Adjoint modeling of stream depletion in groundwater‐surface water systems

Abstract

Groundwater pumping may lead to reduction in surface water flows, which can compromise water supplies and habitat. In light of these threats, the need to minimize stream depletion, defined as the reduction in the flow rate in streams and rivers caused by groundwater pumping, becomes paramount. We develop adjoint equations to calculate stream depletion due to aquifer pumping. We consider a coupled groundwater and surface water system in which both the river head and river flow rate are impacted by drawdown in the aquifer as a result of pumping. Through an illustrative example, we show that the adjoint method for calculating stream depletion produces accurate results if the model is approximately linear. With only one simulation of the adjoint equations, stream depletion can be calculated for pumping at a well at any location in the model domain, which results in a substantial reduction in computational time as compared to the standard method of calculating stream depletion.