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Switch Between El Nino and La Nina is Caused by Subsurface Ocean Waves Likely Driven by Lunar Tidal Forcing


The El Nino-Southern Oscillation (ENSO) is the dominant interannual variability of Earth’s climate system, and strongly modulates global temperature, precipitation, atmospheric circulation, tropical cyclones and other extreme events. However, forecasting ENSO is one of the most difficult problems in climate sciences affecting both interannual climate prediction and decadal prediction of near-term global climate change. The key question is what cause the switch between El Nino and La Nina. For the past 30 years, ENSO forecasts have been limited to short lead times after ENSO sea surface temperature (SST) anomaly has already developed, but unable to predict the switch between El Nino and La Nina. Here, we demonstrate that the switch between El Nino and La Nina is caused by a subsurface ocean wave propagating from western Pacific to central and eastern Pacific and then triggering development of SST anomaly. This is based on analysis of all ENSO events in the past 136 years using multiple long-term observational datasets. The wave’s slow phase speed and decoupling from atmosphere indicate that it is a forced wave. Further analysis of Earth’s angular momentum budget and NASA’s Apollo Landing Mirror Experiment suggests that the subsurface wave is likely driven by lunar tidal gravitational force.


The 1876–1877 eastern hemisphere drought and resultant Great Famine caused a death toll of 17 million people in China, India, Indonesia, Australia and South Africa, and prompted the discovery of ENSO1,2,3. ENSO is a 3–6 year oscillation of Earth’s climate system, which is the first principle component of global monthly sea surface temperature anomaly, and contributes 18% of the total variance4,5,6,7,8. ENSO strongly modulates global temperature9, precipitation10, droughts11, tropical cyclones12, tornadoes13, extratropical cyclones14 and other extreme events15, and also plays an important role in global warming projections16,17,18.

However, forecasting ENSO is one of the most difficult problems in atmospheric sciences19,20,21,22. The long-lasting unanswered question is what cause the switch between El Nino and La Nina. For the past 30 years, ENSO forecasts have been limited to short lead time of 6–9 months after ENSO sea surface temperature anomaly has already developed (Supplementary Fig. 1). Most of the ENSO forecast models cannot predict the switch between El Nino and La Nina19,20,21,22 which requires a lead time of 12 months or longer (Supplementary Fig. 2). This is the case not only for statistical models, but also for most of the dynamical coupled general circulation models (CGCMs). State-of-the-art CGCMs have substantial difficulty in simulating the correct oscillation period and amplitude of ENSO16,23, which is connected to their biases in simulating tropical mean state and ocean-atmosphere feedbacks24,25. This affects not only their ENSO predictions, but also their decadal to multi-decadal predictions of near-term global climate change26,27,28,29,30.

The existing ENSO theories can be categorized into six groups31,32,33 (Supplementary Fig. 3) including (1) slow coupled mode theories3,34,35,36, (2) stochastic forcing theories37,38, (3) recharge oscillator theory39, (4) delayed oscillator theory40,41,42, (5) advective-reflective oscillator theory43, and (6) western Pacific oscillator theory44. Ocean-atmosphere feedback mechanisms are emphasized by the first three theories, but coupled climate models with ocean-atmosphere feedbacks still have difficulty in simulating ENSO and are quite sensitive to different physical parameterizations. Free ocean waves, including equatorial Kelvin and Rossby waves, are emphasized by the other three theories, and have been found in both observations45,46,47,48,49 and models41,50,51,52,53,54. The phase speeds of the free Kelvin waves are generally 2–3 m/s, while those of the free Rossby waves are 0.5–1 m/s. These waves are driven by anomalous westerly or easterly winds55, which are often associated with the intraseasonal Madden-Julian Oscillation (MJO)56,57,58,59, and show clear horizontal and vertical propagations associated with different types of El Nino60. However, the propagation speeds of free ocean waves are too fast to explain the 3–6 year time-scale of ENSO.

Sea surface state variables, including sea surface temperature (SST), sea level pressure (SLP), surface winds and sea surface height (SSH), are the predictors generally used by statistical ENSO models, and also serve as initial fields for dynamical ENSO models. However, during the transition phase between El Nino and La Nina, which is often called “neutral phase”, the SST, SLP, SSH and surface wind anomalies are very weak, and cannot provide good predictors for long-lead ENSO prediction.

Here, we demonstrate that the switch between El Nino and La Nina is caused by a subsurface ocean wave propagating from western Pacific to central/eastern Pacific, and then trigger the development of sea surface temperature anomaly there. This is based on analysis of all ENSO events in the past 136 years using multiple long-term observational datasets. See Methods section for detailed information about the datasets and methods.

The Subsurface Ocean Wave Associated with ENSO Lifecycle

Supplementary Fig. 4 shows vertical cross-section of climatological mean ocean subsurface temperature along the equator averaged between 5N-5S for three observational datasets: (a) TAO buoy array for 23 years (1993–2015), (b) UKMO ocean analysis for 61 years (1955–2015), and (c) SODA ocean reanalysis for 133 years (1880–2012). All datasets show the well-defined temperature contrast between western Pacific warm pool and eastern Pacific cold tongue. The white line is the climatological 23.5 °C line, which is a good representation of thermocline. Supplementary Fig. 5 shows the climatological mean vertical velocity along the equator. Because the equatorial upwelling is driven by the trade winds, there is strong upwelling to the east of dateline from the thermocline to 10 m. The upwelling to the west of dateline is much weaker.

