SENSITIVITY AND MOMENT ANALYSES OF HEAD IN VARIABLY SATURATED REGIMES

A numerical approach for approximating statistical moments of hydrauli c heads of variably saturated flows in multi-dimensional porous media is developed. The approximation relies on a first-order Taylor series expansion of a finite element flow model and an adjoint state numerica l method for variably saturated flows to evaluate sensitivities. This approach can be employed to analyze uncertainties associated with pred ictions of head of steady-state or transient flows in variably saturat ed porous media, with any type of boundary and initial conditions. Lim itations of stochastic analytical methods such as spectral/perturbatio n approaches and the time-consuming Monte Carlo simulation technique a re thus alleviated. An example is given to demonstrate the utility of the approach and to investigate the temporal evolution of head varianc es in a variably saturated flow regime. Results show that the fluctuat ion of the water table can have significant impacts on the propagation of the head variance. (C) 1998 Elsevier Science Limited. All rights r eserved.