Self consistent and computationally efficient EOF calculation from incomplete oceanographic data sets

We present a new self-consistent method to infer missing data from oceanographic data series and to extract the relevant empirical orthogonal functions. As a by-product, the new method allows to detect the number of statistically significant EOFs by a cross-validation procedure for a complete or incomplete data set as well as the noise level and interpolation error. Since for the proposed filling and analysis method there is no need for a priori information about the error covariance structure, the method is self-consistent and parameter free. The method is exemplified on a synthetic data set as well as real satellite data with cloud coverage.