Figure 1 illustrates the lag-correlation of UKMO ocean analysis subsurface temperature with Nino3.4 SST from (a) −24 months (La Nina) to (h) −3 months (3 months before El Nino) for all ENSO events in 61 years from 1955–2015. Figure 1 demonstrates three key points. First, there is a clear subsurface ocean wave propagating eastward along the thermocline from western Pacific to central and eastern Pacific (Fig. 1A–F). The warm temperature anomaly already starts off from western Pacific at the peak of La Nina (Fig. 1A), and quickly passes the dateline within 3 months when the surface temperature in central and eastern Pacific still shows significant cold anomaly of La Nina (Fig. 1B). Secondly, as soon as the ocean wave passes the dateline and enters the eastern Pacific (Fig. 1B), the strong mean-state upwelling in eastern Pacific starts to advect the warm temperature anomaly from the thermocline (at 30–120 meters depth in the eastern Pacific) towards the surface, with a vertical speed of 2–10 meters per month (Supplementary Fig. 5). The warm advection starts earlier in central Pacific (Fig. 1B), but the thermocline is deeper there and it takes more time for the warm anomaly to reach the surface. The warm advection starts much later in far east Pacific close to the coast of South America (Fig. 1F), but the thermocline is much shallower there and the warm anomaly can quickly reach the surface. This warm advection likely contributes to the decay of La Nina from −21 months to −12 months (Fig. 1B–E), and then initiates the warm SST anomalies and triggers the Bjerknes feedback, leading to development of El Nino at −6 months to −3 months (Fig. 1G,H). The corresponding amplitude of temperature variations is above 1 °C (not shown), which is similar to the amplitude in the delayed oscillator model41, and thus sufficient to cause the switch. Thirdly, during the neutral transition phase at −12 months and −9 months (Fig. 1E,F), there is no significant surface temperature anomaly, but the subsurface ocean wave anomaly is highly significant and provides an excellent predictor for ENSO forecast.

Figure 1
figure 1

Eastward propagation of ocean subsurface wave leading to switch from La Nina to El Nino. Shadings show lag-correlation of UKMO ocean analysis subsurface temperature along the equator (5N-5S) with Nino3.4 SST from (A) −24 months to (H) −3 months for all ENSO events in 61 years from 1955–2015. Black stars denote the grids with lag-correlation above 95% confidence level. The white dashed line is the climatological 23.5 °C line from Supplementary Fig. 4b.

The switch from El Nino to La Nina is shown in Fig. 2. Again, at the peak of El Nino when the entire central and eastern Pacific are occupied by significant warm surface temperature anomalies (Fig. 2A), cold subsurface ocean wave has already started off from western Pacific. When the surface temperature anomalies have disappeared during the neutral transition phase from +9 months (Fig. 2D) to +15 months (Fig. 2F), cold subsurface ocean wave anomaly is highly significant, providing important predictors for the forthcoming La Nina.

Figure 2
figure 2

Same as Fig. 1 but for switch from El Nino to La Nina for (A) 0 month (El Nino) to (H) +21 months after El Nino.

Similar results are obtained from 33 years (1993–2015) of raw TAO buoy data (Supplementary Figs 6 and 7). Extending our analysis to all ENSO events in 133 years (1880–2012) using SODA ocean reanalysis, which assimilates all available ocean subsurface temperature observations, also reveals the same results (Supplementary Figs 8 and 9). Therefore, the eastward propagation of subsurface ocean wave associated with ENSO lifecycle is a highly robust physical phenomena.

What Drives the Subsurface Ocean Wave?

There are three types of ocean waves: free ocean wave, free ocean-atmosphere coupled wave, and forced ocean wave. First, we determine if the observed wave is a free ocean wave by calculating the phase speed of propagation. Figure 3 provides a summary of wave propagation along the thermocline for all three observational datasets. All three datasets consistently demonstrate an eastward propagation with a phase speed of 0.2–0.3 m/s, which is much slower than the phase speeds of free ocean waves40. The free Kelvin waves driven by westerly wind bursts associated with the MJO generally have a phase speed of 2–3 m/s56,57,58,59, which is an order of magnitude larger than the phase speed of the wave found here. Therefore, the observed wave is not a free ocean wave.

Figure 3
figure 3

Eastward propagation of ocean subsurface wave along the thermocline associated with ENSO lifecycle in three observational datasets. (A) TAO buoy array for 23 years (1993–2015), (B) UKMO ocean analysis for 61 years (1955–2015), and (C) SODA ocean reanalysis for 133 years (1880–2012). Shadings show lag-correlation with Nino3.4 SST for ocean temperature averaged between 5N-5S along the thermocline (climatological 23.5 °C depth). Black stars denote the grids with lag-correlation above 95% confidence level. White dashed lines are the 0.26 m/s phase speed line.

