Spatiotemporal groundwater modeling for hazard analyses in the San Francisco Bay region

Many hazards, including precipitation-induced landslides and coseismic liquefaction, are strongly influenced by the variability of groundwater levels. Simplified or coarse-resolution groundwater models are available for regional-scale studies of infrastructure networks; however, these models often do not consider spatial and temporal variations observed within wells and may not provide sufficient local resolution for critical hazard studies. We extend a conventional, physics-based groundwater model to include spatial and temporal variability based on Gaussian process (GP) interpolation to better understand the local and temporal variation of groundwater between well observations. In this probabilistic model, the physics-based groundwater elevation model serves as an ergodic function and the GP interpolation serves as a model of the well observation residuals. We demonstrate the applicability and accuracy of the model by developing phreatic groundwater estimates for an approximately 10,000 km2 area surrounding San Francisco Bay, California, USA. The resulting model accurately estimates the seasonally variable groundwater depth in a blind holdout dataset within 1.11 m with 90% confidence. The model is well constrained with a standard deviation of approximately 1.1 m near wells, but the uncertainty increases dramatically in mountainous terrain where well observations are limited. The model results also indicate that the average seasonal variability is typically modest relative to non-seasonal events, but nonetheless could have significant impacts on hazard evaluations such as earthquake-induced liquefaction or shallow slope instability.