Fig. 3

The El Niño-Southern Oscillation (ENSO) and its Combination Mode. a EOF1 (ENSO) and b EOF2 (ENSO Combination Mode) of ERA5 (Hersbach et al. 2020) detrended joint u and v 10 m wind monthly anomalies displayed as regression coefficients in physical units following the methodology and applied to the same spatial domain (100°E–60°W, 10°S–10°N; area-weighted; normalized PCs regressed on the anomalies over the larger domain shown here) as described in Stuecker et al. (2013). Shading is the zonal wind component. c Power spectral density [PSD; using the Multi-Taper Method (MTM) with 5 tapers and nfft = 1024 (Thomson 1982)] of the normalized leading two principal components (PCs) of the ERA5 10 m wind anomalies EOF analysis. The confidence level (CL) for spectral peaks was calculated from the respective percentile at each frequency of 10,000 power spectra generated from discrete AR(1) processes with the same lag(-1) autocorrelation r and data length as the respective PC time series (\({\lambda }^{-1}=\sim 4.3\) months for PC1 and \({\lambda }^{-1}=\sim 2.6\) months for PC2). The time series representing the C-mode (spectrum in yellow line) was created using Eq. 4 with T_ENSO = PC1 following Stuecker et al. (2013). The grey boxes represent the approximate frequency range of ENSO (f_E) and the near-annual combination tones (1-f_E and 1 + f_E). d The same as c but for the normalized leading two PCs of the same EOF analysis (same domain) applied to surface wind stress monthly anomalies (the Combination Mode is reflected in the second PCs of 10 m surface winds as well as in wind stress; see results in Stuecker et al. (2013) and McGregor et al. (2012)) from a 1000-year preindustrial control simulation of the CESM2 climate model (using 7 instead of 5 tapers). The EOF patterns are not shown but are very similar to the ERA5 patterns (explained variance: 18% and 12% for EOF1 and EOF2; \({\lambda }^{-1}=\sim 6.8\) months for PC1 and \({\lambda }^{-1}=\sim 2.2\) months for PC2)