Enhanced El Niño predictability from climate mode interactions

The conceptual XRO model (XROM) introduced recently by Zhao et al. (Nature, 2024) is extended here by including state dependence of the external noise forcing on ENSO as well as a seasonal modulation of both the additive and state-dependent parts of the forcing. These features of the forecast model, the XDROM+, require the use of Maximum Likelihood Estimation for parameter inference, which is much more costly than fitting the XROM to data by linear regression via matrix inversion. Yet, it pays, yielding the best ENSO forecast skill yet. I also make a few points of caveat via introducing and discussing four concepts, those of the apparent, theoretical maximum, climatological, and true prediction skills. Most importantly, I explain that (i) the true skill—unlike the apparent skill determined from historical data—cannot be defined by a correlation coefficient and demonstrate that (ii) the said two types of skill do not correlate across possible realisations of the statistical process generated by the XDROM+.