The subsurface ocean wave is not likely a free ocean-atmosphere coupled slow mode because during the neutral transition phases (Figs 1E–F and 2D–F), there is no significant SST anomaly and the strong subsurface ocean wave is totally decoupled from the atmosphere. During these periods, the wave still keeps the slow phase speed of 0.2–0.3 m/s (Fig. 3) and thus is not a free wave emanating from the source region.

The third possibility is forced ocean wave. The major external forcing for ocean is the tidal gravitational force. The thermocline is associated with the strongest vertical temperature gradient and thus tend to show the largest temperature anomaly when driven by tidal vertical motion, which is consistent with the depth of the subsurface ocean wave. The moon’s revolution around the Earth is from the west to the east in the same direction as the Earth’s rotation, which is consistent with the eastward propagation of the subsurface ocean wave. Connection between the observed subsurface wave with tide is also supported by the evolution of zonal mean ocean temperature associated with ENSO lifecycle (Supplementary Fig. 10), which can be compared with subsurface wave propagation along the equator (Fig. 1). When the warm subsurface wave propagates from western Pacific to central Pacific (Fig. 1A–D), zonal mean temperature shows clear warm anomaly at the 100–300 m depth of the wave (Supplementary Fig. 10a–d). When the subsurface wave rises up in eastern Pacific and triggers the El Nino (Fig. 1E–H), zonal mean temperature shows clear process that the wave breaks through the cold temperature anomaly of La Nina, and pushes it away from the equator in both hemispheres (Supplementary Fig. 10e–h). SODA ocean reanalysis shows similar results for all ENSO events in 133 years (Supplementary Fig. 11). The zonal mean structure is similar to the lunar semidiurnal tides in the ocean61 and atmosphere62. Because the tidal force at the equator doubles that at the pole, the largest amplitude occurs in the tropics. For a vertically propagating gravity wave, upward (downward) phase propagation implies downward (upward) energy dispersion. For the lunar atmospheric tide, the forcing is strongest at the Earth’s surface where rising sea level forces the atmosphere, so tidal energy disperses upward and phase propagates downward62. In contrast, for the lunar oceanic tide, the forcing is strongest at the ocean surface because tidal force increases with the distance to the center of the Earth and vertical displacement is largest at the top of tidal bulge63, so tidal energy disperses downward and phase propagates upward.

Is there lunar tidal forcing at ENSO’s time-scale? The three commonly used ENSO indices consistently demonstrate that the generally-thought wide spectral peak of ENSO between 3–7 years in fact consists of two main spectral peaks at 3 years and 6 years, respectively (Supplementary Fig. 12). Lunar tidal gravitational force calculated from NASA Apollo Landing Mirror Experiment64,65 and Earth’s angular momentum budget consistently show two sharp peaks at 6 years and 9 years, respectively (Supplementary Fig. 13). The western Pacific subsurface temperature at the thermocline depth also demonstrates sharp 6-year and 9-year peaks (Supplementary Fig. 14), suggesting a strong link between the lunar tidal force and the Earth’s ocean subsurface temperature. The 6-year peak of lunar tidal force matches very well with the 6-year component of ENSO. Lag-correlations between the 6-year component of lunar tidal forcing with equatorial ocean subsurface temperature demonstrate clearly the subsurface ocean wave propagating from western Pacific to central and eastern Pacific and triggering SST anomaly there, suggesting that the 6-year component of lunar tidal forcing drives the 6-year component of ENSO (Supplementary Figs 15 and 16).

The 6-year and 9-year peaks of lunar tidal forcing are key lunar tidal constituents at the interannual time-scale65,66,67, although the 6-year component did not draw much attention in research. The three different lunar months: draconic (nodal passage: 27.212208 days), sidereal (inertial space period: 27.321661 days), and anomalistic (perigee to perigee: 27.554551 days) combine to give periods of 6.00 years, 8.85 years and 18.6 years65,66,67. Global mean surface temperature demonstrates 6-year and 9-year oscillations, which have been proposed to be driven by lunar tidal forcing67,68. The 3-year component of ENSO may be generated by the sub-harmonics of the 6-year tidal forcing, or the interactions of 6-year and 9-year forcings with seasonal cycle and other high-frequency oscillations.

The observed oscillation periods of ENSO are irregular, which are known to be affected by the background state associated with longer-period oscillations and ocean-atmosphere feedback23. The tidal forcing in real world is also “irregular” because it is contributed by many tidal constituents. For example, in order to predict the day-to-day sea level variations along the coast, at least 10 dominant tidal constituents in the diurnal, semidiurnal and quarter-diurnal bands are needed in the global tidal models69. Another example is that the interannual lunar tidal forcing is dominated by the 6-year component between the 1920s and 1940s, but dominated by the 9-year component during other time periods, which coincide well with similar oscillations in observed global mean surface temperature67. Therefore, tidal forcing may also contribute to the observed irregularity of ENSO. In addition, after the El Nino has developed (Figs 1G,H and 2A), equatorial upwelling driven by tidal forcing may affect the amplitude of El Nino.

