McPhaden, M. J., Zebiak, S. E. & Glantz, M. H. ENSO as an integrating concept in earth science. Science 314, 1740–1745 (2006).
Timmermann, A. et al. El Niño–Southern Oscillation complexity. Nature 559, 535–545 (2018).
Cai, W. et al. Changing El Niño–Southern Oscillation in a warming climate. Nat. Rev. Earth Environ. https://doi.org/10.1038/s43017-021-00199-z (2021).
Cane, M. A., Zebiak, S. E. & Dolan, S. C. Experimental forecasts of El Niño. Nature 321, 827–832 (1986).
Barnston, A. G., Tippett, M. K., L’Heureux, M. L., Li, S. & DeWitt, D. G. Skill of real-time seasonal ENSO model predictions during 2002–11: is our capability increasing? Bull. Amer. Meteor. Soc. 93, 631–651 (2012).
Tang, Y. et al. Progress in ENSO prediction and predictability study. Natl Sci. Rev. 5, 826–839 (2018).
L’Heureux, M. L. et al. in El Niño Southern Oscillation in a Changing Climate (eds McPhaden, M. J. et al.) 227–246 (American Geophysical Union, 2020).
Ham, Y.-G., Kim, J.-H. & Luo, J.-J. Deep learning for multi-year ENSO forecasts. Nature 573, 568–572 (2019).
Zhou, L. & Zhang, R.-H. A self-attention–based neural network for three-dimensional multivariate modeling and its skillful ENSO predictions. Sci. Adv. 9, eadf2827 (2023).
Wang, H., Hu, S. & Li, X. An interpretable deep learning ENSO forecasting model. Ocean Land Atmos. Res. 2, 0012 (2023).
Cai, W. et al. Pantropical climate interactions. Science 363, eaav4236 (2019).
Chiang, J. C. H. & Vimont, D. J. Analogous Pacific and Atlantic Meridional Modes of tropical atmosphere–ocean variability. J. Clim. 17, 4143–4158 (2004).
Zhang, H., Clement, A. & Nezio, P. D. The South Pacific Meridional Mode: a mechanism for ENSO-like variability. J. Clim. 27, 769–783 (2014).
Jin, Y. et al. The Indian Ocean weakens ENSO spring predictability barrier: role of the Indian Ocean Basin and dipole modes. J. Clim. 36, 8331–8345 (2023).
Izumo, T., Vialard, J. & Lengaigne, M. Influence of the state of the Indian Ocean Dipole on the following year’s El Niño. Nat. Geosci. https://doi.org/10.1038/NGEO760 (2010).
Jo, H.-S. et al. Southern Indian Ocean Dipole as a trigger for Central Pacific El Niño since the 2000s. Nat. Commun. 13, 6965 (2022).
Ham, Y.-G., Kug, J.-S., Park, J.-Y. & Jin, F.-F. Sea surface temperature in the north tropical Atlantic as a trigger for El Niño/Southern Oscillation events. Nature Geosci. 6, 112–116 (2013).
Ham, Y.-G., Kug, J.-S. & Park, J.-Y. Two distinct roles of Atlantic SSTs in ENSO variability: North Tropical Atlantic SST and Atlantic Niño. Geophys. Res. Lett. 40, 4012–4017 (2013).
Ham, Y.-G. et al. Inter-basin interaction between variability in the South Atlantic Ocean and the El Niño/Southern Oscillation. Geophys. Res. Lett. 48, e2021GL093338 (2021).
Jansen, M. F., Dommenget, D. & Keenlyside, N. Tropical atmosphere–ocean interactions in a conceptual framework. J. Climate 22, 550–567 (2009).
Frauen, C. & Dommenget, D. Influences of the tropical Indian and Atlantic Oceans on the predictability of ENSO. Geophys. Res. Lett. 39, L02706 (2012).
Luo, J.-J. et al. Interaction between El Niño and Extreme Indian Ocean Dipole. J. Climate 23, 726–742 (2010).
Keenlyside, N. S., Ding, H. & Latif, M. Potential of equatorial Atlantic variability to enhance El Nino prediction. Geophys. Res. Lett. 40, 2278–2283 (2013).
Luo, J.-J., Liu, G., Hendon, H., Alves, O. & Yamagata, T. Inter-basin sources for two-year predictability of the multi-year La Nina event in 2010-2012. Sci. Rep. 7, 2276 (2017).
