An Innovative MODFLOW-Based Tool for Managing Groundwater Resources

Groundwater management of water resources has traditionally been based upon the estimation of discharge capture (capture function).    A capture function, at a specified location, is defined as a derivative of the flux across the boundary of an aquifer (such as the interface of groundwater with surface water) with respect to the rate of withdrawal from a pumping well at the same location. The quantification of discharge capture can be used in the assessment of water rights; assessment of groundwater development and issues of sustainability; and optimal location and timing of pumping of wells to minimize capture subject to the constraints of permissible consequences in the ecosystems of the aquifer and surface water supplies.

Capture has traditionally been estimated through analytic means derived from the closed-form Glover-Balmer (1954) equation for stream flow.  To overcome stream-aquifer non-idealities, numerical models are increasingly being used for simulation of groundwater flow and the determination of pumping development on water levels and stream and spring flows.

Traditionally, the strategy used with numerical models for the evaluation of capture functions is a finite difference method to approximate the derivative implied in the capture function. This approach involves (N+1) repetitions of the model simulations, where N denotes the number of nodes in the model grid. When N is of the order of hundreds of thousands (as is common in present practice), this method is prohibitively expensive in time consumed and in physical effort.

This paper presents the application of an alternative algorithm, based on the Adjoint Sensitivity formulation, for the calculation of capture functions. The adjoint method only requires two simulations of the underlying groundwater model. The method has been developed in MODFLOW and this paper will present an example application compared to a recently published perturbation method and will discuss potential application in the groundwater practice.