A universal approach to overcome resolution limitations in the ocean is to parametrize physical processes. The traditional method of parametrizing mesoscale range processes on eddy-permitting mesh resolutions, known as a viscous momentum closure, tends to over-dissipate eddy kinetic energy. To return excessively dissipated energy to the system, the viscous closure is equipped with a dynamic energy backscatter, which amplitude is based on the amount of unresolved kinetic energy (UKE). Our study suggests including the advection of UKE to consider the effects of nonlocality on the subgrid. Furthermore, we suggest incorporating a stochastic element into the subgrid energy equation to account for variability, which is not present in a fully deterministic approach. This study demonstrates increased eddy activity and highlights improved flow characteristics. In addition, we provide diagnostics of optimal scale separation between dissipation and injection operators. The implementations are tested on two intermediate complexity setups of the global ocean model FESOM2: an idealized channel setup and a double-gyre setup.

The parameterization IDEMIX for vertical mixing by breaking internal gravity waves is evaluated in three different non-eddy resolving ocean models. Three different products of wave forcing by tidal flow over topography, representing the current uncertainty, are applied and compared to reference simulations without IDEMIX, allowing the model-independent effects of the new closure to be assessed. Common to all models is larger interior mixing work with stronger horizontal structure due to the inhomogeneous forcing functions in all simulations using IDEMIX, in better agreement to observations. Coherent model responses to the stronger mixing work are changes in the thermocline depth including IDEMIX related to stronger shallow overturning cells in the Indo-Pacific Ocean. Furthermore, deeper mixed layer depths in the subpolar North Atlantic are related to an increase of the Atlantic overturning circulation which brings the model closer to observations, coming along with an increase in northward heat transport. In the Southern Ocean, excessive energy input by one of the forcing products leads to unrealistic deep convection in the Weddell Sea in one of the models. The deep Indo-Pacific overturning circulation and the bottom cell of the Atlantic feature an incoherent model response, which may point towards the importance of excessive numerical mixing in the models.

Scale analysis based on coarse-graining has been proposed recently as an alternative to Fourier analysis. It requires interpolation to a regular mesh for data from unstructured-mesh models. We propose an alternative coarse-graining method which relies on implicit filters using powers of discrete Laplacians. This method can work on arbitrary (structured or unstructured) meshes and is applicable to the direct output of unstructured-mesh models. Illustrations and details are provided for discrete fields placed at vertices of triangular meshes. The placement on triangles is also briefly discussed.

The Alfred Wegener Institute Climate Model (AWI-CM) participates for the first time in the Coupled Model Intercomparison Project (CMIP), CMIP6. The sea ice-ocean component, FESOM, runs on an unstructured mesh with horizontal resolutions ranging from 8 to 80 km. FESOM is coupled to the Max-Planck-Institute atmospheric model ECHAM 6.3 at a horizontal resolution of about 100 km. Using objective performance indices, it is shown that AWI-CM performs better than the average of CMIP5 models. AWI-CM shows an equilibrium climate sensitivity of 3.2°C, which is similar to the CMIP5 average, and a transient climate response of 2.1°C which is slightly higher than the CMIP5 average. The negative trend of Arctic sea ice extent in September over the past 30 years is 20-30% weaker in our simulations compared to observations. With the strongest emission scenario, the AMOC decreases by 25% until the end of the century which is less than the CMIP5 average of 40%. Patterns and even magnitude of simulated temperature and precipitation changes at the end of this century compared to present-day climate under the strong emission scenario SSP585 are similar to the multi-model CMIP5 mean. The simulations show a 11°C warming north of the Barents Sea and around 2 to 3°C over most parts of the ocean as well as a wetting of the Arctic, subpolar, tropical and Southern Ocean. Furthermore, in the northern mid-latitudes in boreal summer and autumn as well as in the southern mid-latitudes a more zonal atmospheric flow is projected throughout the year.

We propose to make the damping time scale, which governs the decay of pseudo-elastic waves in the Elastic Viscous Plastic (EVP) sea ice solvers, independent of the external time step and large enough to warrant numerical stability for a moderate number of internal time steps. In this case, EVP becomes very close to the recently proposed modified EVP (mEVP) method in terms of stability. With the proposed damping time scale, the numerical stability of EVP is independent of mesh resolution in setups where the sea ice model component is called every time step of the ocean model. In a simple test case dealing with sea ice breaking under the action of a moving cyclone, EVP with specified damping time scales can produce linear kinematic features very similar to those from the mEVP method. There is more difference in simulated Arctic sea ice thickness and linear kinematic features in realistic configurations, but the difference is minor considering model uncertainties associated with parameter choices in sea ice models.

