Evaluating the performance of Bayesian geostatistical prediction with physical barriers in the Chesapeake Bay

The Chesapeake Bay is one of the most widely studied bodies of water in the United States and around the world. Routine monitoring of water quality indicators (e.g., salinity) relies on fixed sampling stations throughout the Bay. Utilizing this rich monitoring data, various methods produce surface predictions of water quality indicators to further characterize the health of the Bay as well as to support wildlife and human health research studies. Bayesian approaches for geostatistical modelling are becoming increasingly popular and can be preferred over frequentist approaches because full and exact inference can be computed, along with more accurate characterization of uncertainty. Traditional geostatistical prediction methods assume a Euclidean distance between two points when characterizing spatial dependence as a function of distance. However, Euclidean approaches may not be appropriate in estuarine environments when water-land boundaries are crossed during the modelling process. In this study, we compare stationary and barrier INLA geostatistical models with a classic kriging geostatistical model to predict salinity in the Chesapeake Bay during 4 months in 2019. Cross-validation is conducted for each approach to evaluate model performance based on prediction accuracy and precision. The results provide evidence that the two Bayesian-based models outperformed ordinary kriging, especially when examining prediction accuracy (most notably in the tributaries). We also suggest that the non-Euclidean model accounts for the appropriate water-based distances between sampling locations and is likely better at characterizing the uncertainty. However, more complex bodies of water may better showcase the capabilities and efficacy of the physical barrier INLA model.