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Stochastic uncertainty analysis for unconfined flow systems
Author(s) -
Liu Gaisheng,
Zhang Dongxiao,
Lu Zhiming
Publication year - 2006
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2005wr004766
Subject(s) - mathematics , polynomial chaos , polynomial expansion , covariance , monte carlo method , random variable , standard deviation , karhunen–loève theorem , covariance function , random field , eigenfunction , series expansion , gaussian , eigenvalues and eigenvectors , mathematical analysis , statistics , algorithm , physics , quantum mechanics
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 ( lnK S ) 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 lnK S . Next, head h is decomposed as a perturbation expansion series Σ h ( m ) , where h ( m ) represents the m th‐order head term with respect to the standard deviation of lnK S . Then h ( m ) is further expanded into a polynomial series of m products of orthogonal Gaussian standard random variables whose coefficients 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 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.