Application of Superposition with Nonlinear Head‐Dependent Fluxes

Abstract

While superposition is commonly used to address linear ground water problems, it can also be used to address certain nonlinear problems. In particular, it can be used to address problems with nonlinear head-dependent fluxes, where the problem can be separated conveniently into steady-state and transient-state components. Superposition can be used to simulate the transient-state head changes independently from the steady-state heads. The problems addressable by superposition include phreatophyte discharges, stream-aquifer interactions, spring discharges, and drain discharges. Each of these represents a nonlinear head-dependent flux, where the flux depends on the elevation of the land surface or some other feature. Superposition is applied by referencing elevations to the local steady-state water table and by imposing the negative of the steady-state flux on the transient-state problem.

Capture-Rates and Directions of Groundwater Flow Don't Matter!

“…In fact, if aquifer diffusivity, or distributions of hydraulic conductivity, specific storage, specific yield, and aquifer thickness, are known, complex flow models that compute head are likely to be computationally inferior to the "superposition" or "change" numerical modeling approach that directly computes drawdown and capture. Durbin et al (2008) show how to represent nonlinear head-dependent boundaries in numerical-superposition models. For a perspective on groundwater modeling using flow and superposition modes, see Bredehoeft (2006).…”