El Niño and La Niña, collectively referred to as the El Niño–Southern Oscillation (ENSO), are not only highly consequential1,2,3,4,5,6 but also strongly nonlinear7,8,9,10,11,12,13,14. For example, the maximum warm anomalies of El Niño, which occur in the equatorial eastern Pacific Ocean, are larger than the maximum cold anomalies of La Niña, which are centred in the equatorial central Pacific Ocean7,8,9. The associated atmospheric nonlinear thermal damping cools the equatorial Pacific during El Niño but warms it during La Niña15,16. Under greenhouse warming, climate models project an increase in the frequency of strong El Niño and La Niña events, but the change differs vastly across models17, which is partially attributed to internal variability18,19,20,21,22,23. Here we show that like a butterfly effect24, an infinitesimal random perturbation to identical initial conditions induces vastly different initial ENSO variability, which systematically affects its response to greenhouse warming a century later. In experiments with higher initial variability, a greater cumulative oceanic heat loss from ENSO thermal damping reduces stratification of the upper equatorial Pacific Ocean, leading to a smaller increase in ENSO variability under subsequent greenhouse warming. This self-modulating mechanism operates in two large ensembles generated using two different models, each commencing from identical initial conditions but with a butterfly perturbation24,25; it also operates in a large ensemble generated with another model commencing from different initial conditions25,26 and across climate models participating in the Coupled Model Intercomparison Project27,28. Thus, if the greenhouse-warming-induced increase in ENSO variability29 is initially suppressed by internal variability, future ENSO variability is likely to be enhanced, and vice versa. This self-modulation linking ENSO variability across time presents a different perspective for understanding the dynamics of ENSO variability on multiple timescales in a changing climate.
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Data related to the paper can be downloaded from the following: ORA-S5, https://www.ecmwf.int/en/research/climate-reanalysis/ocean-reanalysis; HadISST v1.1, https://www.metoffice.gov.uk/hadobs/hadisst/; ERSST v5, https://www.ncdc.noaa.gov/data-access/marineocean-data/extended-reconstructed-sea-surface-temperature-ersst-v5/; NCEP/NCAR reanalysis, https://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.derived.surfaceflux.html/; ERA5, https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5; CMIP5, https://esgf-node.llnl.gov/projects/cmip5/; CMIP6, https://esgf-node.llnl.gov/projects/cmip6/; CESM-LENS, http://www.cesm.ucar.edu/projects/community-projects/LENS/data-sets.html; GFDL-CM3, http://www.cesm.ucar.edu/projects/community-projects/MMLEA/; GFDL-ESM2M, http://www.cesm.ucar.edu/projects/community-projects/MMLEA/.
The codes for calculating EOF and the parameter |αD| can be downloaded from https://drive.google.com/open?id=1d2R8wKpFNW-vMIfoJsbqIGPIBd9Z_8rj. All codes are available upon request.
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This work is supported by the Strategic Priority Research Program of Chinese Academy of Sciences, grant number XDB40000000. We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modelling groups for producing and making available their model output. For CMIP, the US Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. We are grateful to various reanalysis groups for make the datasets available to us. PMEL contribution number 5077. W.C., B.N. and A.S. are supported by CSHOR and the Earth System and Climate Change Hub of the Australian Government’s National Environment Science Program. CSHOR is a joint research Centre for Southern Hemisphere Oceans Research between QNLM and CSIRO.
The authors declare no competing interests.
Peer review information Nature thanks Tobias Bayr and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Extended data figures and tables
The results from 40 butterfly effect experiments of the CESM-LE. a, Time series of global mean SST. The red curve represents the ensemble mean. b, Multi-experiment ensemble mean SST and wind stress difference between the last 50-year period (2050–2099) and the initial 50-year period (1920–1969). c, Same as in b but for ocean temperature along the Equator averaged between 5° S–5° N, showing an intensification of stratification along the equatorial upper ocean as in ref. 17, enhancing the ocean–atmosphere coupling. d, E-index variability in the initial 50-year period (blue bars) and the last 50-year period (red bars) for each experiment and the multi-experiment ensemble mean. The error bars represent 1 s.d. value of interexperiment E-index variability for the two periods, respectively.
Extended Data Fig. 2 ENSO properties in initial and future climate in the butterfly effect experiments.
