated flow and solved using a finite element method. Evaporation and transpiration were modeled as a specified flux boundary and internal sink respectively within the vadose zone flow model. The Penman-Monteith equation was selected to estimate potential evapotranspiration, which was partitioned between evaporation and transpiration according to the plant's Leaf Area Index (LAI) and its type. The actual evaporation and transpiration were calculated by introducing soil moisture reduction coefficients, which can be obtained by several methods. A diffusion wave model of overland flow was derived from the Saint-Venant equations, and solved using the finite element method. Several examples were presented to verify the overland flow component, the vadose zone flow component, and the coupled numerical model. These examples showed that each component and the coupled model are reliable and give results similar to analytical solutions, results from other numerical models or experimental data.; Using the coupled model developed in this study, Monte Carlo simulations were conducted to study the effect of uncertain spatial variability in Manning's coefficient, surface elevation and soil saturated hydraulic conductivity on the mean predicted surface water depth, the mean predicted surface runoff, and the prediction uncertainty around these values. The Monte Carlo simulation results showed that the spatial variability of saturated hydraulic conductivity, Manning's coefficient, and microtopography influences the mean surface runoff hydrograph in runoff starting time, ending time, discharge peak and volume. Among the three spatially varied parameters, hydraulic conductivity demonstrates the greatest effect on runoff discharge rate and total volume, while Manning's coefficient has the greatest effect on surface water depth.; A 1-D analytical model, based on stochastic perturbation techniques, was also developed to examine the effects of spatial variability of land surface elevation, surface roughness, and hydraulic conductivity on surface runoff. Expressions were derived for estimating the model prediction uncertainty, and the effective parameter values for hydraulic conductivity, Manning's coefficient, and surface elevation. The analytical model was tested against the Monte Carlo simulations results. The comparison shows that the analytical model agrees reasonably well with the Monte Carlo simulation.