Incorporating correlated nugget effects in multivariate spatial models: An application to Argo ocean data

Accurate analysis of global oceanographic data, such as temperature and salinity profiles from the Argo program, requires geostatistical models that capture complex spatial dependencies. We propose Gaussian and non-Gaussian hierarchical multivariate Matérn-SPDE models with correlated nugget effects that jointly account for small-scale variability and measurement-error correlations between co-located observations. Simulations show that ignoring such correlations biases cross-variable dependence estimates, while incorporating them improves parameter recovery. Applied to 14 years of global Argo data, our models yield lower temperature–salinity dependence than models that assume independent noise, indicating that standard approaches tend to overstate this dependence. Cross-validation shows that the Gaussian model with correlated noise achieves the best point predictions, while the non-Gaussian (NIG) model with independent noise yields better-calibrated probabilistic scores. These findings highlight the importance of relaxing the independent-noise assumption in multivariate hierarchical models.