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.
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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
Thomas, L. N., Tandon, A. & Mahadevan, A. Submesoscale processes and dynamics (2008).
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).
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).
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).
Mahadevan, A. The impact of submesoscale physics on primary productivity of plankton. Annual review of marine science 8(1), 161–184 (2016).
Fox-Kemper, B. & Ferrari, R. Parameterization of mixed layer eddies. part ii: Prognosis and impact. Journal of Physical Oceanography 38(6), 1166–1179 (2008).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
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).
Argo: Argo float data and metadata from Global Data Assembly Centre (Argo GDAC) https://doi.org/10.17882/42182 (2000).
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).
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).
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).
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).
Callies, J., Ferrari, R., Klymak, J. M. & Gula, J. Seasonality in submesoscale turbulence. Nature communications 6(1), 6862 (2015).
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).
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).
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).
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).
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).
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).
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).
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).
Waliser, D. E. & Gautier, C. A satellite-derived climatology of the itcz. Journal of Climate 6(11), 2162–2174 (1993).
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).
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).
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).
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).
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).
Maze, G. pyXpcm: Ocean Profile Classification Model https://doi.org/10.5281/zenodo.3906236 (2018).
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).
(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).
(CMEMS), E. U. C. M. S. I. Global ocean physics reanalysis. Marine Data Store (MDS) DOI:https://doi.org/10.48670/moi-00021 (2023).
McDougall, T. J. & Barker, P. M. Getting started with teos-10 and the gibbs seawater (gsw) oceanographic toolbox. SCOR/IAPSO WG127, 28 (2011).
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).
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).
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LY and JT designed the study. LY performed the analysis. Both authors contributed to the writing of the manuscript.
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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
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DOI: https://doi.org/10.1038/s41598-026-41929-x


