Modeling stream–aquifer interactions with linear response functions

The problem of stream–aquifer interactions is pertinent to conjunctive—use management of water resources and riparian zone hydrology. Closed form solutions expressed as convolution integrals of impulse response and unit step response functions are derived for channel flow and stream–aquifer interactions. The solutions, obtained using Laplace transforms, relate channel reach discharge, stream–aquifer exchange rates, and associated flow volumes to hydrologic processes and regulatory and management control measures. Channel flow is modeled using a simple mass balance equation and the Muskingum linear storage relationship, and groundwater flow is approximated by a linearized representation of the one-dimensional Boussinesq equation. Within a given channel reach, the aquifer is assumed to be homogeneous, separated from the channel by a semipervious layer, and with a time-variable prescribed head or no-flow boundary condition at a finite distance normal to the channel flow direction. Discrete-time unit response functions are derived for arbitrary channel inflow hydrographs and other systemʹs excitations, which extend the utility of the model to a wider spectrum of water management problems. Although the closed-form solutions are based on simplifying assumptions which may limit the utility of the solutions, applications to example flow scenarios nonetheless illustrate the robustness of the solutions to a variety of applications such as the bank storage problem, effect of drought periods, and groundwater–surface water interactions in the presence of water management controls.