Abstract We are reporting on the much studied internal climate variability mode of ENSO, concerning (i) its 20th c. climatology, (ii) the natural fluctuations of the apparent variability as seen in observational data, as well as – our ultimate subject of interest – (iii) the forced change of ENSO variability under anthropogenic forcing, at least as seen in model simulations under scenarios of accelerating global warming. Our analysis is meant to be aided two-fold by fitting a recharge oscillator model (ROM) to model-simulation-data. First, by performing parameter inference via Maximum Likelihood Estimation, we likely have reliable estimates; second, statistical quantities characterising ENSO variability could become attributable to physics via the possible interpretation of the ROM parameters. We find that in the CESMv2 model, (iii) (a) the variance increase in an initial period of moderate forcing is due, to a smaller extent, to excitation external to the ENSO dynamics as well as the forced change of linear feedback parameters, all working in tandem, while (b) the decrease under stronger forcing later, towards the end of the 21st c., is due to a a reversal of the trend of the linear temperature-to-temperature feedback parameter, i.e., the Bjerknes stability index. (c) By performing a dimensional analysis of the ROM, the latter is implicated to play a role also in the decline of ENSO skewness. This is so exclusively in the role of modulating the susceptibility of the skewness; in the late 21st c., almost all of the skewness decline is to do with a forced change of “vertical nonlinear dynamical heating”, on the one hand, to a grater extent, (d) as a forced change of the nonlinearity of the dynamics, as a primary effect, and, on the other hand, to a somewhat smaller extent, as a secondary effect, (c) by the change of the Bjerknes stability index modulating the susceptibility of skewness to nonlinearity. We also find that historically (i) the nonlinearity of the dynamics is dominantly responsible for the positive skewness of the Nin ̃o3 index while state dependent external forcing might even oppose its effect slightly. Underpinning our methodology of studying the forced response (iii), we also demon- strate that, (ii) in view of a formal statistical test, a constant-in-time parameter ROM is consistent with observational data.
Bódai et al. (2025) studied this question.