The air-sea exchange velocity of elemental mercury, one of the major factors of uncertainty in the global mercury cycle, is still most commonly parametrized by using the 10-m wind speed only. The manuscript by Li et al. uses a new parametrization for the air-sea exchange velocity of mercury, also taking into consideration the exchange-suppressing effects of surfactants using total organic carbon concentrations, and the exchange-enhancing effects of wave breaking and bubble injection using the significant wave height. Using the MITgcm ocean model, one parametrization for the exchange suppression by surfactants and four different parametrizations for the exchange enhancement by wave breaking are tested and compared. The relative importance of each effect is constrained through several sensitivity runs. Overall, higher net oceanic elemental mercury evasion is obtained globally by the inclusion of these new parametrizations, when compared to the baseline run. The study also proposes that the non-consideration of surfactants and wave-breaking effects might be the reason why different observational studies obtained very different results for the relationship between exchange velocity and wind speed.

The article is generally well and concisely written, although the conclusion section might need a bit of retouching. All necessary details are given and the provided summary tables are appreciated. The argument is logically developed, and the overall line of thought is easy to follow. Relevant previous work is adequately referenced. This study fits well into the journal's scope, and the topic is interesting and of significant relevance for the mercury community. I also salute the authors for communicating the needs of the modelling community to experimentalists. Nevertheless, before suggesting publication I would like some of my doubts to be dispersed and some minor points to be addressed.

Major comments:

• Section 2.2 & general approach:

Woolf (2005) indeed separated the air-sea exchange velocity into contributions of wave breaking and non-wave breaking. However, for the non-wave breaking part, they state to have used a relationship derived from theoretical considerations and observations in wind-wave tanks. Thus, their representation of the non-wave breaking part, while most likely being influenced by microscale wave breaking as they explicitly state, was probably not influenced by larger scale wave breaking and significant bubble injection. In consequence, the addition of the non-wave-breaking term and another wave-breaking term likely led to no significant "double counting" of effects.

In contrast, in the present work, the authors use for the non-wave breaking part the parametrization of Nightingale (2000), which is based on deliberate tracer experiments in the southern North Sea, i.e. experimental data in the real ocean, spanning a wide range of different wind speeds (and thus likely including some wave-breaking). As such, it is likely that the parametrization of Nightingale already implicitly includes some effect of wave-breaking and bubble injection on the air-sea exchange velocity, even though this is not explicitly quantified.

I fear that by adding to the non-wave breaking part of the air-sea exchange velocity (using the parametrization of Nightingale (2000)) another term that explicitly considers the wave-breaking part, one risks counting the effect of wave-breaking and bubble injection twice, so to speak. This would lead to an overestimation of the total air-sea exchange velocity, which could explain why an overall global increase in the air-sea exchange velocity and the magnitude of oceanic Hg evasion was found in the present work.

I would like the authors to comment on this potential issue.

• Line 115 and line 120: I would like the authors to comment on the possible limitation of extrapolating experimental results concerning biological surfactants in the Atlantic Ocean globally. I would like this possible limitation to be mentioned/shortly discussed somewhere in the manuscript (maybe around those very lines, or in the “Model uncertainty” section).

Minor comments:

