General comment:

This paper presents a new modeling framework to represent the near-surface ocean and its temperature diurnal cycle. By enabling the representation of the temperature profile in the first meters of the ocean, this model shows promise for future applications to study physical interactions between the ocean surface and the atmosphere, between the ocean surface and the ocean interior and in particular processes involving biogeochemical cycles. As exposed in the article, there is a growing interest in understanding and modelling ocean-atmosphere coupled mechanisms at the sub-diurnal time-scale among which these involving atmospheric deep convection (triggering, aggregation). This study is therefore timely and has a high scientific significance. The scientific quality of the approach is excellent with hypotheses being in general discussed clearly and confronted to in situ observations when possible. The article proposes a detailed and complete view of the modeling framework and remains synthetic and clear in the comments of the results and in the discussions.

In conclusion, this is an overall excellent and convincing article which I will be glad to recommend for publication in Geoscientific Model Development after some specific comments have been addressed.

Specific comments:

1- One of the advantages of the proposed model is to represent the evolution of the temperature profile within the first meter of the ocean. However, no attempt to validate these profiles against observations is made. Yet, in situ observations exist for the same cruise (Ward et al 2006 cited in the article). If these data are not available to the authors, the POSH parameterization of Gentemann et al. (2009, cited in the draft) could be of some help to validate DiuSST profiles. This validation could also help the reader see the advantage of the present model compared with the Zeng and Beljaars parameterization that assumes a very steep profile of temperature close to the interface.

2- The authors could precise a bit more the Markov Chain Monte Carlo approach. They argue that they can produce 80 independent samples out of a timeseries containing only 13 full diurnal cycles (Fig. F1). Correlations exist between the different parameters due to the correlation in the training data between the wind speed and shortwave radiation (line 281-284). One is left to wonder if the observation sample is sufficient for a robust estimation of the parameters and for the model validation.

3- With a vertical resolution of 0.1m, the diffusive microlayer of less than a millimeter thickness that is responsible for the cool skin phenomenon is not resolved by DiuSST. This is somehow acknowledged by the authors who speak about a “coarse-grained” cool skin (see discussions lines 295-297, 310-312, 412-416, 540-545). Indeed, static instabilities with vertical extend of the order of 0.1m are larger than the Kolmogorov scale and should lead to convective instability (Saunders 1967, Fairall et al. 1996, Zeng and Beljaars 2005). Therefore, one may argue that the STAB version of the model (instead of LIN, Appendix C) is the most physical and should be used as the main model to represent the subskin temperature. In order to get a proper representation of the interfacial temperature, one would have to add a parameterization for the cool skin such as Fairall et al (1996).  

Saunders, P. M. (1967), The temperature at the ocean-air interface, J. Atmos. Sci., 24, 269 – 273

Technical comments:

Line 87-93: An issue of the Fairall et al. (1996) parameterization is the need to set to zero the diurnal warm layer during the night.

Lines-160-165: When implemented in a model, downwelling longwave radiation can be an input rather than computed from the 10-meters height air temperature. This would help to take into account clouds effects for instance.

Line 173: Can you illustrate the importance of taking into account the refraction angle?

Lines 190-195: By how much vary the integration timesteps? Can you provide some statistics, minimum and maximum?

Line 195: About the limitation of the wind speed: Can you note the maximum diurnal amplitude of the SST at wind higher than 10 ms^-1?

Line 205: Is this 2K oscillation of the air temperature also visible in the MOCE-5 data? Why don’t you set it to a constant?

Line 324 : Is T really the difference relative to T_f? The difference between them actually appears in the sur second and third terms of (15).

Line 344 : noa?

Figure 8 legend: Wind dependence of the « maximum » or « peak » or « amplitude of the » diurnal warming.

Lines 415 : Tu and Tsuang (2005) used 100 mm resolution close to the surface to produce a cool skin with a unidimensional model.

Tu C. Y. and B. J. Tsuang, 2005: Cool-skin simulation by a one-column ocean model, Geophys. Res. Lett.,. 32, L22602, doi:10.1029/2005GL024252, 2005

Lines 445-452 : Can one conclude that OGCMs with 1m resolution close to the surface (e.g. Bernie et al. 2005) suffer from the same problem than the slab model, producing very regular diurnal cycles?

Bernie, D. J., S. J. Woolnough, J. M. Slingo, and E. Guilyardi, 2005: Modeling diurnal and intraseasonal variability of the ocean mixed layer. J. Climate, 18, 1190–1202.

Line 465 : The fact that DiuSST resolves the vertical profile makes it also suitable for an inclusion in an ocean model (or a coupled model) with a resolution of 1 meter or coarser close to the surface. For this kind of application, the warming of the first level of the ocean model should be added to the resolved foundation temperature to compute the fluxes such as Voldoire et al 2022 and Bellenger et al. 2023 (already cited in the text).

Voldoire, A., R. Roehrig, H. Giordani, R. Waldman, Y. Zhang, S. Xie, and M.-N. Bouin, 2022, Assessment of the sea surface temperature diurnal cycle in CNRM-CM6-1 based on its 1D coupled configuration, Geosci. Model Dev., 15, 3347–3370, DOI:10.5194/gmd-15-3347-2022.

Annex F : Maybe add some comments?

Review of "DiuSST: a conceptual model of diurnal warm layers for idealized atmospheric simulations with interactive SST" by Borner et al.

This paper is very well written and presents a novel and simple model of diurnal SST warming.  It is insightful, and as such, I think it should be published subject to one major comment and some minor modifications.

Major comment

I was intrigued that the training data included most of the extremes (minima on 2-4 October, maximum on 13 October). I was wondering if this made the exercise “too easy”, in that you did not have to independently simulate the extremes. What would happen if you trained on 5th-12th October – would the extremes on other days be well simulated?



I understand that to create the best and most useful operational model, including extremes in training is necessary. My comment is mainly out of scientific curiosity – if you don’t train on extremes, can you simulate extremes well?

Minor comments:

Line 3. "strongly, and delicately" seems like a contradiction!



Line 43. Regarding imprint of SST on the moisture field, and, more generally, the atmosphere boundary layer, there is a large body of literature, e.g. reviewed in Seo et al. 2023.   See also Skyllingstad et al. 2019.



Line 80-81 “generally not physics-informed” seems too strong. I looked at just one of the papers listed, and it was physics-informed (Price et al.)



Lines 161-162. There are lots of other major references like Large and Yeager (2009), Fairall et al. 1996, 2003, Edson et al. 2013…



Equation 10: max(2…   )



Line 193. What are typical timesteps of the model?



Line 241. Do you think there is any sensitivity to varying qv ?



Line 357 “on days 6 and 7 (not shown)”



Line 373 “moisture and momentum”



Lines 423-439 discuss the applicability of the model to different environments, but only within the eastern Pacific region of Fig. 3.  Can you say anything about its applicability to other Tropical and non-Tropical regions?  I am not asking for any modification of the model, but maybe you can say whether the background conditions in other regions will make the current model suitable or non-suitable. 



Refs

Seo et al. 2023: Ocean Mesoscale and Frontal-scale Ocean-Atmosphere Interactions and Influence on  Large-scale Climate: A Review.,  J. Clim. 10.1175/JCLI-D-21-0982.1



Skyllingstad et al. 2023: DOI: https://doi.org/10.1175/JAS-D-18-0079.1 .