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Explainable El Niño predictability from climate mode interactions

Nature volume 630, pages 891–898 (2024)Cite this article

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Abstract

The El Niño–Southern Oscillation (ENSO) provides most of the global seasonal climate forecast skill1,2,3, yet, quantifying the sources of skilful predictions is a long-standing challenge4,5,6,7. Different sources of predictability affect ENSO evolution, leading to distinct global effects. Artificial intelligence forecasts offer promising advancements but linking their skill to specific physical processes is not yet possible8,9,10, limiting our understanding of the dynamics underpinning the advancements. Here we show that an extended nonlinear recharge oscillator (XRO) model shows skilful ENSO forecasts at lead times up to 16–18��months, better than global climate models and comparable to the most skilful artificial intelligence forecasts. The XRO parsimoniously incorporates the core ENSO dynamics and ENSO’s seasonally modulated interactions with other modes of variability in the global oceans. The intrinsic enhancement of ENSO’s long-range forecast skill is traceable to the initial conditions of other climate modes by means of their memory and interactions with ENSO and is quantifiable in terms of these modes’ contributions to ENSO amplitude. Reforecasts using the XRO trained on climate model output show that reduced biases in both model ENSO dynamics and in climate mode interactions can lead to more skilful ENSO forecasts. The XRO framework’s holistic treatment of ENSO’s global multi-timescale interactions highlights promising targets for improving ENSO simulations and forecasts.

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Fig. 1: Different sources of ENSO predictability and associated different global impacts.
Fig. 2: Superior efficacy of the XRO in simulating and reforecasting ENSO.
Fig. 3: Quantifying the increased ENSO forecast skills from the coupled influences outside equatorial Pacific during 1979–2022.
Fig. 4: Delineating contributions to ENSO amplitudes from other climate modes.
Fig. 5: Linking biases in the dynamics captured by the XRO to climate model deficiencies in forecasting ENSO during 1979–2022.

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Data availability

Datasets used in this paper are freely available. Observational data have links in Supplementary Table 2; NMME: https://iridl.ldeo.columbia.edu/SOURCES/.Models/.NMME/; 3D-Geoformer ENSO AI model forecast: http://msdc.qdio.ac.cn/data/metadata-special-detail?id=1602252663859298305; CESM1 LENS: https://www.cesm.ucar.edu/community-projects/lens/data-sets; CESM2 LENS: https://www.cesm.ucar.edu/community-projects/lens2/data-sets; MPI-ESM LENS: https://esgf-data.dkrz.de/projects/mpi-ge/; CMIP5 outputs: https://esgf-node.llnl.gov/projects/cmip5/; and MIROC6 LENS and CMIP6 outputs: https://esgf-node.llnl.gov/projects/cmip6/. All the map figures (Fig. 1a,c,d and Supplementary Figs. 1, 2 and 14) were generated using Python Cartopy v.0.22.0 (https://doi.org/10.5281/zenodo.1182735) (ref. 114). The source data for figures in the main text are available at https://doi.org/10.5281/zenodo.10951443 (ref. 115).

Code availability

The XRO model code is deposited at https://doi.org/10.5281/zenodo.10681114 (ref. 116). The code to calculate the predictive skill is available at https://github.com/pangeo-data/climpred.

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Acknowledgements

S.Z. and F.-F.J. were supported by the US National Science Foundation (NSF) grant no. AGS-2219257 and NOAA’s Climate Program Office’s Modelling, Analysis, Predictions, and Projections (MAPP) Program grant no. NA23OAR2007440. M.F.S. was supported by NSF grant no. AGS-2141728. M.F.S. and S.Z. were supported by NOAA’s Climate Program Office’s MAPP Program grant no. NA20OAR4310445. P.R.T. and S.Z. were supported by National Aeronautics and Space Administration grant no. 80NSSC20K1241. J.-S.K. was supported by the National Research Foundation of Korea grant funded by the Korean government (grant no. NRF-2022R1A3B1077622). M.A.C. was supported by NSF award no. OCE-2219829. This is International Pacific Research Center publication 1620, SOEST contribution 11800 and Pacific Marine Environmental Laboratory contribution 5579.

