Bispectral analysis of nonlinear interaction, predictability and stochastic modelling with application to ENSO

Abstract

Non-Gaussianity and nonlinearity have been shown to be ubiquitous characteristics of El Niño Southern Oscillation (ENSO) with implication on predictability, modelling, and assessment of extremes. These topics are investigated through the analysis of third-order statistics of El Niño 3.4 index in the period 1870–2018, namely bicovariance and bispectrum. Likewise, the spectral decomposition of variance, the bispectrum provides a spectral decomposition of skewness. Positive and negative bispectral contributions identify modes contributing respectively to La Niñas and El Niños, mostly in the period range 2–6 years. The ENSO bispectrum also shows statistically significant features associated with nonlinearity. The analysis of bicovariance reveals a nonlinear correlation between the Boreal Spring and following Winter, coming from an asymmetry of the persistence of El Niño, contributing hence to a reduction of Spring Predictability Barrier. The positive skewness and main features of the ENSO bicovariance and bispectrum are shown to be well reproduced by fitting a bilinear stochastic model. This model shows improved forecasts, with respect to benchmark linear models, especially of the amplitude of extreme El Niños. This study is relevant, particularly in a changing climate, to better characterize and predict ENSO extremes coming from non-Gaussianity and nonlinearity.

Keywords:

• ENSO spring predictability barrier
• bispectrum
• El Niño skewness
• nonlinear predictability
• bilinear models

Data availability statement

The data that support the findings of this study are available from the NOAA website: https://www.esrl.noaa.gov/psd/gcos_wgsp/Timeseries/Data/nino34.long.anom.data

Acknowledgments

This research was developed at IDL with the support of the Portuguese Foundation for Science and Technology through the FCT – project UIDB/50019/2020 – IDL – Instituto Dom Luiz (IDL) and FCT – project JPIOCEANS/0001/2019 (ROADMAP: 'The Role of ocean dynamics and Ocean–Atmosphere interactions in Driving cliMAte variations and future Projections of impact–relevant extreme events'). We acknowledge the International Meteorological Institute (IMI) at Stockholm University for hosting Carlos Pires, and also the constructive discussion with Adam Monahan. Two anonymous referees provided constructive comments, which helped improve the manuscript. Many thanks for the undeniable support of the family.

Disclosure statement

The authors declare that there are no conflicts of interest regarding the publication of this paper.