Model simulations of El Niño–Southern Oscillation (ENSO) are usually evaluated by comparing them to observations using a multitude of metrics. However, this approach cannot provide an objective summary metric of model performance. Here, we propose that such an objective model evaluation should involve comparing the full joint probability density functions (pdf’s) of ENSO. For simplicity, ENSO state is defined here as sea surface temperature anomalies over the Niño 3 region and equatorial Pacific thermocline depth anomalies. We argue that all ENSO metrics are a function of the joint pdf, the latter fully specifying the underlying stochastic process. Unfortunately, there is a lack of methods to recover the joint ENSO pdf from climate models or observations. Here, we develop a data-driven stochastic model for ENSO that allows for an analytic solution of the non-Markov non-Gaussian cyclostationary ENSO pdf. We show that the model can explain relevant ENSO features found in the observations and can serve as an ENSO simulator. We demonstrate that the model can reasonably approximate ENSO in most GCMs and is useful at exploring the internal ENSO variability. The general approach is not limited to ENSO and could be applied to other cyclostationary processes.
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