Model Ranking Metrics for Groundwater Vulnerability Assessment Using Bayesian Inference

Abstract: Groundwater vulnerability to pollution, defined as the likelihood of contaminants migrating from the ground surface to the groundwater system, is a critical environmental concern. Traditional assessment methods, often deterministic or empirical, lack a robust probabilistic framework. This study integrates groundwater movement and dynamics into a Bayesian probabilistic framework to assess the vulnerability of groundwater systems to pollution. Bayesian inference treats each parameter in a probabilistic manner, producing a posterior probability density function. The framework is applied to the Burdekin Basin, Queensland, Australia, using hydrological and geological data to incorporate groundwater flow dynamics and contaminant transport mechanisms. Two Bayesian iterative algorithms, Joint Maximum a Posteriori (JMAP) and Variational Bayesian Approximation (VBA), are employed. The sensitivity of these algorithms to different hydrological parameters, as applied to the Burdekin Basin, is evaluated. The functionality of different model ranking metrics, including the 2-norm residual, the posterior Gaussian norm, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Pearson correlation coefficient (R), mean absolute error (MAE), and root mean square error (RMSE), are analyzed to select the optimum values of the inferred coefficients. The posterior Gaussian norm is shown to provide a robust metric for model selection and accuracy assessment, alongside the 2-norm residuals, objective function, and RMSE. The results demonstrate the efficacy of Bayesian methods in capturing groundwater dynamics and assessing groundwater vulnerability. Keywords: Groundwater vulnerability assessment, Bayesian inference, regularization, model ranking metrics