Our key findings are summarized schematically in Fig. 4. We have demonstrated highly robust evidence that the switch between El Nino and La Nina is caused by an ocean subsurface wave propagating along thermocline from western Pacific to central and eastern Pacific, and then triggering the development of SST anomaly there. Our findings suggest two possible ways to improve the current ENSO forecasts: (1) Adding the subsurface ocean wave to statistical ENSO forecast models and improving its representation in CGCMs, which may lead to an improvement of the 12-month ENSO forecast. Right now, none of the statistical models considers the subsurface ocean wave. In fact, the only two ENSO forecast models that can make good 12-month forecast, the NASA GMAO model and GFDL FLOR model (Supplementary Fig. 2), are assimilating carefully subsurface temperature. (2) Adding lunar tidal forcing to statistical models and CGCMs may provide important long-range predictability. Currently, the ocean-atmosphere coupled runs of climate models, such as the IPCC models historical runs and projection runs23,70, are called “free runs” and are not expected to capture the timing of ENSO events in the real world. Adding lunar tidal forcing may help to simulate the correct timing of ENSO events, in addition to improving the simulated oscillation period and amplitude of ENSO. Recently, the ocean modelling community show strong interest in lunar tidal forcing because there are more and more evidences that tidal mixing plays a key role in global ocean circulation71,72,73. Parameterizations of diurnal and semidiurnal tidal mixing have been implemented into several OGCMs such as the GFDL MOM74, HYCOM75, and MIROC76. However, for simulating the interannual tidal components related to ENSO, explicit modelling of time-varying gravitational field is needed. An exciting new progress is that the MPI OM group has developed a tidal forcing option to include explicit time-varying gravitational forcing from the Sun and Moon including the seasonal, annual, interannual and inter-decadal tidal cycles77. For each time step of simulation, the actual positions of the Sun and Moon are calculated using the semi-analytic planetary theory Variations Seculaires des Orbites Planetaires (VSOP87)78, and the associated gravitational forcing is determined. This tidal forcing option has not been used in the MPI model’s climate predictions79 or IPCC runs80. Nevertheless, the MPI model has demonstrated that it is possible to add to GCMs explicit time-varying gravitational forcing from the Sun and Moon. The VSOP87 source code is available online (, and we hope that the climate modelling community could install it to the climate models and conduct long-term coupled ocean-atmosphere experiments, which may provide insights on the relationship between tidal forcing and ENSO as suggested by the our observational study. If the model experiments confirm that lunar tidal forcing drives the observed subsurface ocean waves leading to the switch between El Nino and La Nina, this new physics will provide valuable long-range predictability, and help to improve the ENSO forecasts and decadal to multi-decadal predictions of global climate change26,27,28,29,30.

Figure 4
figure 4

Schematic depiction of the physical mechanisms leading to the switch between El Nino and La Nina.


Datasets used in this study are listed in Table 1. The main ENSO index used in this study is Nino3.4 SST from ERSST dataset. Linear trend and composite seasonal cycle are first removed from all datasets. Maximum entropy spectrum is calculated following Press and Flannery81. The anomalies are then filtered with a 3–6 year butterworth filter (Murakami)82. Lag-correlation is calculated with the ENSO index. Statistical significance is evaluated following Oort and Yienger83.

Table 1 Datasets used in this study.

The anomalies are also filtered with a 6-year butterworth filter and lag-correlation is calculated with the lunar tidal gravitational force. Lunar tidal gravitational force is calculated from two sources. The first is direct calculation from Moon-Earth distance measured by NASA’s Apollo Landing Mirror experiment from 5 mirrors on the Moon deployed by Apollo 11 and others. The second is by calculating the angular momentum of whole Earth system, which is anti-correlated with lunar tidal friction. We calculated the whole atmospheric angular momentum using 6-hourly NCEP reanalysis upper air winds for all levels around the globe for 69 years (1948–2016) following Weickmann and Berry84, and solid Earth angular momentum from Earth’s rotation speed (length of the day measurement) following Rosen et al.85.

Data Availability

Datasets used in this study are from NOAA PMEL TAO Buoy Website, NOAA ESRL climate data archive and NCAR Research Data Archive.


  1. Blanford, H. F. 1884: On the connexion of Himalayan snowfall and seasons of drought in India. Proc. Roy. Soc. London 37, 3–22 (1884).

    Article  Google Scholar 

  2. Walker, G. T. Correlation in seasonal variations of weather. VIII: A preliminary study of world weather. Mem. Indian Meteor. Dept. 24, 75–131 (1923).

    Google Scholar 

  3. Bjerknes, J. Atmospheric teleconnections from the equatorial Pacific. Mon. Weather Rev. 97, 163172 (1969).

    Article  Google Scholar 

  4. Philander, S. G., El Niño, La Nia, and the Southern Oscillation, Academic Press, London, 289 pp (1990).

  5. Wallace, J. M. et al. On the structure and evolution of ENSO-related climate variability in the tropical Pacific: Lessons from TOGA. J. Geophys. Res. 103, 14241–14259 (1998).

