Probabilistic Uncertainty Consideration in Regionalization and Prediction of Groundwater Nitrate Concentration

In this study, we extend our previous work on a two-dimensional convolutional neural network (2DCNN) for spatial prediction of groundwater nitrate, focusing on improving uncertainty quantification. Our enhanced model incorporates a fully probabilistic Bayesian framework and a structure aimed at optimizing both specific value predictions and predictive intervals (PIs). We implemented the Prediction Interval Validation and Estimation Network based on Quality Definition (2DCNN-QD) to refine the accuracy of probabilistic predictions and reduce the width of the prediction intervals. Applied to a model region in Germany, our results demonstrate an 18% improvement in the prediction interval width. While traditional Bayesian CNN models may yield broader prediction intervals to adequately capture uncertainties, the 2DCNN-QD method prioritizes quality-driven interval optimization, resulting in narrower prediction intervals without sacrificing coverage probability. Notably, this approach is nonparametric, allowing it to be effectively utilized across a range of real-world scenarios.