Assessment of the Finite VolumE Sea Ice Ocean Model (FESOM2.0), Part II: Partial bottom cells, embedded sea ice and vertical mixing library CVMIX

The second part of the assessment and evaluation of the unstructured-mesh Finite-volumE Sea ice-Ocean Model version 2.0 (FESOM2.0) is presented. It focuses on the performance of partial cells, embedded sea ice and on the effect of mixing parameterisations available through the CVMIX package. It is shown that partial cells and embedded sea ice lead to significant improvements in the representation of the Gulf Stream and North Atlantic Current as well as the circulation of the Arctic Ocean. In addition to the already existing Pacanowski and Phillander (fesom_PP) and K-profile (fesom_KPP) parameterisations for vertical mixing in FESOM2.0, we document the impact of several mixing parameterisations from the Community Vertical Mixing (CVMIX) project library. Among them are the CVMIX versions of Pacanowski and Phillander (cvmix_PP) and K-profile (cvmix_KPP) parameterisations, the tidal mixing parameterisation (cvmix_TIDAL), a vertical mixing parameterisation based on turbulent kinetic energy (cvmix_TKE) as well as a combination of cvmix_TKE and the recent scheme for the computation of the Internal Wave Dissipation, Energy and Mixing (IDEMIX). The IDEMIX parameterises the redistribution of internal wave energy through wave propagation, nonlinear interactions and the associated imprint on the vertical background diffusivity. Further, the benefit from using a parameterisation of sea ice melt season mixing in the surface layer (MOMIX) for reducing Southern Ocean hydrographic biases in FESOM2.0 is presented. We document the implementation of different model components and illustrate their behaviour. This paper serves primarily as a reference for FESOM users but is also useful to the broader modelling community.


Introduction
Global unstructured-mesh ocean models start to be widely used in climate studies, including the recent CMIP6 simulations (Semmler et al., 2020), although structured-mesh ocean general circulation models are still more mature in terms of features, functionality and complexity due to their long development history.
However, step by step, also the unstructured-mesh ocean models acquire new features and catch up in their to each other. From the CVMIX package we implemented the Pacanowski and Philander 1981, the K-profile parameterization of Large et al. 1994 and the tidal mixing parameterisation of Simmons et al. 2004. Further, the infrastructure of the CVMIX library has been used to implement the turbulent kinetic energy (TKE) scheme of Gaspar et al. (1990) and the scheme for Internal Wave Dissipation and Mixing (IDEMIX) of Olbers and Eden (2013) in the same way as it is done in Gutjahr et al. (2020). It should be mentioned that neither TKE nor IDEMIX is yet part of the official CVMIX package but will hopefully be added to the package in the future.
Beside the prime vertical mixing schemes, like the K-profile scheme, the Pacanowski and Phillander scheme and others that have the purpose to deliver a usable mixing parameterisation for the entire ocean, and vertical mixing schemes like the tidal mixing scheme of Simmons et al. 2004 or IDEMIX that are used to parametrize internal wave processes which then result in a heterogeneous background diffusivity, there are also mixing parameterizations that aim at resolving regional processes. One of them was proposed by Timmerman and Beckmann (2004). It parameterises the wind driven mixing in the Southern Ocean especially when there is insufficient mixing during the melt seasons when other mixing schemes are used. It is used in FESOM2.0 to improve the otherwise too low stratification in the Southern Ocean and Weddell Sea.
The intention of this paper is to document the performance of the newly implemented features --partial bottom cells, "embedded" sea ice, the vertical mixing parameterisations that come with the implementation of CMVIX and the local mixing parameterization of Timmerman and Beckmann (2004), based on comparing the associated hydrographic biases, changes in vertical convection and differences in Meridional Overturning Circulation, using a relatively coarse reference mesh.
The paper is structured as follows. First in Section 2 we describe the mesh configuration and model setup used in the simulations. The description and analysis of partial bottom cells, "embedded" sea ice and vertical mixing schemes is done in Section 3. A discussion and conclusion is given in Section 4.