The results from 40 butterfly effect experiments of the CESM-LE. a, Interexperiment relationship between the E-index and the C-index s.d. for the initial 50-year period (1920–1969). b, As in a, interexperiment relationship between the E-index variability and variability of the EP (5° S–5° N, 150° W–90° W) net heat flux (s.d.). c, d, The same as a, b, respectively, but for the future 50-year period (2050–2099). The blue stars and orange diamonds represent the ten experiments with the weakest and strongest initial E-index variability, respectively. Solid black circles represent other experiments. Experiments with a greater E-index variability systematically produce greater heat flux variability, and greater C-index variability as strong El Niño events lead to strong La Niña events. These properties are seen in both initial and future climate. Statistics (that is, correlation (R) and P value) of a linear fit (red solid line) are shown. The relationship is statistically significant above the 99% confidence level.
Extended Data Fig. 3 Nonlinear thermal damping aggregated over observational datasets and over 27 selected CMIP5 and CMIP6 models.
a, The observed monthly E-index versus normalised monthly surface net heat flux anomalies over the EP (5° S–5° N, 150° W–90° W) for the period of 1979–2017. b, As in a, but for the observed monthly C-index versus normalized monthly surface net heat flux anomalies over the CP (5° S–5° N, 160° E–150° W). Also shown are the quadratic fit (red solid line), for example, with E-index, in terms of NHF(t) = αT(E-index(t))2 + βTE-index(t) + γT, and corresponding thermodynamic nonlinear coefficient αT associated with EP ENSO and CP ENSO. Three SST reanalysis products and two atmospheric reanalyses52,53,54,55,56 are used here (see ‘Atmosphere thermal feedback and its nonlinearity’ in Methods). c, d, As in a, b, respectively, but for 27 selected CMIP5 and CMIP6 models (Extended Data Fig. 7).
Extended Data Fig. 4 ENSO thermal damping and cumulative ocean heat flux in the butterfly effect experiments.
The results from 40 butterfly effect experiments of the CESM-LE. a, b, Time series E-index (black) and net heat flux (red) in the EP (at 0°, 105° W) in experiments with strongest (run 14; a) and weakest (run 24; b) E-index variability in the initial (1920–1969) 50 years. c, EP cumulative net heat flux for the two experiments. Raw monthly net heat flux fields referenced to the 70-year (1850–1919) common monthly climatology before the butterfly effect is constructed first before accumulation. Greater cumulative heat loss by 1969 (end of the initial 50 years, indicated by the vertical black line) is generated owing to greater initial ENSO variability, reducing upper ocean warming due to the greenhouse effect.
The results from 40 butterfly effect experiments of the CESM-LE. a, b, Relationship between the monthly E-index and the monthly net heat flux over the EP (5° S–5° N, 150° W–90° W; a), and between the monthly C-index and the monthly CP (5° S–5° N, 160° E–150° W; b), quadratically detrended net heat flux into ocean (W m−2) for the initial 100 years (1920–2019). Thermal damping takes heat out of the ocean during El Niño and puts heat into the ocean during La Niña, but because El Niño is greater in amplitude, after several ENSO events, net heat is taken out of the ocean. c, Interexperiment relationship showing that greater initial ENSO variability, hence a greater amount of cumulative ocean heat loss (at 0°, 105° W, indicated by the black cross in e, positive out of the ocean), is generated. Raw monthly net heat flux fields referenced to the 70-year (1850–1919) common monthly climatology before the butterfly effect is constructed first before accumulation. The cumulative oceanic heat loss can be surrogated by heat flux variability, as seen in d, showing that a greater cumulative heat loss is associated with greater heat flux variability. The blue stars and orange diamonds in c and d represent the ten experiments with the weakest and strongest initial E-index variability, respectively. Solid black circles represent other experiments. Correlation (R) and P value of a linear fit (red solid line) are shown. e, Interexperiment regression of 40 cumulative heat flux fields onto 40 values of E-index variability, both over the initial 100 years (1920–2019), showing an ENSO pattern of cumulative heat flux. In experiments in which the butterfly effect leads to greater initial ENSO variability, a greater cumulative ocean heat loss is generated along the Equator. Statistical significance above the 90% and 95% confidence levels based on a two-tailed Student’s t-test is indicated as black stippling and the green solid contour, respectively.
Extended Data Fig. 6 Difference between two groups of experiments with strong and weak initial E-index variability.