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Authors and Affiliations

  1. Department of Atmospheric Sciences, School of Ocean and Earth Science and Technology (SOEST), University of Hawai‘i at Mānoa, Honolulu, HI, USA

    Sen Zhao & Fei-Fei Jin

  2. International Pacific Research Center, SOEST, University of Hawai‘i at Mānoa, Honolulu, HI, USA

    Fei-Fei Jin & Malte F. Stuecker

  3. Department of Oceanography, SOEST, University of Hawai‘i at Mānoa, Honolulu, HI, USA

    Malte F. Stuecker & Philip R. Thompson

  4. School of Earth and Environmental Sciences, Seoul National University, Seoul, South Korea

    Jong-Seong Kug

  5. National Oceanic and Atmospheric Administration (NOAA)/Pacific Marine Environmental Laboratory, Seattle, WA, USA

    Michael J. McPhaden

  6. Lamont Doherty Earth Observatory of Columbia University, Palisades, NY, USA

    Mark A. Cane

  7. NOAA/OAR/Geophysical Fluid Dynamics Laboratory, Princeton, NJ, USA

    Andrew T. Wittenberg

  8. Frontiers Science Center for Deep Ocean Multispheres and Earth System, Physical Oceanography Laboratory, and Sanya Oceanographic Institution, Ocean University of China, Qingdao, China

    Wenju Cai

  9. Laoshan Laboratory, Qingdao, China

    Wenju Cai

  10. State Key Laboratory of Loess and Quaternary Geology, Institute of Earth Environment, Chinese Academy of Sciences, Xi’an, China

    Wenju Cai

  11. State Key Laboratory of Marine Environmental Science & College of Ocean and Earth Sciences, Xiamen University, Xiamen, China

    Wenju Cai

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  1. Sen Zhao
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  3. Malte F. Stuecker
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Contributions

F.-F.J., S.Z. and M.F.S. conceptualized the research. S.Z. designed the model and experiments, conducted the analysis, produced the figures, and wrote the initial manuscript, in discussion with F.-F.J. F.-F.J., W.C., M.F.S. and S.Z. structured the paper. A.T.W., M.F.S. and S.Z. designed the LENS perfect model experiments. M.A.C. coined the acronym XRO. All authors contributed to interpreting the results and improving the paper.

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Correspondence to Fei-Fei Jin.

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Extended data figures and tables

Extended Data Fig. 1 Seasonally-modulated strength of mode interactions in observations and CMIP5/6 models, as diagnosed from the linear part of the XRO model.

(a) ENSO recharge-oscillator coefficients, (b) Coupling processes denoted by the contribution of other modes to the tendencies of ENSO SSTA and WWV anomalies, (c) ENSO-forced processes denoted by the contribution of ENSO SSTA and WWV anomalies to the SSTA tendency of other modes, (d) Interactions among NPMM, SPMM, IOB, IOD, SIOD, TNA, ATL3, and SASD. The coefficient \({L}_{{ij}}\) has been normalized by a factor of \({\sigma }_{j}\)/\({\sigma }_{i}\), where \({\sigma }_{i}\) and \({\sigma }_{j}\) are the monthly standard deviations of the indices in row \(i\) and column \(j\), respectively, so that all coefficients are comparable, and the units are year−1. The diagonal panels (blue frames) show the damping rate for each index. The black curves with shading show the XRO fit to the ORAS5 reanalysis (with 10%–90% spread band from the cross-validated fitting excluding 3-year data, see “Cross-validated reforecasts” in Methods), and the red curves with shading show the ensemble mean with 10%–90% spread band of the 91 CMIP5/6 historical simulations. ENSO can be strongly driven by climate modes in extratropical Pacific, Indian Ocean, and Atlantic Ocean, which in some seasons are as important as the dynamics internal to the equatorial Pacific. Most of the non-ENSO modes are more strongly driven by ENSO (and their own damping) than by any of the other non-ENSO modes in other basins. The climate models underestimate the strength of most of the mode interactions and miss the seasonality.

