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Stochastic uncertainty analysis for unconfined flow systems

Water Resources Research

By:
, ,
DOI: 10.1029/2005WR004766

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Abstract

A new stochastic approach proposed by Zhang and Lu (2004), called the Karhunen-Loeve decomposition-based moment equation (KLME), has been extended to solving nonlinear, unconfined flow problems in randomly heterogeneous aquifers. This approach is on the basis of an innovative combination of Karhunen-Loeve decomposition, polynomial expansion, and perturbation methods. The random log-transformed hydraulic conductivity field (InKS) is first expanded into a series in terms of orthogonal Gaussian standard random variables with their coefficients obtained as the eigenvalues and eigenfunctions of the covariance function of InKS- Next, head h is decomposed as a perturbation expansion series ??A(m), where A(m) represents the mth-order head term with respect to the standard deviation of InKS. Then A(m) is further expanded into a polynomial series of m products of orthogonal Gaussian standard random variables whose coefficients Ai1,i2(m)...,im are deterministic and solved sequentially from low to high expansion orders using MODFLOW-2000. Finally, the statistics of head and flux are computed using simple algebraic operations on Ai1,i2(m)...,im. A series of numerical test results in 2-D and 3-D unconfined flow systems indicated that the KLME approach is effective in estimating the mean and (co)variance of both heads and fluxes and requires much less computational effort as compared to the traditional Monte Carlo simulation technique. Copyright 2006 by the American Geophysical Union.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Stochastic uncertainty analysis for unconfined flow systems
Series title:
Water Resources Research
DOI:
10.1029/2005WR004766
Volume
42
Issue:
9
Year Published:
2006
Language:
English
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
Water Resources Research