    ADS  Article  Google Scholar 

  6. Deser, C., Alexander, M. A., Xie, S. P. & Phillips, A. S. Sea surface temperature variability: Patterns and mechanisms. Annu. Rev. Mar. Sci. 2, 115–143 (2010).

    ADS  Article  Google Scholar 

  7. Messie, M. & Chavez, F. Global modes of sea surface temperature variability in relation to regional climate indices. J Climate 24, 4314–4331 (2011).

    ADS  Article  Google Scholar 

  8. Trenberth, K. E. et al. Progress during TOGA in understanding and modeling global teleconnections associated with tropical sea surface temperatures. J. Geophys. Res. 103, 14 291–14 324 (1998).

    ADS  Article  Google Scholar 

  9. Halpert, M. S. & Ropelewski, C. F. Temperature patterns associated with the Southern Oscillation. J. Clim. 5, 577–593 (1992).

    ADS  Article  Google Scholar 

  10. Ropelewski, C. F. & Halpert, M. S. Global and regional scale precipitation patterns associated with the E1 Nino/Southern Oscillation. Mon. Weather Rev. 115, 1606–1626 (1987).

    ADS  Article  Google Scholar 

  11. Schubert, S. D. et al. Global meteorological drought: a synthesis of current understanding with a focus on SST drivers of precipitation deficits. J. Climate 29, 3989–4019 (2016).

    ADS  Article  Google Scholar 

  12. Landsea, C. W., El Nino-Southern Oscillation and the seasonal predictability of tropical cyclones. El Nino: Impacts of Multiscale Variability on Natural Ecosystems and Society, H. F. Diaz and V. Markgraf, Eds, Cambridge University Press, 149–181 (2000).

  13. Sparrow, K. H. & Mercer, A. E. Predictability of US tornado outbreak seasons using ENSO and northern hemisphere geopotential height variability. Geosci. Front. 7, 21–31 (2016).

    Article  Google Scholar 

  14. Eichler, T. & Higgins, W. Climatology and ENSO-related variability of North American extratropical cyclone activity. J. Climate 19, 2076–2093 (2006).

    ADS  Article  Google Scholar 

  15. Larkin, N. K. & Harrison, D. E. On the definition of El Nino and associated seasonal average U.S. weather anomalies. Geophys. Res. Lett. 32, L13705, (2005).

    ADS  Article  Google Scholar 

  16. Guilyardi, E. et al. Fourth CLIVAR workshop on the evaluation of ENSO processes in climate models: ENSO in a changing climate. Bulletin of the American Meteorological Society 97(5), 817–820 (2016).

    ADS  Article  Google Scholar 

  17. Schmidt, G. A., Shindell, D. T. & Tsigaridis, K. Reconciling warming trends. Nat. Geosci. 7, 158–160 (2014).

    ADS  CAS  Article  Google Scholar 

  18. Huber, M. & Knutti, R. Natural variability, radiative forcing and climate response in the recent hiatus reconciled. Nature Geosci. 7(9), 651–656 (2014).

    ADS  CAS  Article  Google Scholar 

  19. Barnston, A. G., Coauthors. Long-lead seasonal forecasts-Where do we stand? Bull. Amer. Meteor. Soc. 75, 2097–2114 (1994).

    Article  Google Scholar 

  20. Battisti, D. & Sarachik, E. Understanding and predicting ENSO. Rev. Geophys., 1367–1376 (1995).

  21. Barnston, A. G., He, Y. & Glantz, M. H. Predictive skill of statistical and dynamical climate models in SST forecasts during the 1997/98 El Nino episode and the 1998 La Nia onset, Bull. Amer. Meteor. Soc. 80, 217244 (1999).

    Google Scholar 

  22. 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).

    Article  Google Scholar 

  23. Lin, J. L. Interdecadal variability of ENSO in 21 IPCC AR4 coupled GCMs. Geophys. Res. Let. 34, L12702, (2007).

    ADS  Article  Google Scholar 

  24. Lin, J. L. The double-ITCZ problem in IPCC AR4 coupled GCMs: Ocean-atmosphere feedback analysis. J. Climate 20, 4497–4525 (2007).

    ADS  Article  Google Scholar 

  25. Li, G. & Xie, S. P. Tropical Biases in CMIP5 Multimodel Ensemble: The Excessive Equatorial Pacific Cold Tongue and Double ITCZ Problems. J. Climate 27, 1765–1780 (2014).

    ADS  Article  Google Scholar 

  26. Meehl, G. A., Coauthors. Decadal prediction: Can it be skillful? Bull. Amer. Meteor. Soc. 90, 1467–1485 (2009).

    Article  Google Scholar 

  27. Meehl, G. A., Hu, A. X. & Tebaldi, C. Decadal prediction in the Pacific region. J. Clim. 23, 2959–2973 (2010).

    ADS  Article  Google Scholar 

  28. Kirtman, B. et al. Near-term climate change: Projections and predictability, in Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, edited by T. F. Stocker et al. pp. 953–1028, Cambridge Univ. Press, Cambridge, U. K., and New York (2013).