Model configurations
We use here the FESOM2.0 coarse mesh configuration core2, which is the same mesh as in part 1. It consists of ~0.13M surface vertices, with a nominal resolution of 1° in the bulk of the ocean, ~25km north of 50°N, 1/3° in the equatorial belt and slightly enhanced resolution in the coastal regions. In the vertical, 48 unevenly distributed layers are used, with a vertical grid spacing stepwise increasing from 5m at the surface to 250 m towards the bottom.
All model simulations are initialised from the Polar Science Center Hydrographic winter Climatology (PHC3.0, updated from Steele et al., 2001) and forced by the CORE interannually varying atmospheric forcing fields (Large and Yeager, 2009)  for eddy stirring (Gent et al., 1995;Gent and Mcwilliams, 1990) and we follow the implementation after Ferrari et al., 2010. The isoneutral tracer diffusion (Redi, 1982) coefficient equals to that of GM, same as in Scholz et al. (2019) and in previous FESOM versions (Wang et al. 2014). GM and Redi are scaled with horizontal resolution with a maximum value of 3000 m²/s at 100 km horizontal resolution and change linearly to zero between a resolution of 40 km and 30 km. In the vertical, they are scaled according to Ferrari et al., 2010 andWang et al., 2014. The simulations use as default the K-profile parameterisation for vertical mixing (KPP, Large et al., 1994), a linear free surface (Scholz et al., 2019), levitating sea ice and a full bottom cell approaches, unless otherwise stated.

Partial bottom cells
The concept of partial cells, as an attempt to improve the bottom representation in general ocean circulation models, which was first introduced for the finite volume approach by Adcroft et al., (1997). Although an early version of partial cells was developed by Cox, (1977), and used by Semtner and Mintz, (1977) and Maier-Reimer et al., (1993), it has never got officially released (Griffies et al., 2000). Adcroft et al. (1997) presented three different cases. The first one is the conventional full cell approach, where the depth of the ocean bottom is approximated with the nearest standard depth level of the vertical model discretization.
The second one is the partial cell approach in which the bottom level can take any intermediate depth within the cell, thus capturing water columns more accurately. In these two cases, the bottom features a "stepped" topography and the jump of the steps is smaller for the partial cell approach (Adcroft et al., 1997). The third case introduced by Adcroft et al., (1997) is a shaved cell approach, which assumes a constant slope within each bottom cell and gives the best approximation for a continuous bottom topography. Adcroft et al. (1997) showed that the shaved cell approach gives the most accurate results, but induces a significant increase in computational demand, whereas the partial cell approach is a good compromise between the low computational demand of the full cell approach and the increased accuracy of the shaved cell approach.
Hence, most ocean models ( For the implementation of partial cells in FESOM2.0 we follow the work of Pacanowski and Gnanadesikan, (1998), which implemented partial cells for the B-grid discretization in MOM2 with efforts to minimize pressure gradient errors and spurious diapycnal mixing. They addressed that calculating horizontal pressure gradients needs some special attention for partial cells since not all grid points within the bottom layer are at the same depth. In FESOM2.0, we compute pressure gradient force based on the density Jacobian approach as used by Shchepetkin, (2003) and not the pressure Jacobian approach proposed by Pacanowski and Gnanadesikan, (1998). The density Jacobian approach is less prone to pressure-gradient error than using pressure Jacobian, and therefore the model is more stable. Furthermore, we limited the thickness of the partial bottom cell to be at least half of the full cell layer thickness to reduce the possibility of violating the vertical Courant-Friedrichs-Lewy (CFL) criterion.
Using a B-grid like discretisation, where the scalars are located at vertices of a triangular mesh while the velocities are located at the centroids of the triangular elements, makes it necessary to define the partial cells at both locations. First, the partial bottom depth is defined at the centroids of the triangular elements based on the real bottom topography considering the aforementioned limitation. Then, the vertice partial bottom depth is derived from the deepest partial bottom of the surrounding triangular elements.
