Advancing Mesoscale Process Representation in Ocean Models with Machine Learning

By: Dr. Anna Denvil-Sommer

Mesoscale eddies, which are swirling, whirlpool-like motions, play a critical role in ocean circulation and the global energy budget. At scales of 10 to 300 km, these dynamic features transfer hydrographic properties (physical and chemical characteristics of seawater, such as temperature and salinity) and redistribute energy across spatial and temporal scales, influencing large-scale ocean dynamics and biogeochemical processes. Representing their effects in ocean models is vital for accurate long-term climate predictions, as mesoscale eddies impact sunlight reaching deeper ocean levels, ecosystem health, and climate feedbacks [Olbers et al., 2012]. 

However, achieving a balance between resolution and computational efficiency remains challenging. High-resolution ocean models, capable of resolving mesoscale eddies (so called eddy-permitting), are computationally expensive (CPU time and storage) and constrained by numerical stability requirements, such as high viscosity and dissipation, and the neglection of Reynolds constraints on eddy Reynolds stress [Zanna et al., 2017]. In their turn, coarse resolution models, used in climate and Earth System Models, fail to explicitly represent mesoscale processes. This underscores the need for innovative methods to improve their representation without excessive computational costs. 

Machine learning (ML), especially deep learning, offers a promising solution. By leveraging large datasets, ML reconstructs missing information across different spatial and temporal scales. For instance, processes invisible to satellites or unresolved by coarse models can now be modelled using ML techniques. A notable example is using deep neural networks to represent all subgrid atmospheric processes in a climate model and successively replace traditional subgrid parameterizations in a global general circulation model [Rasp et al., 2018]. 

One of the driving mechanisms for the emergence of mesoscales features in the ocean is the baroclinic instability (density-driven flow instability), especially in winter [Boccaletti, et al., 2007; Capet et al., 2008; Fox-Kemper and Ferrari, 2008; Mensa et al., 2013; Oiu et al., 2014; Sasaki et al., 2014]. This instability can be measured using the eddy buoyancy flux (u′b′), which quantifies correlations between 3D velocity and tracer anomalies. 

There several studies dedicate to this problem (Bolton & Zanna, 2019; Zanna & Bolton, 2020; Guillaumin & Zanna, 2021; Bodner et al, 2024). In our work we first concentrate on the vertical component of buoyancy flux w′b′. To address these challenges, we test a 3D Convolutional Neural Network (3DCNN) method to reconstruct w′b′ from large-scale ocean variables – temperature, salinity, and velocities. The model is trained on outputs from the eNATL60 simulation, a high-resolution regional configuration of NEMO (a general global model of ocean circulation), covering the North Atlantic with a horizontal resolution of 1/60°x1/60° and 300 vertical levels. This high-resolution dataset explicitly resolves mesoscale processes, providing an ideal foundation for training. The 3DCNN links coarse-resolution inputs to mesoscale fluxes. Testing involves averaging eNATL60 outputs to simulate various coarse resolutions, creating a robust training database.  

Figure 1. Vorticity filed of eNATL60 with the zoom on Gulf Stream region with high meso-scale activity. The grid on the zoomed plot is 1°x1° to show the meso-scale features that can be missed in course resilution model.

By improving mesoscale process representation (Figure 1), this work paves the way for enhanced biogeochemical and physical modelling in climate simulations. Once validated in other ocean regions, the method will contribute significantly to the accuracy of coarse resolution global ocean and climate models. Keep an eye on the scientific literature next year for the outcomes of this project as it progresses. 

References

1. Boccaletti,  G., Ferrari, R.,  and Fox-Kemper, B.  Mixed layer instabilities and restrati cation, Journal of Physical Oceanography,  37(9):  2228-50, doi: 10.1175/JPO3101.1, 2007. 
2. Bodner, A., Balwada, D., Zanna, L. A Data-Driven Approach for Parameterizing Submesoscale Vertical Buoyancy Fluxes in the Ocean Mixed Layer, arXiv preprint arXiv:2312.06972, https://arxiv.org/abs/2312.06972, 2023. 
3. Bolton, T. and Zanna, L. Applications of deep learning to ocean data inference and subgrid parameterization, J. Adv. Model. Earth Sy., 11, 376–399, doi:  2019. 
4. Capet, X., Campos, E.J., and Paiva, M. Submesoscale activity over the Argentinian shelf, Geophysical Research Letters, 35,  2-6, doi:10.1029/2008GL034736, 2008. 
5. Fox-Kemper, B., and Ferrari, R. Parameterization of mixed layer eddies.  Part II: prognosis and impact, Journal of Physical Oceanography, 38, 1166-79, doi: 10.1175/2007JPO3788.1, 2008. 
6. Guillaumin, A. P. and Zanna, L. Stochastic-deep learning parameterization of ocean momentum forcing. Journal of Advances in Modeling Earth Systems, 13(9), e2021MS002534, doi:https://doi.org/10.1029/2021MS002534, 2021. 
7. Mensa,  J.A.,  Z  Garraffo, Z.,  Griffa, A., Ozgokmen, T.M., Haza, A., and Veneziani, M. Seasonality of the submesoscale dynamics in the Gulf Stream region, Ocean Dynamics, 63, 923-41, doi: https://doi.org/10.1007/s10236-013-0633-1, 2013. 
8. Olbers, D., Willebrand, J., Eden, C. Ocean Dynamics, Springer, Heidelberg, 2012. 
9. Rasp, S., Pritchard, M.S., and Gentine, P. Deep learning to represent subgrid processes in climate models, PNAS  115 (39), 9684-9689, https://doi.org/10.1073/pnas.1810286115, 2018. 
10. Sasaki, H.,  Klein,P., Qiu B., and Sasa, Yi.. Impact of oceanic scale interactions on the seasonal modulation of ocean dynamics by the atmosphere, Nature  Communications, 5, 5636 https://doi.org/10.1038/ncomms6636, 2014. 
11. Zanna, L. and Bolton, T.. Data-driven equation discovery of ocean mesoscale closures, Geophys. Res. Lett., 47, e2020GL088376, https://doi.org/10.1029/2020GL088376, 2020. 
12. Zanna, L., P. P. Mana, J. Anstey, T. David, and T. Bolton. Scale-aware deterministic and stochastic parametrizations of eddy-mean flow interaction, Ocean Modelling, 111, 66–80, https://doi.org/10.1016/j.ocemod.2017.01.004, 2017.