  29. Marotzke, J., Coauthors. MiKlip—A National Research Project on Decadal Climate Prediction. Bull. Amer. Meteor. Soc. 97, 2379–2394 (2016).

    Article  Google Scholar 

  30. Cassou, C. et al. Decadal Climate Variability and Predictability: Challenges and Opportunities. Bulletin of the American Meteorological Society 99, 479–490 (2018).

    ADS  Article  Google Scholar 

  31. Neelin, J. D. et al. ENSO theory. J. Geophys. Res. 103(14), 26214,290 (1998).

    Google Scholar 

  32. Wang, C. & Picaut, J. Understanding ENSO physics - A review. In: Earth’s Climate: The Ocean- Atmosphere Interaction. Wang, C., Xie, S.-P. and Carton, J. A. Eds, AGU Geophysical Monograph Series, 147:21–48 (2004).

  33. Lin, J. L. Ocean-atmosphere interaction in the lifecycle of ENSO: the coupled wave oscillator. Chin Ann Math Ser B 2009 30(6), 715–28 (2009).

    MathSciNet  CAS  MATH  Article  Google Scholar 

  34. Lau, K. M. Oscillations in a simple equatorial climate system. J. Atmos. Sci. 38, 248–261 (1981).

    ADS  Article  Google Scholar 

  35. Philander, S. G. H., Yamagata, T. & Pacanowski, R. C. Unstable air-sea interactions in the tropics. J. Atmos. Sci. 41, 604–613 (1984).

    ADS  Article  Google Scholar 

  36. Gill, A. E. Elements of coupled ocean-atmosphere models for the tropics, in Coupled Ocean-AtmosphereModels, El-sevier Oceanogr. Ser., vol. 40, pp. 303–328, Elsevier, New York (1985).

    Chapter  Google Scholar 

  37. McWilliams, J. & Gent, P. A coupled air-sea model for the tropical Pacific. J. Atmos. Sci. 35, 962–989 (1978).

    ADS  Article  Google Scholar 

  38. Lau, K. M. Elements of a stochastic-dynamical theory of long-term variability of the El Niño-Southern Oscillation. J. Atmos. Sci. 42, 1552–1558 (1985).

    ADS  Article  Google Scholar 

  39. Jin, F.-F. An equatorial ocean recharge paradigm for ENSO. Part I: Conceptual model. J. Atmos. Sci. 54, 811829 (1997).

    Google Scholar 

  40. Suarez, M. J. & Schopf, P. S. A delayed action oscillator for ENSO. J. Atmos. Sci. 45, 32833287 (1988).

    Article  Google Scholar 

  41. Schopf, P. S. & Suarez, M. J. Vacillations in a coupled ocean–atmosphere model. J. Atmos. Sci. 45, 549–566 (1988).

    ADS  Article  Google Scholar 

  42. Battisti, D. S. & Hirst, A. C. Interannual variability in the tropical atmosphere-ocean model: influence of the basic state, ocean geometry and nonlineary. J. Atmos. Sci. 45, 16871712 (1989).

    Google Scholar 

  43. Picaut, J., Masia, F. & du Penhoat, Y. An advective-reflective conceptual model for the oscillatory nature of the ENSO. Science 277, 663–666 (1997).

    CAS  Article  Google Scholar 

  44. Weisberg, R. H. & Wang, C. A western Pacific oscillator paradigm for the El Nino-Southern Oscillation. Geophys. Res. Lett. 24, 779782 (1997).

    Article  Google Scholar 

  45. Delcroix, T., Boulanger, J.-P., Masia, F. & Menkes, C. GEOSAT–derived sea level and surface-current anomalies in the equatorial Pacific, during the 1986–1989 El Niño and La Niña. J. Geophys. Res. 99, 25093–25107 (1994).

    ADS  Article  Google Scholar 

  46. Kessler, W. S. & McPhaden, M. J. Oceanic Equatorial Waves and the 1991–93 El Niño. J. Clim. 8, 1757–1776 (1995).

    ADS  Article  Google Scholar 

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

    CAS  Article  PubMed  Google Scholar 

  48. Mosquera, K., Dewitte, B., Illig, S., Takahashi, K. & Garric, G. The 2002/03 El Niño: equatorial wave sequence and their impact on sea surface temperature. Journal of Geophysical Research: Oceans 118, 1–12 (2013).

    Google Scholar 

  49. Hu, S. & Fedorov, A. V. The extreme El Niño of 2015–2016: The role of westerly and easterly wind bursts, and preconditioning by the failed 2014 event. Climate Dynamics. (2017).

    ADS  Article  Google Scholar 

  50. Boulanger, J.-P., Delecluse, P., Maes, C. & Levy, C. Long equatorial waves in a high-resolution OGCM simulation of the tropical Pacific Ocean during the 1985–94 TOGA period. Mon. Wea. Rev. 125, 972–984 (1997).

