This study illustrates a new method to visualize particle number size distributions for atmospheric aerosols, and presents results from one year of data collected at the Amazon Tall Tower Observatory. The authors did a good job with the framing (very neat and clear introduction), and while there are places where the writing could be slightly improved (see below for some suggestions), the manuscript is pretty clear and undeniably useful. Three major comments: 1) 3D pictures are hard to understand and visualize, and 2D projections could be done better here. Descriptions of the 3D shape are sometimes puzzling/unscientific. I commented more on this below. 2) There is a lack of analyses in terms of statistics, so hard to tell how significant some results are. A problem in the figures arising from the 3D representation, but both the 2D projections could do with some measure of significance, and mainly the numbers reported could be better framed. I offer an example in my comment below for Figure 1. Finally, 3) while I want to remark that the manuscript is mostly well written and the results could be of interest so this should not be an obstacle itself to publication, I am unsure if it fits into the category of a “Research Article” or if this should more neatly fit into a “Measurement reports” which ACP clearly states “Analysis of the measurements may include model results and conclusions of more limited scope than in research articles.” This seems to me to be fitting here: it’s only 1 year of measurements, and the statistics are unclear (maybe the authors can convince me otherwise if they present them). Furthermore, while the abstract starts by highlighting the novelty of the approach, the conclusions mostly highlight the results. I think this is up to the Editor to decide, but I would urge the authors to consider changing the scope to a Measurement report so that they can more clearly state what is the relevant part of the manuscript (the approach), offer the year of measurements as a result stemming from the approach, but then more clearly state that future work is needed to produce more statistically robust results. Whatever the decision over the manuscript type, which is not entirely my business to decide, I suggest an eventual publication in ACP after the text and figures are made clearer and after some statistical analyses have been performed.

Some more detailed comments on the text and figures follow.

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1. 85: “data” is here first used as singular and then as plural. I have no strong opinions over the debate, but consistency is probably better either way!

1. 135: 57820 out of how many?

Fig. 1: The figure could be improved for clarity. The 3D numbers in the cube are not really visible. Panel a) does not have the sigma_2 line very visible (and not sure the color matches). Sigmas are also not very clear in Panel c). Lastly, I don’t think you need to specify that the source is you, the authors, if this is your paper, in the caption!

I also have an issue with the description in the text preceding the figure: you use the words “low to a high geometric diameter” and  “broad to a narrow curve” but the differences in D and sigma are quite small: are they statistically significant? They are both pretty squarely in what we consider “accumulation” mode, so it would be helpful to see how much they overlap. How many PNSDs per season, are the numbers comparable? A bit more statistic could be useful here. In line 164 the authors say “broad statistical basis” but unclear 1) what they mean and 2) what the numbers actually are.

Line 184: “Dominated basically by N, the accumulation mode PNSDs are distributed in a geometric figure that resembles a cylinder” That sounds very qualitative, and I can’t really see a cylinder (more a cone). Anyway, not sure what this phrase adds!

In general, Figure 2 could also do with a higher quality: better to have the three plots larger, and more defined. Very hard to tell anything. Potentially better to have the 2D projections as separate plots to appreciate them more.

Line 205: “initial” state.

Line 226: I’m sure the authors can find a more professional term than “birth” here!

Figure 3: absolutely impossible to determine where the seasons actually are. No point in having the 3D version here, as it’s not informative. Suggest changing to 9 plots (3x3) showing the three projections for the three modes, with seasons explicitly written there. Same for Fig. 4, except with 4 points this is easier to follow

Line 246: “confirm” this cycle (you often use the present tense to talk about your work elsewhere, then switch to the past. Use some consistency!).

Line 259: “happening”

Line 315: “Many studies have been reporting” -> “have reported”

Line 393: “The cause of this pattern showed to be linked to the diurnal cycle of precipitation, possibly associated with new particle formation” this should be rewritten for clarity! In general, the conclusions are of a slightly lower quality (clarity-wise) than other pieces of the manuscript. Not a big deal, but it would be good to improve this a bit more!

This paper presents analysis of long-term aerosol particle number size distribution (PNSD) data from the ATTO tower through characterising the PNSD in a three-dimensional phase space represented by 1) the geometric mean diameter; 2) the geometric standard deviation; 3) the number concentration of log-normal modes fitted to the PNSD. The manuscript deals with an important topic: finding new ways to analyse the emerging long-term data sets of aerosol particle characteristics, which are critical for enhancing our understanding on e.g. aerosol-cloud-climate interactions, and is therefore approapriate for the scope of ACP. I think the approach for investigating trends and behavior of the PNSD as a function of various environmental parameters is interesting and novel, although the exact value for potential applications is to be demonstrated in future studies. The manuscript therefore has scientific value that is of potential interest for the readership of ACP. There are, however, some aspects of the manuscript that should be improved before publication can be recommended - related to both the scientific approach and the presentation quality: 



General comments:



- The reference list of the manuscript is rather limited with a high proportion of work from the authors themselves. I understand that when it comes to PNSDs in the tropical atmosphere this is hard to avoid, but perhaps there is previous work on PNSD characteristics from other parts of the world worth mentioning here? Please consider also adding some discussion and comparisons to past work to the Discussion and conclusions section.