Substantial changes have occurred in the Arctic Ocean in the last decades. Not only sea ice has retreated significantly, but also the ocean at mid-depth showed a warming tendency. By using simulations we identified a mechanism that intensifies the upward trend in ocean heat supply to the Arctic Ocean through Fram Strait. The reduction in sea ice export through Fram Strait induced by Arctic sea ice decline increases the salinity in the Greenland Sea, which lowers the sea surface height and strengthens the cyclonic gyre circulation in the Nordic Seas. The Atlantic Water (AW) volume transport to the Nordics Seas and Arctic Ocean is consequently strengthened. This enhances the warming trend of the Arctic AW layer, potentially contributing to the “Atlantification” of the Eurasian Basin. Therefore, the Nordic Seas can play the role of a switchyard for the Arctic sea ice decline to influence the Arctic heat budget at mid-depth.

We examine the historical and projected hydrography in the deep basin of the Arctic Ocean in 23 climate models participating in the sixth phase of the Coupled Model Intercomparison Project (CMIP6). The comparison between historical simulations and observational climatology shows that the simulated Atlantic Water (AW) layer is too deep and too thick among the majority of the models and in the multi-model mean (MMM). Moreover, the halocline is too fresh in the MMM. These issues indicate that there is no visible improvement in the representation of Arctic hydrography in the CMIP6 compared to the CMIP5. The climate projections reveal that the sub-Arctic seas are outstanding warming hotspots, supplying a strong warming trend in the Arctic AW layer. The MMM temperature increase averaged in the upper 700 m till the end of the 21st century in the Arctic Ocean is about 40% and 60% higher than the global mean in the SSP245 and SSP585 scenarios, respectively. Comparing the AW temperature in the present day with its future change among the models shows that the temperature climate change signals are not sensitive to the model biases in the present-day simulations. The upper-ocean salinity is projected to become fresher in the Arctic deep basin in the MMM. However, the salinity spread is rather large and the tendency toward stronger upper ocean stratification in the MMM is not shared among all the models. The identified hydrography biases and spread call for a collective effort for systematic improvements of coupled model simulations.

Using the depth (z) and density (ϱ) frameworks, we analyze local contributions to AMOC variability in a 900-year simulation with the AWI climate model. Both frameworks reveal a consistent interdecadal variability, however the correlation between their maxima deteriorates on year-to-year scales. We demonstrate the utility of analyzing the spatial patterns of sinking and diapycnal transformations through depth levels and isopycnals. The success of this analysis relies on the spatial binning of these maps which is especially crucial for the maps of vertical velocities which appear to be too noisy in the main regions of up- and downwelling because of stepwise bottom topography. Furthermore, we show that the AMOC responds to fast (annual or faster) fluctuations in atmospheric forcing associated with the NAO. This response is more obvious in the ϱ than in the z framework. In contrast, the link between AMOC deep water production south of Greenland is found for slower fluctuations and is consistent between the frameworks.

We examine the historical evolution and projected changes in the hydrography of the deep basin of the Arctic Ocean in 23 climate models participating in the Coupled Model Intercomparison Project Phase 6 (CMIP6). The comparison between historical simulations and an observational climatology shows that the simulated Atlantic Water (AW) layer is too deep and thick in the majority of models, including the multi-model mean (MMM). Moreover, the halocline is too fresh in the MMM. Overall our findings indicate that there is no obvious improvement in the representation of the Arctic hydrography in CMIP6 compared to CMIP5. The climate change projections reveal that the sub-Arctic seas are outstanding warming hotspots, causing a strong warming trend in the Arctic AW layer. The MMM temperature increase averaged over the upper 700 m at the end of the 21st century is about 40\% and 60\% higher in the Arctic Ocean than the global mean in the SSP245 and SSP585 scenarios, respectively. Salinity in the upper few hundred meters is projected to decrease in the Arctic deep basin in the MMM. However, the spread in projected salinity changes is rather large and the tendency toward stronger upper 400 m ocean stratification in the MMM is not simulated by all the models. The identified biases and projection uncertainties call for a concerted effort for major improvements of coupled climate models.

It is generally agreed that the resolution of a regular quadrilateral mesh is the side length of quadrilateral cells. There is less agreement on what is the resolution of triangular meshes, exacerbated by the fact that the numbers of edges or cells on triangular meshes are approximately three or two times larger than that of vertices. However, the geometrical resolution of triangular meshes, i.e. maximum wavenumbers that can be represented on such meshes, is a well defined quantity, known from solid state physics. These wavenumbers are related to a smallest common mesh cell (primitive unit cell), and the set of mesh translations that map it into itself. The wavenumbers do not depend on whether discrete degrees of freedom are placed on vertices, cells or edges. The resolution is defined by the height of triangles.