A flexible data-driven cyclostationary model for the probability density of El Niño-Southern Oscillation

Roman Olson, Yanan Fan, Soon Il An, Soong Ki Kim

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Article number103126
Issue number10
Publication statusPublished - 2021 Oct 1

Bibliographical note

Funding Information:
For their roles in producing, coordinating, and making available the CMIP5 model output, we acknowledge the climate modeling groups, the World Climate Research Programme’s (WCRP) Working Group on Coupled Modeling (WGCM), and the Global Organization for Earth System Science Portals (GO-ESSP). We acknowledge support from the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Nos. NRF-2018R1A5A1024958 and 2020R1A2B5B01094934). Thoughtful discussions with Antonio Napolitano and Axel Timmermann are gratefully acknowledged.

Publisher Copyright:
© 2021 Author(s).

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics


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