[1] 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.Citation: Griebling, S. A., and R. M. Neupauer (2013), Adjoint modeling of stream depletion in groundwater-surface water systems, Water Resour. Res., 49,[4971][4972][4973][4974][4975][4976][4977][4978][4979][4980][4981][4982][4983][4984]

If an aquifer is hydraulically connected to an adjacent stream, a pumping well operating in the aquifer will draw some water from aquifer storage and some water from the stream, causing stream depletion. Several analytical, semi-analytical, and numerical approaches have been developed to estimate stream depletion due to pumping. These approaches are effective if the well location is known. If a new well is to be installed, it may be desirable to install the well at a location where stream depletion is minimal. If several possible locations are considered for the location of a new well, stream depletion would have to be estimated for all possible well locations, which can be computationally inefficient. The adjoint approach for estimating stream depletion is a more efficient alternative because with one simulation of the adjoint model, stream depletion can be estimated for pumping at a well at any location. We derive the adjoint equations for a coupled system with a confined aquifer, an overlying unconfined aquifer, and a river that is hydraulically connected to the unconfined aquifer. We assume that the stage in the river is known, and is independent of the stream depletion, consistent with the assumptions of the MODFLOW river package. We describe how the adjoint equations can be solved using MODFLOW. In an illustrative example, we show that for this scenario, the adjoint approach is as accurate as standard forward numerical simulation methods, and requires substantially less computational effort.

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