Stochastic Analysis of Spatial Variability in Unconfined Groundwater flow
Resource
Stochastic Environmental Research and Risk Assessment 18 (2): 100-108
Journal
Stochastic Environmental Research and Risk Assessment
Journal Volume
18
Journal Issue
2
Pages
100-108
Date Issued
2004
Date
2004
Author(s)
Chen C.-M.
Abstract
In this paper, spatial variability in steady one-dimensional unconfined groundwater flow in heterogeneous formations is investigated. An approach to deriving the variance of the hydraulic head is developed using the nonlinear filter theory. The nonlinear governing equation describing the one-dimensional unconfined groundwater flow is decomposed into three linear partial differential equations using the perturbation method. The linear and quadratic frequency response functions are obtained from the first- and second-order perturbation equations using the spectral method. Furthermore, under the assumption of the exponential covariance function of log hydraulic conductivity, the analytical solutions of both the spectrum and the variance of the hydraulic head produced from the linear system are derived. The results show that the variance derived herein is less than that of Gelhar (1977). The reason is that the log transmissivity is linearized in Gelhar's work. In addition, the analytical solutions of both the spectrum and the variance of the hydraulic head produced from the quadratic system are derived as well. It is found that the correlation scale and the trend in mean of log hydraulic conductivity are important to the dimensionless variance ratio. © Springer-Verlag 2004.
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journal article
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