Bayesian PCA for reconstruction of historical sea surface temperatures

In this work, reconstructions of historical global sea surface temperatures (SST) are performed using Bayesian principal component analysis (PCA). Two PCA models are examined: a model with isotropic noise and a model which takes into account data uncertainty due to sampling errors. Inference is done by variational Bayesian learning. The methods are compared with a more traditional technique, reduced space optimal interpolation (RSOI), that is currently used in producing standard historical SST analyses. New methods were applied to the MOHSST5, an observational data set for 1856-1991 period from the United Kingdom Meteorological Office, that was used in a previously published application of the RSOI. Data uncertainty specification was also identical to the one used in that RSOI application, hence the performances of all reconstructions are directly comparable. Reconstruction results for 1982-1991 period are tested via their comparison with the NOAA monthly 1deg OI (version 2) that blends in situ observations with the much better sampled satellite data. New reconstructions slightly outperform the published RSOI reconstruction in this test and suggest that further improvements are possible.