Nonlinear response of streamflow to groundwater pumping for a hydrologic streamflow model

Groundwater management models that combine optimization methods with coupled stream/aquifer simulation models are considered. Designing algorithms to solve these problems benefits from improved understanding of the nature of the functional relationship between well extraction and streamflow. An analysis is conducted of the nature of this relationship for the Modflow Stream Package stream/aquifer simulation model. Derivatives of the algebraic implementation of the code and numerical testing on a hypothetical problem are used to perform the analysis. Results indicate that a nonlinear relation exists and that it is expected to be bounded and mild under all practical circumstances. The streamflow function may be convex or concave depending on the location of the observation point relative to the well and the ratio of streambed conductance to hydraulic conductivity. For a given setting of well and observation location, the function is likely to be either concave or convex under all practical values of pumping rates and model parameters.