The paper titled “A new process-based and scale-respecting desert dust emission scheme for global climate models – Part I: description and evaluation against inverse modeling emissions” correctly identifies the known problems and challenges in current dust schemes used in GCM/RCM including the effect of threshold friction velocity u*t, wind stress partitioning, boundary layer turbulence, and grid-size-dependency. I appreciate the author’s effort in improving dust emission schemes. The proposed changes are reasonable and have some physical basis. The emission estimates are validated as well. The paper is overall well written. However, there are a few concerns that should be addressed before the paper is accepted.

The resulting emissions are validated using DUSTCOMM data which is reasonable. The author mentions that they plan to implement the code in CESM later, in which case, it should be possible to conduct more robust validation of the results, for example, using DOD data, dust concentrations, and deposition. However, I still think that additional validation of the proposed changes is necessary to justify the added changes.

The proposed changes are numerous, not to mention that the paper is too long. An ideal, effective dust model should be simple in description and should use commonly available input datasets. Such a complex treatment of parameterizations must be justified appropriately. A step-wise validation and analysis of each added term would justify the complexity of the model. In this context, I suggest addressing the following four major points:

1. Validation of threshold friction velocity: For example, threshold friction velocity can be compared with Pu and Ginoux, (2020) who retrieved u*t from MODIS AOD data globally, which are publicly available: https://acp.copernicus.org/articles/20/55/2020/acp-20-55-2020.html
2. Since MERRA2 provides DOD as well, how about calculating the correlation between DOD and estimated emission flux for additional validation? Or how about comparing it with the dust emission fluxes from MERRA2 itself? Can we compare the estimates of dust emissions from this study with the MERRA estimates and show that the estimates from this study better correlate with DUSTCOMM compared to MERRA? 
3. The relative importance of added terms: The proposed changes are exhaustive and the usefulness of their addition has to be clarified. For example, in desert regions, wind explains the most variance of resulting dust emission flux; the other parameters such as threshold friction velocity, soil moisture, clay content, etc., would explain less than 10% of the variance. Figure 1b also supports this point. Therefore, it is important to check which parameter contributes the most or identify in order the relative importance of each parameters for the arid and non-arid regions. I see that emission fluxes are compared on pages 26-28 but it would be useful to present these numbers in a table so that the readers can directly see the relative importance of each added term, separately for arid and nonarid regions. In that way, the model developers would be able to prioritize the inclusion of different terms depending on their relative importance based on the input data available. Also, present the total emissions resulting from the model for arid and nonarid regions (out of 29,300 Tg/year).
4. The paper is exhaustively long to read. Some sections are not very relevant to the main theme of the paper which is to describe the processes of dust emission parameterization proposed. For example, turbulence-driven intermittency (section 3.3) and scaling up of emission (section 4.2) is meant to match the GCM outputs with high-resolution estimates, so do not fall in the core theme of the paper. These two sections could probably form another paper so that this paper can better focus on emission parameterization and its validation alone.

Detailed comments:

Title: scale-aware or scale-invariant instead of scale-respecting?

The title seems self-contradictory to the content because the paper itself compares the emissions at different resolutions which are very different (lines 165-195). So in what sense is the model scale-respecting? And why limit it only to GCMs, it should be applicable to RCMs as well. Perhaps a better title could be ‘Towards a scale-invariant process-based dust emission scheme for climate models ……

Line 43: I understand that you scaled up your high-resolution data so that it can be compared to GCM outputs. However, I don’t see why scaling up high-resolution gridded dust emissions to the coarse resolution of GCMs would be so important so as to develop such an additional methodology, which also diverts the focus of the paper. The world is moving towards a high-resolution era and actually, the opposite would be more beneficial – to convert GCM outputs to high-resolution emissions.

Line 51-52, this may not be entirely true, for example, Osipov et al. (2022) show that anthropogenic aerosols contribute more than 90% of PM:

https://www.nature.com/articles/s43247-022-00514-6

Line 55: Literature on dust-climate interaction should be expanded to include the most recent developments: e.g.,

1. Jin et al. (2021): Interactions of Asian mineral dust with Indian summer monsoon: Recent advances and challenges, https://www.sciencedirect.com/science/article/pii/S0012825221000611
2. Froyd et al. (2022): Dominant role of mineral dust in cirrus cloud formation revealed by global-scale measurements, https://www.nature.com/articles/s41561-022-00901-w
3. Parajuli et al. (2022): Effect of dust on rainfall over the Red Sea coast based on WRF-Chem model simulations, https://acp.copernicus.org/articles/22/8659/2022/

113-116: I am not sure about it because I think the main challenge is to represent small-scale roughness elements of grounds and rocks, not vegetation. The vegetation roughness effect is already taken into account in calculating friction velocity in most models in terms of displacement height and ground surface roughness, although crudely. So we need to be careful not double-accounting the effect of roughness.

122-123: that is true for GCMs but not for RCMs (e.g. WRF) which typically use model time steps in seconds.

