See attached.

This is a fairly straight forward and interesting paper that makes a useful contribution to understanding how constrained computational resources should be used in climate change scenarios. The paper focuses upon Eddy Kinetic Energy (EKE) and how to make reliable estimates of how this might change as a result of climate change. To do so, the authors use an ensemble of eddy-permitting models alongside a configuration specifically designed to better represent the Southern Ocean. I found the conclusion that only a single realisation of a given model is needed to appreciate how climate change affects EKE compelling. This paper makes a useful contribution to on-going discussion in the literature regarding the impact of climate change on the Southern Ocean and its mesoscale eddy field.

Most of my comments regarding the paper are quite minor. There isn’t complicated analysis here, which is a strength of the paper as it makes it simple to understand. However, the paper’s clarity could be improved, particularly in Section 2. In addition, there are some choices in the analysis, such as using geostrophic surface EKE for one model and subsurface full EKE for another, that need stronger justification.

As a final point, from the title I was expecting something more technical, like using single precision maths, alongside the use of FESOM’s non-uniform resolution. The paper is really using a carefully designed spinup procedure with an equally carefully put together finite element model and forcing dataset. The title should be altered to reflect this.

Specific Comments

In Section 2.1 it is currently tricky to understand which model is which resolution and whether they are coupled or ocean-only. After reading the paper there should be three; the high resolution SO3 configuration, a medium-resolution ocean-only model used to supply SO3 with initial conditions, and the coupled AWI-CM-1 ensemble. At the moment this isn’t entirely clear up front. The first paragraph made me think that SO3 was coupled, while the third paragraph makes it clear that it is ocean-only. It also isn’t clear here that AWI-CM-1 is an ensemble instead of a single model run. In the case of AWI-CM-1, whilst details are elsewhere and a citation is given, it would be much clearer to tell the reader that this is a five member ensemble and how that ensemble is generated in a sentence or two. The “medium-resolution eddy-permitting, ocean-only transient simulation” isn’t used in detail, but its existence is a little obfuscated here. At the beginning of the second paragraph it is stated that “model experiments with SO3 consist of a medium-resolution…”, whilst the third paragraph tells us the SO3 is “the higher-resolution ocean grid”. This can be easily remedied, but certainly caused me to pause on first read through.

Section 2.4 describes how the geostrophic velocities are calculated to facilitate how the models are compared. There are a few issues here that should be dealt with. Firstly, no explanation is given why geostrophic surface velocity wasn’t used for SO3. This would be a simpler way to guarantee that all ageostrophic motions are removed and make for a better comparison with the AWI-CM-1 ensemble and altimetry. If SSH is available for SO3, a quick comparison would validate the use of subsurface velocities instead. If there is a substantial difference, then this would require further work to ensure that the rest of the paper still stands. Secondly, equations (1) and (2) should be relocated to the middle of the first paragraph, where they are referred to. They are currently orphaned at the end of the paragraph. They are also incorrect; the pre-multiplier to the differential should be g/f, not gf, although I suspect this is purely a typo given that this would grossly alter the order of magnitude of the EKE.

The method used to test ensemble agreement seems idiosyncratic. It isn’t a standard procedure that I’m aware of, although this obviously doesn’t guarantee that this isn’t the case. I expected some sort of statistical analysis to confirm whether or not the ensemble members were in agreement and this, much simpler, approach took me by surprise. A more in-depth explanation of how to interpret what is being calculated might help. For example, should Figure 4 be interpreted as showing where the ensemble members share a common standard deviation? Does this measure imply anything about the range of values found as five days means?

In Section 4 it is hypothesised that the lack of EKE change in SO3 at 1oC could be due to a stronger wind stress causing an increase in relative wind stress damping. It is certainly the case that relative wind damping has an influence over Southern Ocean EKE (Munday et al., 2021). It is a bit of a shame to leave this has a hypothesis; changes in relative wind damping can be tested by calculating the actual damping using Reynolds averaging of the geostrophic wind power input. In addition, the expected power budget of the Southern Ocean is wind power input being balanced by bottom kinetic energy dissipation due to friction (Abernathey et al., 2021). As such, it could also be the case that the alignment of SO3’s wind stress and surface current is such that there isn’t the increased power input required to drive a stronger eddy field.

