go through: Dr. Thomas Wilder
The term “numerical gray zone” may seem abstract to many, but for those involved in atmospheric and ocean modelling, it represents a challenging dilemma. The numerical gray zone describes any numerical model that can resolve processes in some regions but not others, such as mesoscale eddies at low and high latitudes respectively. Mesoscale eddies are high-energy rotating currents with length scales of 10 – 100 kilometers found throughout the global ocean. Similar difficulties surrounding the gray zone arise in convection-permitting atmospheric models.
Ocean patterns that allow eddies suffer from this numerical gray area, making accurate representation of eddies extremely difficult. For example, the Met Office Hadley Center globally coupled medium-resolution climate model used in CMIP6 performed poorly in the Southern Ocean. In particular, the current flowing through the Drake Passage, the Antarctic Circumpolar Current, is thought to be weaker due to the warm temperature bias (Kuhbrodt et al., 2018). The reason for these problems is thought to be due to the poor representation of mesoscale processes in the NEMO ocean model components. Ocean models that allow for eddies have the potential to address more important processes while not being too computationally expensive to run. Ideally, higher resolution models would be used to address this issue. Unfortunately, we are limited by computational limitations.
The Southern Ocean is a major region of water transformation, with deep water rising and interacting with the atmosphere and cryosphere. The Southern Ocean is also home to the Antarctic Circumpolar Current, a violent eddy field. In this region, eddies transport heat poleward, serving as a potential mechanism for transporting warm water across the continental shelf onto ice shelves. In addition, eddies also contribute to the ventilation of surface and internal seawater, affecting air-sea exchange of properties such as heat and carbon, and even affecting cloud properties and rainfall. The importance of the Southern Ocean is obvious and accurate representation of mesoscale eddy processes is crucial.
As part of the Future Earth System Models 2025 project, our mission is to try to improve the Southern Ocean circulation in the eddy-permitting NEMO model by implementing a new eddy parameterization. A parameterization is an equation that approximates the effects of processes occurring below the resolution of the model grid. Here, we are interested in the Leith viscosity parameterization, which represents mesoscale turbulence more faithfully than other more common closures (Bachman et al., 2017). There are two Leith schemes: 2D Leith is proportional to relative vorticity; QG Leith is proportional to quasi-geostrophic vorticity. One benefit of Leith closures is that they can be used as Gent-McWilliams (GM) diffusion coefficients. GM parameterization works by modeling the eddy transport of ocean tracers such as temperature and salinity. Adopting a typical GM scheme at the eddy-allowed resolution will reduce the eddies that the model has explicitly resolved. Through the Leith scheme used in GM, they were considered to parameterize unresolved eddies without weakening resolved eddies. Additional developments have also been undertaken by the Met Office (MO), including the use of weak GM coefficients when the model cannot resolve eddies unambiguously. The development of these MOs has shown promising results (Guiavarc'h et al., 2024).
So far we have performed simulations examining the effects of Leith viscosity parameterization in the NEMO model ORCA025 that allows eddies. More specifically, we run the Met Office's global ocean sea ice 9 configuration. The image above shows the results of transmission through the Drake channel during a spin cycle. We intend to analyze the second cycle soon. The line labeled biharm is the standard simulation developed by MO. Their respective dashed lines are the same simulations without changes in MO. The other rows show the results of the Liss scheme. With the Leith scheme, we see an increase in transmission of about 10-20 Sverdrups (Sv), which is exactly what we want to see, considering the observed value is about 170 Sv.
Our analysis is still in its infancy and many questions still require answers. Did Project Leith reduce temperature bias in the Southern Ocean? Do we see any changes in the formation of water masses? In the Southern Ocean, do we see reduced sensitivity of zonal transport and overturning circulation to wind speed changes? By improving ocean circulation through Leith closures, we hope better use of eddies will allow models to make long-term climate predictions. Please look out for a publication later this year.
Further reading:
Bachman, SD, Fox-Kemper, B., & Pearson, B. (2017). Scale-aware subgrid patterns for quasi-geostrophic turbulence. J. Geophys. resource. Ocean, 122(2), 1529–1554. https://doi.org/10.1002/2016JC012265
Guiarc'h, C., Stokey, D., Black, AT, Blockley, E., Megan, A., Hewitt, HT,. . . Ann, B. (May 2024). GOSI9: UK global ocean and sea ice configuration. EGU Fields, 1-38. https://doi.org/10.5194/egusphere-2024-805
Kubrod, T., Jones, C., Thaler, A., Stockey, D., Blockley, E., Stringer, M.,. . . Walton, J. (November 2018). Low-resolution version of HadGEM3 GC3.1: development and assessment of global climate. J.Adv. Model. Earth Systems, 10(11), 2865–2888. https://doi.org/10.1029/2018ms001370
