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Stochastic uncertainty analysis for unconfined flow systems
Liu, Gaisheng Zhang, Dongxiao Lu, Zhiming
Liu, Gaisheng
Zhang, Dongxiao
Lu, Zhiming
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Abstract
[1] 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 (lnKS) 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 lnKS. Next, head h is decomposed as a perturbation expansion series Σh(m), where h(m) represents the mth-order head term with respect to the standard deviation of lnKS. Then h(m) is further expanded into a polynomial series of m products of orthogonal Gaussian standard random variables whose coefficients image 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 image 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.
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This is the published version. Copyright American Geophysical Union
Date
2006-09-19
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American Geophysical Union
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liu_unconfined.pdf
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Liu, Gaisheng, Dongxiao Zhang, and Zhiming Lu. "Stochastic Uncertainty Analysis for Unconfined Flow Systems." Water Resources Research Water Resour. Res. 42.9 (2006): n. pag. DOI:10.1029/2005WR004766