In order to demonstrate the effect of the partial cells on the simulated ocean state we performed two model simulations using the full cell and partial cell approaches, respectively. We investigate, first, the temperature biases of the full cell approach with respect to the data of the World Ocean Atlas 2018 (WOA18, Locarnini et al., 2018;Zweng et al., 2018, in the left column of Fig. 1) and, second, the temperature differences between partial cell and full cell (partial-full) averaged over five different depth ranges 0-250m, 250-500m, 500-1000m, 1000-2000m and 2000-4000m (in the right column of Fig. 1).
The full cell setup ( Fig. 1, left) shows positive climatological temperature biasin the northern and southern Pacific, the Atlantic equatorial ocean as well as in the central Indian Ocean through the depth ranges of 0-250m, 250-500m and 500-1000m. In the same depth ranges there are also negative biases in the North Atlantic (NA) subtropical gyre and in the equatorial and southern subtropical Pacific. The depth ranges of 250-500m and 500-1000m indicate cold biases in the Southern Ocean (SO) and around the coast of Antarctica. The deeper depth ranges (1000-2000m and 2000-4000m.) indicate small negative temperature biases in most of the world oceans, except for the Atlantic and Arctic Ocean (AO), which possess a small warming bias in the depth ranges. The Arctic warming anomaly at these depths originates largely from a vertically too much extended Atlantic water inflow branch (not shown), which is a typical fea ture of coarse resolution models (e.g., Ilicak2016).
Using partial cells (   Using partial cells leads to an increase in salinity throughout all depth ranges of the AO relative to using full cells. Further, a salinity increase at the position of the "cold blob", in the GIN sea, in the eastern South Atlantic and parts of the SO can be observed within the upper three depth ranges. Compared to full cells, using partial cells reduces salinity along the pathway of the GS, the Antarctic Circumpolar Current (ACC) in the South Atlantic and along the coast of Antarctica.
The differences in the horizontal velocity speed between partial and full cells ( reveal that partial cells lead to a weakening and a slight southwards shift of the NAC between -45°W and -30°W, and a more pronounced tendency towards a northwest bend of the NAC between -30°W and -15°W, which is nevertheless still too far eastward. By using partial cells the pathway of the Irminger Current (IC) moves closer to the continental slope.
In terms of absolute and anomalous northern and southern hemispheric maximum mixed layer depth (MLD), using partial cells leads to a slight MLD decrease in the southern LS, IS and northern Greenland-Iceland-Norwegian (GIN) Seas, and a slight MLD increase along the pathway of the IC and in the southern and central GIN Seas (Fig. 4c). In the southern hemisphere, partial cells have a more pronounced effect, leading Sv. One can summarize that partial cells lead to a clear improvement of the circulation pattern, especially regarding the branch of the Gulf Stream and NAC even in rather coarse resolved configurations.

Embedded sea ice
As described in Scholz et al. (2019), FESOM2.0 supports the full free surface formulation with two possible options, zlevel and zstar (Adcroft and Campin, 2004). Both options allow for surface freshwater exchanges which can modify the thickness of the surface layer and thus decrease or increase salinity in the surface layer. This avoids the need of virtual salinity fluxes, which are required in the linear free surface (linfs) approach when the layer thicknesses are kept fixed. Using virtual salinity fluxes has the potential to affect the model integrity on long timescales and change local salinities with certain biases (Scholz et al., 2019).
