I think that the most significant forcing function for ENSO is QBO, which is a global oscillation in wind direction.
This is an excerpt from the Chikamoto paper:
> "This enhanced multi-year predictability in central Pacific SLP can be explained by the fact that SLP, and in particular wind variability, are more sensitive to variations in the zonal gradient of SST rather than to the nearly homogeneous SST warming 22 induced by GHGs increases. We find that, unlike in the case of SST, natural variability explains 4 80% of the total variance of the SLP anomalies over major parts of the tropics (Supplementary Fig. 1). In the central tropical Pacific, therefore, the natural atmosphere–ocean variability is the major contributor for multi-year predictability"
So what causes the QBO to reverse direction every 2.3 years? Is this a strong resonance condition in the upper atmosphere, possibly being pumped by the Walker circulation as they show:
I glanced at the paper and found this figure representing their "hindcasting and forecasting ensemble mean". It looks as if it is very conservative based on the sparse number of simulation points given and the size of the error bars:
As usual, I can't comment too much because I have no feel for how their simulations work.