Efficient modeling methods for estimating stream depletion

摘要

Stream depletion is the reduction in stream flow rate caused by pumping from a groundwater well in an aquifer that is hydraulically connected to the stream. To aid in choosing the location for a new well, simulations are often conducted to estimate stream depletion that would occur if pumping was done at any of the candidate well locations. The results are then used to eliminate candidate well locations that would lead to stream depletion above a pre-determined threshold. With this approach, one simulation must be run for each candidate well location, which may be computationally expensive. Instead, an adjoint approach can be used. With only one adjoint simulation, stream depletion can be calculated for a well at any location in the aquifer. The adjoint approach is based on sensitivity analysis, and the adjoint equation is developed by considering the sensitivity of the stream flow rate to the pumping rate. This sensitivity is approximated as a first derivative, and therefore assumes a linear relationship between the system states and the pumping rate. If the assumption of linearly is invalid, the adjoint approach introduces error into the stream depletion calculations. In this work, we use the MODFLOW, a commonly-used groundwater flow simulator, to simulate stream depletion using both standard and adjoint approaches. We investigate the limitations of the adjoint approach and the extent of the error introduced by the assumption of linearity between the system states and pumping rate.