Regularised empirical orthogonal functions

Empirical orthogonal functions, extensively used in weather/climate research, suffer serious geometric drawbacks such as orthogonality in space and time and mixing. The present paper presents a different version, the regularised (or smooth) empirical orthogonal function (EOF) method, by including a regularisation constraint, which originates from the field of regression/correlation of continuous variables. The method includes an extra unknown, the smoothing parameter, and solves a generalised eigenvalue problem and can overcome, therefore, some shortcomings of EOFs. For example, the geometrical constraints satisfied by conventional EOFs are relaxed. In addition, the method can help alleviate the mixing drawback. It can also be used in combination with other methods, which are based on downscaling or dimensionality reduction. The method has been applied to sea level pressure and sea surface temperature and yields an optimal value of the smoothing parameter. The method shows, in particular, that the leading sea level pressure pattern, with substantially larger explained variance compared to its EOF counterpart, has a pronounced Arctic Oscillation compared to the mixed North Atlantic Oscillation/Arctic Oscillation pattern of the leading EOF. The analysis of the remaining leading patterns and the application to sea surface temperature field and trend EOFs are also discussed.