Extended Data Fig. 2 Decadal change in the ENSO forecast correlation skill.

a, The all-months correlation skill of the 3-month running mean Niño3.4 index verified on 1950–1970 for the out-of-sample XRO fitted on 1973–2022 (red curve), out-of-sample nRO fitted on 1973–2022 (magenta curve), in-sample XRO fitted on 1950–1970 (black dashed curve) and in-sample XRO fitted on the full-period 1950–2022 (blue dashed curve). The bottom inset shows the time series of Niño3.4 index for out-of-sample training (blue) and verifying (orange) periods, respectively. b-c, same as a, but verifying on 1972–1992 and 2002–2022, respectively. The XRO is superior to the nRO regardless the verifying periods and decadal changes of ENSO forecast skill.

Extended Data Fig. 3 Test of additivity (i.e., linearity) of the sensitivity experiments.

a, Regression slope and linear correlation coefficients for the Niño3.4 SSTA forecasts between the effects of the uninitialized ExPO+IO + AO experiment (\({\rm{XRO}}-{U}_{{\rm{ExPO}}+{\rm{IO}}+{\rm{AO}}}\)) and the sum of the effects of the individual uninitialized ExPO, IO, and AO experiments (\(3\ast {\rm{XRO}}-{U}_{{\rm{ExPO}}}-{U}_{{\rm{IO}}}-{U}_{{\rm{AO}}}\)). b and c, same as a, but for decoupling experiments (\({\rm{XRO}}-{D}_{{\rm{ExPO}}+{\rm{IO}}+{\rm{AO}}}\) vs. \(3\ast {\rm{XRO}}-{D}_{{\rm{ExPO}}}-{D}_{{\rm{IO}}}-{D}_{{\rm{AO}}}\)) and relaxing towards observation experiments (\({\rm{XRO}}-{R}_{{\rm{ExPO}}+{\rm{IO}}+{\rm{AO}}}\) vs. \(3\ast {\rm{XRO}}-{R}_{{\rm{ExPO}}}-{R}_{{\rm{IO}}}-{R}_{{\rm{AO}}}\)), respectively. d, e the all-months correlation skill (d) and RMSE (e) of the 3-month running mean Niño3.4 index, as a function of the forecast lead month in the control experiment (black line) and sensitivity experiments: the uninitialized ExPO+IO + AO experiment (solid red line) and sum of uninitialized ExPO, IO, and AO individually (dashed red line), the decoupling ExPO+IO + AO experiment (solid blue line) and sum of decoupling ExPO, IO, and AO individually (dashed blue line), and the relaxing ExPO+IO + AO to observation experiment (solid magenta line) and sum of relaxing ExPO, IO, and AO to observation individually (dashed magenta line). The individual basin uninitialized experiments are additive with the slopes and correlations at all lead months being very close to 1. But the individual basin decoupling experiments and the individual relaxation towards observations experiments are not additive, owing to a nonlinear dependence on the operator parameters. The sum of the effects of decoupling ExPO, IO, and AO individually is much larger than the effect of decoupling ExPO+IO + AO, suggesting that the decoupling experiment framework overestimates the contribution of each basin, given the presence of indirect pathways due to interactions among basins.

Extended Data Fig. 4 Influence of the memory effect outside the equatorial Pacific on ENSO forecast skill.

Shown are the all-months correlation skill (a) and RMSE (b) of the 3-month running mean Niño3.4 index, as a function of the forecast lead month in the XRO forecast (black), the nRO forecast (grey triangle), and the “Losing memory” sensitivity experiments (colour curves) by adding different damping rates (ranging from a strong damping rate of –(5 day)−1 implying no memory to a weak damping rate of –(360 day)−1 implying longer memory) to the non-ENSO modes (See “Losing memory experiments” in Methods). The initial condition memory effect of the climate modes outside equatorial Pacific extends the skill of ENSO forecasts.

Extended Data Fig. 5 Contribution of each climate mode’s initialization to ENSO correlation skill.

Shown is the forecast skill difference of the Niño3.4 SSTA index, as a function of initial time and target month, between the control and uninitialized climate mode sensitivity experiments for the NPMM, SPMM, IOB, IOD, SIOD, TNA, ATL3, and SASD, respectively. The contributions of the IOD, NPMM, and TNA dominate the ENSO forecast skill improvement.

