A combined wave‐number‐‐frequency and time‐extended EOF approach for tracking the progress of modes of large‐scale organized tropical convection

An algorithm combining filtering in the wave‐number‐‐frequency domain with time‐extended empirical orthogonal function (EEOF) analysis is developed and applied to diagnose and track signals associated with modes of organized moist deep convection in the Tropics. The wave‐number‐‐frequency spectrum of outgoing long‐wave radiation (OLR) is broken down into five broad filter bands in order to concentrate signals associated with the Madden–Julian oscillation, convectively coupled equatorial Rossby, Kelvin, and mixed Rossby–gravity waves, easterly waves, and low‐frequency variations such as the El Niño/Southern Oscillation (ENSO). The EEOF patterns are obtained from analysis of the filtered data, and principal component (PC) time series are generated by projection of temporally smoothed, but otherwise unfiltered data onto the EEOF patterns. Filtered data are reconstructed by taking the product of the EEOF patterns and the corresponding PCs. These reconstructed data compare well with unfiltered OLR anomalies and with OLR anomalies filtered in the wave‐number‐‐frequency domain for the same modes. The method is easily applied in real time since results are not influenced by the proximity to the end of the dataset.