In reality part of sea ice is embedded in the ocean with impact on the ocean pressure below. In the model, when the sea ice loading is omitted, the "levitating" sea ice (Campin et al., 2008) does not impose pressure on the ocean. This is the default case in the case of linfs but also applicable to zlevel and zstar. The other case when ice-loading is considered has "embedded" sea ice (Rousset et al., 2015), which depresses the sea surface according to its mass. Since it affects the layer thicknesses, this case is only available for the full free surface cases of zlevel and zstar. Although freezing and melting have no direct effect on the oceanic pressure, the divergence of the ice transport does modify the ice-loading fields and influences the hydrostatic pressure (Campin et al., 2008). As mentioned by Campin et al., 2008, this effect could be compensated by the divergence of the oceanic transport in the special case where sea ice and ocean velocities match, but in reality sea ice and ocean velocities are rarely identical especially in the presence of high frequency wind forcing. Therefore, sea ice dynamics in combination with the ice-loading coupling can be a source of oceanic variability especially near the ice-edge where ice divergence/convergence is large (Campin et al., 2008).
However, using embedded sea ice harbours the risk that the amount of sea ice loading due to excessive accumulation and the resulting depression in the surface elevation may result in a depletion of the surface layer thickness, when the zlevel option is used, where only the surface layer is allowed to change. To avoid this issue, we limit in FESOM2.0 the maximum ice loading to a sea ice height of 5m when the zlevel option is used. In case of using zstar, the problem is less severe, since here the change in elevation is distributed over all vertical layers, except for the bottom one. This makes zstar to be the recommended option when using embedded sea ice, as also stated by Campin et al., 2008. To show the effect of embedded sea ice on the simulated ocean state, two simulations were carried out using the zstar option of FESOM2.0, one with levitating (omitting the effect of sea ice loading on ocean pressure) the other with embedded sea ice (including the effect of sea ice loading on ocean pressure). shelf of the AO that shows negative anomalies in the depth ranges of 0-250 m, 250-500 m and 500-1000 m.
The changes in temperature and salinity can be explained by the changes in ocean currents. Figure 8 depicts the speed of the horizontal currents in levitating (1 st column) and embedded (2 nd column) sea ice cases as well as their difference (3 rd column). Using embedded sea ice leads to an increase in the speed along the entire boundary current of the Eurasian Basin and along the Lomonosov Ridge, that can be found in all three presented depth ranges. The increase in the velocity of the boundary currents, caused by using embedded sea ice, leads to an enhanced heat and salt transport in the Atlantic water layer originating from the Fram Strait, which results in a warmer and more saline intermediate depth in the Arctic Ocean. The increase in temperature and salinity, especially in the surface layers of the AO using embedded sea ice reduces existing local biases (see Fig. 1 and Fig. 2) that occur when using levitating sea ice. On the whole it can be stated that using embedded sea ice instead of levitating sea ice has some significant effect on the ocean dynamics of the AO, but no effect in the Southern Ocean or Antarctic marginal seas.

Implementation and evaluation of vertical mixing schemes
Besides the already existing Pacanowski and Philander (fesom_PP, Pacanowski and Philander, 1981) and   . Although cvmix_TKE and IDEMIX are not yet a part of the CVMIX project, they use its libraries in the background and will join the project in the future. CVMIX is used by a variety of models, such as MOM6, POP, MPAS or ICON and provides an opportunity of a cross model-spanning vertical mixing implementation that allows for an enhanced cross-model intercomparison.

Comparison of cvmix_KPP, cvmix_PP with previous fesom_KPP and fesom_PP implementation
In FESOM2.0 we implemented cvmix_PP and cvmix_KPP in addition to its previous implementations fesom_PP and fesom_KPP that were adopted from FESOM1.4. The difference between cvmix_PP and fesom_PP lies in the background coefficient for viscosity which is considered in cvmix_PP but not in fesom_PP when computing the diffusivity, following the experience with FESOM1.4 which did not need to be more diffusive. The difference between cvmix_KPP and fesom_KPP lies mainly in the treatment of the Fesom_KPP and fesom_PP produced rather small temperature and salinity differences (note different colorbar ranges between 1 st & 2 nd and 3 rd & 4 th column), considering the biases with respect to the WOA18 climatology. Employing fesom_PP has the tendency to be slightly warmer almost everywhere in the subsurface layers and slightly saltier especially in the AO and fresher in the surface layer of the subtropical and equatorial ocean compared to using fesom_KPP. column) between cvmix_KPP and fesom_KPP (cvmix_KPP minus fesom_KPP) averaged over five different depth ranges. The last column presents the fesom_KPP vertical diffusivity as a reference. Also here, the temperature and salinity differences are rather small compared to the climatological biases shown in Suppl.
