  Argo floats measure seawater temperature and salinity in the upper 2,000 m of
the global ocean. 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 fine-scale
variation as a means to account for non-Gaussian heavy tails in ocean
temperature data. Cross-validation studies comparing the proposed approach with
the existing state-of-the-art demonstrate clear improvements in point
predictions and show that accounting for the nonstationarity and
non-Gaussianity is crucial for obtaining well-calibrated uncertainties. This
approach also provides data-driven local estimates of the spatial and temporal
dependence scales for the global ocean which are of scientific interest in
their own right.
