Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Intensification of Pacific tropical instability waves over the recent three decades

Nature Climate Change volume 14, pages 163–170 (2024)Cite this article

Subjects

Abstract

Tropical instability waves (TIWs) arise from shear instabilities of equatorial Pacific Ocean currents and are important for the tropical climate and the El Niño–Southern Oscillation. Yet the long-term evolution of TIW activity under climate change remains unclear due to the difficulty in estimating equatorial current velocity. Here we use in situ, satellite altimeter and sea surface temperature observations along with a realistic eddy-resolving ocean simulation to show that TIW activity has intensified in the central equatorial Pacific at ∼12 ± 6% per decade over the recent three decades. The extended satellite data and the ocean model simulation show that the increased TIW activity is probably caused by an enhanced cross-equatorial asymmetric warming in the eastern tropical Pacific. The intensified TIWs lead to increased eddy dynamic heating effects of ∼70% since the 1990s near the equator, with implications for predicting and projecting tropical Pacific climate changes.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Sea surface temperature and velocity in the tropical Pacific.
Fig. 2: Trends of TIW intensity.
Fig. 3: Trends of EKE budget based on OFES2 simulation.
Fig. 4: Multidecadal variability of TIW intensity.
Fig. 5: Trends of the tropical Pacific climate and ocean circulation.

Similar content being viewed by others

Data availability

The NOAA OISST v.2.1 is available at https://www.ncei.noaa.gov/data/sea-surface-temperature-optimum-interpolation/v2.1/. The AVISO SSH is available at https://resources.marine.copernicus.eu/product-detail/SEALEVEL_GLO_PHY_L4_NRT_OBSERVATIONS_008_046/DATA-ACCESS. The OSCAR v.2.0 is available at https://doi.org/10.5067/OSCAR-25F20. The NOAA NBS v.2.0 wind is available at https://www.ncei.noaa.gov/products/blended-sea-winds. The TAO observations are available at https://www.pmel.noaa.gov/tao/drupal/disdel/. The drifter-derived climatological mean zonal currents are available at https://www.aoml.noaa.gov/phod/gdp/mean_velocity.php. The reconstruction dataset for temperature and salinity is available at http://www.ocean.iap.ac.cn/?navAnchor=home. The OFES2 simulation and 10-member ensemble output are available at https://www.jamstec.go.jp/ofes/ofes2.html. The GLORYS12V1 is available at https://data.marine.copernicus.eu/product/GLOBAL_MULTIYEAR_PHY_001_030/description. The ERSST v.5 is available at http://apdrc.soest.hawaii.edu/dods/public_data/NOAA_SST/ERSST/monthly_v5. The ECMWF ORAS5 reanalysis is available at https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-oras5?tab=form. The JMA JRA55-do reanalysis is available at https://climate.mri-jma.go.jp/pub/ocean/JRA55-do/. The CMIP6 HighResMIP1 ensemble is available at https://esgf-node.llnl.gov/projects/cmip6/. The processed data68 used in this study are publicly available in MATLAB format at https://doi.org/10.6084/m9.figshare.24633639.

Code availability

The diagnostic model67 for the TIW surface currents is available at https://doi.org/10.6084/m9.figshare.24633606.v1 via MATLAB codes. All analyses and figures68 in this manuscript are reproducible via MATLAB codes found in the repository (https://doi.org/10.6084/m9.figshare.24633639).

References

  1. Li, G. & Xie, S.-P. Tropical biases in CMIP5 multimodel ensemble: the excessive equatorial Pacific cold tongue and double ITCZ problems. J. Clim. 27, 1765–1780 (2014).

    Article  ADS  Google Scholar 

  2. Willett, C. S., Leben, R. R. & Lavín, M. F. Eddies and tropical instability waves in the eastern tropical Pacific: a review. Prog. Oceanogr. 69, 218–238 (2006).

