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.

Advertisement

Scientific Reports
  • View all journals
  • Search
  • My Account Login
  • Content Explore content
  • About the journal
  • Publish with us
  • Sign up for alerts
  • RSS feed
  1. nature
  2. scientific reports
  3. articles
  4. article
Global climatology of submesoscale restratification using machine learning
Download PDF
Download PDF
  • Article
  • Open access
  • Published: 20 March 2026

Global climatology of submesoscale restratification using machine learning

  • Leyu Yao1 na1 &
  • John R. Taylor1 na1 

Scientific Reports , Article number:  (2026) Cite this article

  • 754 Accesses

  • Metrics details

We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.

Subjects

  • Climate sciences
  • Ocean sciences

Abstract

Submesoscale eddies are important in setting the stratification in the ocean surface mixed layer and transporting energy between large and small scale motions. However, the study of submesoscale on a global scale has been hindered by a shortage of global, long-term datasets. To meet this need, we apply an unsupervised machine learning method adapted from the profile classification model (PCM) to density profiles collected by Argo floats over the global ocean from 2000-2021, producing the first global observational climatology of submesoscale restratification. The method classifies individual vertical profiles based on the shape of the density profile in the ocean surface mixed layer. The fraction of profiles that exhibit a shape characteristic of submesoscale is referred to as the submesoscale restratification (SR) index. The SR index peaks in spring in both hemispheres and lags the maxima of mixed layer depth by one month, suggesting that submesoscale eddies play an important role in restratifying the mixed layer. Hotspots of SR index can be found in the Norwegian Sea and the Drake Passage in spring. This method enables the study of the spatial and temporal distributions of submesoscale restratification on a global scale.

Similar content being viewed by others

Simulated Sea Surface Salinity Data from a 1/48° Ocean Model

Article Open access 23 May 2024

Oceanic eddy with submesoscale edge drives intense air-sea exchanges and beyond

Article Open access 24 October 2024

Observed large-scale and deep-reaching compound ocean state changes over the past 60 years

Article Open access 25 November 2025

Data availability

This study has been conducted using E.U. Copernicus Marine Service Information (product https://doi.org/10.48670/moi-00181, https://doi.org/10.48670/moi-00016) and Copernicus Climate Change Service Climate Data Store (product https://doi.org/10.24381/cds.f17050d7).

Code availability

Code for fetching and processing the Argo data, training the PCM and making all the plots for the paper is available here: https://github.com/Nataliely/Argo-PCM-code.

References

  1. Thomas, L. N., Tandon, A. & Mahadevan, A. Submesoscale processes and dynamics (2008).

  2. McWilliams, J. C. Submesoscale currents in the ocean. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472(2189), 20160117. https://doi.org/10.1098/rspa.2016.0117 (2016).

    Google Scholar 

  3. Taylor, J. R. & Thompson, A. F. Submesoscale dynamics in the upper ocean. Annual Review of Fluid Mechanics 55(1), 103–127. https://doi.org/10.1146/annurev-fluid-031422-095147 (2023).

    Google Scholar 

  4. Lévy, M., Ferrari, R., Franks, P. J., Martin, A. P. & Rivière, P. Bringing physics to life at the submesoscale. Geophysical Research Letters 39(14), (2012).

  5. Mahadevan, A. The impact of submesoscale physics on primary productivity of plankton. Annual review of marine science 8(1), 161–184 (2016).

    Google Scholar 

  6. Fox-Kemper, B. & Ferrari, R. Parameterization of mixed layer eddies. part ii: Prognosis and impact. Journal of Physical Oceanography 38(6), 1166–1179 (2008).

    Google Scholar 

  7. Su, Z., Wang, J., Klein, P., Thompson, A. & Menemenlis, D. Ocean submesoscales as a key component of the global heat budget. Nature Communications https://doi.org/10.1038/s41467-018-02983-w (2018).

    Google Scholar 

  8. Boccaletti, G., Ferrari, R. & Fox-Kemper, B. Mixed layer instabilities and restratification. Journal of Physical Oceanography 37(9), 2228–2250. https://doi.org/10.1175/JPO3101.1 (2007).

    Google Scholar 

  9. Fox-Kemper, B., Ferrari, R. & Hallberg, R. Parameterization of mixed layer eddies. part i: Theory and diagnosis. Journal of Physical Oceanography 38(6), 1145–1165. https://doi.org/10.1175/2007JPO3792.1 (2008).

