Locally stationary spatio-temporal interpolation of Argo 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 non-stationary 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 non-stationary anomaly fields without the need to explicitly model the non-stationary 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 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. Joint work with Michael L. Stein (UChicago).