    Article  ADS  Google Scholar 

  3. Holmes, R. M., Thomas, L. N., Thompson, L. & Darr, D. Potential vorticity dynamics of tropical instability vortices. J. Phys. Oceanogr. 44, 995–1011 (2014).

    Article  ADS  Google Scholar 

  4. Wang, M., Xie, S.-P., Shen, S. S. P. & Du, Y. Rossby and Yanai modes of tropical instability waves in the equatorial Pacific Ocean and a diagnostic model for surface currents. J. Phys. Oceanogr. 50, 3009–3024 (2020).

    Article  ADS  Google Scholar 

  5. Kennan, S. C. & Flament, P. J. Observations of a tropical instability vortex. J. Phys. Oceanogr. 30, 2277–2301 (2000).

    Article  ADS  Google Scholar 

  6. Shi, W. & Wang, M. Tropical instability wave modulation of chlorophyll-a in the Equatorial Pacific. Sci. Rep. 11, 22517 (2021).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  7. Zheng, G., Li, X., Zhang, R. H. & Liu, B. Purely satellite data-driven deep learning forecast of complicated tropical instability waves. Sci. Adv. 6, eaba1482 (2020).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  8. Lyman, J. M., Johnson, G. C. & Kessler, W. S. Distinct 17- and 33-day tropical instability waves in subsurface observations. J. Phys. Oceanogr. 37, 855–872 (2007).

    Article  ADS  Google Scholar 

  9. Liu, C., Wang, X., Köhl, A., Wang, F. & Liu, Z. The northeast‐southwest oscillating equatorial mode of the tropical instability wave and its impact on equatorial mixing. Geophys. Res. Lett. 46, 218–225 (2019).

    Article  ADS  Google Scholar 

  10. Brown, J. N., Godfrey, J. S. & Wijffels, S. E. Nonlinear effects of tropical instability waves on the equatorial Pacific circulation. J. Phys. Oceanogr. 40, 381–393 (2010).

    Article  ADS  Google Scholar 

  11. Holmes, R. M. & Thomas, L. N. Modulation of tropical instability wave intensity by equatorial Kelvin waves. J. Phys. Oceanogr. 46, 2623–2643 (2016).

    Article  ADS  Google Scholar 

  12. Small, R. J. et al. Air–sea interaction over ocean fronts and eddies. Dyn. Atmos. Oceans 45, 274–319 (2008).

    Article  ADS  Google Scholar 

  13. Li, T., Yu, Y., An, B., Luan, Y. & Chen, K. Tropical instability waves in a high-resolution oceanic and coupled GCM. Ocean Model. 182, 102169 (2023).

    Article  Google Scholar 

  14. Ascani, F., Firing, E., Dutrieux, P., McCreary, J. P. & Ishida, A. Deep equatorial ocean circulation induced by a forced-dissipated Yanai beam. J. Phys. Oceanogr. 40, 1118–1142 (2010).

    Article  ADS  Google Scholar 

  15. Tanaka, Y., Hibiya, T. & Sasaki, H. Downward lee wave radiation from tropical instability waves in the central equatorial Pacific Ocean: a possible energy pathway to turbulent mixing. J. Geophys. Res. Oceans 120, 7137–7149 (2015).

    Article  ADS  Google Scholar 

  16. Farrar, J. T. Barotropic Rossby waves radiating from tropical instability waves in the Pacific Ocean. J. Phys. Oceanogr. 41, 1160–1181 (2011).

    Article  ADS  Google Scholar 

  17. Warner, S. J. et al. Buoyant gravity currents released from tropical instability waves. J. Phys. Oceanogr. 48, 361–382 (2018).

    Article  ADS  Google Scholar 

  18. Santos-Ferreira, A. M., da Silva, J. C. B., St-Denis, B., Bourgault, D. & Maas, L. R. M. Internal solitary waves within the cold tongue of the Equatorial Pacific generated by buoyant gravity currents. J. Phys. Oceanogr. https://doi.org/10.1175/JPO-D-22-0165.1 (2023).