    Google Scholar 

  10. Fox-Kemper, B. et al. Parameterization of mixed layer eddies. iii: Implementation and impact in global ocean climate simulations. Ocean Modelling 39(1–2), 61–78 (2011).

    Google Scholar 

  11. Smith, K. et al. The doe e3sm version 2.1: overview and assessment of the impacts of parameterized ocean submesoscales. Geoscientific Model Development Discussions 2024, 1–38 (2024).

    Google Scholar 

  12. Dong, J., Fox-Kemper, B., Zhang, H. & Dong, C. The seasonality of submesoscale energy production, content, and cascade. Geophysical Research Letters 47(6), 2020–087388. https://doi.org/10.1029/2020GL087388 (2020).

    Google Scholar 

  13. Yao, L., Taylor, J. R., Jones, D. C. & Bachman, S. D. Identifying ocean submesoscale activity from vertical density profiles using machine learning. Earth and Space Science 12(1), 2022–002618. https://doi.org/10.1029/2022EA002618 (2025).

    Google Scholar 

  14. Maze, G. et al. Coherent heat patterns revealed by unsupervised classification of Argo temperature profiles in the North Atlantic Ocean. Progress in Oceanography 151, 275–292. https://doi.org/10.1016/j.pocean.2016.12.008 (2017).

    Google Scholar 

  15. Desbruyères, D., Chafik, L. & Maze, G. A shift in the ocean circulation has warmed the subpolar North Atlantic Ocean since 2016. Communications Earth & Environment 2(1), 1–9. https://doi.org/10.1038/s43247-021-00120-y (2021).

    Google Scholar 

  16. Boehme, L. & Rosso, I. Classifying oceanographic structures in the amundsen sea, antarctica. Geophysical Research Letters 48(5), 2020–089412. https://doi.org/10.1029/2020GL089412 (2021).

    Google Scholar 

  17. Jones, D. C., Holt, H. J., Meijers, A. J. S. & Shuckburgh, E. Unsupervised clustering of Southern Ocean Argo float temperature profiles. Journal of Geophysical Research: Oceans 124(1), 390–402. https://doi.org/10.1029/2018JC014629 (2019).

    Google Scholar 

  18. Rosso, I. et al. Water mass and biogeochemical variability in the kerguelen sector of the Southern Ocean: A machine learning approach for a mixing hot spot. Journal of Geophysical Research: Oceans 125, 2019–015877. https://doi.org/10.1029/2019JC015877 (2020).

    Google Scholar 

  19. Houghton, I. A. & Wilson, J. D. El niño detection via unsupervised clustering of argo temperature profiles. Journal of Geophysical Research: Oceans 125(9), 2019–015947. https://doi.org/10.1029/2019JC015947 (2020).

    Google Scholar 

  20. Taylor, J. R., Smith, K. M. & Vreugdenhil, C. A. The influence of submesoscales and vertical mixing on the export of sinking tracers in large-eddy simulations. Journal of Physical Oceanography 50(5), 1319–1339 (2020).

    Google Scholar 

  21. Bachman, S. D., Taylor, J. R., Adams, K. A. & Hosegood, P. Mesoscale and submesoscale effects on the mixed layer depth in the Southern Ocean. J. Phys. Ocean. 47, 2173–2188 (2017).

    Google Scholar 

  22. Callies, J. & Ferrari, R. Note on the rate of restratification in the baroclinic spindown of fronts. Journal of Physical Oceanography 48(7), 1543–1553. https://doi.org/10.1175/JPO-D-17-0175.1 (2018).

    Google Scholar 

  23. Argo: Argo float data and metadata from Global Data Assembly Centre (Argo GDAC) https://doi.org/10.17882/42182 (2000).

  24. Sinha, A., Callies, J. & Menemenlis, D. Do submesoscales affect the large-scale structure of the upper ocean?. Journal of Physical Oceanography 53(4), 1025–1040 (2023).

    Google Scholar 

  25. Mahadevan, A., Tandon, A. & Ferrari, R. Rapid changes in mixed layer stratification driven by submesoscale instabilities and winds. Journal of Geophysical Research: Oceans https://doi.org/10.1029/2008JC005203 (2010).

