Spatial-depth functional estimation of ocean temperature from non-separable covariance models

Spatial-depth functional regression is applied for the estimation of ocean temperature, with projection onto the eigenvectors of the empirical covariance operator of the functional response (i.e., onto the Empirical Orthogonal Functions in space and depth). Moment-based estimation is performed to approximate the regression operators in the subspace generated by the empirical eigenvectors associated with nonnull eigenvalues. In addition, Bayesian estimation is performed to approximate the regression operators in the subspace generated by the empirical eigenvectors associated with almost null eigenvalues. The cross-validation results obtained, together with the spatial-depth residual correlation analysis carried out on a real data set for the South Atlantic area, to the east of Argentina and the Falkland Islands, represent an improvement on those provided by the wavelet-based approach recently proposed in Fernandez-Pascual (Stoch Environ Res Risk Assess 30:523-557, 2016).