  19. Holmes, R. M. & Thomas, L. N. The modulation of equatorial turbulence by tropical instability waves in a regional ocean model. J. Phys. Oceanogr. 45, 1155–1173 (2015).

    Article  ADS  Google Scholar 

  20. Inoue, R., Lien, R.-C., Moum, J. N., Perez, R. C. & Gregg, M. C. Variations of equatorial shear, stratification, and turbulence within a tropical instability wave cycle. J. Geophys. Res. Oceans 124, 1858–1875 (2019).

    Article  ADS  Google Scholar 

  21. Imada, Y. & Kimoto, M. Parameterization of tropical instability waves and examination of their impact on ENSO characteristics. J. Clim. 25, 4568–4581 (2012).

    Article  ADS  Google Scholar 

  22. Eddebbar, Y. A. et al. Seasonal modulation of dissolved oxygen in the equatorial Pacific by tropical instability vortices. J. Geophys. Res. Oceans 126, e2021JC017567 (2021).

    Article  ADS  CAS  Google Scholar 

  23. Jochum, M. & Murtugudde, R. Temperature advection by tropical instability waves. J. Phys. Oceanogr. 36, 592–605 (2006).

    Article  ADS  Google Scholar 

  24. Maillard, L., Boucharel, J. & Renault, L. Direct and rectified effects of tropical instability waves on the eastern tropical Pacific mean state in a regional ocean model. J. Phys. Oceanogr. 52, 1817–1834 (2022).

    Article  ADS  Google Scholar 

  25. Maillard, L., Boucharel, J., Stuecker, M. F., Jin, F.-F. & Renault, L. Modulation of the Eastern Equatorial Pacific seasonal cycle by tropical instability waves. Geophys. Res. Lett. 49, e2022GL100991 (2022).

    Article  ADS  Google Scholar 

  26. Moum, J. N. et al. Sea surface cooling at the equator by subsurface mixing in tropical instability waves. Nat. Geosci. 2, 761–765 (2009).

    Article  ADS  CAS  Google Scholar 

  27. Cherian, D. A. et al. Off-equatorial deep-cycle turbulence forced by tropical instability waves in the equatorial Pacific. J. Phys. Oceanogr. 51, 1575–1593 (2021).

    Article  ADS  Google Scholar 

  28. Whitt, D. B. et al. Simulation and scaling of the turbulent vertical heat transport and deep-cycle turbulence across the equatorial Pacific cold tongue. J. Phys. Oceanogr. 52, 981–1014 (2022).

    Article  ADS  Google Scholar 

  29. Xue, A., Zhang, W., Boucharel, J. & Jin, F. F. Anomalous tropical instability wave activity hindered the development of the 2016/17 La Niña. J. Clim. 34, 5583–5600 (2021).

    ADS  Google Scholar 

  30. Wang, S. et al. El Niño/Southern Oscillation inhibited by submesoscale ocean eddies. Nat. Geosci. 15, 112–117 (2022).

    Article  ADS  CAS  Google Scholar 

  31. An, S.-I. Interannual variations of the tropical ocean instability wave and ENSO. J. Clim. 21, 3680–3686 (2008).

    Article  ADS  Google Scholar 

  32. Holmes, R. M., McGregor, S., Santoso, A. & England, M. H. Contribution of tropical instability waves to ENSO irregularity. Clim. Dyn. 52, 1837–1855 (2019).

    Article  Google Scholar 

  33. Wengel, C. et al. Future high-resolution El Niño/Southern Oscillation dynamics. Nat. Clim. Change 11, 758–765 (2021).

    Article  ADS  Google Scholar 

  34. Wang, M., Du, Y., Qiu, B., Xie, S.-P. & Feng, M. Dynamics on seasonal variability of EKE associated with TIWs in the eastern equatorial Pacific Ocean. J. Phys. Oceanogr. 49, 1503–1519 (2019).

