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 transient climate response (TCR) is 20% higher in the Alfred Wegener Institute Climate Model (AWI-CM) compared to the Max Planck Institute Earth System Model (MPI-ESM) whereas the equilibrium climate sensitivity (ECS) is only by less than 10% higher in AWI-CM. These results are largely independent of the two considered model resolutions for each model. The two coupled CMIP6 models share the same atmosphere-land component ECHAM6.3 developed at the Max Planck Institute for Meteorology (MPI-M). However, ECHAM6.3 is coupled to two different ocean models, namely the MPIOM sea ice-ocean model developed at MPI-M and the FESOM sea ice-ocean model developed at the Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research (AWI). A reason for the different TCR is related to ocean heat uptake in response to greenhouse gas forcing. Specifically, AWI-CM simulations show stronger surface heating than MPI-ESM simulations while the latter accumulate more heat in the deeper ocean. The vertically integrated ocean heat content is increasing slower in AWI-CM model configurations compared to MPI-ESM model configurations in the high latitudes. Weaker vertical mixing in AWI-CM model configurations compared to MPI-ESM model configurations seems to be key for these differences. The strongest difference in vertical ocean mixing occurs inside the Weddell Gyre and the northern North Atlantic. Over the North Atlantic, these differences materialize in a lack of a warming hole in AWI-CM model configurations and the presence of a warming hole in MPI-ESM model configurations. All these differences occur largely independent of the considered model resolutions.

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.

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.

Many state-of-the-art climate models do not simulate the Atlantic Water (AW) layer in the Arctic Ocean realistically enough to address the question of future Arctic Atlantification and its associated feedback. Biases concerning the AW layer are commonly related to insufficient resolution and exaggerated mixing in the ocean component as well as unrealistic Atlantic-Arctic Ocean exchange. Based on sensitivity experiments with FESOM1.4, the ocean-sea ice component of the global climate model AWI-CM1, we show that even if all impediments for simulating AW realistically are addressed in the ocean model, new biases in the AW layer develop after coupling to an atmosphere model. By replacing the wind forcing over the Arctic with winds from a coupled simulation we show that a common bias in the atmospheric sea level pressure (SLP) gradient and its associated wind bias lead to differences in surface stress and Ekman transport. Fresh surface water gets redistributed leading to changes in steric height distribution. Those changes lead to a strengthening of the anticyclonic surface circulation in the Canadian Basin, so that the deep counterflow carrying warm AW gets reversed and a warm bias in the Canadian Basin develops. An underestimation of sea ice concentration can significantly amplify the induced ocean biases. The SLP and anticyclonic wind bias in the Nordic Seas weaken the cyclonic circulation leading to reduced AW transport into the Arctic Ocean through Fram Strait but increased AW transport through the Barents Sea Opening. These effects together lead to a cold bias in the Eurasian Basin.

The Atlantic Meridional Overturning Circulation (AMOC) is one of the most essential mechanisms influencing our climate system. By comparing constant depth (z-AMOC) and density (ρ-AMOC) frameworks under pre-industrial, historical and abrupt 4xCO2 scenarios we analyze how the circulation mean state and variability differ amongst them. Water mass transformations are also assessed as a matter of analyzing surface-induced and interior-mixing-induced transformations. As expected, both location and strength of AMOC maxima are deeply affected by the framework choice, with the AMOC reaching a maximum transport of 21 Sv at around 35°N under constant depth coordinates, as opposed to ∼25 Sv at 55°N when diagnosed from density surfaces for both pre-industrial and historical climate. When quadrupling the CO2, both frameworks exhibit an abrupt AMOC weakening followed by a steady recovery to maximum values of 10-15 Sv. The z-AMOC maxima timeseries correlates more with those at 26°N (r ∼0.7) than with the ρ-AMOC maxima (r ∼-0.3), due to the flatter isopycnals in the z framework even in the subpolar North Atlantic, where isopycnals are, in fact, steeper. Based on this discrepancy, we argue that the density framework is more coherent to the physics of this circulation by directly incorporating water mass transformations and their density structure. We suggest that more analysis across timescales and under different conditions must be performed with density surface outputs being provided by as many models as possible, to enable a more comprehensive analysis of these two frameworks and their applications.