Groundwater response to changing water‐use practices in sloping aquifers using convolution of transient response functions

Abstract

This study examines the impact of a sloping base on the movement of transients through groundwater systems. Dimensionless variables and regression of model results are employed to develop functions relating the transient change in saturated thickness to the distance upgradient and downgradient from recharge or withdrawal. Convolution of these transient response functions (made possible due to linearity of partial differential equations in the model) enables computation of changes in saturated thickness over recharge/withdrawal that varies over space and time. Establishing the criteria and form of these functions led to the discovery of fundamental underlying properties: upgradient and downgradient responses may be scaled to achieve a symmetrical relationship, expressions are developed to compute change in saturated thickness at the location of water use, and downgradient response at large times form a S‐shaped curve that effectively adds a diffusive component to the average velocity of the kinematic wave approximation, where the hydraulic gradient is equal to the bed slope. Hydrogeologic data for three study regions in the High Plains Aquifer are summarized, and model results are presented for changes in saturated thickness. The transient response functions are used to reconstruct and interpret groundwater response to historical water‐use practices and to predict future changes in saturated thickness for a series of hypothetical alternative water‐use scenarios. Depressions in groundwater elevation are observed both upgradient and downgradient from areas of high water use; however, these depressions preferentially move downgradient over time and may continue to spread downgradient far into the future. This approach quantifies and provides understanding of the impacts of changes in natural and anthropogenic hydrologic forcings on aquifer systems.