Correlated Nugget Effects in Multivariate SPDE Models: Enhancing Ocean Data Predictions

Accurate modeling of multivariate spatial processes is essential for interpreting complex environmental datasets, such as those collected by the Argo project on ocean temperature and salinity. Traditional geostatistical models often assume independent measurement errors, which can lead to biased parameter estimates and inaccurate spatial predictions, especially in the presence of correlated noise and high small-scale variability. This study advances the conventional geostatistical framework by integrating a correlation term within the nugget effect, thereby accommodating correlated measurement errors in bivariate Matérn Stochastic Partial Differential Equations (SPDE) models.

We analyzed global Argo profile data spanning from 2007 to 2020 to assess the impact of the correlated nugget effect on variable estimation and spatial prediction. Enhanced models were developed for both Gaussian and non-Gaussian (Normal-Inverse Gaussian) driving noises. Our findings indicate that neglecting measurement noise correlation distorts the estimated dependencies between variables, resulting in substantial misestimation of the true dependence structure, particularly under strong noise correlations.

Applying our methodology to real-world Argo data, we employed a moving-window approach alongside the Matérn-SPDE model to predict temperature and salinity at unobserved oceanic locations. Cross-validation metrics, including the Continuous Ranked Probability Score (CRPS) and Mean Squared Error (MSE), demonstrated that models incorporating the correlated nugget effect consistently outperformed traditional models. This improvement was particularly notable in capturing small-scale variations and underlying dependencies, thereby enhancing interpretability and predictive accuracy.

These results underscore the critical importance of accounting for measurement noise correlation in multivariate geostatistical analyses. By refining dependence structures and improving predictive accuracy, our work contributes to more robust multivariate spatial analyses in climate and oceanography, encouraging further research into non-stationary and higher-dimensional extensions within environmental geostatistics.