Unconditional and conditional analysis of flow and solute transport in variably saturated porous media

Abstract

A numerical first order approach is proposed to conduct stochastic analyses of head and concentration under variably saturated conditions. The approach is based on a first-order Taylor series expansion and an adjoint state method. To implement the approach in different flow and transport regimes, numerical models are adopted to evaluate sensitivities of head and concentration with respect to hydrological parameters. This provides the possibility of conducting stochastic analyses of flow and transport problems with any kind of boundary and initial conditions. As a result, limitations of analytical approaches such as the spectral/perturbation approach can be avoided. In addition, the use of adjoint state method also alleviates the computational burden encountered in Monte Carlo simulation by allowing us to evaluate the sensitivities of head and concentration only at interesting/measurement locations. Several numerical simulations are performed to examine the sensitivities and moments of head and concentration under different flow conditions. The results show that the existence of water tables in the simulation domain can have a significant impact on the moment calculation of head and concentration. The calculated statistical moments are used to estimate log-conductivity by cokriging. The conditioning effect of head, concentration, and arrival time in estimating log-conductivity is investigated under different flow conditions. The results show steady state head is the best secondary information compared to solute concentration and arrival time in estimating conductivity by providing stable and consistent results. Estimates can be error prone when concentration measurements are used to estimate LnKs because of the nonlinear relationship between concentration and LnKs and the large variability in the simulated solute plumes. A sequential estimating technique is shown to be able to overcome some of these inadequacies of using concentration measurements. Arrival time, requiring a large amount of CPU time, does not show any advantage over concentration and head in estimating conductivity.