1. McPhaden, M. J. Genesis and evolution of the 1997–98 El Niño. Science 283, 950–954 (1999).

2. Maloney, E. D. & Hartmann, D. L. Modulation of eastern North Pacific hurricanes by the Madden–Julian oscillation. J. Clim. 13, 1451–1460 (2000).

3. Klotzbach, P. J. & Oliver, E. C. Modulation of Atlantic basin tropical cyclone activity by the Madden–Julian oscillation (MJO) from 1905 to 2011. J. Clim. 28, 204–217 (2015).

4. Joseph, S., Sahai, A. & Goswami, B. Eastward propagating MJO during boreal summer and Indian monsoon droughts. Clim. Dyn. 32, 1139–1153 (2009).

5. Jia, X., Chen, L., Ren, F. & Li, C. Impacts of the MJO on winter rainfall and circulation in China. Adv. Atmos. Sci. 28, 521–533 (2011).

6. Wheeler, M. C., Hendon, H. H., Cleland, S., Meinke, H. & Donald, A. Impacts of the Madden–Julian oscillation on Australian rainfall and circulation. J. Clim. 22, 1482–1498 (2009).

7. Pohl, B. & Camberlin, P. Influence of the Madden–Julian oscillation on East African rainfall. I: intraseasonal variability and regional dependency. Q. J. R. Meteorol. Soc. 132, 2521–2539 (2006).

8. Lorenz, D. J. & Hartmann, D. L. The effect of the MJO on the North American monsoon. J. Clim. 19, 333–343 (2006).

9. Grimm, A. M. Madden–Julian Oscillation impacts on South American summer monsoon season: precipitation anomalies, extreme events, teleconnections, and role in the MJO cycle. Clim. Dyn. 53, 1–26 (2019).

10. Carvalho, L. M. V., Jones, C. & Liebmann, B. The South Atlantic convergence zone: intensity, form, persistence, and relationships with intraseasonal to interannual activity and extreme rainfall. J. Clim. 17, 88–108 (2004).

11. Weller, E. et al. Human-caused Indo-Pacific warm pool expansion. Sci. Adv. 2, e1501719 (2016).

12. Lazo, J. K., Lawson, M., Larsen, P. H. & Waldman, D. M. US economic sensitivity to weather variability. Bull. Am. Meteorol. Soc. 92, 709–720 (2011).

13. Bertrand, J.-L. & Brusset, X. Managing the financial consequences of weather variability. J. Asset Manag. 19, 301–315 (2018).

14. Kessler, W. S. EOF representations of the Madden–Julian oscillation and its connection with ENSO. J. Clim. 14, 3055–3061 (2001).

15. Zhang, C. Madden–Julian oscillation: bridging weather and climate. Bull. Am. Meteorol. Soc. 94, 1849–1870 (2013).

16. Cassou, C. Intraseasonal interaction between the Madden–Julian Oscillation and the North Atlantic Oscillation. Nature 455, 523–527 (2008).

17. Stan, C. et al. Review of tropical-extratropical teleconnections on intraseasonal time scales. Rev. Geophys. 55, 902–937 (2017).

18. Garfinkel, C. I., Feldstein, S. B., Waugh, D. W., Yoo, C. & Lee, S. Observed connection between stratospheric sudden warmings and the Madden–Julian Oscillation. Geophys. Res. Lett. 39, L18807 (2012).

19. Madden, R. A. & Julian, P. R. Observations of the 40–50-day tropical oscillation—a review. Mon. Weath. Rev. 122, 814–837 (1994).

20. Maloney, E. D., Adames, Á. F. & Bui, H. X. Madden–Julian oscillation changes under anthropogenic warming. Nat. Clim. Change 9, 26–33 (2019).

21. Adames, Á. F., Kim, D., Sobel, A. H., Del Genio, A. & Wu, J. Changes in the structure and propagation of the MJO with increasing CO 2 . J. Adv. Model. Earth Syst. 9, 1251–1268 (2017).

22. Oliver, E. C. & Thompson, K. R. A reconstruction of Madden–Julian Oscillation variability from 1905 to 2008. J. Clim. 25, 1996–2019 (2012).

23. Oliver, E. C. Blind use of reanalysis data: apparent trends in Madden–Julian Oscillation activity driven by observational changes. Int. J. Climatol. 36, 3458–3468 (2016).

24. Jones, C. & Carvalho, L. M. V. Changes in the activity of the Madden–Julian Oscillation during 1958–2004. J. Clim. 19, 6353–6370 (2006).

25. Pohl, B. & Matthews, A. J. Observed changes in the lifetime and amplitude of the Madden–Julian oscillation associated with interannual ENSO sea surface temperature anomalies. J. Clim. 20, 2659–2674 (2007).

26. Slingo, J. M., Rowell, D. P., Sperber, K. R. & Nortley, E. On the predictability of the interannual behaviour of the Madden–Julian Oscillation and its relationship with El Nino. Q. J. R. Meteorol. Soc. 125, 583–609 (1999).

27. Arnold, N. P., Kuang, Z. & Tziperman, E. Enhanced MJO-like variability at high SST. J. Clim. 26, 988–1001 (2013).

28. Zhang, C. & Ling, J. Barrier effect of the Indo-Pacific Maritime Continent on the MJO: perspectives from tracking MJO precipitation. J. Clim. 30, 3439–3459 (2017).

29. Foltz, G. R. & McPhaden, M. J. The 30–70 day oscillations in the tropical Atlantic. Geophys. Res. Lett. 31, L15205 (2004).