Extended Data Fig. 6 Impacts of climate-mode initialization to ENSO forecasts.

Shown is the difference of Niño3.4 SSTA (shading) and WWV anomalies (contours with interval of 0.6 m, positive in red and negative in black dashed, zero omitted), as a function of forecast lead and target time, between control and uninitialized climate mode experiments for NPMM, SPMM, IOB, IOD, SIOD, TNA, ATL3, and SASD, respectively. Vertical reference dashed lines denote December of El Niño (red) and La Niña (blue) years, respectively. The normalized time series of each climate mode SSTA index is indicated in the bottom axis; the black arrows indicate the flow of forecast integration started from the selected time in the bottom. The XRO sensitivity experiments quantify how the initial states of key climate modes affect subsequent ENSO events.

Extended Data Fig. 7 Impacts on ENSO forecast skill of correcting biases in the XRO parameters fitted to individual CMIP simulations.

Shown is the difference of the all-months correlation skill for the Niño3.4 SSTA index, between the corrected-parameter forecast experiment and the XROm experiment trained solely on CMIP model outputs. (a) Effect of correcting linear operators (\({{\rm{X}}{\rm{R}}{\rm{O}}}_{{\bf{L}}}^{m}\)- XROm), (b) effect of correcting ENSO internal linear dynamics (\({{\rm{X}}{\rm{R}}{\rm{O}}}_{{{\bf{L}}}_{{\rm{E}}{\rm{N}}{\rm{S}}{\rm{O}}}}^{m}\)- XROm), (c) effect of correcting remote climate mode feedbacks onto ENSO (\({{\rm{X}}{\rm{R}}{\rm{O}}}_{{{\bf{C}}}_{1}}^{m}\)- XROm), and (d) effect of correcting ENSO teleconnections to remote climate modes (\({{\rm{X}}{\rm{R}}{\rm{O}}}_{{{\bf{C}}}_{2}}^{m}\)- XROm). The model is sorted by the averaged correlation skill of the XROm forecast at 6–15 lead months. Reforecasts using the XRO trained on global climate model output show that correcting CGCMs’ dynamical biases in ENSO and climate mode interactions lead to more skilful ENSO forecasts. Most important is correcting ENSO biases (which improves skill at longest lead-times), followed by correcting the remote climate mode impact on ENSO (which improves skill at intermediate leads). Less skill is gained by improving ENSO’s teleconnection to the remote modes.

Extended Data Fig. 8 Correlation forecast skill for the Indian Ocean Dipole, using the XRO trained with climate model outputs.

(a) The correlation skill of the IOD index in Sep-Oct-Nov (SON) as a function of forecast lead, in the XROm trained solely on 91 individual CMIP model outputs (grey curves), the XRO trained on observations (red curve), and the original (not XRO) multi-model mean of the ensemble means of the forecasts from the NMME models (black). (b) the ensemble mean and 10%–90% spread band of the changes in correlation skill for the IOD index, obtained by correcting the ENSO internal linear dynamics (\({{\rm{X}}{\rm{R}}{\rm{O}}}_{{{\bf{L}}}_{{\rm{E}}{\rm{N}}{\rm{S}}{\rm{O}}}}^{m}\)- XROm, red), or the remote-mode feedbacks onto ENSO (\({{\rm{X}}{\rm{R}}{\rm{O}}}_{{{\bf{C}}}_{1}}^{m}\)- XROm, magenta), or the ENSO teleconnections to remote modes (\({{\rm{X}}{\rm{R}}{\rm{O}}}_{{{\bf{C}}}_{2}}^{m}\)- XROm, blue). Reforecasts using the XRO trained on climate model output show that reducing CGCM biases in the dynamics of ENSO’s climate mode interactions improves IOD forecasts.

Extended Data Table 1 Details of the XRO forecasting experiments based on observations (1979–2022)
Full size table
Extended Data Table 2 Details of the XRO forecasting experiments using global climate model output as training data
Full size table

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Zhao, S., Jin, FF., Stuecker, M.F. et al. Explainable El Niño predictability from climate mode interactions. Nature 630, 891–898 (2024). https://doi.org/10.1038/s41586-024-07534-6

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