125: Are you talking about wind gusts that could be better represented in a sub-grid scale? Turbulence and subgrid variability of winds are two things. Wind gusts are probably better represented with the increase in resolution. Turbulence is usually understood differently in relation to large convective cells so it could be confusing.

290-291: since Bit is constant u*it is proportional to u*ft0, I don’t understand how it is going to change the simulated spatiotemporal distribution of dust as mentioned. u*ft also includes soil moisture term fm in addition to u*ft0 (which is only a function of Dp and air density) so u*ft will show more variability, isn’t it so?

314-316: This is an interesting formulation but I am concerned that roughness could be double-accounted because roughness is already used in calculating u* (law of the wall) in most GCM/RCM.

328: delete comma

384-385: Perhaps Chappel and Webb (2016) consider both since it uses satellite albedo, which has been recently implemented by Legrand et al. (2022).

Chappel and Webb (2016): https://gmd.copernicus.org/preprints/gmd-2022-157/

Legrand et al. (2022): https://www.sciencedirect.com/science/article/pii/S1875963716300957?via%3Dihub

Eq 14: Using a constant Dp in arid regions is fine but it does not make much sense to use a variable Dp in vegetated areas which are not the dominant dust sources anyway. The question is: is adding such complexity worth that will likely not have any significant effect on the results of dust emission? In the vegetated areas, roughness/drag force will dominantly govern threshold friction velocity and the Dp will not likely have a remarkable effect on the resulting dust emission. Another concern is that fm already depends upon clay content so using clay content again in this formulation of Dp may double-account the effect of clay/silt content on dust emission.

Eq 15, again there is a possibility that zos is double-accounted as u* already uses this term.

Eq 7, as far as I remember the equation is dp/30, not 2*dp/30, e.g., see https://hal.archives-ouvertes.fr/hal-00677875/document

Page 26 Line 38: You mentioned earlier that the K14 scheme is increasingly used in GCM/RCMs. The description of this model was already published and validated. Could you explain why this model still gives such a high estimate of dust emission flux (29,300 Tg/year)?

313-315 Was Z03 also conducted at the same spatial resolution?

313-315: Since this scheme uses an additional representation of drag partition, which is not in the Z03 scheme, wouldn't it make more sense to compare the results with another dust scheme that also contains a drag partition scheme, for example, Marticorena and Bergametti 1995 dust scheme which has been discussed in the paper:

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/95JD00690

Section 5: The limitation section is too detailed, which somehow undermines the value of the study itself. This section could be shortened to highlight only the key limitations associated with estimates of dust emission fluxes.  

General comments

This paper concerns the improvement of the representation of dust emission processes in current global climate models and land surface models. The paper is novel, interesting, overall well written. I have some suggestions however, which might be helpful for improving the readability of the paper. Overall I share some similar thoughts as those from Anonymous Referee #1 as regards the paper’s length. In particular, the length is not totally justified as some sections are really too long (more appropriate for a book/report/PhD thesis rather than for a research paper). I would suggest improving the readability and the novelty by focusing more on the validation of the proposed scheme(s), showing its performance against that obtained by other schemes available in the literature: as the RMSE is of the order of Tg/year, which might be considered high, how about adding also a normalized error (or percentage)? In summary, I would suggest focusing more on the results and their discussion trying to shorten a bit the considerations made to derive the scheme. This would make the reading much clearer and the novelty carried out might emerge more clearly.

Specific comments

Lines 53-56: This is true in general for all aerosols, and mineral dust does not make an exception.

Lines 83-85: The listed properties are not only those from soil but also from the atmosphere and aerosol.

Line 88: Which kind of soil properties and how do they affect the dust emission threshold?

Line 172: This detail about R is probably not needed at this point of the work.

Line 243, 245, 247, …: “moment” would be “momentum”?

Lines 180-462: These subsections are quite long and descriptive. I would suggest to do some efforts in summarizing the description in these subsections.

Lines 465-480: This subsection entitled “Input data and model description” is not appropriate as a subsection of Section 2 “Current dust emission schemes in climate models”. Revise the structure.

Figure 1 d: There is consistent spread for arid soils, which is masked by the goodness of the fit driven for nonarid soils. This might indicate reduced agreement for arid soils which are the more relevant for this study. Indeed, the fit-line slope is essentially good, but this might depend on the fact that the regression is driven by the non arid values.

Lines 003-005: Please provide justifications for such statement (one year used as a climatological dataset?); also, please provide further details on “other input data”.

Line 224: Change “spatiaotemporal” to “spatio”.

Line 238: Change “infinity” to “infinite”.

Lines 342-359: Perhaps this comparative analysis of performance would be better if provided in a table and discussed in the main text, providing reasons. It would be also nice to provide percentage values for comparison: for instance, as from figure 10 b it might be observed that the differences are more relevant in some regions, which might correspond or not to regions of significant dust emissions. As such, the introduction of a normalized or a percentage value could be helpful.

Figure 10: in figure 10 b it could be discussed better the reasons of the differences, more relevant in some regions than in ot