- The manuscript needs to be improved for readability and precise use of terms and language. Some examples are provided in the specific comments below, but generally e.g. references to analysis or figures that are only to be presented later in the manuscript should be kept to minimum, and concepts and terms should be referred to as precisely as possible. 



- It would be interesting if the authors could, for example at the end of the introduction section, reflect on the potential research questions that could be answered using the approach presented here - beyond following temporal patterns and responses to precipitation events. What larger-scale implications might the results presented here have? 



- My main potentially scientifically major comment has to do with the fact that it appears from Fig. 2 and the text that the division between the "sub-50 nm" and "Aitken" modes was somewhat arbitrary - if I understand correctly, a predefined size-cut at 50 nm was simply used instead of letting the fitting algorithm find the best number of modes and their parameters. This constraint makes it difficult to use the fitted "sub-50" and "Aitken" mode bevior for analysis of the underlying microphysics and chemistry - because it is not clear whether one can justify the choice of the modes in terms of them representing clearly different aerosol populations. Could the authors please clarify their methodological choices in this regard and reflect on the potential implications for the interpretation and usefulness of the presented results?  



Specific comments:



- Abstract, p. 1, e.g. lines 23-24 and 25-26: The abstract should be stand-alone and understandable without having to read the manuscript in detail. It is very difficult to understand e.g. what it means that "the sub-50 nm mode appears as a curved cone, the Aitken mode as a semi-sphere, and the accumulation mode as a cylinder" without looking at the plots in the manuscript. Also what does a "positive linear slope" mean in "The diurnal cycle of sub-50 nm particles in the dry season shows a positive linear slope as a function of all three fit parameters." -  i.e. which variable has a positive linear slope as a function of the three fit parameters? Do you perhaps mean that all three fit parameters have a positive linear slope as a function of time? Please revise the abstract for readability through e.g. defining which modes where fitted to the data, accurate definition of parameters and clearly highlighting the key conclusions that can be summarized without having to read the entire mansucript.



- p. 2, lines 46-48: PLease revise the sentence starting with "Improving aerosols parameterizations..." for clarity, English language and readability.



- p. 2, line 64 and p. 3, line 66: What do you refer to with the term "comparatively" - as compared with what? Please specify if possible.



- p 3, lines 89-91: Perhaps it is appropriate also to refer to the study by Hussein et al. from 2005 (Hussein, T., Dal Maso, M., Petäjä, T., Koponen, I. K., Paatero, P., Aalto, P. P., Hämeri, K., & Kulmala, M. (2005). Evaluation of an automatic algorithm for fitting the particle number size distributions. Boreal Environment Research, 10(5), 337-355. http://www.borenv.net/BER/pdfs/ber10/ber10-337.pdf) here? Also, what do you mean by "isolating the variability of isolated modes" - please consider revising for readability. 



- p. 4, lines 130-131: Was it always appropriate to fit three modes or were there instances when a different number of modes would have represented the size distribution better? If yes, what kind of error might the choice of three modes introduce to the results presented? Furthermore, did you fix the size ranges assumed for the three modes or let the code decide this. What might this imply for the results? Please add a brief elaboration on these questions and a justification of the chosen approach (in terms of numbers of modes and size ranges assumed).



- p. 7, line 72: Please revise the expression commenting that  "the SMPS used was limited to 10 nm" for accuracy. I guess you want to say that the lower detection limit of the SMPS was 10 nm.



- p. 7, line 76: Instead of "constant dispersion" do you mean "constant standard deviation"? Can this depend on the the size ranges that you have constrained (if that is the case)?



- p. 8, lines 215-216: Please revise the sentence starting "the accumulation mode dominates...". I believe you want to say that "accumulation mode dominates over Aitken mode" and at the end "prevalent" instead of "equivalent".



- p. 9, lines 242-243, the sentence saying "reaching a maximum during the night probably due to late afternoon rainfalls": Whatabout the importance of boundary layer dynamics?



- p.  9, line 243: with "initiates" do you perhaps mean "begins"?



- p. 12, lines 305-306: Please revise the the sentence "Since lightning and precipitation peak simultaneously (Mattos et al., 2017) the following results (Figure 5) are intercomparable, promoting a complete characterization of the aerosol-precipitation interaction." for clarity and readability.



- p. 13, line 314: Instead of "sensible" do you perhaps mean "pronounced" or something similar?



- p. 13, line 317: Please revise the sentence starting as "In addition, it was shown..." for readability and English language.



- Same as above, the sentence starting "In fact, it can be seen...": Where exactly can this be seen? Please specify.



- p. 14, line 327: Please revise the sentence for readability, clarity and precise use of English. Specifically, what do you mean by "background trajectories" - please specify.