Quantifying uncertainty in groundwater depth from sparse well data in the California Central Valley

Groundwater is a critical freshwater resource for irrigation in the California Central Valley, particularly in times of drought. Groundwater depth has dropped rapidly in California's overdrafted basins, but irregular monitoring across space and time limits the accuracy of the groundwater depth projections in the Groundwater Sustainability Plans required by the California Sustainable Groundwater Management Act (SGMA). This work constructs a Bayesian hierarchical model for predicting groundwater depth from sparse monitoring data in three Central Valley counties. We apply this model to generate 300 m resolution monthly groundwater depth estimates for drought years 2013-2015, and compare our smoothed groundwater depth map to smoothed rasterized maps published by the CA Department of Water Resources. Finally, we quantify uncertainty in groundwater depth predictions that are made by imputing missing well data and interpolating predictions across the study domain, which is helpful in directing future sampling efforts towards areas with high uncertainty. The BHM model accurately captures the spatiotemporal pattern in groundwater depth, as evidenced by 94.54% of withheld test samples' true depth being covered by the 95% prediction interval drawn from the BHM posterior distribution. The model converged despite a very sparse dataset, demonstrating broad applicability for evaluating changes in regional groundwater depth as required by SGMA. Depth prediction intervals can also help prioritize future groundwater depth sampling activity and increase the utility of groundwater depth maps in total storage predictions by enabling sensitivity analysis.