Summary and recommendation

This manuscript proposes a modeling hierarchy, DINO, intended to act as a testbed for eddy parameterizations. The new hierarchy extends NeverWorld2, a previous such testbed, by including both temperature and salinity, an (idealized) nonlinear equation of state, an inter hemispheric overturning circulation, and diabatic processes. All of these either influence or are influence by mesoscale eddies, so DINO would provide a more stringent and comprehensive test of eddy parameterizations. The ocean modeling community is in desperate need of such standardized testbeds and DINO stands to be a very useful contribution. The manuscript is generally well-written and the hierarchy carefully documented, with a few exceptions detailed under my specific comments. The comments primarily ask for clarification, although I do have concerns about the design of the freshwater forcing and the shortness of the period analyzed. I support publication if the authors can address these comments and concerns.

Specific comments

1. Two of the design decisions seem unusual or arbitrary. While they are unlikely to impact the ability of DINO to serve as a testbed for parameterizations, they deserve a few lines of additional justification
1. The reentrant part of the domain spans 20º. This is significantly wider than than the width of Drake Passage, which is about 8º wide. What is the rationale for choosing this width? To match NeverWorld2?
2. Why is a minimum depth 2000 m? Neverworld2 has a minimum depth of 200 m, which is a reasonable (if deep) value for continental shelves. In nature, the upper part of the North Atlantic deep western boundary current (associated with Labrador Sea Water) is found around 1000 m depth (Bower and Hunt 2000) and the interactions of the DWBC with the slope are thought to impact the Gulf Stream (Zhang and Vallis 2007). It would thus seem desirable to have the DWBC flow along the sloping topography rather than against the free-slip wall. However, Figure 5 shows that most of the southward flow of the mid-depth overturning cell is found at densities of 27 kg m^–3 or lighter, which figure 6 shows is shallower than 2000 m. 
2. It should be clarified that the equation of state (equation 6) is not an approximation to the in situ density, but the potential density (apparently referenced to the surface). The in situ density has a pressure dependence that leads to a nearly linear increase in density of about 4.5 kg m^–3 per km of depth. This, if the density at the surface is about 1026 kg m^–3, the density at 2000 m should be about 1035 kg m^–3. The potential density referenced to 2000 m (used in figures 5 and 6) should therefore be in the 30s rather than the 20s. It might be simpler to use potential density referenced to the surface in these figures—the numerical values are unlikely to change much, but they’d be closer to what people would expect for potential density. 
3. Lines 112–114: Note that AABW and NADW have essentially the same density at the surface, but AABW is denser than NADW at depth due to the thermobaric effect (Nycander et al. 2015). Since DINO’s equation of state supports the thermobaric effect, surface forcing that produces AABW that is denser than NADW at the surface may result in AABW that is excessively dense at depth.
4. Lines 189–190: It is not clear how starting from rest ensures conservation or what is being conserved.
5. The approach to freshwater forcing does not seem adequate. Salinity resorting is indeed unrealistic, but five years is unlikely to be sufficient to produce a stable climatology of moisture fluxes and four years is not long enough for the circulation to adjust to the change in the boundary conditions. Since the procedure for producing the freshwater forcing is repeated independently for each model resolution, this leads to each resolution being subjected to different freshwater forcing. This is undesirable for a model hierarchy that is supposed to only differ by resolution and subgridscale parameterizations. In lieu of devising a new freshwater forcing scheme (which would require expensive recomputations), it would be more straightforward and clarifying to simply forgo freshwater forcing and analyze the cases with salinity restoring. 
6. Similarly, four years does not seem sufficient to characterize the mean state of higher resolution models.
7. Page 12: The rationale for the approach to separating the mean and eddy heat fluxes is not clear. A three month average doesn’t seem sufficient to separate mesoscale eddy timescales from the mean—why not use an average over the full four years available? Also, considering that resolved eddies still play a role in the R1 simulation, why are the effect of these not also diagnosed and added to the GM contribution?

