The authors present a Bayesian inversion approach to estimate particle number measurements in sampling lines. They find that physics process can influence and bias estimates (as expected) and their method addresses these with some uncertainty quantifications as well. I think this is a generally excellent manuscript and should be published. It’s well written, well argued, and well presented. I have written down some comments that the authors can choose to address in a possible revision, but none of these comments is blocking (i.e., feel free to ignore them).

Two general comments:

• In Section 2, I understand (and support) the decision by the authors to only address select physics processes that are most relevant here. For completion, there are other processes that can be accounted for in potential expansion of the model. Below, I give one example about charges. I encourage the authors to include more examples of potential processes that could be accounted for — are there processes you suspect could be important for future studies?
• In Section 4, it is readily clear how one would assess the synthetic data (we know the full ground truth) but how could one address the case of measurements in Section 4.3 where we don’t know the full ground truth? Any thoughts on a potential *experiment* to further constrain the estimates (and test your method)?

Some comments I wrote while reading the manuscript:

• L105: provide a proper citation for SciPy (e.g., see this file https://github.com/scipy/scipy/blob/main/CITATION.bib)
• L115 and thereabouts: it is ok to ignore other factors, but a reader may be interested to follow up. I would add a few citations here to other works that dealt with other aspects of coagulation. For example, some recent work dealt with charging effects on collisions (e.g., 10.5194/acp-21-3827-2021, 10.5194/acp-23-6703-2023, 10.1029/2021GL092758, 10.1073/pnas.2313897121). You can probably find more references on other topics. There’s no need to delve too deeply into any of this, but providing some references for the interested reader will be sufficient and helpful
• L200 and thereabouts: Do you think charges on the walls play a role in deposition? See the following which is related to the above papers: 10.1080/02786826.2020.1757032
• L216: What’s the n and B for? Please define them here (also, define the M below in L220 as well)
• Section 2: I am not sure a full derivation of already established material (2.1.1, 2.1.2, 2.2) is needed (consider trimming). It’s okay to keep as-is though. Sometimes repeating already known material is beneficial :)
• L375: “inversion crime” is vague; please elaborate
• Fig 7: I would consider flipping the b panel (so that dn/dlogdp can still be on the y-axis). Also, why do the axes change? dN/dlogdm in an and then dN/dlogdp in b. Maybe a typo? Also, is there a normalized version of the density such that it adds up to 1?
• L466: Why not drop the zeros for these plots? (i.e., make them NaN)
• L500 and thereabouts: see my above comment about charging; in general, I think you can cite some works on extra confounding factors, but no need to delve too deep into them. As you cite the Seinfeld & Pandis book on coagulation, see the appendix of the chapter where coagulation is treated for more info (Appendix 13.1 in the 2016 book, 3rd edition)
• L508: there might be additional wall losses too (related to charges on walls, smoothness of walls, wetness of walls, etc.)

Dear authors, thank you for one of the hardest reviews I have ever had to complete. The presented work using Bayesian inversion to account for particle losses and coagulation is sampling lines is extremely well presented, I have found it very difficult to find any issues that could be improved upon prior to publication. The paper gives sufficient detail in all aspects and presents a well throught out argument alongside rigorous methods and their application. I see no reason why the paper should not be published as it is.



While reading the manuscript I made some notes, many were answered in subsequent paragraphs, and many are simply due to this not directly being my area of research. I did have one simple question: In section 2.2 there is discussion regarding wall deposition. It is stated that aerosol particles adhere when they collide with a surface, does their adherence change the deposition rate for future aerosols? I.e. does deposition/diffusion accelerate or decelerate any future deposition?



And one more complicated question: Could this method be applied to sampling other atmospheric pollutants?

Thank you for a very interesting article.

The manuscript focuses on addressing challenges in particle number emission measurements from vehicles, specifically the alterations in particle size distribution caused by coagulation and diffusion losses during sampling. The authors propose a Bayesian method for reconstructing the initial particle size distribution from distorted measurements. Their method incorporates detailed physical processes, such as particle morphology and van der Waals/viscous forces, while systematically quantifying uncertainty and leveraging prior information. The method offers flexibility for designing measurement setups and facilitates comparisons across different sampling locations.

The manuscript is very well-written and after reading the previous two referee's comments, I agree that it could be published after addressing referee#1's comments.