The results from 40 butterfly effect experiments of the CESM-LE. The difference indicates the impact due to different ENSO variability between the two groups. a, SST (°C) and wind stress (N m−2) difference between the ten experiments with the strongest E-index variability in the initial 50-year period (1920–1969) and the ten experiments with the weakest E-index variability for the same period (see Fig. 1b, orange diamonds and blue stars, respectively). b, Same as in a but for the upper 150-m ocean temperature (°C). Stippling indicates where the difference between the two ensembles is significant above the 90% confidence level, based on a two-tailed Student’s t-test, and the green solid contour represents the 95% confidence level.
The results are for 27 models, that is, 18 out of 34 CMIP5 models and 9 out of 15 CMIP6 models, that produce both a dynamic nonlinear coefficient αD less than −0.155, that is, greater than 50% of the observed amplitude17 and a thermodynamic nonlinear coefficient αT less than 0 with all but one simulating 50% of the observed value. In general, a greater αT is associated with a greater αD, with a correlation coefficient of 0.47 using all models. Selected models are marked by symbols filled in different colours, while non-selected models are indicated in black and grey without filling. Each ensemble member and the multimember ensemble mean for CESM-LE are shown in filled blue and red circles, respectively.
a, b, Intermodel relationship of E-index variability with strong ENSO frequency and with EP (5° S–5° N, 150° W–90° W) heat flux variability, respectively, for the initial 50-year period (1900–1949). c, d, The same as a, b, respectively, but for the last 50-year period (2050–2099). Models with a higher E-index variability systematically generate a higher frequency of strong ENSO events and a stronger heat flux variability. The results are for 27 models, that is, 18 out of 34 CMIP5 models and 9 out of 15 CMIP6 models, that produce both a dynamic nonlinear coefficient αD of less than −0.155, that is, greater than 50% of the observed amplitude17 and a thermodynamic nonlinear coefficient αT less than 0. Strong ENSO frequency in a, c is defined as the total number per 50 years of strong El Niño events (E-index more than 1.5 s.d.) plus the total number of strong La Niña events (C-index less than −1.5 s.d.) in the ENSO peak season of December–February. Correlation (R) and P value of a linear fit (red solid line) are shown. In all scatter plots, the relationship is statistically significant above the 99% confidence level.
a, Intermodel relationship between the last (2050–2099) and initial (1900–1949) 50-year period in E-index variability, showing an inverse relationship that is statistically significant above the 99% confidence level, that is, models that generate a greater variability in the initial period systematically produce a smaller future variability. The results are for 27 models, that is, 18 out of 34 CMIP5 models and 9 out of 15 CMIP6 models, that produce both a dynamic nonlinear coefficient αD less than −0.155 (greater than 50% of the observed amplitude17) and a thermodynamic nonlinear coefficient αT less than 0. b, Evolution of E-index variability, measured by a 50-year running window, moving forward every year from 1900 and recorded at the initial year, for ten models with strong initial E-index variability (red box in a) and ten models with weak initial E-index variability (blue box in a). Solid red (blue) lines and red (blue) shadings indicate multimodel average and intermodel spread (1 s.d. value), respectively, of the ten models with strong (weak) initial E-index variability. ENSO variability in models with weaker initial variability shows a faster increase in response to greenhouse warming during the ensuing periods, with a final amplitude that exceeds that in models with stronger initial ENSO variability. Different running window lengths (for example, 40 years or 60 years) and different sample sizes of model groups for averaging (for instance, 7 or 13 models with largest initial E-index variability versus 7 or 13 models with smallest initial E-index variability, respectively) produce qualitatively similar behaviour.
Extended Data Fig. 10 Initial ENSO variability and its future change in all available runs of CMIP5 and CMIP6 models.
The results are for the 27 selected models, that is, 18 out of 34 CMIP5 models and 9 out of 15 CMIP6 models, that produce both a dynamic nonlinear coefficient αD less than −0.155 (greater than 50% of the observed amplitude17) and a thermodynamic nonlinear coefficient αT less than 0. a, Intermodel relationship between initial 50-year (1900–1949) E-index variability and its future change (2050–2099 minus 1900–1949) scaled by the corresponding global-mean SST warming in each model. b, As in a, but for C-index. Run numbers are indicated next to the model names (for example, r1, r2 and so on).
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Cai, W., Ng, B., Geng, T. et al. Butterfly effect and a self-modulating El Niño response to global warming. Nature 585, 68–73 (2020). https://doi.org/10.1038/s41586-020-2641-x
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