30. Wheeler, M. C. & Hendon, H. H. An all-season real-time multivariate MJO index: development of an index for monitoring and prediction. Mon. Weath. Rev. 132, 1917–1932 (2004).

31. Yoo, C., Feldstein, S. & Lee, S. The impact of the Madden–Julian Oscillation trend on the Arctic amplification of surface air temperature during the 1979–2008 boreal winter. Geophys. Res. Lett. 38, L24804 (2011).

32. Song, E. J. & Seo, K. H. Past-and present-day Madden–Julian Oscillation in CNRM-CM5. Geophys. Res. Lett. 43, 4042–4048 (2016).

33. Roxy, M. Sensitivity of precipitation to sea surface temperature over the tropical summer monsoon region—and its quantification. Clim. Dyn. 43, 1159–1169 (2014).

34. Cravatte, S., Delcroix, T., Zhang, D., McPhaden, M. & Leloup, J. Observed freshening and warming of the western Pacific warm pool. Clim. Dyn. 33, 565–589 (2009).

35. Dong, L. & McPhaden, M. J. The role of external forcing and internal variability in regulating global mean surface temperatures on decadal timescales. Environ. Res. Lett. 12, 034011 (2017).

36. Suematsu, T. & Miura, H. Zonal SST difference as a potential environmental factor supporting the longevity of the Madden–Julian Oscillation. J. Clim. 31, 7549–7564 (2018).

37. Sobel, A., Wang, S. & Kim, D. Moist static energy budget of the MJO during DYNAMO. J. Atmos. Sci. 71, 4276–4291 (2014).

38. Kim, D., Kug, J.-S. & Sobel, A. H. Propagating versus nonpropagating Madden–Julian Oscillation events. J. Clim. 27, 111–125 (2014).

39. Gonzalez, A. O. & Jiang, X. Winter mean lower tropospheric moisture over the Maritime Continent as a climate model diagnostic metric for the propagation of the Madden–Julian oscillation. Geophys. Res. Lett. 44, 2588–2596 (2017).

40. Tokinaga, H., Xie, S.-P., Deser, C., Kosaka, Y. & Okumura, Y. M. Slowdown of the Walker circulation driven by tropical Indo-Pacific warming. Nature 491, 439–443 (2012).

41. Hermes, J. C. et al. A sustained ocean observing system in the Indian Ocean for climate related scientific knowledge and societal needs. Front. Mar. Sci. 6, 355 (2019).

42. Subramanian, A. et al. Ocean observations to improve our understanding, modeling, and forecasting of subseasonal-to-seasonal variability. Front. Mar. Sci. 6, 427 (2019).

43. Vitart, F. & Robertson, A. W. The sub-seasonal to seasonal prediction project (S2S) and the prediction of extreme events. npj Clim. Atmos. Sci. 1, 3 (2018).

44. Straub, K. H. MJO initiation in the real-time multivariate MJO index. J. Clim. 26, 1130–1151 (2013).

45. Liu, P. et al. A revised real-time multivariate MJO index. Mon. Weath. Rev. 144, 627–642 (2016).

46. Wolding, B. O. & Maloney, E. D. Objective diagnostics and the Madden–Julian oscillation. Part II: application to moist static energy and moisture budgets. J. Clim. 28, 7786–7808 (2015).

47. Ventrice, M. J. et al. A modified multivariate Madden–Julian oscillation index using velocity potential. Mon. Weath. Rev. 141, 4197–4210 (2013).

48. Hendon, H. H., Wheeler, M. C. & Zhang, C. Seasonal dependence of the MJO–ENSO relationship. J. Clim. 20, 531–543 (2007).

49. Schreck, C., Lee, H.-T. & Knapp, K. HIRS outgoing longwave radiation—daily climate data record: application toward identifying tropical subseasonal variability. Remote Sens. 10, 1325 (2018).

50. Kikuchi, K., Wang, B. & Kajikawa, Y. Bimodal representation of the tropical intraseasonal oscillation. Clim. Dyn. 38, 1989–2000 (2012).

51. Seo, K.-H. & Kumar, A. The onset and life span of the Madden–Julian oscillation. Theor. Appl. Climatol. 94, 13–24 (2008).

52. Wheeler, M. & Kiladis, G. N. Convectively coupled equatorial waves: analysis of clouds and temperature in the wavenumber–frequency domain. J. Atmos. Sci. 56, 374–399 (1999).

53. Roundy, P. E., Schreck, C. J. III & Janiga, M. A. Contributions of convectively coupled equatorial Rossby waves and Kelvin waves to the real-time multivariate MJO indices. Mon. Weath. Rev. 137, 469–478 (2009).

54. Zeileis, A., Kleiber, C., Krämer, W. & Hornik, K. Testing and dating of structural changes in practice. Comput. Stat. Data Anal. 44, 109–123 (2003).

55. Bai, J. & Perron, P. Computation and analysis of multiple structural change models. J. Appl. Econ. 18, 1–22 (2003).

56. Schwarz, G. Estimating the dimension of a model. Ann. Stat. 6, 461–464 (1978).

57. Hirsch, R. M., Slack, J. R. & Smith, R. A. Techniques of trend analysis for monthly water quality data. Wat. Resour. Res. 18, 107–121 (1982).

58. Cohen, P., West, S. G. & Aiken, L. S. Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences (Psychology Press, 2014).

59. Kendall, M. G. Rank Correlation Methods 2 edn (C. Griffin, 1948).