• Graphical abstract: I salute the authors for having included a nice graphical abstract, which is additional effort but – in my opinion – adds quality to a manuscript. However, I advise the authors to be mindful about making everything well-readable. Currently, most of the text (especially in the lower left corner) is quite hard to read.
• Figures 1, 2, and 4: Please increase the font size of the numbers and text in the legend, it is currently very hard to read. It would also be advisable to increase the font size of the panel labelling (a, b, c, d).
• Lines 16-17: “(…) results in an increase of over twofold in the transfer velocity of Hg0 relative to the baseline model.” – I feel like there should be a range given, considering that the increase in transfer velocity depends on which of the 4 parametrizations for wave breaking is used.
• Line 57: Please indicate the section of Woolf (1997) where the 30% is mentioned, as I cannot find it explicitly stated. Or was this value derived using figures or tables in Woolf (1997), for instance Table 6.2?
• Line 61: It seems like this should be "Reichl", not "Reichel"
• Line 86: The name “Darwin model” was not explicitly mentioned in Dutkiewicz et al., 2012. Was this term later added? Maybe there is some reference missing?
• Line 93: Where does the "doubled" come from? From Loose et al. (2014): "The model indicates that effects from shear and convection in the sea ice zone contribute an additional 40 % to the magnitude of keff, beyond what would be predicted from an estimate of keff based solely upon a wind speed parameterization"
• Line 96-97: “(…) is the Henry’s law constant (…)” - Should this not be the dimensionless Henry's law constant?
• Line 143: I cannot find an Asher et al. (2002) in the reference list. Please correct.
• Line 155: A word appears to be missing here.
• Line 172: Considering that the unit of suppression is in percentage (%) such that 100% = 1, shouldn’t this read: (100-suppression [%])/100 ?
• Table 1: Even if somewhat redundant, it may still be helpful for the reader here to indicate the naming of the parametrizations (e.g AW98, A02) next to the corresponding equations
• Line 223: high variation
• Line 224-225: Another point where it could be explicitly mentioned that the surfactant parametrization used here was based on data from the Atlantic Ocean, and that extrapolation adds uncertainty.
• Line 263: Minor detail, but maybe it would be better to write "comparatively small" instead of “relatively small” to make clear that the magnitude of effect on CO2 is evaluated in comparison to the effect on Hg0. I wouldn’t call a 30-40% increase in CO2 exchange “relatively small”.
• Line 321: One has to be careful with what is what is ment with “lifetime” here. If it is lifetime against deposition, then it shouldn’t be increased by increased atmospheric Hg concentrations. If it is lifetime against permanent burial, then this argument could be made because of more efficient reemission from the ocean. I advise to clearly state here what is ment with “lifetime”.
• Line 344: I think this should say REpresent, not present
• Line 346: In THE Southern Ocean
• Line 379-380: This sentence feels off at the moment. Maybe “(…) is CURRENTLY the only USED”?
• Line 387-388: This is weirdly worded at the moment and not clearly understandable, please reformulate.
• Line 391: observationS
• Line 392: it "is reduced by concentration change" is unclear. Is something missing here?
• Line 397: Maybe better: “even higher”
• Line 399: I suggest to tone this down a bit, e.g. “may have resulted”
• Line 400: “(…) as the exclusive proxy.” - proxy for what? It should be explicitly said. I guess this is the gas exchange velocity.
• Line 405-408: This is quite a long sentence that might be better split into 2.
• Supplementary Figure S2: The figure is very useful, but the text is very small. I suggest to just increase the figure size on the page, considering that there is no real space limitation in the supplementary material.
• Supplementary Figure S4: Please increase font size in the figure legend.

Other suggestions:

• It may be interesting to mention for experimentalists if, for improvement of the parametrizations, observational data from certain oceanic regions would be especially useful, for example because model results in certain regions are especially sensitive to the used parametrization.

This work is the first to evaluate the impact of wave breaking and surfactants on the air-sea exchange of mercury, building on recent advances in the measurement of Hg fluxes and the general understanding of the gas exchange process. The authors inserted new parameterizations into a global coupled model for Hg that had been previously validated, also testing different schemes for solving the wave breaking process. The manuscript is well conceived and presented and the results are of broad interest. Indeed, the flux from the ocean to the atmosphere is considered to be one of the largest in the global Hg cycle but is still not well constrained. The manuscript could be further improved with some adjustments, especially in the methodology section.

Introduction 

I suggest adding some background information on the estimated magnitude of global air–sea exchange of Hg and the associated uncertainties to emphasize the knowledge gap and the importance of the research question. A summary of how different model configurations and parameterizations have affected these estimates in previous modeling efforts (e.g., Zhang et al., 2019, 2023) would be interesting.

