Quantifying Uncertainty in Groundwater Vulnerability Assessment: a Bayesian Approach

Assessing groundwater vulnerability is essential for understanding the risk of pollutants infiltrating groundwater systems after being introduced at the ground surface. Traditional methods for groundwater vulnerability assessment (GVA) often rely on deterministic or empirical approaches, lacking a robust probabilistic framework. This study introduces Bayesian inference as a comprehensive method for GVA, focusing on nitrate concentrations as a proxy for contamination risk in agricultural areas. The proposed model defines a linear relationship between nitrate levels and various hydrological and geological parameters. Two Bayesian algorithms, Joint Maximum a Posteriori (JMAP) and Variational Bayesian Approximation (VBA), are applied to GVA in the Burdekin Basin, an agricultural catchment in Queensland, Australia. Different model ranking metrics are used to compare the models, revealing the Bayesian posterior to be a robust metric for model ranking. Additionally, the Bayesian framework demonstrates superior performance compared to traditional GVA methods in terms of Pearson correlation coefficients (R) between observed and predicted nitrate concentrations. This research highlights the benefits of Bayesian methods in GVA, offering improved model ranking, parameter estimation, and uncertainty quantification.