Empirical orthogonal teleconnections

A new variant is proposed for calculating functions empirically and orthogo nally from a given space-time dataset. The method is rooted in multiple lin ear regression and yields solutions that are orthogonal in one direction, e ither 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 spat ial pattern is the regression coefficient between the base point and all ot her 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 proce dure is repeated exactly as before for the second, third, etc., modes. Thes e new functions are named empirical orthogonal teleconnections (EOTs). This is to emphasize the similarity of EOT to both teleconnections and (biortho gonal) empirical orthogonal functions (EOFs). One has to choose the orthogo nal direction for EOT. In the above description of the normal space-time se tup, picking successive base points in space, the time series are orthogona l. One can reverse the role of time and space-in this case one picks base p oints in time, and the spatial maps will be orthogonal. If the dataset cont ains biorthogonal modes, the EOTs are the same for both setups and are equa l to the EOFs. When applied to four commonly used datasets, the procedure w as found to work well in terms of explained variance (EV) and in terms of e xtracting familiar patterns. In all examples the EV for EOTs was only sligh tly 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 cro ss validation the EOTs seem to fare well in terms of explained variance on independent data las good as EOF). The EOT procedure can be implemented ver y easily and has, for some (but not all) applications, advantages over EOFs . These novelties, advantages, and applications include the following. 1) O ne can pick certain modes (or base point) first-the order of the EOTs is fr ee, and there is a near-infinite set of EOTs. 2) EOTs are linked to specifi c points in space or moments in time. 3) When linked to Row at specific mom ents in time, the EOT modes have undeniable physical reality. 4) When linke d to flow at specific moments in time, EOTs appear to be building blocks fo r empirical forecast methods because one can naturally access the time deri vative. 5) When linked to specific points in space, one has a rational basi s to define strategically chosen points such that an analysis of the whole domain would benefit maximally from observations at these locations.