Methodology

Several equations (6, 8, 9, 10, 11, 12 and 13) are found both in the text and in Table 1. I suggest retaining them only in Table 1 and referring to them in the text with equation numbers. Referring to the equations could also reduce some confusion and redundancy elsewhere in the text. For example, in lines 87-103, many repetitions could be avoided by small rearrangements, e.g.:

The air–sea exchange of Hg0 (eq.1) is calculated from the exchange velocity (kwHg0) and the concentration gradient of Hg0 across the air–sea interface corrected for Henry’s law constant (Cw-Ca/H) (Andersson et al., 2008). H […] quantifies the ability of the dissolved phase to […]. [This is general, not only for baseline]. In the baseline parameterization, the exchange velocity of Hg0 on the ocean side (eq.2) is estimated following the quadratic relationship with wind speed proposed by Nightingale et al. (2000) for CO2 (eq. 3) adjusted for the Schmidt number of Hg0 [add somewhere the eq. of ScHg0 to show the relationship with diffusivity and temperature], and for the proportion of ice-free sea surface areas.

The terms kwexch, kHg0, kwHg0, and kw are used somewhat ambiguously in the manuscript and should be homogenized. It might be convenient to have Eqs. 2 and 14 close together to make it clear that the latter is the modified version of the former. Thus, lines 170-173  might best be inserted after line 103 to introduce subsections 2.2. and 2.3 (where a detailed explanation of the terms introduced in eq. 14 is given). Similarly, lines 175-178 should be placed outside the section on wave breaking. They could be moved together with the previous paragraph or to another subsection dedicated to the simulations (together with lines 104-106).

Still concerning the equations:

• pisvelo is a gas transfer velocity normalized to the Schmidt number of CO2 in freshwater at a temperature of 20 °C, called k600 in Nightingale et al. and elsewhere in the literature. I suggest using k600 also in this text.
• in eq. 14 and elsewhere a more concise name could be found for “suppression of kw” (e.g. Ssurf, Skw?)

As for surfactants (lines 108-110), marine bacteria also seem to be involved in their production (see e.g. Kurata et al. 2016 in Sci Rep), which at least partly explains why TOC is a better proxy than Chla. The marine bacteria are indeed shown in the graphical abstract, but they are neglected in the text. Also, I find it somewhat inaccurate to say that PP is "commonly represented" by Chla. I would rather say that it is "estimated from" Chla for operational reasons (i.e. remote sensing). I suggest to critically revise this paragraph to clarify the current understanding of surfactant dynamics.

Tables 

The readability of Table 1 must be improved (e.g. add the associated parameterization names for k_bub, use - or not - horizontal lines consistently in all rows, remove apex letters for references from the equations of k_bub).

Table 2. I suggest simplifying the names of the parameterizations (eg. SUR1, WB1, WB2, WB3, WB4?) and distinguishing the sensitivity simulations from the other ones by using different names (e.g., CaseA-CaseC instead of 5-7).

Results

Can the results from Wurl et al., 2011 be used to validate the modeled distribution of surfactants, at least qualitatively?

line 394: the net flux of Hg0 evasion for the baseline simulation is 3841 Mg/a, higher than 3000 Mg/a given in Zhang et al., 2019 for the offline coupled model. Is this due to only the different initial conditions used in the model?

Minor Comments

line 39 I suggest changing "production" with "activity"

lines 40-42: I suggest using "they" instead of repeating surfactants and using a comma rather than a period before "Second"

line 63 reword "more significant for Hg0 with lower solubility."

line 126 the subsection number needs to be corrected

line 135 I suggest rewording as follows: […] we attempt to use four different parameterization schemes, all considering the significant wave height (Hs), which has been proved to be [...]

line 168 add the article a to dimensionless

line 223 highly should be high

line 224 therefore, the suppression relationship may not be linear?

line 280 please specify stronger than …

line 294 but lower than

line 362 another verb would fit best than implied

line 365 revise “The highly spatial-temporal variations in short-term and seasonal of surfactants”

line 366 chemical composition has been already discussed at lines 359-361

line 380  the only parameter considered. 

line 384  sensitivity

line 398 the word research is uncountable

line 391 add an s to observation