Enhancing groundwater vulnerability assessment through Bayesian inference

This study introduces a Bayesian regularization framework for the assessment of groundwater vulnerability, which is applied to the Burdekin Basin, an agricultural catchment in Queensland, Australia. In this method, the Bayesian maximum a posteriori (MAP) estimate is used to estimate a linear model between major hydrological variables and nitrate concentrations - as a proxy for groundwater vulnerability - using the available nitrate data. This model is then applied to the entire Burdekin Basin within a Geographical Information System. Outputs include the model parameter coefficients and their uncertainties, and groundwater vulnerability maps for the catchment. To handle unknown parameters, two iterative Bayesian algorithms are used: the Bayesian joint maximum a posteriori (JMAP) estimate and the variational Bayesian approximation (VBA). These are compared to the index-based DRASTIC and DRASTICL methods widely used for groundwater vulnerability assessment, and a least squares regularization method with thresholding (SINDy algorithm). Compared to index-based methods, the Bayesian algorithms lead to higher Pearson correlation coefficients between measured and predicted nitrate concentrations (from 0.20 to 0.39 for 8 parameters), with a further improvement (0.60) using Fourier-filtered nitrate data. The inferred groundwater vulnerability maps were also quite different. This study demonstrates several advantages of the Bayesian framework, including the ranking of models, the calculation of model parameters and the quantification of their uncertainties.