    Article  ADS  Google Scholar 

  35. Wang, M. et al. Mechanism of seasonal eddy kinetic energy variability in the eastern equatorial Pacific Ocean. J. Geophys. Res. Oceans 122, 3240–3252 (2017).

    Article  ADS  Google Scholar 

  36. Boucharel, J. & Jin, F.-F. A simple theory for the modulation of tropical instability waves by ENSO and the annual cycle. Tellus A 72, 1–14 (2020).

    Article  Google Scholar 

  37. Xue, A., Jin, F.-F., Zhang, W., Boucharel, J. & Kug, J.-S. Parameterizing the nonlinear feedback on ENSO from tropical instability waves (TIWs) by nonlinear eddy thermal diffusivity. Clim. Dyn. https://doi.org/10.1007/s00382-023-06744-4 (2023).

  38. Kosaka, Y. & Xie, S.-P. Recent global-warming hiatus tied to equatorial Pacific surface cooling. Nature 501, 403–407 (2013).

    Article  ADS  CAS  PubMed  Google Scholar 

  39. England, M. H. et al. Recent intensification of wind-driven circulation in the Pacific and the ongoing warming hiatus. Nat. Clim. Change 4, 222–227 (2014).

    Article  ADS  Google Scholar 

  40. Hu, S. N. & Fedorov, A. V. Cross-equatorial winds control El Niño diversity and change. Nat. Clim. Change 8, 798–802 (2018).

    Article  ADS  Google Scholar 

  41. Martínez-Moreno, J. et al. Global changes in oceanic mesoscale currents over the satellite altimetry record. Nat. Clim. Change 11, 397–403 (2021).

    Article  ADS  Google Scholar 

  42. Johnson, E. S., Bonjean, F., Lagerloef, G. S., Gunn, J. T. & Mitchum, G. T. Validation and error analysis of OSCAR sea surface currents. J. Atmos. Ocean. Technol. 24, 688–701 (2007).

    Article  ADS  Google Scholar 

  43. He, W.-B., Yang, Y. & San Liang, X. Mechanisms for generating and connecting the Yanai-mode and Rossby-mode tropical instability waves in the equatorial Pacific. Deep Sea Res. I Oceanogr. Res. Pap. 197, 104041 (2023).

    Article  CAS  Google Scholar 

  44. Sasaki, H. et al. A global eddying hindcast ocean simulation with OFES2. Geosci. Model Dev. 13, 3319–3336 (2020).

    Article  ADS  CAS  Google Scholar 

  45. Sasaki, H., Qiu, B., Klein, P., Nonaka, M. & Sasai, Y. Interannual variations of submesoscale circulations in the subtropical northeastern Pacific. Geophys. Res. Lett. 49, e2021GL097664 (2022).

    Article  ADS  Google Scholar 

  46. Nonaka, M., Sasaki, H., Taguchi, B. & Schneider, N. Atmospheric-driven and intrinsic interannual-to-decadal variability in the Kuroshio Extension jet and eddy activities. Front. Mar. Sci. 7, 547442 (2020).

    Article  Google Scholar 

  47. Tsujino, H. et al. JRA-55 based surface dataset for driving ocean–sea-ice models (JRA55-do). Ocean Model. 130, 79–139 (2018).

    Article  ADS  Google Scholar 

  48. Jean-Michel, L. et al. The Copernicus global 1/12 oceanic and sea ice GLORYS12 reanalysis. Front. Earth Sci. 9, 698876 (2021).

    Article  Google Scholar 

  49. Haarsma, R. J. et al. High resolution model intercomparison project (HighResMIP v1.0) for CMIP6. Geosci. Model Dev. 9, 4185–4208 (2016).

    Article  ADS  Google Scholar 

  50. Yue, S. & Wang, C. The Mann–Kendall test modified by effective sample size to detect trend in serially correlated hydrological series. Water Resour. Manage. 18, 201–218 (2004).

    Article  Google Scholar 

  51. Wang, S. et al. Weakened submesoscale eddies in the equatorial Pacific under greenhouse warming. Geophys. Res. Lett. 49, e2022GL100533 (2022).