    ADS  Article  Google Scholar 

  51. Dewitte, B., Reverdin, G. & Maes, C. Vertical structure of an OGCM simulation of the equatorial Pacific Ocean in 1985–94. J. Phys. Oceanogr. 29, 1542–1570 (1999).

    ADS  Article  Google Scholar 

  52. Delcroix, T., Dewitte, B., Dupenhoat., Y., Masia, F. & Picaut, J. Equatorial waves and warm pool displacements during the 1992–98 ENSO events: observations and modelling. J. Geophys. Res. 105, 26045–26062 (2000).

    ADS  Article  Google Scholar 

  53. Vialard, J. et al. Oceanic mechanisms driving the SST during the 1997–1998 El Niño. J. Phys. Oceanogr. 31, 1649–1675 (2001).

    ADS  Article  Google Scholar 

  54. Puy, M. & Coauthors, 2017: Influence of westerly wind events stochasticity on El Niño amplitude: The case of 2014 vs. 2015. Climate Dyn., (2017).

    ADS  Article  Google Scholar 

  55. Lengaigne, M., J.-P. Boulanger, C. Menkes, P. Delecluse, and J. Slingo: Westerly wind events in the tropical Pacific and their influence on the coupled ocean-atmosphere system. Earth Climate: The Ocean-Atmosphere Interaction, Geophys. Monogr., Vol. 147, Amer. Geophys. Union, 49–69 (2004).

  56. Madden, R. A. & Julian, P. R. Detection of a 40–50 day oscillation in the zonal wind in the tropical Pacific. J. Atmos. Sci. 28, 702–708 (1971).

    ADS  Article  Google Scholar 

  57. Madden, R. A. & Julian, P. R. Observations of the 40-50 day tropical oscillation: A review. Mon. Weather Rev. 112, 814–837 (1994).

    ADS  Article  Google Scholar 

  58. Zhang, C. Madden-Julian oscillation. Rev. Geophys. 43, 2003RG, (2005).

    ADS  Article  Google Scholar 

  59. Lin, J. L. et al. Tropical intraseasonal variability in 14 IPCC AR4 climate models, Part I: convective signals. J. Climate 19, 2665–2690, (2006).

    ADS  Article  Google Scholar 

  60. Zhang, Z., Ren, B. & Zheng, J. Leading modes of tropical Pacific subsurface ocean temperature and associations with two types of El Nino. Sci Rep 7, 42371, (2017).

    ADS  CAS  PubMed Central  Article  PubMed  Google Scholar 

  61. Lyard, F., Lefevre, F., Letellier, T. & Francis, O. Modelling the global ocean tides: Modern insights from FES2004. Ocean Dyn. 56(5–6), 394–415 (2006).

    ADS  Article  Google Scholar 

  62. Kohyama, T. & Wallace, J. M. Lunar gravitational atmospheric tide, surface to 50 km in a global, gridded data set. Geophys. Res. Lett. 41, 8660–8665 (2014).

    ADS  Article  Google Scholar 

  63. Knauss, J.A. Introduction to physical oceanography. Third edition. Waveland Press. 310pp.(2017).

  64. Dickey, J. O. et al. Lunar laser ranging: A continuing legacy of the Apollo program. Science, 265, 482–490.

    ADS  CAS  Article  PubMed  Google Scholar 

  65. Murphy, T. W. Lunar laser ranging: the millimeter challenge. Rep. Prog. Phys. 76, 076901, (2013).

    ADS  CAS  Article  PubMed  Google Scholar 

  66. Wood, F. J. Tidal Dynamics. Reidel, 558 pp (1986).

  67. Keeling, C. D. & Whorf, T. P. Possible forcing of global temperatures by the oceanic tides. Proc. Natl. Acad. Sci. USA 94, 8321–8328 (1997).

    ADS  CAS  Article  PubMed  PubMed Central  Google Scholar 

  68. Scafetta, N. Empirical evidence for a celestial origin of the climate oscillations and its implications. Journal of Atmospheric and Solar-Terrestrial Physics 72, 951–970 (2010).

    ADS  Article  Google Scholar 

  69. Stammer, D. et al. Accuracy assessment of global barotropic ocean tide models. Rev. Geophys. 52, 243–282, (2014).

    ADS  Article  Google Scholar 

  70. Bellenger, H., Guilyardi, E., Leloup, J., Lengaigne, M. & Vialard, J. ENSO representation in climate models: From CMIP3 to CMIP5. Climate Dyn. 42, 1999–2018 (2014).

    ADS  Article  Google Scholar 

  71. Loder, J. W. & Garrett, C. The 18.6 year cycle of sea surface temperature in shallow seas due to variations in tidal mixing. J. Geophys. Res. 83, 1967–1970 (1978).

    ADS  Article  Google Scholar 

  72. Schmittner, A., Green, J. A. M. & Wilmes, S.-B. Glacial ocean overturning intensified by tidal mixing in a global circulation model. Geophys. Res. Lett. 42, 4014–4022 (2015).

    ADS  Article  Google Scholar 

  73. Melet, A., Legg, S. & Hallberg, R. Climatic impacts of parameterized local and remote tidal mixing. J. Climate 29, 3473–3500 (2016).

