Range change data, obtained from Synthetic Aperture Radar satellites, form the basis for estimates of aquifer volume change in California's Central Valley. The estimation algorithm incorporates a function penalizing changes far from known well locations, linking the aquifer volume changes to agricultural, industrial, and municipal pumping within the Tulare basin. We show that the range changes are compatible with the hypothesis that the source of aquifer volume changes are variations in effective pressure around documented wells. Specifically, inclusion of the well distance penalty does not degrade the fit to the observations, inversions with and without it both give variance reductions of 99.6%. The patterns of aquifer volume change vary significantly from the drought year, between October 2015 and October 2016, to a wet year in 2017, and into 2018, a year with near average rainfall. The 2.3 million acre-feet of estimated volume reduction, a lower bound on the amount of water extracted from the basin between October 2015 and 2016, agrees with independent estimates of 1.8 and 2.3 million acre-feet. The aquifer volume reduction is also compatible with a loss of 3.1 km3 (2.5 million acre-feet) in groundwater volume derived from Gravity Recovery and Climate Experiment (GRACE) satellite data.