Keenlyside, N. et al. in Interacting Climates of Ocean Basins: Observations, Mechanisms, Predictability, and Impacts (ed. Mechoso, C. R.) 258–292 (Cambridge Univ. Press, 2020).
Exarchou, E. et al. Impact of equatorial Atlantic variability on ENSO predictive skill. Nat. Commun. 12, 1612 (2021).
Alexander, M. A., Shin, S.-I. & Battisti, D. S. The influence of the trend, basin interactions, and ocean dynamics on tropical ocean prediction. Geophys. Res. Lett. 49, e2021GL096120 (2022).
Kido, S., Richter, I., Tozuka, T. & Chang, P. Understanding the interplay between ENSO and related tropical SST variability using linear inverse models. Clim. Dyn. 61,1029–1048 (2023).
Stuecker, M. F. et al. Revisiting ENSO/Indian Ocean dipole phase relationships. Geophys. Res. Lett. 44, 2016GL072308 (2017).
Zhang, W., Jiang, F., Stuecker, M. F., Jin, F.-F. & Timmermann, A. Spurious North Tropical Atlantic precursors to El Niño. Nat. Commun. 12, 3096 (2021).
Lee, S.-K. et al. On the fragile relationship between El Niño and California rainfall. Geophys. Res. Lett. 45, 907–915 (2018).
Jeong, H., Park, H.-S., Stuecker, M. F. & Yeh, S.-W. Distinct impacts of major El Niño events on Arctic temperatures due to differences in eastern tropical Pacific sea surface temperatures. Sci. Adv. 8, eabl8278 (2022).
McPhaden, M. J. A 21st century shift in the relationship between ENSO SST and warm water volume anomalies. Geophys. Res. Lett. 39, 2012GL051826 (2012).
Choi, J., An, S.-I. & Yeh, S.-W. Decadal amplitude modulation of two types of ENSO and its relationship with the mean state. Clim. Dyn. 38, 2631–2644 (2012).
Zhao, Y., Jin, Y., Capotondi, A., Li, J. & Sun, D. The role of Tropical Atlantic in ENSO predictability barrier. Geophys. Res. Lett. 50, e2022GL101853 (2023).
Anderson, B. T. On the joint role of subtropical atmospheric variability and equatorial subsurface heat content anomalies in initiating the onset of ENSO events. J. Clim. 20, 1593–1599 (2007).
Larson, S. M., Pegion, K. V. & Kirtman, B. P. The South Pacific Meridional Mode as a thermally driven source of ENSO amplitude modulation and uncertainty. J. Clim. 31, 5127–5145 (2018).
Stuecker, M. F. Revisiting the Pacific Meridional Mode. Sci. Rep. 8, 3216 (2018).
Park, J.-H. et al. Mid-latitude leading double-dip La Niña. Int. J. Climatol. 41, E1353–E1370 (2021).
Ding, R. et al. Multi-year El Niño events tied to the North Pacific oscillation. Nat. Commun. 13, 3871 (2022).
Geng, T. et al. Increased occurrences of consecutive La Niña events under global warming. Nature 619, 774–781 (2023).
Kug, J.-S. & Kang, I.-S. Interactive feedback between ENSO and the Indian Ocean. J. Climate 19, 1784–1801 (2006).
Hasan, N. A., Chikamoto, Y. & McPhaden, M. J. The influence of tropical basin interactions on the 2020–2022 double-dip La Niña. Front. Clim. 4, 1001174 (2022).
Iwakiri, T. et al. Triple-Dip La Niña in 2020–23: North Pacific atmosphere drives 2nd year La Niña. Geophys. Res. Lett. 50, e2023GL105763 (2023).
Zhao, S. et al. Improved predictability of the Indian Ocean dipole using a stochastic dynamical model compared to the North American multimodel ensemble forecast. Weather Forecast. 35, 379–399 (2020).
Chen, H.-C., Jin, F.-F., Zhao, S., Wittenberg, A. T. & Xie, S. ENSO dynamics in the E3SM-1-0, CESM2, and GFDL-CM4 climate models. J. Clim. 34, 9365–9384 (2021).
Chen, D., Cane, M. A., Kaplan, A., Zebiak, S. E. & Huang, D. Predictability of El Niño over the past 148 years. Nature 428, 733–736 (2004).
