Stochastic analysis of solute transport in heterogeneous aquifers subject to spatiotemporal random recharge

This paper extends the work of Li and Graham [1998] to deal with the unconditional moments of head, velocity, and concentration under transient flow conditions, which are assumed to be caused by a spatiotemporally random recharge. Semianalytical solutions are derived for the unconditional covariances for transient velocity with a constant mean recharge using a Fourier transform approach. Results demonstrate that the velocity covariance derived for the steady state random recharge field is a limiting case of the spatiotemporally variable velocity covariance with an infinite temporal correlation scale. Another limiting case indicates that introduction of temporally random but spatially uniform recharge has no effect on the velocity covariances (over that induced by the mean recharge on the mean head gradient). Thus for this limiting case there is no increased effect on the ensemble mean concentration plume spreading or the concentration prediction uncertainty. Following Deng et al. [1993], the equations for mean concentration and macrodispersive flux under zero mean transient recharge are decoupled in the Laplace‐Fourier domain and solved using a fast Fourier transform algorithm, which significantly reduces the computational demand. The first‐order concentration variance is solved using three different approximate techniques: an approximate fast Fourier transform technique, a finite element method, and a direct numerical integration. The simulation results show that introduction of a spatiotemporally random recharge enhances both longitudinal and lateral mean concentration plume spreading compared to the no recharge case. However, transient recharge produces less spreading and less concentration prediction uncertainty than the steady state spatially random recharge case.