Aquifer-scale flow equations as generalized linear reservoir models for strip and circular aquifers: Links between the Darcian and the aquifer scale

Abstract

[1] An analytical treatment of aquifer flow is presented to establish a link between runoff models and aquifer properties. Recently developed one-dimensional analytical solutions for transient flows in homogeneous aquifers produce expressions for the flux between the aquifer and the surface water, and the difference between the average hydraulic head in the aquifer and the surface water. It is shown that the ratio between these large-scale variables (i.e., the aquifer-scale hydraulic conductivity) can assume one of three asymptotic values. A non-Darcian aquifer-scale flow equation is derived for the average head in the aquifer minus the surface water level. This first-order ordinary differential equation has nonconstant coefficients based in part on the aquifer-scale conductivity. The aquifer-scale equation is a generalization of linear reservoir models: when the aquifer-scale conductivity is stationary, its solution has an exponential term (like a linear reservoir) with a reservoir coefficient that depends on external factors, and a constant term. The solution applies to a wider range of problems than conventional linear reservoir models. The aquifer's characteristic time (derived from the solution) shows that dense drainage networks can make aquifers behave like linear reservoirs most of the time, while large systems never will. When the asymptotic values are used before the time period for which they become valid (i.e., shortly after a perturbation in the surface water level or recharge/extraction), the predicted fluxes can be very inaccurate, and possibly have the wrong sign. In such cases, the full analytical solutions should be used.