A potential problem with extended EOF analysis of standing wave fields

The extended empirical orthogonal function (EEOF) analysis of signals containing a standing wave component is considered. It is shown using a simple analytical model that for a single time-lag EEOF analysis, two EEOF patterns describe the standing wave, and that their associated eigenvalues become degenerate if the lag chosen is close to a zero of the sample autocovariance function of the standing wave time series. This degeneracy strongly affects the relative magnitudes of the two sectors of each EEOF pattern and the structure of the associated spatial pattern. A set of EEOF analysis of varying lags is performed on a tropical Pacific sea level pressure (SLP) dataset, known to be dominated by standing variance, and the predictions of the analytical model are verified. As well, it is seen that at degeneracy there is a reduction in the quality of the spatial patterns produced by the EEOF analysis.