Locally stationary spatio-temporal interpolation of Argo profiling float data

Argo floats measure sea water temperature and salinity in the upper 2,000 m of the global ocean. The statistical analysis of the resulting spatio-temporal dataset is challenging due to its nonstationary structure and large size. We propose mapping these data using locally stationary Gaussian process regression where covariance parameter estimation and spatio-temporal prediction are carried out in a moving-window fashion. This yields computationally tractable nonstationary anomaly fields without the need to explicitly model the nonstationary covariance structure. We also investigate Student-$t$ distributed microscale variation as a means to account for non-Gaussian heavy tails in Argo data. We use cross-validation to study the point prediction and uncertainty quantification performance of the proposed approach. We demonstrate clear improvements in the point predictions and show that accounting for the nonstationarity and non-Gaussianity is crucial for obtaining well-calibrated uncertainties. The approach also provides data-driven local estimates of the spatial and temporal dependence scales which are of scientific interest in their own right.