Liu, T., Song, X., Tang, Y., Shen, Z. & Tan, X. ENSO predictability over the past 137 years based on a CESM ensemble prediction system. J. Clim. 35, 763–777 (2022).
Weisheimer, A. et al. Variability of ENSO forecast skill in 2-year global reforecasts over the 20th century. Geophys. Res. Lett. 49, e2022GL097885 (2022).
Lou, J., Newman, M. & Hoell, A. Multi-decadal variation of ENSO forecast skill since the late 1800s. npj Clim. Atmos. Sci. 6, 89 (2023).
Jin, F.-F. et al. in El Niño Southern Oscillation in a Changing Climate (eds McPhaden, M. J. et al.) 119–151 (American Geophysical Union, 2020).
Jin, F.-F. An equatorial ocean recharge paradigm for ENSO. Part I: conceptual model. J. Atmos. Sci. 54, 811–829 (1997).
Hasselmann, K. Stochastic climate models, Part I. Theory. Tellus 28, 473–485 (1976).
Frankignoul, C. & Hasselmann, K. Stochastic climate models, Part II. Application to sea-surface temperature anomalies and thermocline variability. Tellus 29, 289–305 (1977).
Stuecker, M. F. The climate variability trio: stochastic fluctuations, El Niño, and the seasonal cycle. Geosci. Lett. 10, 51 (2023).
Meinen, C. S. & McPhaden, M. J. Observations of warm water volume changes in the Equatorial Pacific and their relationship to El Niño and La Niña. J. Climate 13, 3551–3559 (2000).
Richter, I., Stuecker, M. F., Takahashi, N. & Schneider, N. Disentangling the North Pacific Meridional Mode from tropical Pacific variability. npj Clim. Atmos. Sci. 5, 94 (2022).
Klein, S. A., Soden, B. J. & Lau, N. C. Remote sea surface temperature variations during ENSO: evidence for a tropical atmospheric bridge. J. Climate 12, 917–932 (1999).
Xie, S.-P. et al. Indian Ocean capacitor effect on Indo-Western Pacific climate during the summer following El Niño. J. Climate 22, 730–747 (2009).
Saji, N. H., Goswami, B. N., Vinayachandran, P. N. & Yamagata, T. A dipole mode in the tropical Indian Ocean. Nature 401, 360–363 (1999).
Webster, P. J., Moore, A. M., Loschnigg, J. P. & Leben, R. R. Coupled ocean–atmosphere dynamics in the Indian Ocean during 1997–98. Nature 401, 356–360 (1999).
Enfield, D. B. & Mayer, D. A. Tropical Atlantic sea surface temperature variability and its relation to El Nino southern oscillation. J. Geophys. Res.-Oceans 102, 929–945 (1997).
Zebiak, S. Air-sea interaction in the Equatorial Atlantic Region. J. Clim. 6, 1567–1568 (1993).
Nnamchi, H. C. et al. Thermodynamic controls of the Atlantic Niño. Nat. Commun. 6, 8895 (2015).
Rodrigues, R. R., Campos, E. J. D. & Haarsma, R. The impact of ENSO on the South Atlantic Subtropical Dipole mode. J. Clim. 28, 2691–2705 (2015).
Jin, F.-F., Kim, S. T. & Bejarano, L. A coupled‐stability index for ENSO. Geophys. Res. Lett. 33, (2006).
An, S.-I., Tziperman, E., Okumura, Y. M. & Li, T. in El Niño Southern Oscillation in a Changing Climate (eds McPhaden, M. J. et al.) 153–172 (American Geophysical Union, 2020).
An, S.-I. & Jin, F.-F. Nonlinearity and asymmetry of ENSO. J. Climate 17, 2399–2412 (2004).
Kang, I.-S. & Kug, J.-S. El Niño and La Niña sea surface temperature anomalies: asymmetry characteristics associated with their wind stress anomalies. J. Geophys. Res. Atmos. 107, 1–10 (2002).
Choi, K.-Y., Vecchi, G. A. & Wittenberg, A. T. ENSO transition, duration, and amplitude asymmetries: role of the nonlinear wind stress coupling in a conceptual model. J. Climate 26, 9462–9476 (2013).
Geng, T., Cai, W. & Wu, L. Two types of ENSO varying in tandem facilitated by nonlinear atmospheric convection. Geophys. Res. Lett. 47, e2020GL088784 (2020).
