Empirical Orthogonal Teleconnections

Abstract

A new variant is proposed for calculating functions empirically and orthogonally from a given space?time dataset. The method is rooted in multiple linear regression and yields solutions that are orthogonal in one direction, either space or time. In normal setup, one searches for that point in space, the base point (predictor), which, by linear regression, explains the most of the variance at all other points (predictands) combined. The first spatial pattern is the regression coefficient between the base point and all other points, and the first time series is taken to be the time series of the raw data at the base point. The original dataset is next reduced; that is, what has been accounted for by the first mode is subtracted out. The procedure is repeated exactly as before for the second, third, etc., modes. These new functions are named empirical orthogonal teleconnections (EOTs). This is to emphasize the similarity of EOT to both teleconnections and (biorthogonal) empirical orthogonal functions (EOFs). One has to choose the orthogonal direction for EOT. In the above description of the normal space?time setup, picking successive base points in space, the time series are orthogonal. One can reverse the role of time and space?in this case one picks base points in time, and the spatial maps will be orthogonal. If the dataset contains biorthogonal modes, the EOTs are the same for both setups and are equal to the EOFs. When applied to four commonly used datasets, the procedure was found to work well in terms of explained variance (EV) and in terms of extracting familiar patterns. In all examples the EV for EOTs was only slightly less than the optimum obtained by EOF. A numerical recipe was given to calculate EOF, starting from EOT as an initial guess. When subjected to cross validation the EOTs seem to fare well in terms of explained variance on independent data (as good as EOF). The EOT procedure can be implemented very easily and has, for some (but not all) applications, advantages over EOFs. These novelties, advantages, and applications include the following. 1) One can pick certain modes (or base point) first?the order of the EOTs is free, and there is a near-infinite set of EOTs. 2) EOTs are linked to specific points in space or moments in time. 3) When linked to flow at specific moments in time, the EOT modes have undeniable physical reality. 4) When linked to flow at specific moments in time, EOTs appear to be building blocks for empirical forecast methods because one can naturally access the time derivative. 5) When linked to specific points in space, one has a rational basis to define strategically chosen points such that an analysis of the whole domain would benefit maximally from observations at these locations.