Anthony J. Smith

Weakly Nonlinear Approximation of Periodic Flow in Phreatic Aquifers

Published frequency-domain solutions of periodic flow in aquifers apply strictly to mathematically linear systems that arise when aquifer diffusivity is assumed constant in space and time. This assumption can be invalid in phreatic aquifers that experience spatiotemporal variation in the free surface position and consequent variation in saturated thickness. A weakly nonlinear approach to formulating and solving periodic flow problems in the frequency domain can be applied in situations where conventional linearized approximations break down. The weakly nonlinear equations provide robust approximations of the true nonlinear response and require much less computational effort and time to solve than the full nonlinear problem. Nondimensional rules of thumb are presented for choosing between linear, weakly nonlinear and nonlinear solution strategies.

Assessment of Managed Aquifer Recharge Potential Using Ensembles of Local Models

A simple quantitative approach for assessing the artificial recharge potential of large regions using spatial ensembles of local models is proposed. The method extends existing qualitative approaches and enables rapid assessments within a programmable environment. Spatial discretization of a water resource region into continuous local domains allows simple local models to be applied independently in each domain using lumped parameters. The ensemble results can be analyzed directly or combined with other quantitative and thematic information and visualized as regional suitability maps. A case study considers the hydraulic potential for surface infiltration across a large water resource region using a published analytic model for basin recharge. The model solution was implemented within a geographic information system and evaluated independently in >21,000 local domains using lumped parameters derived from existing regional datasets. Computer execution times to run the whole ensemble and process the results were in the order of a few minutes. Relevant aspects of the case study results and general conclusions concerning the utility and limitations of the method are discussed.