Effects of Heterogeneity and Uncertainties in Sources and Initial and Boundary Conditions on Spatiotemporal Variations of Groundwater Levels

Abstract:

Effects of aquifer heterogeneity and uncertainties in source/sink, and initial and boundary conditions in a groundwater flow model on the spatiotemporal variations of groundwater level, h(x,t), were investigated. Analytical solutions for the variance and covariance of h(x, t) in an unconfined aquifer described by a linearized Boussinesq equation with a white noise source/sink and a random transmissivity field were derived. It was found that in a typical aquifer the error in h(x,t) in early time is mainly caused by the random initial condition and the error reduces as time goes to reach a constant error in later time. The duration during which the effect of the random initial condition is significant may last a few hundred days in most aquifers. The constant error in groundwater in later time is due to the combined effects of the uncertain source/sink and flux boundary: the closer to the flux boundary, the larger the error. The error caused by the uncertain head boundary is limited in a narrow zone near the boundary but it remains more or less constant over time. The effect of the heterogeneity is to increase the variation of groundwater level and the maximum effect occurs close to the constant head boundary because of the linear mean hydraulic gradient. The correlation of groundwater level decreases with temporal interval and spatial distance. In addition, the heterogeneity enhances the correlation of groundwater level, especially at larger time intervals and small spatial distances.