    Google Scholar 

  26. Thompson, A. F. et al. Open-ocean submesoscale motions: A full seasonal cycle of mixed layer instabilities from gliders. Journal of Physical Oceanography 46(4), 1285–1307. https://doi.org/10.1175/JPO-D-15-0170.1 (2016).

    Google Scholar 

  27. Yu, X. et al. An annual cycle of submesoscale vertical flow and restratification in the upper ocean. Journal of Physical Oceanography 49(6), 1439–1461. https://doi.org/10.1175/JPO-D-18-0253.1 (2019).

    Google Scholar 

  28. Callies, J., Ferrari, R., Klymak, J. M. & Gula, J. Seasonality in submesoscale turbulence. Nature communications 6(1), 6862 (2015).

    Google Scholar 

  29. Buckingham, C. E. et al. Seasonality of submesoscale flows in the ocean surface boundary layer. Geophysical Research Letters 43(5), 2118–2126. https://doi.org/10.1002/2016GL068009 (2016).

    Google Scholar 

  30. Thomas, L. N. Destruction of potential vorticity by winds. Journal of Physical Oceanography 35(12), 2457–2466. https://doi.org/10.1175/JPO2830.1 (2005).

    Google Scholar 

  31. Thomas, L. N. & Lee, C. M. Intensification of ocean fronts by down-front winds. Journal of Physical Oceanography 35(6), 1086–1102. https://doi.org/10.1175/JPO2737.1 (2005).

    Google Scholar 

  32. Thomas, L. & Ferrari, R. Friction, frontogenesis, and the stratification of the surface mixed layer. Journal of Physical Oceanography 38(11), 2501–2518. https://doi.org/10.1175/2008JPO3797.1 (2008).

    Google Scholar 

  33. Soloviev, A. & Lukas, R. Observation of large diurnal warming events in the near-surface layer of the western equatorial pacific warm pool. Deep Sea Research Part I: Oceanographic Research Papers 44(6), 1055–1076. https://doi.org/10.1016/S0967-0637(96)00124-0 (1997).

    Google Scholar 

  34. Kawai, Y. & Wada, A. Diurnal sea surface temperature variation and its impact on the atmosphere and ocean: A review. J. Oceanogr 63, 721–744. https://doi.org/10.1007/s10872-007-0063-0 (2007).

    Google Scholar 

  35. Matthews, A. J., Baranowski, D. B., Heywood, K. J., Flatau, P. J. & Schmidtko, S. The surface diurnal warm layer in the indian ocean during cindy/dynamo. Journal of Climate 27(24), 9101–9122. https://doi.org/10.1175/JCLI-D-14-00222.1 (2014).

    Google Scholar 

  36. Moulin, A. J., Moum, J. N. & Shroyer, E. L. Evolution of turbulence in the diurnal warm layer. Journal of Physical Oceanography 48(2), 383–396. https://doi.org/10.1175/JPO-D-17-0170.1 (2018).

    Google Scholar 

  37. Waliser, D. E. & Gautier, C. A satellite-derived climatology of the itcz. Journal of Climate 6(11), 2162–2174 (1993).

    Google Scholar 

  38. Schneider, T., Bischoff, T. & Haug, G. H. Migrations and dynamics of the intertropical convergence zone. Nature 513(7516), 45–53. https://doi.org/10.1038/nature13636 (2014).

    Google Scholar 

  39. Berry, B. & Reeder, M. J. Objective identification of the intertropical convergence zone: Climatology and trends from the era-interim. Journal of Climate 27(5), 1894–1909. https://doi.org/10.1175/JCLI-D-13-00339.1 (2014).

    Google Scholar 

  40. Boyer Montégut, C., Madec, G., Fischer, A. S., Lazar, A. & Iudicone, D. Mixed layer depth over the global ocean: An examination of profile data and a profile-based climatology. J. Geophys. Res. https://doi.org/10.1029/2004JC002378 (2004).

    Google Scholar 

  41. Kara, A., Rochford, P. & Hurlburt, H. An optimal definition for ocean mixed layer depth. Journal of Geophysical Research 105, 20. https://doi.org/10.1029/2000JC900072 (2000).

    Google Scholar 

  42. Maze, G. & Balem, K. argopy: A python library for argo ocean data analysis. Journal of Open Source Software 5(53), 2425. https://doi.org/10.21105/joss.02425 (2020).