2. cvmix_KPP has the tendency to produce in the marginal seas of the AO a slightly fresher surface ocean, while the central AO shows an increase in salinity by ~0.1 psu.
The absolute value of the vertical diffusivity in fesom_KPP is larger than that in cvmix_KPP in the surface layers as well as in regions of unstable stratification (buoyancy frequency < 0), superimposed on a non-

Effects of tidal mixing parameterization of Simmons et al. (2004)
The tidal mixing parameterization of Simmons et al., (2004) provided by CVMIX has been added to To further understand the effect of the tidal vertical mixing, Fig. 14 shows the global zonal mean temperature and salinity differences between the case of cvmix_KPP ando the WOA18 (a, c) and the differences between cvmix_KPPTIDAL and cvmix_KPP (b, d). The temperature of cvmix_KPP shows a rather strong warming bias until 1000 m for the tropical and subtropical ocean as well as until ~2500 m for the ocean north of 50°N with respect to WOA18 (Fig. 14a). The deep ocean features small negative temperature anomalies for the tropical and subtropical ocean and slightly positive biases for the deep SO, when compared to WOA18. The salinity biases of the cvmix_KPP case (Fig. 14c) indicate a more heterogeneous but nevertheless similar picture.
Also here positive salinity biases can be seen in the tropical and subtropical ocean until around 1000m as well as until ~2500m for the ocean north of 50°N. Looking at the temperature and salinity difference between cvmix_KPPTIDAL and cvmix_KPP, it can be seen that the tidal mixing of Simmons et al.,

Effects of Turbulent-Kinetic-Energy (TKE) mixing parameterisation
More elaborate parameterizations of the vertical mixing in the ocean can be achieved by using closure schemes of turbulent kinetic energy (TKE) and the associated turbulent mixing within the mixed layer and below. One of these turbulent closure schemes is by Gaspar et al. (1990)  for the interior mixing (10e-6 m 2 /s 2 ).

Effects of energy consistent combination of TKE with the Internal Wave Dissipation Energy and Mixing (IDEMIX) parameterisation
Besides the standard implementation of vertical background diffusivity in cvmix_TKE using a constant minimum value of TKE to parameterize the effect of breaking of internal waves, cvmix_TKE also allows for the usage of a more sophisticated parameterization of internal wave breaking when combined with the IDEMIX parameterization (Olbers and Eden, 2013;    General cooling biases can be seen for the equatorial and mid-latitudinal surface oceans, between a depth of 1000m to 2000m as well as for the very deep ocean. The salinity biases for cvmix_TKE (Fig. 18c) show too high salinities for the high-latitude ocean north of 40°N and for the surface SO. Small salinity biases can be found in the equatorial and mid-latitudinal surface layers as well as around 40°N between ~1000 and 3000 m.
The temperature differences between cvmix_TKE with and without IDEMIX (Fig. 18b) shows that the IDEMIX leads to a general warming of the equatorial and mid-latitudinal oceans especially between ~500 m and ~2000 m, but a cooling in the northern and southern high-latitude oceans. The salinity differences between cvmix_TKE with and without IDEMIX reveal a similar pattern with an increase in salinity for the equatorial and mid-latitudinal ocean from the surface until a depth ~2000m and a freshening bias in the same depth range for the high-latitudinal oceans and for the entire deep ocean as well.
The corresponding vertical diffusivity difference is shown in Fig. 18e. There, using IDEMIX results in an increase in vertical diffusivity along the bottom topographic slopes in the SO and north of 50°N until 70°N.
