Reduced Space Approach to the Optimal Analysis of Historical Marine Observations: Accomplishments, Difficulties, and Prospects

Observed historical climate fields are characterized by comparatively precise data and good coverage in the last few decades, and by poor observational coverage prior to then. The technique of the reduced space optimal analysis of such fields (i.e. estimating them in projections onto a low-dimensional space spanned by the leading patterns of the signal variability) is presented in the context of more traditional approaches to data analysis. Advantages of the method are illustrated on examples of reconstructions of near-global monthly fields of sea surface temperature and sea level pressure from the 1850s to the present, along with verified error bars. The limitations of the technique as regards quality and robustness of estimating a priori parameters, representation of long-term and small-scale types of variability, assumption of stationarity of means and covariances, and incompleteness of coverage are discussed, and possible ways to overcome these problems are suggested.