Technical Corrections

Line 12 : it would be less mysterious to tell us what the “cost-efficient, high-resolution modelling approaches” are at this point in the abstract.

Line 18 : it is fairly normal to get about a 50% at 1/4o grid spacing. Perhaps mention that here?

Line 22 :”despite full ensemble agreement” regarding the project EKE increase?

Line 47-50 : a very long sentence that could be split at “but shortcomings remain”.

Line 51 : “they” is ambiguous; what must vary in space?

Line 64-66 : mesoscale eddies also play an active role in setting the general stratification/pycnocline depth (see Marshall et al., 2002).

Line 70-73 : a good point, not something I’ve seen phrased this way before.

Line 77-78 : I found this sentence ambiguous, it could be interpreted as meaning that the wind stress and heat fluxes, etc, won’t change in a forced ocean simulation. In practise, they of course will, and this isn’t what the authors mean. Its the prescribed atmospheric temperature, 10 m winds, etc, that can’t change.

Line 130, 140, 45 : why AWI-CM-1-1MR instead of AWI-CM-1?

Line 135 : “the medium resolution: opening the sentence is repetitive, maybe replace it with SO3 to make it clear which model we’re talking about.

Line 162-164 : Has the drift vs. the climate change forcing been quantified?

Section 2.2 : this only discusses the setup of SO3, which is fine because the reader is directed to the other setups in the previous section. But it would be interesting to summarise here the number of nodes, etc, to compare with SO3.

Line 174-175 : the references on these lines have got the brackets in the wrong place, they should be around the year only.

Line 184-185 : there are two interpolations to get the forcing variables from the donor grid to the SO3 grid. This seems like it could exacerbate potential impacts, such as not conserving certain variables. Did any special care have to be taken with this process?

Line 210 : there’s a rogue “e.” at the beginning of the line. Is this a remnant of an old labelling scheme?

Line 214 and 218 : the prime isn’t the same symbol as actually used in equation (3).

Line 220 : There is currently no explanation why the EKE is coarsened to five-day means. This would be expected to reduce the EKE and may harm the comparison.

Line 222-223 : the averaging region is initially described as being from 45oS to 60oS and then as having the area northward of 40oS removed. Why is this necessary if the averaging starts at 45oS? And why is the Brazil/Malvinas confluence removed?

Line 235 : the 50% underrepresentation of the observations would be clearer if you noted the change in y-axis between panels here.

Line 236-237 : is the “less Gaussian” appearance the result of a specific test or the use of the eyeball norm?

Line 238-240 : does a deviation from normality have a physical interpretation reflecting eddy behaviour? Similarly, would multimodality or skewness reflect something physical about the circulation?

Figure 1 caption : why “Real” magnitudes of EKE for panels a-c? In the description for panel (c) SO3 isn’t fully capitalised.

Line 254-256 : this short of regional discrepancy could be because of the use of EKE at depth, instead of the surface geostrophic EKE.

Line 280-281 : It is noted that “other factors” may contribute to SO3 not showing an increase in EKE. But what are they? If the authors have such factors in mind, listing them here for later discussion would help the reader.

Line 341 : what is “spurious” about such decline? Declines such as this could occur due to a change in the position of the mean eddy field, which would not be unexpected if the change in forcing results in a change in the mean circulation. A region of strong EKE being relocated by a few 10’s of km could result in a large decrease in local EKE.

Figure 5 : the individual panels haven’t been labelled

Line 361 : Is -> is

Line 417 : extra bracket in the Hewitt reference.

References

Abernathey, R., J. Marshall, and D. Ferreira, 2011: The dependence of Southern Ocean meridional overturning on wind stress., J. Phys. Oceanogr., 41, 2261–2278.

Marshall, J., H. Jones, R. Karsten, and R. Wardle, 2002: Can eddies set ocean stratification?, J. Phys. Oceanogr.,32, 26–38.

Munday, D. R., X. Zhai, J. Harle, A. C. Coward, and A. J. G. Nurser, 2021: Relative vs. absolute wind stress in a circumpolar model of the Southern Ocean., Ocean Model., 168, 101891, doi:10.1016/j.ocemod.2021.101891.