Further, an increase in vertical diffusivity can be observed for almost the entire upper ocean until ~2000 m with deeper reaching positive anomalies between -60°S -30°S and 30°N -50°N. A reduction of the vertical diffusivity can be observed for the entire AO from the surface to bottom, for the equatorial and midlatitudinal deep ocean >3000 m as well as for the deep (>4000 m) SO.
The effect of IDEMIX on the MLD is presented in Fig. 19, which shows the northern hemisphere March a) and southern hemisphere September b) cvmix_TKE MLD and the corresponding anomalies between cvmix_TKE with and without IDEMIX. It indicates that the use of IDEMIX leads to an increase in northern hemisphere MLD within the boundary currents of the LS by up to ~1000 m and in the southeastern GIN Seas by up to ~1800 m. In the southern hemisphere September, IDEMIX leads to a significant increase of the Weddell Sea MLD up to ~1800 m. We observe that using cvmix_KPPTiDAL or cvmix_TKEIDEMIX the model cannot maintain the upper halocline in the Weddell Sea. Hence the warm water that shall stay deep is exposed to the surface and the ocean loses heat. It can be well seen from Fig. 14.b and 18.b as blobs of negative temperature differences beneath the surface. As a consequence, the enlarged MLDs in the Weddell Sea appear. We therefore recommend to combine cvmix_KPPTiDAL or cvmix_TKEIDEMIX with the partial bottom cell approach, which has a compensating effect on the stratification in the Weddell Sea (see section 3.1 and Suppl. 1) due to improvements of the current circulation in the Weddell Sea.

Implementation of Monin-Obukhov length dependent vertical mixing
In this section the effect of the Monin-Obukhov length vertical mixing (MOMIX) of Timmermann and Beckmann (2004)  winter deep convection in the Weddell Sea, thus affecting the basin wide ocean-and meridional overturning circulation (Timmermann and Beckmann, 2004). MOMIX computes the Monin-Obukhov length based on heat flux, freshwater flux, wind stress, sea ice concentration and sea ice velocity following the approach of Lemke (1987), and subsequently increases the vertical diffusivity within the Monin-Obukhov length to a value of 0.01m²/s.
Due to its success in reducing the aforementioned mean biases, MOMIX is applied at the moment in  cell is reduced by ~1 Sv when using MOMIX. We conclude that using MOMIX helps to alleviate the problem of large MLDs in the Weddell Sea which we addressed above. Hence, the options cvmix_KPPTiDAL or cvmix_TKEIDEMIX are strongly recommended to be used in combination with MOMIX, which is per default active only South of -50°S.

Discussion and Conclusions
This paper describes the two new features --partial cells and embedded sea ice introduced to FESOM2.0 and the implementation of the vertical mixing library CVMIX (cvmix_PP, cvmix_KPP, cvmix_TKE, IDEMIX and cvmix_TIDAL), together with the elaboration of the effect of MOMIX. These new features expand the functionality of FESOM2.0, its applicability and its ability to be better compared to other state of the art ocean general circulation models. With its model components implemented, FESOM2.0 is mature for its practical applications and holds its leading role in the competition of the global unstructured ocean models.
We demonstrate the effect of using partial cells by comparing them against the full cell approach. It is shown that partial cells lead to an improved representation of the Gulf Stream branch, with a reduction in the cold bias in the northwest corner of the North Atlantic associated with an improved NAC pathway. Further, partial cells lead to a "northwest corner like" meridional deflection of the NAC between -30°W and -15°W which is still too far east, but leads to an improved representation in a rather coarse configuration which would otherwise be dominated by a rather zonal NAC. Partial cells also lead to a general speed up of the boundary currents shown as an example for the North Atlantic.
