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

Understanding 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. Plain Language Summary: Groundwater pumping is causing shallow groundwater levels, or the water table, to lower in unsustainable ways. Because groundwater observations are typically sparse and uncertain, so we do not always know where water tables are dropping or how fast they drop. In this study, we introduced a new mathematical method of accurately estimating water table changes and the related losses in groundwater storage while not needing to know all of the uncertain properties of the ground. We tested this method for make‐up cases and cases of the High Plains Aquifer in the central United States. The results demonstrate that the method is both fast and accurate and can be applied for other aquifers. Key Points: New highly parameterized linear inverse method was developed for unconfined aquifers with unknown initial and boundary conditionsSynthetic and field inversions demonstrate accurate and reasonable results with spatiotemporally sparse and uncertain head observationsThe new inverse method yielded accurate water table change and depletion rates despite large uncertainty in hydraulic conductivity [ABSTRACT FROM AUTHOR]