    Article  ADS  Google Scholar 

  52. Li, G. et al. Increasing ocean stratification over the past half-century. Nat. Clim. Change 10, 1116–1123 (2020).

    Article  ADS  Google Scholar 

  53. Xie, S.-P. et al. Eastern Pacific ITCZ dipole and ENSO diversity. J. Clim. 31, 4449–4462 (2018).

    Article  ADS  Google Scholar 

  54. Imada, Y., Kimoto, M. & Chen, X. Impact of the atmospheric mean state on tropical instability wave activity. J. Clim. 25, 2341–2355 (2012).

    Article  ADS  Google Scholar 

  55. Friedman, A. R., Hwang, Y. T., Chiang, J. C. & Frierson, D. M. Interhemispheric temperature asymmetry over the twentieth century and in future projections. J. Clim. 26, 5419–5433 (2013).

    Article  ADS  Google Scholar 

  56. Meehl, G. A., Hu, A., Arblaster, J. M., Fasullo, J. & Trenberth, K. E. Externally forced and internally generated decadal climate variability associated with the Interdecadal Pacific Oscillation. J. Clim. 26, 7298–7310 (2013).

    Article  ADS  Google Scholar 

  57. Watanabe, M. & Tatebe, H. Reconciling roles of sulphate aerosol forcing and internal variability in Atlantic multidecadal climate changes. Clim. Dyn. 53, 4651–4665 (2019).

    Article  Google Scholar 

  58. Kang, S. M., Xie, S.-P., Deser, C. & Xiang, B. Zonal mean and shift modes of historical climate response to evolving aerosol distribution. Sci. Bull. 66, 2405–2411 (2021).

    Article  CAS  Google Scholar 

  59. Beech, N. et al. Long-term evolution of ocean eddy activity in a warming world. Nat. Clim. Change 12, 910–917 (2022).

    Article  ADS  Google Scholar 

  60. Yang, H. et al. Poleward shift of the major ocean gyres detected in a warming climate. Geophys. Res. Lett. 47, e2019GL085868 (2020).

    Article  ADS  Google Scholar 

  61. Shi, J.-R., Talley, L. D., Xie, S.-P., Peng, Q. & Liu, W. Ocean warming and accelerating Southern Ocean zonal flow. Nat. Clim. Change 11, 1090–1097 (2021).

    Article  ADS  Google Scholar 

  62. Chassignet, E. P. et al. Impact of horizontal resolution on global ocean–sea ice model simulations based on the experimental protocols of the Ocean Model Intercomparison Project phase 2 (OMIP-2). Geosci. Model Dev. 13, 4595–4637 (2020).

    Article  ADS  Google Scholar 

  63. Graham, T. The importance of eddy permitting model resolution for simulation of the heat budget of tropical instability waves. Ocean Model. 79, 21–32 (2014).

    Article  ADS  Google Scholar 

  64. An, S.-I. & Jin, F.-F. Nonlinearity and asymmetry of ENSO. J. Clim. 17, 2399–2412 (2004).

    Article  ADS  Google Scholar 

  65. Shin, N.-Y. et al. More frequent central Pacific El Niño and stronger eastern Pacific El Niño in a warmer climate. NPJ Clim. Atmos. Sci. 5, 101 (2022).

    Article  ADS  Google Scholar 

  66. Laurindo, L. C., Mariano, A. J. & Lumpkin, R. An improved near-surface velocity climatology for the global ocean from drifter observations. Deep Sea Res. I Oceanogr. Res. Pap. 124, 73–92 (2017).

    Article  ADS  Google Scholar 

  67. Wang, M. A diagnostic model for TIW currents from SSH. Dataset. figshare https://doi.org/10.6084/m9.figshare.24633606.v1 (2023).

  68. Wang, M. Intensification of Pacific tropical instability waves over the recent three decades. Dataset. figshare https://doi.org/10.6084/m9.figshare.24633639.v1 (2023).

