Stochastic Groundwater Flow Modeling Using the Second-Order Method

摘要

Stochastic groundwater flow modeling by means of a second-order uncertainty analysis technique is discussed. This technique is based on a Taylor series expansion of the state variables of interest (hydraulic heads and Darcian velocities) about the expected values of the model parameters. The method has been incorporated into the computer code PORSTAT, which solves the two-dimensional stochastic groundwater flow equation coupled with the deterministic heat transfer and mass transport equation using integrated finite differences coupled to a direct-equation solver. Uncertain variables that can be considered in the application of PORSTAT are (1) hydraulic conductivities (x- and y-direction), (2) specific storage, (3) boundary conditions, and (4) initial conditions. The output from PORSTAT consists of the expected values, variances, and covariances of hydraulic heads and Darcian velocities. The application of PORSTAT to a sample problem is also presented. This problem was also solved by means of a Monte Carlo groundwater flow program (PORMC) to assess the accuracy of the second-order method. It was observed that as the coefficient of variation of the input parameters increases, the difference between the standard deviations predicted by PORSTAT and those prediced by Monte Carlo codes increases. For coefficients of variation of hydraulic conductivity in these test cases of less than about one, the agreement between the results of PORSTAT and Monte Carlo codes appear to be reasonably close. However, it is not possible to generalize this conclusion since results are, in general, problem dependent. 16 refs., 16 figs. (ERA citation 10:028913)