The term “numerical grey zone” might seem abstract to many, but for those involved in atmospheric and oceanic modeling, it represents a challenging predicament. The numerical grey zone describes any numerical model that can resolve processes in some regions but not others, e.g. mesoscale eddies in low and high latitudes, respectively. Mesoscale eddies are energetic rotating currents with length scales of 10 – 100 km that populate the global ocean. Similar difficulties surrounding the grey zone arise in convective permitting atmospheric models.
Eddy-permitting ocean models suffer from this numerical grey zone, making it inextricably difficult to accurately represent eddies. For example, the Met Office Hadley Centre global coupled medium resolution climate model used in CMIP6 performed poorly in the Southern Ocean. In particular, the current flowing through Drake passage, the Antarctic Circumpolar Current, was took weak, owing to a warm temperature bias (Kuhlbrodt et al., 2018). The cause of these issues was reasoned to be because of the poor representation of mesoscale processes in the NEMO ocean model component. Eddy-permitting ocean models have the potential to resolve more important processes while not being too computationally expensive to run. Ideally, higher-resolution models would be used to navigate this problem. Unfortunately, we are constrained by computational limits.
The Southern Ocean is a major region of water mass transformations, where deep waters upwell and interact with the atmosphere and cryosphere. The Southern Ocean is also home to the Antarctic Circumpolar Current that hosts a vigorous eddy field. In this region, eddies transport heat polewards, acting as a potential mechanism for the cross-shelf transport of warm waters onto ice shelves. Moreover, eddies also contribute to the ventilation of surface and interior ocean waters, influencing the air-sea exchange of properties like heat and carbon, and even affecting cloud properties and rainfall. The Southern Ocean’s importance is clear, with it being vital to accurately represent mesoscale eddy processes.
As part of the project “Earth System Models for the Future 2025” our task was to try and improve Southern Ocean circulation in the eddy-permitting NEMO model by implementing a new eddy parameterisation. A parameterisation is an equation that approximates the effect of processes that take place below the model’s grid resolution. Here, we are interested in the Leith viscosity parameterisations, which more faithfully represent mesoscale turbulence compared with 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. A benefit of the Leith closures is their utility in being used as the Gent-McWilliams (GM) diffusivity coefficient. The GM parameterisation works by mimicking the eddy transport of oceanic tracers like temperature and salinity. Employing the typical GM scheme at eddy-permitting resolution degrades eddies that have been resolved explicitly by the model. With the Leith schemes used in GM, they are argued to simultaneously not weaken resolved eddies while parameterising unresolved eddies. Added developments have also been carried out by the Met Office (MO), which include a weak GM coefficient used when the model cannot explicitly resolve eddies. These MO developments have shown promising results (Guiavarc’h et al., 2024).
To date, we have carried out simulations examining the impact of the Leith viscosity parameterisations in the eddy-permitting NEMO model, ORCA025. More specifically, we run the Met Office’s Global Ocean Sea Ice 9 configuration. The above figure shows the results of the transport through Drake passage during the spin-up cycle. We intend to analyse the second cycle soon. The line labelled biharm is the standard simulation developed by the MO. Its respective dotted line is the same simulation without the MO changes. The other lines show the results of the Leith schemes. With the Leith schemes, we see an increase in transport of around 10-20 Sverdrups (Sv), which is exactly what we want to see, considering that observations are around 170 Sv.
Our analysis is still in its infancy with many questions still requiring an answer. Do the Leith schemes reduce the Southern Ocean temperature biases? Do we see any changes to the formation of water masses? In the Southern Ocean, do we see any reduction in sensitivity of zonal transport and overturning circulation to wind speed changes? By improving the ocean circulation with the Leith closures, we hope to better utilise eddy-permitting models for long-range climate projections. Watch out for a publication later in the year.
Further reading:
Bachman, S. D., Fox-Kemper, B., & Pearson, B. (2017). A scale-aware subgrid model for quasi-geostrophic turbulence. J. Geophys. Res. Oceans, 122 (2), 1529–1554. https://doi.org/10.1002/2016JC012265
Guiavarc’h, C., Storkey, D., Blaker, A. T., Blockley, E., Megann, A., Hewitt, H. T., . . . An, B. (2024, May). GOSI9: UK Global Ocean and Sea Ice configurations. EGUsphere, 1–38. https://doi.org/10.5194/egusphere-2024-805
Kuhlbrodt, T., Jones, C., Sellar, A., Storkey, D., Blockley, E., Stringer, M., . . . Walton, J. (2018, November). The Low-Resolution Version of HadGEM3 GC3.1: Development and Evaluation for Global Climate. J. Adv. Model. Earth Syst.,10 (11), 2865–2888. https:doi.org/10.1029/2018ms001370