    ADS  Article  Google Scholar 

  74. Schiller, A. & Fiedler, R. Explicit tidal forcing in an ocean general circulation model. Geophys. Res. Lett. 34, L03611 (2007).

    ADS  Article  Google Scholar 

  75. Arbic, B. K., Wallcraft, A. J. & Metzger, E. J. Concurrent simulation of the eddying general circulation and tides in a global ocean model. Ocean Modell. 32, 175–187 (2010).

    ADS  Article  Google Scholar 

  76. Tanaka, Y., Yasuda, I., Hasumi, H., Tatebe, H. & Osafune, S. Effects of the 18.6-year modulation of tidal mixing on the North Pacific bidecadal climate variability in a coupled climate model. J. Clim. 25(21), 7625–7642 (2012).

    ADS  Article  Google Scholar 

  77. Muller, M., Cherniawsky, J. Y., Foreman, M. G. G. & von Storch, J.-S. Global M2 internal tide and its seasonal variability from high resolution ocean circulation and tide modelling. Geophys. Res. Lett. 39, L19607, (2012).

    ADS  Article  Google Scholar 

  78. Bretagnon, P. & Francou, G. Planetary theories in rectangular and spherical variables—VSOP 87 solutions. Astron. Astrophys. 202, 309–315 (1988).

    ADS  MATH  Google Scholar 

  79. Baehr, J. et al. The prediction of surface temperature in the new seasonal prediction system based on the MPI-ESM coupled climate model. Climate Dynamics 44, 2723–2735 (2015).

    ADS  Article  Google Scholar 

  80. Müller, W. A. et al. A higher-resolution version of the Max Planck Institute Earth System Model (MPI-ESM1.2-HR). Journal of Advances in Modeling Earth Systems 10, 1383–1413 (2018).

    ADS  Article  Google Scholar 

  81. Press, W. H. & Flannery, B. P. Numerical recipes: The Art of Scientific Computing. Cambridge University Press. 781pp (1989).

  82. Murakami, M. Large-scale aspects of deep convective activity over the GATE area. Mon. Wea. Rev. 107, 994–1013 (1979).

    ADS  Article  Google Scholar 

  83. Oort, A. H. & Yienger, J. J. Observed long-term variability in the Hadley circulation and its connection to ENSO. J. Climate 9, 2751–2767 (1996).

    ADS  Article  Google Scholar 

  84. Weickmann, K. M. & Berry, E. The tropical Madden–Julian Oscillation and the global wind oscillation. Mon. Wea. Rev. 137, 1601–1613 (2009).

    ADS  Article  Google Scholar 

  85. Rosen, R. D., Salstein, D. A., Eubanks, T. M., Dickey, J. O. & Steppe, J. A. An El Nino signal in atmospheric angular momentum and Earth rotation. Science 225, 411–414 (1984).

    ADS  CAS  Article  PubMed  Google Scholar 

  86. Huang, B. et al. Further Exploring and Quantifying Uncertainties for Extended Reconstructed Sea Surface Temperature (ERSST) Version 4 (v4). Journal of Climate 29, 3119–3142 (2015).

    ADS  Article  Google Scholar 

  87. McPhaden, M. J. The Tropical Atmosphere Ocean (TAO) Array is Completed. Bulletin of the American Meteorological Society 76(5), 739–741 (1995).

    ADS  Article  Google Scholar 

  88. Good, S. A., Martin, M. J. & Rayner, N. A. EN4: quality controlled ocean temperature and salinity profiles and monthly objective analyses with uncertainty estimates. Journal of Geophysical Research: Oceans 118, 6704–6716 (2013).

    ADS  Google Scholar 

  89. Giese, B. S., Seidel, H. F., Compo, G. P. & Sardeshmukh, P. D. An ensemble of ocean reanalyses for 1815–2013 with sparse observational input. J. Geophys. Res. Oceans 121, 6891–6910 (2016).

    ADS  Article  Google Scholar 

  90. Dee, D. P. et al. The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q. J. Roy. Meteorol. Soc. 137, 553–597 (2011).

    ADS  Article  Google Scholar 

  91. Kalnay et al. The NCEP/NCAR 40-year reanalysis project. Bull. Amer. Meteor. Soc. 77, 437–470 (1996).

    Article  Google Scholar 

  92. Compo, G. P. et al. The Twentieth Century Reanalysis Project. Quarterly. J. Roy. Meteorol. Soc. 137, 1–28 (2011).

    ADS  Article  Google Scholar 

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We are indebted to the two anonymous reviewers for their constructive and stimulating comments, which helped to improve significantly the manuscript. Datasets used in this study are from NOAA PMEL TAO Buoy Website, NOAA ESRL climate data archive and NCAR Research Data Archive.

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J.L. and T.Q. jointly analysed the datasets, wrote the manuscript text and prepared all the figures.

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Correspondence to Jialin Lin.

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Lin, J., Qian, T. Switch Between El Nino and La Nina is Caused by Subsurface Ocean Waves Likely Driven by Lunar Tidal Forcing. Sci Rep 9, 13106 (2019).

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