An Adjoint Approach To Estimating Stream Depletion
Neupauer, Roseanna M. 1 ; McCarl, Daniel F. 2
2 Presenting Author
1 University of babyֱapp
2 University of babyֱapp
Pumping groundwater can draw water from a nearby stream and decrease the flow rate of water in the stream. We call this effect “stream depletion.” Stream depletion is quantified as the difference between the river flow rate in the absence of pumping and in the presence of pumping. Stream depletion has many negative consequences; for example, stream depletion can disturb riparian habitats and infringe on water rights. Thus, when a new well is to be drilled, it may be desirable to choose a well location that will minimize stream depletion. To find such a location, previous methods required that a separate computer simulation be run for each possible well location. We develop an adjoint-based method. Our adjoint-based method requires only one computer simulation to determine the stream depletion at all possible well locations. Thus, the adjoint method is computationally more efficient. Previously, the equations for the adjoint-method have been derived for (1) a model in which the streambed was assumed to a “wide” rectangle and (2) a model in which the streambed was rectangular and the water level in the river was independent of groundwater pumping. We derive the equations for a model with a generic rectangular streambed, and we assume that the water level in the river is dependent on pumping. In the future, we will derive equations for more complex streambed geometries, including an eight-point cross section.
Neupauer, R.M., and S.A. Griebling, 2011, Adjoint Simulation of Stream Depletion Due to Aquifer Pumping, Ground Water, doi:10.11/j.1745-6584.2011.00901.x.
Sykes, J.F., J.L. Wilson, and R.W. Andrews, 1985, Sensitivity analysis for steady state groundwater flow using adjoint operators, Water Resources Research 21, no. 3: 359-371.