Review of “Development and evaluation of a new 4DEnVar-based weakly coupled ocean data assimilation system in E3SMv2” by Shi et al. for GMD.

The manuscript describes the implementation of a new weakly coupled ocean data assimilation in the E3SMv2. The authors show that using this assimilation method helps reduce temperature and salinity bias and RMSE in general in both surface and deeper ocean layers. The results of the manuscript are promising and will be valuable for the community. It is overall well-written and easy to follow. That being said I believe that more work must be done on this manuscript before being published.  A lot of things need to be clarified or added to improve the clarity and robustness of the results.

As a general comment here, before going into details, the authors need to be more quantitative, in the text and in the abstract, when describing results in addition to saying increase/decrease or cold/warm biases please indicate some values. Also, units of temperature and salinity are missing on every figure, please add units in both figures and captions as otherwise, it makes things hard to understand, i.e. figure 10 see comment below.

One other main concern here is about section 3.6 on the influence of ocean data assimilation on the regional climate over land. Although this is an interesting topic, it is most likely a manuscript in itself. The results presented in this section are highly preliminary, no details on observations (definitely not enough to only briefly mention it in the Figure 11’s caption) or methodology used are given. Very little can be said with certainty on the influence of ocean data assimilation on regional climate over land with only the figure and analysis presented (fig 11). This needs a much more rigorous analysis to be able to draw robust conclusions. In my opinion, this section should be removed and can’t be published as is in this manuscript.

More specific comments below:

Line 114-116: As the manuscript focuses on ocean, more info is needed on the ocean model set-up here. Does the ocean model has the same horizontal resolution as the atmosphere ? how many vertical layers, vertical resolution ? What is the vertical mixing scheme used ? …

On section 2.2: Just by reading this, for an external reader, it is not very clear what is this product (EN4.2.1) and thus what is assimilated. Those are profiles with spatiotemporal variability (right ?), what are the typical depths where observations are available? Typically, what are the regions where we have a lot or few observations, and thus can/should we expect improvement in these areas or not? In summary, a better description of this product here would help us understand better the results presented after.

Line 150: “significantly reducing”: by how much the computational resources are reduced ?

Line 207: what do you mean by “observed external forcing” ? what is this ?

Line 211: “across sixty ocean layers” Is this all the model ocean layers ? if not what’s the depth of the 60^th layer and why only 60. Please clarify this.

Line 237-238: what is the reason for the initial jump  in the cost function reduction from -12% to -4% ?

Line 246: “nine ocean layers”: why did you choose to show specifically these 9 layers ? Is 85m the last layer where observations are assimilated ? if not why not showing anything below ? This need to be clarified.

Moreover, is it necessary to show these nine as they relatively show the same results, maybe you could only show 5m, 45 and 85m ..? Reading further, you’re showing profiles up to 1000m so why not showing maps of the deeper ocean here as well ? 85m is not ‘deep ocean’, depending on region and/or season this is still in the ocean mixed layer.

On that note, it could be interesting to show seasonal maps as well. Is there any seasonal variability on these results, i.e. if maybe there are fewer observations during winter months does the ASSIM still perform better ?

On Figure 4 : Is there any ocean current-related impact ? As it seems that the RMSE is somewhat increased near strong ocean currents (i.e. Gulf Stream separation, ACC from Agulhas to East Australian current with some sort of dipole increased/decreased RMSE)? and/or near upwelling regions California coast, Northwest Africa ..? any reasons on why the assimilation would not do better there? As in Figure 6 and 7 statistical significance should be added on both Figure 4 and 5, this will make the result more robust and these increased RMSE might not turn out to be significant (?).

Also please indicate how the significance is calculated.

Line 256: Again, 85m is not “deep-ocean dynamics”..  

Line 274-276: It seems a good hypothesis with maybe hints of this in Figure4 as well showing reduced RMSE on temperature in this region. Since you have both the observations and simulations it would be interesting to confirm and show this, if assimilation actually helps representing El Nino/La Nina better.

Otherwise one can wonder why the correlation is largely increase in the Pacific compare to, i.e, the Atlantic.

Line 276: “considerable”: considering the values in the Indian Ocean this vocabulary might be too strong.. otherwise the Southern Ocean have similar magnitude, is that also “considerable improvements”..?

Line 277-278: “complex ocean dynamics” This term was used before in the text, but this is a bit too generic to explain differences and especially to explain the diminished performance, you have to be more specific or don't use this. what is "complex ocean dynamics" ? In that regard, then it means that the simulation without assimilation (CTRL) is doing better at these "complex ocean dynamics", then why?

I believe here, from the stippling on the figure, it doesn't seem that these reduced correlations are statistically significant (whereas all the increased ones are) and thus, this might just be due to internal variability of the ocean model ?

Line 286: Again, this doesn't seem to be statistically significant ?

Figure 8: Related to previous comment on ocean model depth. Here, why stop the profiles at 1106m, nothing below ? 1106m which is rather a very specific depth..? and thus why showing only up to 85 m on the previous panels, Figure 4 to 7? As previously mentioned, it would be interesting to see maps at deeper ocean levels as well as it seems here that the assimilation is improving significantly deeper in the ocean ? Instead of showing 9 layers in the first 90m which are showing very similar results..

Line 299: “gradually decrease as depth increases” but it does increase again below 300m ? Is it not significant ?

Line 306-307 and Figure 9: it could be useful to show the average over different depths not only 0-1000m. i.e. 0-300m, 0-700m, 0-1000m. From fig 8, doesn't this “systematic overestimation of temperature” come from 300m and below ? if looked at the surface or over different depths it may not systematically overestimate the temperature ? This would give more insight into what is improved or not depending on the depth, as in Fig8. Similar thing could be done for salinity.

Also, is there a spin-up period to take into account to analyze the result or when doing this kind of assimilation? it seems to take 10~15 years for the bias to approach the 0 line (Fig 9a,c). Maybe a comment on that would be useful.

Figure 10: What are the units here ? The colorbar is the same for both temperature and salinity ? is it up to 3 Deg C difference and 3 psu difference or is it in % ? This need to be clarified. if in % please quantify in the text how much in degC/psu.

Figure 10b,d Should be “ASSIM minus Obs”, it would then be much easier to appreciate the improvements in ASSIM in comparison to panels (a,c). Right now it is not clear or difficult to see actually how much the biases are reduced (or not) in ASSIM.

Line 323-324: Again, quantify better how much.

Line 325-326: could be worthwhile to note the large high bias in salinity in the Mediterranean Sea as the bias trend seems to be opposite to the global ocean, and it seems to be improved in the ASSIM as well.

Line 378-380: In light of my previous comment, I believe this statement should be also removed.

See report attached.