Building Asymmetry into PCA and Application to ENSO

A novel technique is introduced for building asymmetry into Principal Component Analysis (PCA). This technique, Iterative Asymmetric PCA, finds the general solution to segmented regression with one breakpoint at zero. The approach is formulated from least-squares and builds on the iterative PCA algorithm of van den Dool (2011) that can be used to find the leading Empirical Orthogonal Functions (EOFs) through repeated projection. Properties and details of the technique are discussed, and then it is applied to boreal winter sea-surface temperature and outgoing longwave radiation over the tropical Pacific. The resultant leading mode (AEOF-1) provides a good representation of the El Niño Southern Oscillation (ENSO), and a comparison with EOF-1 (and EOF-2) is made in order to quantify ENSO asymmetry. ENSO asymmetry is statistically significant and accounts for 1/6th of the interannual variance of ENSO. Consistent with past results, the spatial structure during La Niña is clearly not equal and opposite to that during El Niño, and ENSO has more asymmetry in the atmosphere compared with the ocean. This asymmetry explains nearly all variation in the EOF-1-EOF-2 plane suggesting that basic asymmetry dominates ENSO nonlinearity.