Download references

Acknowledgements

M.W. and Y.D. at SCSIO/CAS were supported by the National Natural Science Foundation of China (42090042, 42106024) and the Chinese Academy of Sciences (133244KYSB20190031, 183311KYSB20200015, LTOZZ2203, SCSIO202201). S.-P.X. was supported by the US NSF (AGS 2105654). H.S. was supported by JSPS KAKENHI Grant Number JP19H05701. The numerical computation was supported by the Earth Simulator in the Japan Agency for Marine-Earth Science and Technology (JAMSTEC), and the High-Performance Computing Division in the South China Sea Institute of Oceanology, Guangzhou, China.

Author information

Authors and Affiliations

  1. State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China

    Minyang Wang & Yan Du

  2. Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA, USA

    Shang-Ping Xie

  3. Application Laboratory, Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan

    Hideharu Sasaki & Masami Nonaka

  4. University of Chinese Academy of Sciences, Beijing, China

    Yan Du

Authors
  1. Minyang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shang-Ping Xie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hideharu Sasaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Masami Nonaka
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yan Du
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

M.W., S.-P.X. and Y.D. conceived the study. M.W. conducted the analyses, wrote the initial manuscript draft and produced all figures. H.S. conducted the global ocean model simulation (OFES2), and M.N. conducted the OFES2 ensemble simulations. All authors contributed to the interpretation of the results and the writing and revision of the paper.

Corresponding authors

Correspondence to Shang-Ping Xie or Yan Du.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Climate Change thanks Julien Boucharel, Ryan Holmes and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Observed trends of equatorial wavenumber-frequency spectra.

1993–2021 trends (color shading) are superimposed with the mean states (contour, in log scale): a, SSTy variance spectrum, contour initiating from – 0.8 with interval of 0.2, (10−6 °C m−1)2; b, SST variance spectrum, contour initiating from – 2.6 with interval of 0.2, °C2; c, SSH-derived surface kinetic energy (KE) spectrum, contour initiating from – 0.2 with interval of 0.2, J m−3; d, SSH variance spectrum, contour initiating from – 1.4 with interval of 0.2, cm2. The period is shown on the y-axis in red text. Red dashed box represents the TIW spectral domain with westward wavelength ≤ 3000 km and period ≤ 40 days. Black dashed curves denote dispersion relations of free equatorial waves of the first baroclinic mode, with the phase velocity of long gravity wave at 2.8 m s−1: ‘R0’, ‘R1–3’ and ‘K’ denote the mixed Rossby-gravity, first–third meridional-mode Rossby, and Kelvin waves, respectively. The trends are based on the 9-year running average of the spectra that are calculated over 160°W–100°W at each year, then averaged between (1°S–1°N) / (2°S–2°N) for (a,c) / (b,d). Dotted regions pass the 95% confidence level based on the modified Mann–Kendall test.

Extended Data Fig. 2 Trends based on annual mean time series.

a,b, Satellite-observed \(\overline{{{{\rm{SST}}^{\prime} }_{y}}^{2}}\), c,d, altimeter-derived EKE, and e,f, OFES2-simulated surface EKE. Left panels represent time series averaged in the dashed box of right panels (160°W–100°W and 1°S–1°N): annual (thin blue curves) and 9-yr running mean (bold blue curves); Dashed lines denote their fitted linear trends (thin magenta/red for annual mean over 1993–2015/2021, and bold red for 9-yr running mean over 1993–2021). T, p, and n represent the trends (per decade) ± uncertainties (estimated as the s.e.m.), p values, and n numbers for the statistics. Right panels represent 1993–2021 trends based the annual mean time series.

