The authors present a new numerical method to calculate sea spray induced heat fluxes given a sea spray generation function. Specifically, the authors propose the Gaussian Quadrature (GQ) method as a computationally efficient alternative to the spectrum integral method, and more accurate method than simplifications of the integral method. The results show improved agreement of the GQ method with the spectrum integral in comparison to the simplified parameterization. Impact of such difference in the context of world’s oceans are presented using a coupled ocean-atmospheric-wave model.

Overall, the manuscript is interesting and the modelling community may benefit significantly from the proposed GQ-method. However, the authors are not clear in the type of advancement and implications their work has on current and future works. The method does not improve the physics of sea spray induced heat fluxes, instead it improves the numerical accuracy of solving the involved equations. While I nevertheless believe this is important work worthy to be published, it is an important distinction that is currently not appropriately phrased nor discussed. I therefore recommend a major revision.

Major concerns

• As per the above, I believe that the authors need to be more explicit in what their method is improving. I think that the authors haven’t necessarily overstated their conclusions, but the interpretations of some statements are right now too ambiguous or sometimes incorrect. This largely involves the word ‘improved’ throughout the manuscript, including the title and abstract, where it reads as if the parameterizations are improved. This is not really true, it is actually the numerical method used to solve the parameterizations that has been improved (at least against the simplified parameterization discussed in the manuscript). Thus, when these different methods are compared when implemented in the applied coupled model, the authors are not improving the bulk parameterizations, but simply presenting the numerical error of the methods discussed in the context of the coupled model. Importantly, it is the numerical error assuming that the sea spray generation function is correct.
• A related point is the absence of a clear discussion on the interpretation of the results. As mentioned by the authors, the sea spray generation function has an uncertainty of several orders of magnitude. Thus, if the RMSE of the proposed GQ method reduces the numerical error by say 1-10 W/m2 (e.g., figs 3-5), how relevant is such an improvement in the broader context of the physics and model uncertainty? Such uncertainty in the physics could perhaps get into the 100s of W/m2. I’m not suggesting the GQ method proposed here is therefore irrelevant, but it does change the interpretation and application of the model/results in practice, for now and the future. This also brings up some other questions regarding the interpretation of the improved SST as observed in Figs 6 and 7. The uncertainty in the physics of sea spray is considerable larger than the improvement in approximating the spectral integral using the GQ method. Thus, any improvements in the modelled SST cannot be reliably be assigned to the usage of the GQ method.

Minor comments:

• Line 66: ‘huge amount’ sounds a bit vague. Especially later on the authors actually provide a number, so they can be more accurate here.
• Line 70: ‘apt to produce significant bias’, more a numerical error. However, as per one of my major concerns, is this bias/error of significance in the context of the existing uncertainty in sea spray parameterizations?
• Line 86: ‘thus provided reliable hourly estimates’, is very vague. Either provide a reference about its reliability, or simply state that this dataset is used.
• Line 100: This sentence reads a bit odd. ‘based on eddy correlation observations’ refers to the turbulent heat fluxes in cited papers, not the sea spray induced heat flux.
• Line 108: ‘requires huge amount’, just say is computationally expensive
• Line 123-124: somewhat confusing, please rephrase sentence
• 166: ’36 times’ this is an interesting and useful statistic. Perhaps consider to provide what this means in terms of the fully coupled model run, i.e., is it still saving much time percentage wise?
• Line 201-202: confusing sentence, please repharse
• Line 204: ‘fig 12g’ best practice is to keep order of figures intact.
• Line 233: ‘significant improvements’, I disagree. Fig. 8c and 9c seem to show very similar RMSE. Their variability after day 18 is very similar.
• Line 260: This manuscript would greatly benefit from a separate and in-depth discussion on the interpretation and implications of the results.