On the Interpretation of EOF Analysis of ENSO, Atmospheric Kelvin Waves, and the MJO

Abstract Empirical orthogonal function (EOF) analysis is frequently applied to derive patterns and indexes used to identify and track weather and climate modes as expressed in state variables or proxies of convection. Individual EOFs or pairs of EOFs are often taken to be a complete description of the phenomenon they are intended to index. At the same time, in the absence of projection of the phenomenon onto multiple EOFs yielding multiple similar eigenvalues, each EOF is often assumed to represent a physically independent phenomenon. This project analyzed the leading EOFs of the earth’s skin temperature on the equator and outgoing longwave radiation (OLR) anomalies filtered for atmospheric equatorial Kelvin waves. Results show that the leading two EOFs of the skin temperature data—including east Pacific El Niño and El Niño Modoki—frequently evolve as a quadrature pair during El Niño events, even though the first EOF explains roughly 6 times as much variance as the second. They together diagnose the longitude of the SST anomaly maximum, and their linear combination frequently shows eastward or westward propagation. Analysis of the filtered OLR anomalies shows that the first six EOFs each represent Kelvin wave signals, with the first, second, and third pairs representing Kelvin waves characterized by zonal wavenumbers 2, 3, and 4, respectively. This result demonstrates that if a phenomenon occurs across a range of spatial scales, it is described by multiple EOFs at different scales. A similar analysis demonstrates that the Madden–Julian oscillation probably exhibits spread across a range of spatial scales that would also require multiple EOFs for full characterization.