New Analytical Models for Flow Induced by Pumping in a Stream-Aquifer System: A New Robin Boundary Condition Reflecting Joint Effect of Streambed Width and Storage

Abstract

A Robin type boundary condition (BC), commonly adopted at stream-aquifer interface, excludes a term associated with streambed accounting for the effects of streambed storage and width. This study presents two new analytical models for describing confined flow induced by pumping in a stream-aquifer system. One model considers a single-zone aquifer and treats the streambed as a lagging Robin BC with a time lag parameter related to the effects. The other considers a two-zone aquifer consisting of aquifer and streambed zones. A Dirichlet BC for stream water level is specified at the edge of the streambed. The time-domain solutions of both models are developed to describe spatiotemporal drawdown and temporal stream filtration/depletion rate (SDR). The finite element solutions (FESs) of both models are also built. Results suggest the lag time equals the half of the squared streambed width divided by the streambed hydraulic diffusivity. The effects of streambed width and storage on SDR should be considered when their lumped parameter exceeds 0.1. Neglecting their effects causes 25% difference in SDR when the lumped parameter equals 10. Based on the FESs, the use of the lagging Robin BC takes nearly a tenth of computing time of obtaining accurate steady-state SDR for the simulation of the two-zone aquifer. In addition, the present solutions agree to a field SDR experiment conducted by Hunt et al. (2001, ). To conclude, this study presents two new models for describing groundwater flow in a stream-aquifer system and explores the joint effect of streambed width and storage on SDR. Key Points Two new analytical solutions are developed to estimate aquifer drawdown and stream depletion rate in a pumped stream-aquifer system One treats streambed as a Robin type boundary based on the lagging theory while the other considers streambed as a finite-width zone The lag time in the Robin boundary equals the half of squared streambed width divided by the streambed hydraulic diffusivity