The improvement of the NAC pathway and the speedup of the boundary currents especially in the subpolar gyre by using partial cells is described by a variety of publications (e.g. Barnier et al., 2006;Käse et al., 2001;Myers, 2002). Besides all its advantages, partial cells also harbor the risk of increasing the existing biases, like in our coarse configuration the deep Arctic warm bias, which is largely inherited from the Atlantic Water inflow branch that expands too deep. The tendency of partial cells to increase the velocity in the boundary currents leads to an enhancement of the Atlantic Water inflow to the Arctic Ocean. As the temperature in the Arctic Atlantic Water layer is already overestimated without using partial cells, the warm bias becomes even larger when partial cells are used. However, this is not the principle drawback of partial cells, but rather an issue of model tuning for the pan-Arctic region, which is part of our on-going work (for example, evaluating different numerical schemes of momentum viscosity). In the southern hemisphere, using partial cells leads to a significant reduction of the otherwise rather high MLD in the Weddell Sea. Regarding The second feature that was presented, is the effect of embedded sea ice vs. the standard case of levitating sea ice. Embedded sea ice allows for a further step towards a more realistic and physical ocean-sea ice interaction by adding the sea ice loading to the ocean pressure. This has the potential of increasing ocean variability especially near the sea ice edge. Our results indicate that the embedded sea ice has only a minor effect on the sea ice distribution itself. Nevertheless the effect is the strongest for the Northern Hemisphere summer, when the sea ice edge retracts towards the Arctic Ocean interior. Here embedded sea ice leads to an up to 9% increase in the sea ice concentration in the eastern Arctic Ocean marginal seas, which also leads to an increase in the bias of the sea ice edge, and to a 6% decrease in the marginal seas of the western Arctic Ocean, which slightly reduces the sea ice extent bias there. The effect of embedded sea ice on the hydrography of the Arctic Ocean is much more significant, with an increase in temperature and salinity of up to 0.5°C and 0.1psu, respectively through most of the upper 1000 m. The increase in temperature and salinity is connected to a particular increase of the boundary currents especially along the eastern boundaries of the Eurasian Basin but also to a strengthening of the cyclonic current along the Lomonosov Ridge, which was otherwise rather weakly represented in the levitating sea ice case. The deficiencies of the Arctic Ocean currents representation in our model configuration can be partially attributed to the rather coarse resolution.
However, with embedded sea ice we seem to be able to at least partly counteract the effect of low resolution and improve the Arctic Ocean current structure at rather low costs. We note that embedded sea ice could also deteriorate the model results in some cases. Since the boundary currents around the Eurasian Basin get enhanced, the already existing Atlantic Water layer biases get enhanced. However, as mentioned above, this is an issue of model tuning with this coarse resolution setup, not a drawback of embedded sea ice itself.
To further expand the functionality and comparability of FESOM2.0 we implemented the vertical mixing library CVMIX and its components, which in our implementation include cvmix_PP, cvmix_KPP, cvmix_TIDAL, cvmix_TKE and cvmix_TKE+IDEMIX. At first, the vertical mixing parameterizations fesom_KPP and fesom_PP, which have been already implemented in FESOM2.0, are briefly evaluated. It is shown that fesom_PP produces a slightly colder tropical and subtropical but warmer polar oceans on the surface, with a largely warmer ocean below the surface layer depth range, when compared to fesom_KPP.
This makes between these two, fesom_KPP the preferred vertical mixing option at least in terms of mean temperature biases. In terms of salinity biases, fesom_PP performs better in the surface and subsurface AO as well as in the equatorial Atlantic and Indian Ocean, while otherwise fesom_KPP indicates smaller biases.
In the next instance, fesom_KPP and cvmix_KPP have been compared to each other, since there are slight differences in their implementation. The difference in implementation leads only to minor differences in temperature throughout all considered depth ranges. Regarding the salinity differences, cvmix_KPP produces a considerably fresher surface AO compared to fesom_KPP, which is attributed to a reduced near surface vertical diffusivity in cvmix_KPP that leads to an over-stabilisation of the AO halocline. This enhances the  Pacanowski and Philander (1981).