An, S.-I. et al. Main drivers of Indian Ocean Dipole asymmetry revealed by a simple IOD model. npj Clim. Atmos. Sci. 6, 93 (2023).
Lübbecke, J. F. & McPhaden, M. J. Symmetry of the Atlantic Niño mode. Geophys. Res. Lett. 44, 965–973 (2017).
Gebbie, G., Eisenman, I., Wittenberg, A. & Tziperman, E. Modulation of westerly wind bursts by sea surface temperature: a semistochastic feedback for ENSO. J. Atmos. Sci. 64, 3281–3295 (2007).
Jin, F.-F., Lin, L., Timmermann, A. & Zhao, J. Ensemble-mean dynamics of the ENSO recharge oscillator under state-dependent stochastic forcing. Geophys. Res. Lett. 34, 2006GL027372 (2007).
Zhao, S., Jin, F.-F. & Stuecker, M. F. Improved predictability of the Indian Ocean dipole using seasonally modulated ENSO forcing forecasts. Geophys. Res. Lett. 46, 9980–9990 (2019).
Chen, H.-C. & Jin, F.-F. Simulations of ENSO phase-locking in CMIP5 and CMIP6. J. Clim. 34, 5135–5149 (2021).
Harrell, F. E. Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis (Springer, 2001).
Vimont, D. J. Analysis of the Atlantic meridional mode using linear inverse modeling: seasonality and regional influences. J. Clim. 25, 1194–1212 (2012).
Zhao, Y., Jin, Y., Li, J. & Capotondi, A. The role of extratropical Pacific in crossing ENSO spring predictability barrier. Geophys. Res. Lett. 49, e2022GL099488 (2022).
Rayner, N. A. et al. Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century. J. Geophys. Res. Atmos. 108, 4407 (2003).
Huang, B. et al. Extended reconstructed sea surface temperature, version 5 (ERSSTv5): upgrades, validations, and intercomparisons. J. Clim. 30, 8179–8205 (2017).
Hirahara, S., Ishii, M. & Fukuda, Y. Centennial-scale sea surface temperature analysis and its uncertainty. J. Clim. 27, 57–75 (2014).
Köhl, A. Evaluating the GECCO3 1948–2018 ocean synthesis – a configuration for initializing the MPI-ESM climate model. Q. J. R. Meteorolog. Soc. 146, 2250–2273 (2020).
Behringer, D. & Xue, Y. Evaluation of the global ocean data assimilation system at NCEP: the Pacific Ocean. In Proc. Eighth Symposium on Integrated Observing and Assimilation Systems for Atmosphere, Oceans, and Land Surface AMS 84th Annual Meeting (AMS, 2004).
Zuo, H., Balmaseda, M. A., Tietsche, S., Mogensen, K. & Mayer, M. The ECMWF operational ensemble reanalysis–analysis system for ocean and sea ice: a description of the system and assessment. Ocean Sci. 15, 779–808 (2019).
de Boisséson, E., Balmaseda, M. A. & Mayer, M. Ocean heat content variability in an ensemble of twentieth century ocean reanalyses. Clim. Dyn. 50, 3783–3798 (2018).
Yin, Y., Alves, O. & Oke, P. R. An ensemble ocean data assimilation system for seasonal prediction. Mon. Wea. Rev. 139, 786–808 (2011).
Carton, J. A. & Giese, B. S. A reanalysis of ocean climate using Simple Ocean Data Assimilation (SODA). Mon. Wea. Rev. 136, 2999–3017 (2008).
Hersbach, H. et al. The ERA5 global reanalysis. Q. J. R. Meteorolog. Soc. 146, 1999–2049 (2020).
Xie, P. P. & Arkin, P. A. Global precipitation: a 17-year monthly analysis based on gauge observations, satellite estimates, and numerical model outputs. Bull. Amer. Meteor. Soc. 78, 2539–2558 (1997).
Kirtman, B. P. et al. The North American Multimodel Ensemble: phase-1 seasonal-to-interannual prediction; phase-2 toward developing intraseasonal predictio. Bull. Amer. Meteor. Soc. 95, 585–601 (2014).
Mu, B., Qin, B. & Yuan, S. ENSO-ASC 1.0.0: ENSO deep learning forecast model with a multivariate air–sea coupler. Geosci. Model Dev. 14, 6977–6999 (2021).
