General comment

This paper reports an analysis of the contributions of sources to fine and ultrafine particles in Budapest. A receptor model was applied to particle number size distributions. The analysis is based on a remarkably long dataset that was accurately post-processed. I believe that it is a valuable contribution for the scientific community. However, there are a few aspects ot completely clear that need to be addressed in a revision step (see my specific comments).

Specific comments

Line 69. Please define WS the first time that it is used.

Lines 87-96. Regarding the use an the performances of receptor models, I suggest to mention the work of Belis et al (Atmospheric environment: X 5, 100053, 2020).

Line 105. Better sources rather than source.

Lines 110-117. If I have well understood the measurements were taken at the second site only during one year and not in parallel and a direct comparison of the two sites was not provided. In the time series analysed, the data have been put all together? This should be mentioned here.

Lines 168-179. What values are used for A? In addition, the C3 value of 0.2 was used for each channel or only for the total concentrations (i.e. the sum of all channels)?

It is interesting the comparison between the traditional PMF and that corrected with ventilation coefficient. I have not understood if the correction has been done at hourly level in the dataset. If yes, how calm of wind or absence of wind have been treated? In addition, the comments in lines 599-605 seems to be oriented in looking at the corrected PMF as more reliable, however, this is not demonstrated. Is there any reason to think that results with correction are more reliable than the traditional ones? If not, better to modify this sentence.

Discussion of Figure 1. The midday peak seems actually to be present only during the warm seasons, rather than in every season as it seems to be mentioned here. Better to adda a legend on Fig. 1.

Line 339. I would not say contributions. The factors are loaded with NOx meaning that there is an association among particles in these factors and gas but not a contribution. The same for line 396.

Section 3.2.3. Is it possible that this source includes a contribution from resuspended dust, for example road dust resuspended by traffic? This may be possible for particles around 0.5 µm or more, see for example Conte et al. (Environmental Pollution 251, 830-838, 2019).

General comments

This manuscript presents a source apportionment study on a considerably long dataset composed of particle number concentrations coupled with other major air pollutants. The study was performed by using positive matrix factorization applied both to original data and dispersion-corrected data to evaluate the effect of atmospheric dilution. The results provide interesting information about the sources of fine particles in Budapest. The manuscript is overall written in clear English, although the “Introduction and objectives” could benefit from a revision especially focused on fixing convoluted sentences (see my specific comments below). I believe this manuscript is of interest to the scientific community and is coherent with the aims of this journal. Nevertheless, in my opinion few issues need to be addressed before the manuscript can be accepted for publication.

Specific comments

The Abstract and the first section “Introduction and objectives” should emphasize more the novelty of this work and its importance for the scientific community. In particular, the abstract gives a simple summary of the results without highlighting their relevance and impact.

Throughout the text, the authors put a lot of emphasis on the importance of correcting data for the ventilation coefficient to take into account atmospheric dilution also in the model output, which is of great interest. However, the results focus very little on this aspect. The authors merely discuss the DC-PMF results only in a few lines in Section 3.3 (lines 551-558 and 599-605), being very generic on the findings. For example, it is not very clear if (and eventually how) the dispersion correction altered the diel patterns of the sources and if the correction effects were more visible on specific sources. I would suggest expanding more the discussion of the DC-PMF and adding some results in the Supplementary Material (e.g., the equivalent plots of Figures 2-4 and S6-S8 for the DC-PMF factors).

Line 34: the meaning of “criteria” in this sentence is not very clear, please rephrase.

Lines 42-43: this sentence is not very clear. Do the authors mean that inhalation of small insoluble particles can lead to increased health risk compared to the one related to coarse or fine particles having similar chemical composition? If yes, please rephrase this sentence.

Line 55: “particles are usually emitted into the air”: do the authors mean that these particles are typically emitted as primary aerosol? If yes, please specify.

Line 62: particle number concentrations and size distributions cannot be considered as “pollutants” (also because gases are included in primary pollutants). I would suggest modifying this sentence as “Primary pollutants (including particle number concentrations and size distributions of primary particles)…”.

Line 73-75: This sentence is long and not fluent; please, rephrase it.

Lines 147-150: I did not understand if the subsets on which the PMF was run included all seasons for the 11 years or if a single PMF run was performed on each season of each year. Can the author provide more details on how many subsets the PMF was run?

Lines 187-188: the authors chose a seasonal value of VC. Can the author better specify what they mean? Is it the mean over all the years or a different mean VC value was calculated for each season and each year? This question is connected to my previous doubts related to lines 147-150.

Line 198-199: what are the final values chosen for the uncertainty parameters?

Lines 202-203: I would suggest inserting summary results of the bootstrap and displacement analysis in the Supplementary Material, or at least comment a little bit on the results of these analyses.

Figures 2, 3, and 4: for sake of clarity, it would be very useful to highlight inside these figures what factor they are referring to (e.g., adding the name of the factor as a title, in the legend, inside the plots or in the y-axis label). Moreover, I did not understand why the figures related to only the first three factors were reported in the manuscript and the remaining ones were displayed in the Supplementary Material. Of course, adding too many figures in the main text is not advisable, and I also think that putting all these details into a single figure would not be straightforward; maybe the authors can at least comment on why they gave more importance to the first three factors.

Line 487: “become negligible”: If I understood correctly, I would not use the word “negligible”, because the patterns in winter and summer are just slightly smaller than the spring one. I would rather say that the contributions are simply smaller.

Figure S9: I found this figure quite hard to understand. Firstly, I would recommend adding on the top of the plots aside to the season label also “uncorrected PMF” and “(DC-PMF-uncorrected PMF)”. Secondly, I would also suggest adding the plots related to DC-PMF results, otherwise it is very difficult to figure out their features only just looking at the (DC-PMF-uncorrected PMF) differences.

Technical corrections

Line 36: add a comma after “Despite that”.

Line 103: I would suggest adding “atmospheric” before “dispersion correction” for sake of clarity.

Line 157: I would suggest citing the original work by Paatero (1999) for the ME-2 solver (the reference already listed in lines 773-774).

Line 168: add a space between “N” and “represents”.

Line 172-173: please provide references for this statement.

Line 182: “This effect can be corrected for by…”: eliminate “for”.

Line 223: add a comma between “winter” and “and”.