Extended Data Fig. 3 Trends in \({{{{\boldsymbol{(}}{\overline{{\mathbf{SST}}}}_{\boldsymbol{yy}}{\boldsymbol{)}}}^{\mathbf{2}}}}\), \({{\overline{{\boldsymbol{v}^{\prime}}}^{\mathbf{2}}}}\), \({{\overline{{\boldsymbol{v}^{\prime}}}^{\mathbf{2}} {({\overline{{\mathbf{SST}}}}_{\boldsymbol{yy}})}^{\mathbf{2}}}}\), and \({\overline{{{{\mathbf{SST}}}^{\prime}}}_{\boldsymbol{y}}^{\mathbf{2}}}\) of Eq. 3.

a,e,i, \(({{\overline{{\rm{SST}}}}_{{yy}}})^{2}\). b,f,j, \({{\overline{{{v}^{\prime}}}^{{2}}}}\). c,g,k, \({{\overline{{{v}^{\prime}}}^{{2}} {({\overline{\rm{{SST}}}}_{{yy}})}^{{2}}}}\). d,h,l, \({\overline{{{\rm{{SST}}^{\prime}}_{{y}}}^{{2}}}}\). a–d, e–h and i–l are on the basis of satellite observations, GLORYS12V1 reanalysis (1993–2020), and OFES2 simulation over 1993–2021, respectively. They were averaged between 160°W–100°W, standardized by maximum values of the climatological mean in meridional direction. Data are represented as the trends ± uncertainties (grey shading, estimated as the s.e.m.) at the equator, with n numbers shown. The results demonstrate the proportional relationship: \(\overline{{{{\rm{SST}}^{\prime}}} }_{y}^{2}\propto \overline{{{v^{\prime}}}}^{2}{{ \overline{{\rm{SST}}}}_{{yy}}}^{2}\), at the equator (Eq. 3, Methods).

Extended Data Fig. 4 Validation of EKE with in situ observations.

Upper and lower panels denote two sites at 140°W and 110°W equator of the TAO array, respectively. a,d, Depth-temporal variation of subsurface EKE from TAO; Black curves denote thermocline defined as the depth of 20 °C isotherm (D20). b,e, Multidecadal mean of EKE profile from altimeter (dots on the surface), OFES2 (in CMYK color), and TAO (in RGB color) between 1993–2006 (blue curves) and 2007–2020 (red curves); Color shading denotes the standard deviation of the time series. c,f, Interannual variability of EKE from altimeter (red), OFES2 at 30 m depth (blue), and TAO at 30 m depth (black), 1993–2020 mean removed. The r, p, and n denote the correlation coefficients, p values, and n numbers of the altimeter and OFES2 EKE time series with TAO based on the Student’s t test.

Extended Data Fig. 5 Meridional structures of \({\overline{{{{\mathbf{SSH}}^{\prime}}}}_{\boldsymbol{y}}^{\mathbf{2}}}\), EKE, surface zonal current, and SST trends.

Left/right panels are trends/mean over 1993–2021, averaged between 160°W–100°W. a,b, \({\overline{{{\rm{{SSH}}^{\prime}}}}_{{y}}^{{2}}}\). c,d, EKE. e,f, surface zonal current. g,h, SST. They are on the basis of satellite observation or derivation (red), GLORYS12V1 reanalysis (magenta), and OFES2 simulation (blue). Black curve in f denotes surface zonal currents from historical drifter trajectories66. Trends marked with circles pass the 95% confidence level based on the modified Mann–Kendall test.

Extended Data Fig. 6 Mean states of EKE budget based on OFES2.

Similar to Fig. 3, but for the climatological mean. a, Mean EKE and the budget terms (shaded bars); Error bars denote uncertainties as the standard deviations between 1993–2021 mostly due to interannual variability; Data are represented as the mean ± uncertainties, with n numbers of 24, 28, 26, 24, and 25 from left to right. b–d, Meridional transects of mean EKE (colour shading) with zonal current (contours, cm s−1) (b), BTR (colour shading) with (1 − Uyy/β) (contours, dimensionless) (c) and BCR (colour shading) with temperature (contour, °C) (d), 160° W–100° W averaged. e, 9-yr running mean time series of EKE (red), BTR (solid magenta), BCR (dashed magenta) averaged between 160°W–100°W, 2°S–2°N, and 0–50 m depth, and SEC speed (black) averaged between 0°–4°N.