Gao, C., Zhou, L. & Zhang, R.-H. A transformer-based deep learning model for successful predictions of the 2021 second-year La Niña condition. Geophys. Res. Lett. 50, e2023GL104034 (2023).
Kay, J. E. et al. The Community Earth System Model (CESM) Large Ensemble Project: a community resource for studying climate change in the presence of internal climate variability. Bull. Am. Meteorol. Soc. 96, 1333–1349 (2015).
Rodgers, K. B. et al. Ubiquity of human-induced changes in climate variability. Earth Syst. Dyn. 12, 1393–1411 (2021).
Shiogama, H. et al. MIROC6 Large Ensemble (MIROC6-LE): experimental design and initial analyses. Earth Syst. Dyn. 14, 1107–1124 (2023).
Maher, N. et al. The Max Planck Institute Grand Ensemble: enabling the exploration of climate system variability. J. Adv. Model. Earth Syst. 11, 2050–2069 (2019).
Brady, R. X. & Spring, A. climpred: verification of weather and climate forecasts. J. Open Source Softw. 6, 2781 (2021).
Zhang, Z., Ren, B. & Zheng, J. A unified complex index to characterize two types of ENSO simultaneously. Sci. Rep. 9, 8373 (2019).
Stein, K., Timmermann, A., Schneider, N., Jin, F.-F. & Stuecker, M. F. ENSO seasonal synchronization theory. J. Climate 27, 5285–5310 (2014).
Levine, A. F. Z. & McPhaden, M. J. The annual cycle in ENSO growth rate as a cause of the spring predictability barrier. Geophys. Res. Lett. 42, 5034–5041 (2015).
Zhao, S., Jin, F.-F. & Stuecker, M. F. Understanding lead times of warm water volumes to ENSO sea surface temperature anomalies. Geophys. Res. Lett. 48, e2021GL094366 (2021).
Okumura, Y. M., Ohba, M., Deser, C. & Ueda, H. A proposed mechanism for the asymmetric duration of El Niño and La Niña. J. Clim. 24, 3822–3829 (2011).
DiNezio, P. N. & Deser, C. Nonlinear controls on the persistence of La Niña. J. Climate 27, 7335–7355 (2014).
Iwakiri, T. & Watanabe, M. Mechanisms linking multi-year La Niña with preceding strong El Niño. Sci. Rep. 11, 17465 (2021).
Iwakiri, T. & Watanabe, M. Multiyear ENSO dynamics as revealed in observations, climate model simulations, and the linear recharge oscillator. J. Clim. 35, 7625–7642 (2022).
Kim, J.-W., Yu, J.-Y. & Tian, B. Overemphasized role of preceding strong El Niño in generating multi-year La Niña events. Nat. Commun. 14, 6790 (2023).
Kim, J.-W. & Yu, J.-Y. Single- and multi-year ENSO events controlled by pantropical climate interactions. npj Clim. Atmos. Sci. 5, 88 (2022).
Chen, H.-C., Jin, F.-F. & Jiang, L. The phase-locking of Tropical North Atlantic and the contribution of ENSO. Geophys. Res. Lett. 48, e2021GL095610 (2021).
Jiang, F. et al. Resolving the Tropical Pacific/Atlantic interaction vonundrum. Geophys. Res. Lett. 50, e2023GL103777 (2023).
Trenberth, K. E. The definition of El Niño. Bull. Am. Meteorol. Soc. 78, 2771–2778 (1997).
Enfield, D. B., Mestas-Nuñez, A. M., Mayer, D. A. & Cid-Serrano, L. How ubiquitous is the dipole relationship in tropical Atlantic sea surface temperatures? J. Geophys. Res. Oceans 104, 7841–7848 (1999).
Elson, P. et al. SciTools/cartopy v.0.22.0. Zenodo https://doi.org/10.5281/zenodo.1182735 (2023).
Zhao, S. Source data for ‘Explainable El Niño predictability from climate mode interactions’. Zenodo https://doi.org/10.5281/zenodo.10951443 (2024).
Zhao, S. Extended nonlinear recharge oscillator (XRO) model for ‘Explainable El Niño predictability from climate mode interactions’. Zenodo https://doi.org/10.5281/zenodo.10681114 (2024).