In many environmental applications, high quality in-situ measurements are too sparse to resolve the fine scale patterns needed for process understanding and management. We investigated a Bayesian Kriging framework to densify two different coastal data sets: (i) Sea Surface Temperature (SST) in the Algarve region (Portugal), where poin scale measurements (~10km spacing) were densified to a 300m grid and (ii) chlorophyll concentration in the La Spezia embayment (Italy), where satellite and in-situ based 500m measurements were refined to 30m. The model treats the variogram parameters as random variables with weakly informative priors, which are updated by MCMC sampling to yield joint posterior distributions. This hierarchical formulation propagates both measurement noise and structural (variogram) uncertainty to the predictions, producing posterior means and credible intervals at every grid node. Cross validation confirmed robust predictive skill in both pilot sites. The Bayesian Kriging model successfully reconstructed fine scale thermal structures in the Algarve, even when neighbouring SST measurements were separated by several kilometres, underscoring the method’s ability to borrow spatial information and maintain consistent local predictions under severe data sparsity. In La Spezia, the same framework accurately resolved chlorophyll gradients (variability of spatial changes) and estuarine features at 30m resolution. Credible intervals naturally widened in areas far from any measurement yet remained sufficiently narrow elsewhere to guide interpretation, illustrating that the hierarchical formulation captures uncertainty without sacrificing practical detail. Overall, the study shows that Bayesian Kriging can generate high resolution, uncertainty maps from heterogeneous and sparse data records, making it a versatile tool for enhancing remote sensing products and supporting coastal monitoring workflows.
Andronis et al. (Wed,) studied this question.