Stochastic analysis of steady state groundwater flow in a bounded domain: 1. One‐dimensional simulations

Abstract

A stochastic analysis of one‐dimensional steady state groundwater flow through a bounded domain is carried out by using Monte Carlo simulation techniques. The flow domain is divided into a finite set of discrete blocks. Hydraulic conductivity values in neighboring blocks are autocorrelated by assuming the spatial variations in conductivity can be represented by a first‐order nearest‐neighbor stochastic process model. An integral scale is defined to characterize the average distance over which conductivity values in the block system are autocorrelated. This model leads to a realistic representation of the spatial variations in hydraulic conductivity in a discrete block medium. Results of the simulations provide estimates of the output distributions in hydraulic head. It is shown that the ratio of the integral scale for conductivity to the distance between boundary points is a fundamental parameter in modeling the stochastic behavior of a bounded statistically homogeneous medium. The output distributions on the prediction variables must be interpreted in light of this parameter. The standard deviation in hydraulic head increases with an increase in either the standard deviation in hydraulic conductivity or the strength of the correlation between neighboring conductivity values. The standard deviation in head does not significantly depend upon the block size or the total number of blocks included along the flow line, provided a sufficiently accurate representation of the autocorrelation function is made. Although direct comparisons cannot be made, the Monte Carlo solution shows a similar behavior to the spectral solution of the stochastic flow equation in one dimension.