Stochastic modeling of vertically averaged concentration uncertainty in a perfectly stratified aquifer

Solute concentration which results from transport in an aquifer with unknown variability in hydraulic conductivity can be subject to large predictive uncertainty. This uncertainty can be modeled using a stochastic approach in which conductivity is represented by a random field with known probabilistic structure. In this work we use Monte Carlo methods of stochastic modeling to study the uncertainty in vertically flux-averaged concentration for transport in the simplified case of a perfectly stratified aquifer. We assume steady flow parallel to bedding and negligible transverse dispersion. We measure uncertainty with the ensemble coefficient of variation of concentration and find it to be large in most conditions examined. We consider the validity of an ergodic assumption (practical equivalence of ensemble mean and single-realization concentrations) by investigating the dependence of uncertainty upon the vertical averaging length. Even for averaging over a depth of 100 times the vertical correlation scale of conductivity, uncertainty is large enough (around 20%) to be considered significant in many predictive situations. We conclude that prediction based solely on the ensemble mean concentration would be inappropriate for this simple system and emphasize the importance of the ensemble variance for quantification of predictive uncertainty in stochastic modeling of solute transport.