This work identifies several errors in the definition of ocean skin temperatures in the ECMWF ocean mixed layer model (OML). The authors propose a modified OML model that corrects for these errors, and evaluate its performance compared with the previous model. Although the methods and results presented in the paper suggest that this new model improves on its predecessor, which is indeed an important result and worth reporting, the layout of the manuscript and the diagnostics used here are not sufficiently convincing. I recommend resubmitting after addressing the following comments.

Major comments

• The language in the manuscript needs a major rewrite. I’ve included a few comments below but perhaps professional editing will be helpful.
• There are many acronyms defined but rarely used, and it is distracting from those variables that are important for the work presented here. I suggest emphasizing which variables are the most relevant and try to minimize the use of other acronyms and definitions throughout.
• On that note, I found the explanation of the various SST definitions very confusing, and in particular how come only the upper 5 meters or so are affected by the diurnal cycle where we should also expect mixing effects (due to surface forcing) to extend far below that. Please rewrite this while taking into account other OML models and how they treat the vertical profile of temperature (you have some discussion on this in lines 117-126 but it contradicts your original assumption that SST does not change below 5-10m).
• The main motivation, as presented in the manuscript, is due to inconsistent patterns in Tint given by ECMWF (figs 1-2), however it is hard to judge just based on the text that these patterns are sufficiently wrong. It would be helpful to show a more quantitative metric (rather than the present qualitative one) that motivates the error. If the main motivation is the error in equation 1 then you should start with that and then use the plots to demonstrate further.
• K_w in eq. 1 is redefined to to be the heat diffusivity on the order of 10^-7, instead of thermal conductivity in the original equation, which was on the order of 0.6. These are many orders of magnitude that have likely affected the model performance and stability. I think it is important to add some discussion on this issue.
• It appears that there is some error in the transition between equation 3 and 4 after the k_w is redefined. Because k_w = h_w\rho_w c_w ==> k_w^2 = h_w^2 \rho_w^2 c_w^2 however in equation 3: \rho_w * c_w are not squared, which is either a typo or not an equality with equation eq 4.
• The change in the modified model produces a (desired) smoother simulated Tint compared with the original ECMF (fig 5-6), however, the magnitude also seems to be sufficiently changed. It would be good to add some discussion on why this might be and what are the implications. Also, please clarify whether Tfnd is expected to change based on the new model.
• It is hard to asses whether a mean deviation of 0.1K and standard deviation of 0.5K is a strong result given how sensitive Tint is (eg line 45 in the introduction). Can you compare with a different baseline model here to make this claim stronger?
• The conclusion would benefit from additional discussion on the implications of this work, a comparison with other models, and what might the next steps be.
• It was not clear to me how the ATLAS data was used to derive the stability functions based on the current explanation in the appendix. It may be helpful to add an additional sections on this topic to accompany the figures shown in the main manuscript.

Minor comments

• Line 12: replace “and” after “ECMWF with comma.
• Line 45: replace “evidenced” with “evident”.
• Lines 47-48: this last sentence is out of context. You haven’t told the reader that models have problems with heat budgets. Also, what are related phenomena? Please rephrase.
• Line 54: odd sentence, please reword.
• Line 57: what deficiencies? Can you be more clear? Are these based on figures 1-2? If so the reader hasn’t seen them yet.
• Lines 58-61: please reword this entire paragraph as it is currently without context.
• First paragraph in section 2a may be better suited for the intro.
• Line 66: “misunderstanding”?
• Line 76: what do “int” and “fnd” stand for?
• Line 78: there must be some signal of the diurnal cycle below 5-10m as the mixed layer is sensitive to changes in heat flux and wind stress. Please clarify.
• Line 79: what are conventional measurements?
• Line 80: Can you expand on the type of bulk models used in NWP? It is important in the context of the vertical profile you are alluding to in finding a better SSTfnd.
• Line 80: replace ”deal” with “examine” and remove the following “with”.
• Lines 90-91: I believe you are comparing different times in UTC and not time zones (which will refer to longitudinal differences)?
• Line 94: please reword the description of figure 1.
• Line 105: can winds no affect SST on the order of one hour? Is this not represented in the ECMWF model?
• Can you show an equivalent of figure 7 for the original ECMWF model for comparison?
• Lines 139: please provide references for the replacement of k_w with thermal diffusivity.
• Line 155: replace ” it turned out” with something less casual.
• Lines 199-205: very confusing paragraph. Please reword and clarify procedure.
• Line 216: which parameterizations?
• Line 230: please be more specific with the term “statistics”
• Line 251-25: please reword
• Line 266: Do you mean ERA5 here or the new prediction of Tint?

The manuscript titled “A revised ocean mixed layer model for better simulating the diurnal variation of ocean skin temperature” focuses on the fine-tuning and validation of an ocean mixed layer model (OMLM) used at ECMWF. The authors initially describe the shortcomings of the existing OMLM, then rectify the typographical errors in the model, and subsequently validate the results.

However, the manuscript, in its current form, lacks proper organization and sequence. The methodology is described before the dataset is introduced, leading to confusion. Various SST definitions and terminologies are introduced without context, puzzling the reader. The authors should first provide a detailed description of the data used, including sources, resolution, etc., followed by the methodology. This should include defining various SST terms and explaining each term's source from the dataset.

Figures 3 and 4 should also include comparisons with the original ECMWF model. Although the authors state that the revised model has the same error range, it would be beneficial to compare the scatter plots from the original model for clarity.

The manuscript does not present any significant scientific advancements in the present form beyond correcting typographical errors in the original model. While the authors have contributed by identifying and fixing these mistakes, this could have been addressed in a technical internal note rather than a peer-reviewed publication. Furthermore, the practical implications of the errors in the mixed layer model are not clearly articulated, aside from the improper simulation of diurnal variability. The authors should emphasize the practical benefits gained from correcting the OMLM.

The manuscript requires major modification incorporating above suggestions/comments, before it can be considered for the publication.