Stochastic Modeling of Groundwater Systems

Abstract

This research developed important new results on the use of spectral analysis techniques to evaluate groundwater resources. The linear theory of aquifer spectral response in the frequency domain is developed, including effects of aquifer slope, vertical flow, variable transmissivity and other features. Numerical simulations of the nonlinear effects in the spectral domain are developed and show that the nonlinear effects are typically quite small, thus making the simple linear theory applicable for most field situations. Some additional features which are explored are the effects of spatial variability of hydraulic conductivity and the influence of transient flow in the partially saturated zone above the water table. Through spectral analysis in the wave number domain, an error criterion is established for a simple observation network which is used to measure groundwater flow. The effects of storage in the partially saturated zone on the frequency spectrum of groundwater fluctuations are estimated and found to be negligible in most cases. The theoretical results are applied to evaluate, through spectral analysis, time series of groundwater levels, precipitation and stream stage for a site in Kansas. From these data, using a procedure based on the linear spectral theory, estimates of aquifer transmissivity and storativity are developed. The procedure yields parameter estimates which are in agreement with those obtained from pumping tests. The results of the study should be applicable under specified conditions to the estimation of aquifer parameters from natural fluctuations of groundwater level.