A theoretical model of strong and moderate El Niño regimes

  • Ken Takahashi
  • Christina Karamperidou
  • Boris Dewitte


The existence of two regimes for El Niño (EN) events, moderate and strong, has been previously shown in the GFDL CM2.1 climate model and also suggested in observations. The two regimes have been proposed to originate from the nonlinearity in the Bjerknes feedback, associated with a threshold in sea surface temperature (\(T_c\)) that needs to be exceeded for deep atmospheric convection to occur in the eastern Pacific. However, although the recent 2015–16 EN event provides a new data point consistent with the sparse strong EN regime, it is not enough to statistically reject the null hypothesis of a unimodal distribution based on observations alone. Nevertheless, we consider the possibility suggestive enough to explore it with a simple theoretical model based on the nonlinear Bjerknes feedback. In this study, we implemented this nonlinear mechanism in the recharge-discharge (RD) ENSO model and show that it is sufficient to produce the two EN regimes, i.e. a bimodal distribution in peak surface temperature (T) during EN events. The only modification introduced to the original RD model is that the net damping is suppressed when T exceeds \(T_c\), resulting in a weak nonlinearity in the system. Due to the damping, the model is globally stable and it requires stochastic forcing to maintain the variability. The sustained low-frequency component of the stochastic forcing plays a key role for the onset of strong EN events (i.e. for \(T>T_c\)), at least as important as the precursor positive heat content anomaly (h). High-frequency forcing helps some EN events to exceed \(T_c\), increasing the number of strong events, but the rectification effect is small and the overall number of EN events is little affected by this forcing. Using the Fokker–Planck equation, we show how the bimodal probability distribution of EN events arises from the nonlinear Bjerknes feedback and also propose that the increase in the net feedback with increasing T is a necessary condition for bimodality in the RD model. We also show that the damping strength determines both the adjustment time-scale and equilibrium value of the ensemble spread associated with the stochastic forcing.


El Niño ENSO Nonlinearity Bjerknes feedback Recharge-discharge model Fokker–Planck equation Eastern Pacific 



The authors thank Drs. S.-I. An, F.-F. Jin, J.-S. Kug, A. Levine, K. Stein, A. Timmermann for useful discussions. KT was supported by the Manglares-IGP project (IDRC 106714) and PPR 068 “Reducción de Vulnerabilidad y Atención de Emergencias por Desastres”. CK was supported by U.S. NSF Grants OCE-1304910 and AGS-1602097. BD was supported by LEFE-GMMC (project STEPPE) and FONDECYT (projects 1171861 and 1151185). Calculations and plots were done with GNU Octave, GNU Fortran, GrADS, and R. The implementation in R of the dip test is by M. Mächler ( and the code for the Silverman test is from the website of G. Mukherjee (

Supplementary material

382_2018_4100_MOESM1_ESM.pdf (534 kb)
Supplementary material 1 (PDF 535 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Instituto Geofísico del PerúLimaPeru
  2. 2.Department of Atmospheric SciencesUniversity of Hawai’i at MānoaHonoluluUSA
  3. 3.Centro de Estudios Avanzado en Zonas Áridas (CEAZA)CoquimboChile
  4. 4.Departamento de Biología, Facultad de Ciencias del MarUniversidad Católica del NorteCoquimboChile
  5. 5.Laboratoire d’Etudes en Géophysique et Océanographie SpatialesToulouseFrance

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