The effect of implementing cvmix_TIDAL in combination with cvmix_KPP was further assessed.
cvmix_TIDAL serves here as a resourceful way to heterogenize the effect of tidally induced internal wave breaking that is otherwise homogenized in a constant or latitude dependent value for the background diffusivity. Using cvmix_TIDAL clearly leads to an enhancement of the vertical diffusivity along the slopes of the bottom topography, where tidally related internal wave breaking is induced. This leads especially in the high-latitude marginal seas, e.g. Sea of Okhotsk and Bering Sea but also Arctic Ocean and Southern Ocean, to a decrease in temperature and salinity due to the enhanced mixing along their shelfs. This enables cvmix_TIDAL to improve some of the existing local temperature and salinity biases within FESOM2.0 at rather low computational costs. However, the enhanced vertical diffusivity along the shelf of the Weddell Sea weakens the stratification and leads to a further increase in the MLD of the Weddell Sea of up to 1000 m.
Further, the implications of TKE vertical mixing parameterisation in FESOM2.0, added by  and Gutjahr et al. (2020) to the CVMIX library, was evaluated based on a comparison with fesom_KPP. It is shown that the mean temperature and salinity differences between cvmix_TKE (Fig. 17) and fesom_KPP ( Fig. 9) show very similar patterns. cvmix_TKE tends to produce a generally colder tropical and extratropical ocean together with slightly warmer polar oceans when compared to fesom_KPP. The salinity differences between cvmix_TKE and fesom_KPP shows that cvmix_TKE tends to produce a significantly saltier surface layer AO, revealing a much smaller salinity bias for the Arctic Ocean interior. This is largely connected to enhanced surface vertical mixing along the Arctic Ocean shelf break (not shown) within cvmix_TKE, that helps to partly destabilize the AO halocline. The improvement of the Arctic Ocean hydrography when using cvmix_TKE is also found by Gutjahr et al. (2020)  which is accompanied by positive temperature and salinity anomalies between cvmix_TKE and fesom_KPP.
Following the comparison of cvmix_TKE and fesom_KPP, a side by side comparison of cvmix_TKE with and without IDEMIX was carried out. Here IDEMIX provides an alternative formulation of the background diffusivity in cvmix_TKE using a radiative transfer equation of weakly interacting internal waves (Olbers and Eden 2013), where energy is transferred from sources of internal waves to wave sinks, such as the breaking of internal waves, which provide a source for TKE, leading to an energetically more consistent treatment of internal mixing . As compared to the tidal background mixing parameterization of Simmons et al (2004), IDEMIX allows not only for the generation of internal waves by barotropic tides interacting with marine topography, but also for their propagation in the horizontal and vertical directions away from region of generation and their damping due to wave-wave interaction or interaction with the continental shelf. Further, IDEMIX allows for the excitation of internal waves at the base of the mixed layer by high frequency wind forcing ).
The combined TKE + IDEMIX approach was already applied in a couple of publications , Nielsen et al. 2018, Gutjahr et al. 2020

20
This is in contrast to the findings of Gutjahr et al. 2020, who found that in their coupled MPI-ESM1.2 simulation, IDEMIX led to a reduction of the vertical mixing in the Weddell Sea allowing for more local stratification. On possibility to overcome the lack of performance of IDEMIX but also of cvmix_TIDAL in the Southern Ocean and Weddell Sea could be its combination with partial bottom cells, which had the tendency to significantly reduce the deep convection in the Weddell Sea. At this point it needs further studies also with FESOM2.0 to analyse the different behaviour of IDEMIX that could be influenced by local resolution, coupled ocean-atmosphere feedback or just different background water mass structure.
Nevertheless, the achievable energetic consistency with the combined cvmix_TKE+IDEMIX approach is an interesting feature that should find more applications in the ocean modelling community, although there is still some way to go to better understand and improve its integration.
The last part in this paper deals with the vertical mixing parameterisation MOMIX of Timmermann and      (Cavalieri et al., 1996) contour of the 15% sea ice extent. The lower row shows the corresponding sea ice concentration anomalies between embedded and levitating sea ice (embedded minus levitating ) averaged over the same period.