Uncertainty-based saltwater intrusion prediction using integrated Bayesian machine learning modeling (IBMLM) in a deep aquifer.

Data-driven machine learning approaches are promising to substitute physically based groundwater numerical models and capture input-output relationships for reducing computational burden. But the performance and reliability are strongly influenced by different sources of uncertainty. Conventional researches generally rely on a stand-alone machine learning surrogate approach and fail to account for errors in model outputs resulting from structural deficiencies. To overcome this issue, this study proposes a flexible integrated Bayesian machine learning modeling (IBMLM) method to explicitly quantify uncertainties originating from structures and parameters of machine learning surrogate models. An Expectation-Maximization (EM) algorithm is combined with Bayesian model averaging (BMA) to find out maximum likelihood and construct posterior predictive distribution. Three machine learning approaches representing different model complexity are incorporated in the framework, including artificial neural network (ANN), support vector machine (SVM) and random forest (RF). The proposed IBMLM method is demonstrated in a field-scale real-world "1500-foot" sand aquifer, Baton Rouge, USA, where overexploitation caused serious saltwater intrusion (SWI) issues. This study adds to the understanding of how chloride concentration transport responds to multi-dimensional extraction-injection remediation strategies in a sophisticated saltwater intrusion model. Results show that most IBMLM exhibit r values above 0.98 and NSE values above 0.93, both slightly higher than individual machine learning, confirming that the IBMLM is well established to provide better model predictions than individual machine learning models, while maintaining the advantage of high computing efficiency. The IBMLM is found useful to predict saltwater intrusion without running the physically based numerical simulation model. We conclude that an explicit consideration of machine learning model structure uncertainty along with parameters improves accuracy and reliability of predictions, and also corrects uncertainty bounds. The applicability of the IBMLM framework can be extended in regions where a physical hydrogeologic model is difficult to build due to lack of subsurface information.

Bayesian machine learning ensemble approach to quantify model uncertainty in predicting groundwater storage change.

Agricultural water demand, groundwater extraction, surface water delivery and climate have complex nonlinear relationships with groundwater storage in agricultural regions. As an alternative to elaborate computationally intensive physical models, machine learning methods are often adopted as surrogate to capture such complex relationships due to their high computational efficiency. Inevitably, using only one machine learning model is prone to underestimate prediction uncertainty and subjected to poor accuracy. This study presents a novel machine learning-based groundwater ensemble modeling framework in conjunction with a Bayesian model averaging approach to predict groundwater storage change and improve overall model predicting reliability. Three different machine learning models have been developed namely artificial neural network, support vector machine and response surface regression. To explicitly quantify uncertainty from machine learning model parameter and structure, Bayesian model averaging is employed to produce a forecast distribution associated with each machine learning prediction. Model weights and variances are obtained based on model performance to construct ensemble models. Then, the developed individual and Bayesian model averaging machine learning ensemble models are applied, evaluated and validated at different spatial scales including subregional and regional scales in an overdrafted agricultural region-the San Joaquin River Basin, through independent training and testing dataset. Results shows the machine learning models have remarkable predicting capability without sacrificing accuracy but with higher computational efficiency. Compared to a single-model approach, the ensemble model is able to produce consistently reliable predictions across the basin, yet it does not always outperform the best model in the ensemble. Additionally, model results suggest that groundwater pumping for agricultural irrigation is the primary driving force of groundwater storage change across the region. The modeling framework can serve as an alternative approach to simulating groundwater response, especially in those agricultural regions where lack of subsurface data hinders physically-based modeling.