Modeling groundwater levels in California's Central Valley by hierarchical Gaussian process and neural network regression

TL;DR

The 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.

Abstract

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.

Figures (16)

• Figure 1: Extent of CV outlined in black with groundwater subbasins. (Left) Sacramento and San Joaqin Valley areas have been colored by purple and red. Mapped extent of the Corcoran clay is shown in lime green. (Right) Nomenclature of the CV's groundwater subbasins.
• Figure 2: (Left) Well locations colored by the frequency of data samples. Wells shown in the right plot are highlighted with black crosses. (Right) Water levels measurements at three wells are shown in blue circles. Best fitting long term and seasonal trend line, estimated using equation \ref{['eq:linearReg1']}, is overlain in red on well data.
• Figure 3: Water level long-term and seasonal model parameters fitted by linear regression on well time series data.
• Figure 4: Depth to layer tops (top row), coarse-grained sediment thickness (middle row) and fine-grained sediment thickness (bottom row) for three different texture model layers. Top of layer 6 corresponds to top of Corcoran clay.
• Figure 5: Chi-square Q-Q plots for testing GP (top row) vs. GP-DNN (bottom row) predictive posteriors. Empirical quantiles in the left and second from left columns are derived using 100 and 1 random samples respectively from predictive distribution at each well location in the test set. Empirical quantiles in the second from right and right columns are derived using real data in the test and robust test sets respectively. The $R^2$ coefficient of determination of the best linear fit (blue line) is listed on top.