Using Adjoint Methodology to Quantify Stream Depletion.

As the availability of water for human consumption, irrigation, and environmental health is threatened by increasing demand from growing populations and a potential reduction in supply due to changes in climactic patterns, the need to minimize the depletion of flows in streams and rivers caused by groundwater pumping becomes paramount. Stream depletion is defined as the decrease in stream flow due to groundwater pumping. Several analytical and numerical approaches for quantifying stream depletion have been developed and can be applied when the well location is known. If a new well location is to be chosen to minimize stream depletion, the existing methods prove inefficient as they require a separate simulation for each potential well location. In this work, we develop adjoint equations of a coupled groundwater and surface water system that can be solved to calculate stream depletion. We use MODFLOW with the stream package to solve the adjoint equations, and, unlike previous work, we allow the head and resulting flow in the river to change as a result of depletion. With only one simulation of the adjoint equations, stream depletions can be calculated for a well at any location in the aquifer, making it an efficient method for siting future wells.