Extended Data Fig. 1: Seasonally-modulated strength of mode interactions in observations and CMIP5/6 models, as diagnosed from the linear part of the XRO model.

(a) ENSO recharge-oscillator coefficients, (b) Coupling processes denoted by the contribution of other modes to the tendencies of ENSO SSTA and WWV anomalies, (c) ENSO-forced processes denoted by the contribution of ENSO SSTA and WWV anomalies to the SSTA tendency of other modes, (d) Interactions among NPMM, SPMM, IOB, IOD, SIOD, TNA, ATL3, and SASD. The coefficient \({L}_{{ij}}\) has been normalized by a factor of \({\sigma }_{j}\)/\({\sigma }_{i}\), where \({\sigma }_{i}\) and \({\sigma }_{j}\) are the monthly standard deviations of the indices in row \(i\) and column \(j\), respectively, so that all coefficients are comparable, and the units are year⁻¹. The diagonal panels (blue frames) show the damping rate for each index. The black curves with shading show the XRO fit to the ORAS5 reanalysis (with 10%–90% spread band from the cross-validated fitting excluding 3-year data, see “Cross-validated reforecasts” in Methods), and the red curves with shading show the ensemble mean with 10%–90% spread band of the 91 CMIP5/6 historical simulations. ENSO can be strongly driven by climate modes in extratropical Pacific, Indian Ocean, and Atlantic Ocean, which in some seasons are as important as the dynamics internal to the equatorial Pacific. Most of the non-ENSO modes are more strongly driven by ENSO (and their own damping) than by any of the other non-ENSO modes in other basins. The climate models underestimate the strength of most of the mode interactions and miss the seasonality.