  Modeling groundwater levels continuously across California's Central Valley
(CV) hydrological system is challenging due to low-quality well data which is
sparsely and noisily sampled across time and space. The lack of consistent well
data makes it difficult to evaluate the impact of 2017 and 2019 wet years on CV
groundwater following a severe drought during 2012-2015. A novel machine
learning method is formulated for modeling groundwater levels by learning from
a 3D lithological texture model of the CV aquifer. The proposed formulation
performs multivariate regression by combining Gaussian processes (GP) and deep
neural networks (DNN). The hierarchical modeling approach constitutes training
the DNN to learn a lithologically informed latent space where non-parametric
regression with GP is performed. We demonstrate the efficacy of GP-DNN
regression for modeling non-stationary features in the well data with fast and
reliable uncertainty quantification, as validated to be statistically
consistent with the empirical data distribution from 90 blind wells across CV.
We show how the model predictions may be used to supplement hydrological
understanding of aquifer responses in basins with irregular well data. Our
results indicate that on average the 2017 and 2019 wet years in California were
largely ineffective in replenishing the groundwater loss caused during previous
drought years.