    Google Scholar 

  43. Maze, G. pyXpcm: Ocean Profile Classification Model https://doi.org/10.5281/zenodo.3906236 (2018).

  44. Hersbach, H. et al. Era5 monthly averaged data on single levels from 1940 to present. Copernicus Climate Change Service (C3S) Climate Data Store (CDS) https://doi.org/10.24381/cds.f17050d7 (2023).

    Google Scholar 

  45. (CMEMS), E. U. C. M. S. I. Global ocean monthly mean sea surface wind and stress from scatterometer and model. Marine Data Store (MDS) https://doi.org/10.48670/moi-00181 (2023).

  46. (CMEMS), E. U. C. M. S. I. Global ocean physics reanalysis. Marine Data Store (MDS) DOI:https://doi.org/10.48670/moi-00021 (2023).

  47. McDougall, T. J. & Barker, P. M. Getting started with teos-10 and the gibbs seawater (gsw) oceanographic toolbox. SCOR/IAPSO WG127, 28 (2011).

  48. Mahadevan, A., D’Asaro, E., Lee, C. & Perry, M. J. Eddy-driven stratification initiates north atlantic spring phytoplankton blooms. Science 337(6090), 54–58. https://doi.org/10.1126/science.1218740 (2012).

    Google Scholar 

Download references

Acknowledgements

This study has been conducted using E.U. Copernicus Marine Service Information (product DOI: 10.48670/moi-00181, 10.48670/moi-00016) and Copernicus Climate Change Service Climate Data Store (product DOI: 10.24381/cds.f17050d7).

Author information

Author notes
  1. These authors contributed equally: Leyu Yao and John R. Taylor.

Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK

    Leyu Yao & John R. Taylor

Authors
  1. Leyu Yao
    View author publications

    Search author on:PubMed Google Scholar

  2. John R. Taylor
    View author publications

    Search author on:PubMed Google Scholar

Contributions

LY and JT designed the study. LY performed the analysis. Both authors contributed to the writing of the manuscript.

Corresponding author

Correspondence to John R. Taylor.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note

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

Supplementary Information

Supplementary Information. (download PDF )

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yao, L., Taylor, J.R. Global climatology of submesoscale restratification using machine learning. Sci Rep (2026). https://doi.org/10.1038/s41598-026-41929-x

Download citation

  • Received: 06 November 2025

  • Accepted: 23 February 2026

  • Published: 20 March 2026

  • DOI: https://doi.org/10.1038/s41598-026-41929-x

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Submesoscale eddy
  • Profile classification model (PCM)
  • Argo float
Download PDF

Advertisement

Explore content

  • Research articles
  • News & Comment
  • Collections
  • Subjects
  • Follow us on Facebook
  • Follow us on X
  • Sign up for alerts
  • RSS feed

About the journal

  • About Scientific Reports
  • Contact
  • Journal policies
  • Guide to referees
  • Calls for Papers
  • Editor's Choice
  • Journal highlights
  • Open Access Fees and Funding

Publish with us

  • For authors
  • Language editing services
  • Open access funding
  • Submit manuscript

Search

Advanced search

Quick links

  • Explore articles by subject
  • Find a job
  • Guide to authors
  • Editorial policies

Scientific Reports (Sci Rep)

ISSN 2045-2322 (online)

nature.com footer links

About Nature Portfolio

  • About us
  • Press releases
  • Press office
  • Contact us

Discover content

  • Journals A-Z
  • Articles by subject
  • protocols.io
  • Nature Index

Publishing policies

  • Nature portfolio policies
  • Open access

Author & Researcher services

  • Reprints & permissions
  • Research data
  • Language editing
  • Scientific editing
  • Nature Masterclasses
  • Research Solutions

Libraries & institutions

  • Librarian service & tools
  • Librarian portal
  • Open research
  • Recommend to library

Advertising & partnerships

  • Advertising
  • Partnerships & Services
  • Media kits
  • Branded content

Professional development

  • Nature Awards
  • Nature Careers
  • Nature Conferences

Regional websites

  • Nature Africa
  • Nature China
  • Nature India
  • Nature Japan
  • Nature Middle East
  • Privacy Policy
  • Use of cookies
  • Legal notice
  • Accessibility statement
  • Terms & Conditions
  • Your US state privacy rights
Springer Nature

© 2026 Springer Nature Limited

Nature Briefing Anthropocene

Sign up for the Nature Briefing: Anthropocene newsletter — what matters in anthropocene research, free to your inbox weekly.

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