Modeling the large-scale dynamics of saturated ground flow using spatial-filtering theory: 2. Numerical evaluation

The objective of this paper is to numerically evaluate the spatially filtered flow theory of Beckie et al. [this issue]. We perform two suites of tests to evaluate the theory. In the first suite of tests we examine the accuracy of the spatially filtered Darcy's law approximations. To do this, we use exact filtered conductivities and head gradients in the spatially filtered Darcy's laws to calculate the approximate filtered flux and then compare the approximate flux field to the exact flux field. We determine the exact fields by numerically filtering the primitive fields. In the second suite of tests we solve the model equations to determine the approximate flux solution. We present a simple numerical-perturbation strategy to solve the model equations. The first suite of tests shows that over a range of filter widths the error in the resolved-scale flux computed from the second- order approximate spatially filtered Darcy's law is up to 3 orders of magnitude lower than the zeroth-order approximation. The second suite of tests, which more closely correspond to the way the theory would be applied in practice, show that the model accuracy and convergence properties are degraded by error from the numerical-perturbation strategy.