Stochastic analysis of nonstationary subsurface solute transport; 1, Unconditional moments
Graham Wendy; McLaughlin Dennis
Water Resources Research 25(2): 215-232
ISSN/ISBN: 0043-1397 DOI: 10.1029/wr025i002p00215
Partial differential equations for three unconditional ensemble moments (the concentration mean, concentration covariance, and velocity concentration cross covariance) are derived by applying perturbation techniques to the governing transport equation for a conservative solute. Concentration uncertainty is assumed to be the results of unmodeled small-scale fluctuations in a steady-state velocity field. The moment expressions, which describe how each moment evolves over time and space, resemble the classic deterministic advection-dispersion equation and can be solved using similar methods. A solution procedure based on a Galerkin finite element algorithm is illustrated with a hypothetical two-dimensional example.