Technical corrections

1. Remove indent on line following equation (5).

References

Bower, A. S., and H. D. Hunt, 2000: Lagrangian observations of the deep western boundary current in the North Atlantic Ocean. Part I: Large-scale pathways and spreading rates. J. Phys. Oceanogr., 30 (5), 764–783.

Nycander, J., M. Hieronymus, and F. Roquet, 2015: The nonlinear equation of state of sea water and the global water mass distributions. Geophys. Res. Lett., 42, 7714–7721.

Zhang, R., and G. K. Vallis, 2007: The role of bottom vortex stretching on the path of the North Atlantic western boundary current and on the Northern Recirculation Gyre. J. Phys. Oceanogr., 37 (8), 2053–2080.

Reviewer: Elizabeth Yankovsky

Overall I found this to be a very relevant and useful study, with excellent figures and well-written text. Please see my minor comments below:

Introduction first paragraph: First sentence — there isn’t really a scale separation between “underlying processes” and “changes in Earth’s climate”, there are changes and dynamics on a continuum and they’re all linked/interact with each other. Second sentence “their” isn’t obviously grammatically related to “climate simulations”. Line 16: There’s a difference between mesoscale eddies and geostrophic turbulence (the latter is a broader term); I’d say something like “mesoscale eddies are the most salient feature arising from geostrophic turbulence”.

Introduction second paragraph: It’s not just winds sustaining the PE reservoir but also heterogeneous buoyancy forcing. Line 19: There’s a cascade of energy into the first baroclinic mode as well, so it’s an upscale and downscale cascade of energy (see Smith and Vallis 2001 Fig. 4 for example). In the barotropic mode there’s an upscale transfer, but in the higher modes the energy transfers go both ways and funnel energy into the 1st baroclinic mode.

How valid are the parameter values chosen for the linear EOS when considering high-latitude vs. low-latitude behavior (where S vs. T are respectively more dominant in setting density)?

Can you explain more what is meant by the NW2 style bathymetry introducing an “undesirable separation into two basins with respect to dense water formation and overturning”? The real ocean does have this feature so I’m not sure where this hypothesis came from. We found that the ridge was important to setting some of the vertical structure properties of the eddies and potentially the broader circulation (Yankovsky, Zanna, Smith, 2022).

There is no mention of the dissipation scheme being used until Table 2, I recommend stating this in the model equations/setup. In NW2 we had to think at length about a viscosity scheme that could be applied in a consistent way across resolutions (ended up using biharmonic Smagorinsky). This isn’t being done here, the viscosity parameterizations in R1 are different in formulation than R4 and R16; could the authors speak more about the reasons and implications of this?

Lines 171-179: Is GM by default added to the higher resolution simulations as well, just with a lower coefficient? I would be more explicit about this. This is in itself a “parameterization” choice that may conflict with other choices the users make on top of that to test other eddy parameterization schemes. For example, in my work on backscatter parameterizations, I found that backscatter can replace the need for GM in eddy permitting simulations (and using the two simultaneously is problematic, see Yankovsky et al. 2024).

Line 186: Can you show a figure verifying that the tracers have reached a quasi-equilibrated state? This can be incorporated as a panel into one of the first several figures. I’m curious what is meant by “quasi” here, are the tracers in the deep ocean still evolving? How far out of equilibrium are the higher-resolution simulations? Would be helpful to visualize this in a figure as well. In the higher-resolution simulations, it would be helpful to have more discussion of what the lack of equilibration can introduce error-wise into the analysis.

How do you propose accounting for the unresolved submesoscale dynamics? Is there any parameterization for those effects implemented, and how might that conflict with the mesoscale parameterization?

Might be interesting to consider referencing some of the recent work being done on the Oceananigans model in light of the more traditional modeling efforts/studies addressed here. One can make the argument that rather than layering more complex parameterization schemes on top of each other, we should instead focus on developing modeling frameworks that are able to resolve down to submesoscales through GPU-based architectures.  See Silvestri et al. 2025 (https://doi.org/10.1029/2024MS004465)