A New Highly Parameterized Linear Inversion of Water Table Change and Groundwater Depletion Rate Tested With the High Plains Aquifer, U.S.A.

Abstract

AbstractUnderstanding groundwater resource dynamics is limited by the sparsity of observations of water levels, pumping rates, and hydraulic properties relative to their spatiotemporal heterogeneity. To address some of this complexity, we proposed a new highly parameterized linear inverse method to quantify water table change and groundwater depletion rate in unconfined aquifers that does not require initial or boundary conditions. The method requires linearization, and we tested the performance of six proposed water table functions with three coordinate systems with synthetic models, finding that water table functions by the dimensionless method achieve the lowest errors. Our inverted water table changes and depletion rates remained stable and accurate with head measurement error of 5%. However, inversions became less accurate when head observations contained large temporal gaps. Next, we applied the inversion for water table changes and depletion rates in the Texas High Plains Aquifer (HPA) and the HPA during 2000–2015. To address sparse water levels and uncertain hydraulic conductivity measurements, two modifications were made to improve data constraints for inversion: (a) calculating winter‐time water levels for wells with >1 head observation by linear interpolation and (b) using hydraulic conductivity geostatistical realizations. The inverted water table change and depletion rate expected mean values and uncertainties were reasonable compared to the known pumping records of the Texas HPA. With relatively minor data curation, the new inverse method can quantify spatiotemporally continuous water table change, depletion rates, and their uncertainty for heterogeneous aquifers with temporally sparse and noisy water level observations.