The Recharge Oscillator (RO) is a simple mathematical model of the El Niño Southern Oscillation (ENSO). In its original form, it is based on two ordinary differential equations that describe the evolution of equatorial Pacific sea surface temperature and oceanic heat content. These equations make use of physical principles that operate in nature: (i) the air-sea interaction loop known as the Bjerknes feedback, (ii) a delayed oceanic feedback arising from the slow oceanic response to near-equatorial winds, (iii) state-dependent stochastic forcing from intraseasonal wind variations known as westerly wind bursts (WWBs), and (iv) nonlinearities such as those related to deep atmospheric convection and oceanic advection. These elements can be combined in different levels of RO complexity. The RO reproduces ENSO key properties in observations and climate models: its amplitude, dominant timescale, seasonality, and warm/cold phases amplitude asymmetry. We discuss the RO in the context of timely research questions. First, the RO can be extended to account for ENSO pattern diversity (with events that either peak in the central or eastern Pacific). Second, the core RO hypothesis that ENSO is governed by tropical Pacific dynamics is discussed from the perspective of influences from other basins. Finally, we discuss the RO relevance for studying ENSO response to climate change, and underline that accounting for ENSO diversity, nonlinearities, and better links of RO parameters to the long term mean state are important research avenues. We end by proposing important RO-based research problems.

The use of large ensembles of model simulations is growing due to the need to minimize the influence of internal variability in evaluation of climate models and the detection of climate change induced trends. Yet, exactly how many ensemble members are required to effectively separate internal variability from climate change varies from model to model and metric to metric. Here we analyze the first three statistical moments (i.e., mean, variance and skewness) of detrended precipitation and sea surface temperature (interannual anomalies for variance and skewness) in the eastern equatorial Pacific from observations and ensembles of Coupled Model Intercomparison Project Phase 6 (CMIP6) climate simulations. We then develop/assess the equations, based around established statistical theory, for estimating the required ensemble size for a user defined uncertainty range. Our results show that — as predicted by statistical theory — the uncertainties in ensemble means of these statistics decreases with the square root of the time series length and/or ensemble size. Further to this, as the uncertainties of these ensemble-mean statistics are generally similar when computed using pre-Industrial control runs versus historical runs, the pre-industrial runs can sometimes be used to estimate: i) the number of realizations and years needed for a historical ensemble to adequately characterize a given statistic; or ii) the expected uncertainty of statistics computed from an existing historical simulation or ensemble, if a large ensemble is not available.