Extended Data Fig. 7 Trends of upper ocean stratifications in the equatorial Pacific.

1993–2021 trends (color shading) are superimposed with the mean states (contour, same unit as the trends without ‘/ dec’): a,b, Temperature; c,d, Vertical stratification (buoyancy frequency square, \({N}^{2}=-{b}_{z}\), where the buoyancy \(b=-\frac{\rho }{{\rho }_{0}}g\)); e,f, Meridional buoyancy gradient square (\({{b}_{y}}^{2}\)). \({{b}_{y}}^{2}\) is calculated using monthly data before the average. Left/right panels are from IAP reconstruction/OFES2, averaged between 160°W–100°W. Dashed and solid black curves are climatological mean mixed layer depth (MLD) and D20, respectively. Note that the left and right have different ranges of colorbar and contour intervals in order to magnify the structure of the trends.

Extended Data Fig. 8 Trends of the tropical Pacific climate and ocean surface currents in OFES2 simulation.

Same as Fig. 5a,c but for the OFES2 simulation. a, 1993–2021 trends of simulated SST (colour shading) and 10-m wind from JRA55-do reanalysis (vector, accelerating in bold red; decelerating in thin blue). b, 1993–2021 trends of simulated SSH (colour shading) and surface currents (vector, accelerating in bold red; decelerating in thin blue). The JRA55-do reanalysis is the atmospheric forcing of the OFES2 simulation.

Extended Data Fig. 9 CMIP6 HighResMIP1-simulated and projected \({\overline{{{{\mathbf{SST}}^{\prime}}}}_{\boldsymbol{y}}^{\mathbf{2}}}\) trends.

a, Climatological mean as a function of latitude; b, Long-term evolution (9-yr running mean, standardized by the 1993–2014 mean). Scatter diagrams of the standardized \(\overline{{{{\rm{SST}}^{\prime}}}}_{y}^{2}\) (y axis) vs. \({{\overline{{\rm{SST}}}}_{{yy}}}^{2}\) (x axis): c, the 1993–2014 mean (standardized by the observation), d, the 1993–2014 and e, 2015–2050 trends (markers with black edge pass the 95% confidence level), averaged between 160°W–100°W and 1°S–1°N. Black curves in a,b and grey pentagrams in c,d denote the observation. Bold colored curves (blue/red denotes historical run/future projection) in a,b, and grey squares in c,d,e denote multi-model ensemble mean (MME) with spreads (1 s.d. of ensemble with n number of 6). The used CMIP6 HighResMIP1 ensemble consists of six coupled atmosphere-ocean models (thin curves or colored markers) with historical radiative forcing (Hist-1950 experiment: 1950–2014) and future SSP585 forcing (Highres-future experiment: 2015–2050).

Extended Data Fig. 10 Trends of TIW-induced EDH.

1993–2021 trends (color shading) are superimposed with the mean states (contour, same unit as the trends without ‘/ dec’): a, Satellite-derived surface EDH; b, 160°W–100°W average of a along with the uncertainties in percentage form, standardized by maximum values (∼2 °C month−1) of the climatological mean in the meridional direction; Data are represented as the trends ± uncertainties (estimated as the s.e.m.) at the equator, with n numbers of 25. c, Meridional transect of OFES2-simulated subsurface EDH averaged between 160°W–100°W. The OFES2 simulation underestimates the EDH trends because the \(\overline{{{{\rm{SST}}^{\prime}}}}_{y}^{2}\) trend is biased to be negative (Extended Data Fig. 3l). The OFES2 results suggest that the heating effects are amplified near the surface.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, M., Xie, SP., Sasaki, H. et al. Intensification of Pacific tropical instability waves over the recent three decades. Nat. Clim. Chang. 14, 163–170 (2024). https://doi.org/10.1038/s41558-023-01915-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41558-023-01915-x

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing