Harni et al. used positive matrix factorisation to explore the particle number size distributions simultaneously collected at two spatially adjacent urban sites. The dataset presented here is unique, as simultaneous particle size distribution measurements are still very rare. Using the well-established PMF methods to explore such a unique dataset is of high interest to the aerosol community. However, the current version of the manuscript is not well written. The way in which data are presented, and the use of language significantly affects the quality of the research. The manuscript needs major revision to enhance the overall quality. I would support the final publication after addressing my comments below and polishing the language.

Major Comments

1. Lines 36 – 45: The current summary of source apportionment approaches is not comprehensive enough. The authors are expected to provide a compact summary of various source apportionment approaches used in particle size distribution data. In addition, the authors should provide a rationale for why the PMF was chosen as the source apportionment method in this study.
2. Lines 42 – 44: Why is conducting source apportionment solely based on NSD data and using auxiliary data only challenging? If it is indeed challenging, why did the authors still choose to use source apportionment in the study? What is the novelty of this study? More explanations should be provided here.
3. Section 2.2: Have the two DMPS systems been compared against each other? If not, please comment on whether the different instrumentation could affect the PMF analysis.
4. Lines 165 – 167: It is still unclear why the five-factor solution is the best solution in terms of mathematical and physical aspects. As a PMF user, I typically present the Q/Qexp values, residuals, relative residuals and scaled residuals of different PMF solutions, when analysing the PMF results of aerosol mass spectra data. Presenting these aspects will strengthen the statistical significance of the chosen PMF solution. In addition, why does the five-factor solution have the best physical meaning? To convince the readers, the authors are encouraged to present other factor solutions that neighbour the chosen PMF solution in the Supplement.
5. Lines 185 – 187: Based on S3 – S12, I found it difficult to recognise whether the trends calculated using the seasonal Theil-Sen estimator and the Theil-Sen estimator calculated from data without seasonal variability were almost identical. Can the authors specify the trends mentioned in Line 185 with proper cross reference? In addition, the authors are expected to provide a quantitative comparison between the two types of estimated trends, instead of subjective observations.
6. Lines 209 – 211: The complex sentence and grammatical mistakes make it very difficult to understand the mathematical and physical meanings of the contributions presented in Fig 4. Please rephrase the sentence.
7. Lines 234 – 244: I agree that TRA2 is a traffic-related factor. The author also claims that TRA2 is slightly aged and atmospherically processed. However, the paragraph lacks a description of these two features. It is unclear “(~ minutes to an hour)” mentioned in the sentence. How can the authors come up with this aging time scale? In addition, how did the cooling, dispersion, and mixing impact TRA2?

Minor Comments

1. It is very confusing how the authors define the degree of Pearson correlation coefficients shown in Table 3 and the corresponding sentences. What is “strong”, “significant”, or “weak” in the context of Pearson correlation coefficients?
2. Please summarise any other studies that conducted PMF analysis on urban NSD data in the introduction.
3. This is not the 1^st study on the data simultaneously collected from the Street Cayon and Urban Background Station in Helsinki. In the Introduction, please provide a summary of the main findings from the literature that focuses on the data collected from these two sites.
4. Section 2.2: To improve readability, please include a table in the main text outlining the instruments and measured parameters.
5. Figure 1: For such long-term data, it is worthwhile to provide better statistics of the data. Please include the minimum, maximum and interquartile.
6. Lines 129 – 130: “The interpolation needs to be done on a logarithmic x-axis …”, is very hard for general readers to understand. Could the authors provide visualized examples of interpolations on both logarithmic and linear x-axis in the supplement?
7. Lines 159 – 160: The sentence is hard to follow. What was the set C3 in this study?
8. Lines 168 – 169: What is the dispersion correction? Could the authors provide a detailed description of that and references?
9. Figure 2: To understand the statistical robustness of the PMF solution for the long-term dataset, it is better to provide the histograms to visualise the relative residuals for all NSD at each size.
10. Figure 3: Please include the R-squared values as a function of particle size for each year in the lowest panel.
11. Line 193: In the sentence “The observed NSD at SC…”, what is the size range of the nanosize particles?
12. Line 197: What is the size range of the nanosize particles?
13. Figure 4: For the bottom three contribution plots, please provide the maximum, minimum and interquartile ranges.
14. Line 224 – 225: I cannot see how the finding from Ronkko et al (2017) is associated with the TRA1 data here. If not relevant, please remove the sentence.
15. Figure 5: It is unnecessary to separate the NO_x and BC into two plots. Please combine them into one by introducing one extra Y axis.
16. R-squared value vs Pearson Correlation Coefficient: I find that the R-squared value was used for data presented in Figure 3, while Pearson Correlation Coefficient was used for data presented in Figures 5 and 6 and Table 3. What is the difference between the R-squared value and the Pearson Correlation Coefficient? What is the right occasion to use one, not the other, and vice versa?
17. Line 240: Please clarify “a slightly larger area”.
18. Lines 240 – 241: According to Table 3, the correlation of TRA2 with NO_x and NO emissions at SC is also significant as well. Please comment on this.
19. Line 244: If the boundary layer was shallow, should we expect SCA and SecA to have similar monthly trends as TRA2 due to the accumulation of pollutants?
20. Lines 246 – 247: It is unclear why the weak correlation between SCA and auxiliary data is expected for atmospherically processed aerosol. Please clarify this in the main text.
21. Figure 6: It is unnecessary to separate the NO_x and m/z 60 into two plots. Please combine them into one by introducing one extra Y axis.
22. Line 295: Why did SecA have a high contribution during summertime?
23. Line 304: Different from what?
24. Line 328: What is meaning of “development of technology”? Please clarify the sentence.
25. Lines 331 – 332: “More data (years)… the better they hypothetical test is” is unclear. Is the decreasing trend for this study or Luoma et al., 2021?
26. Table 4: What does “no significance” mean? Please add discussion in the paragraph associated with Table 4.
27. Line 356: What does “immediate emissions of traffic” mean?

Technical Comment

1. A bunch of sentences are very hard for the readers to understand due to grammatical mistakes. I would encourage the authors to find professional language services or native speakers to polish the language. E.g.,
   • Lines 15 – 16: “This study aims to … sources using a novel approach to positive matrix factorisation (PMF)”
   • Line 235 – 237: “The mode particle size was … growing the particle size (Ning & Sioutas, 2010) ”
   • Line 248 – 249: “The strongest Pearson correlation ... during both workdays and weekends”
   • Lines 346 – 347: “TRA2 peaked approximately 1 h later … being much more aged”
   • Lines 359 – 360: “Although the contribution from biomass combustion in traffic environment includes high uncertainty”.
2. Provide labels (e.g., (a), (b), (c)) for each subfigure in the main text and SI. To enhance the readability, please correct the cross-references throughout the whole text.
3. Lines 18 – 19: “The data is combined into one file so that the data from both stations has the same timestamps. Then PMF finds profiles for the unified data” are too descriptive. They are better to be placed in section 2, Experimental, instead of Abstract.
4. Lines 30 – 31: What are the concentrations in the sentence “Of these, anthropogenic… concentrations.” Are they number or mass concentrations?
5. Lines 32 – 33: Please specify what are the indirect financial consequences.
6. Line 82: Instead of using the smallest particles here, please provide the particle size range where the charging difficulties occurred.
7. Lines 107 – 108: Provide reference(s) for “These relatively relative criteria for … in the traffic environments.”
8. Lines 117 – 118: “So the factor profile … between the stations.” The sentence is too long to read. Please rephrase the sentence.
9. Figure 3: Please increase the font size and clearly label the year for each subfigure.
10. Line 241: Is it supposed to be Table 3?
11. Line 282: Add a space for Barreiraet al., 2021.
12. Table 4: Is the unit supposed to be “cm^-3”

The manuscript under review utilizes a more than valuable dataset from a northern European urban area, centered around long-term PNSD measurements from two stations of different characteristics (urban background vs street canyon). These data are complemented by various equally valuable measurements and can be characterized as a unique dataset that should be analyzed and published. However, the presented analysis lacks depth and focus. Is the method proposed or the results/findings that are important? After some necessary improvement and quite some language editing, the article can be suited for publication.

General Comments

1. The introduction can definitely be improved, in terms of providing the context and pinpointing the gaps that this study aims to fill, but especially when the authors are setting the scientific goals of the study, that are now only presented in one sentence (Lines 58-59). Furthermore, this very stated goal, i.e. “to explore how well the sources of urban aerosols are statistically separatable based on the number size distribution data using positive matrix factorization”, does not seem to be addressed in the main text. How did the authors explore the source separating power of PMF on PNSDs. Did they compare with other approaches (e.g. clustering)? Did they compare with PMF that also included other variables? Furthermore, what were the statistical tools used to asses the above?
2. The authors should try to provide more details on why they selected to combine the two datasets in a single PMF input by concatenating the data matrices horizontally? What was the scientific goal behind such a choice? How was the PMF result, i.e. a single timeseries for both stations advantageous in characterizing the sources affecting the sites? Why not perform PMF in each station separately? Or for instance, why not perform a standard multi-site PMF (Pandolfi et al., 2020; van Pinxteren et al., 2016) given that the authors state in Line 117 that “the same factors were solved for both sites”?
3. In order to justify applying PMF this way, a comparison with a standard PMF on each site separately, as well as with a standard multi-site PMF should be added and the performance of the proposed method should be assessed in a quantitative way. In general, the method description is not verry straightforward. A step-by-step schematic of the measurement matrix manipulation before feeding PMF should be added in the main text or supplement.
4. I believe that the reasoning behind the selection of the presented 5-factor solution is poorly presented in the manuscript. To my opinion more quality metrics should be presented (e.g. Q/Qexp, temporal trends in residuals etc). Such analysis should be presented in the context of comparison to more and less factor solutions. For instance, how do such metrics change when moving from a 6-factor to a 5-factor and then to a 4-factor solution. The robustness of the solution should be examined and presented. Was bootstrap resampling or displacement analysis performed? Is the solution repeatable among different runs starting from different random seeds? How was rotational ambiguity addressed?
5. The discussion regarding the SCA factor needs more detail, given that this factor is presented to include various types of combustion related aerosol. What seems odd is that, while it is stated that it also represents biomass burning contributions, its average contribution does not exhibit a wintertime enhancement. Don’t the authors expect a more pronounced contribution of biomass burning at the UB site? Is that reflected in the results?
6. Wind regression analysis would greatly help the interpretation of the results and add to the quality of the presented analysis.

Specific Comments

1. Lines 15-16: See general comment #2.
2. Lines 18-19: The sentences “The data is combined… for the unified data.” Are not that well written and generally don’t seem to belong to the abstract. In general, there should be some more effort for the abstract to capture the highlights of this research adequately. For instance, there is no single word on the trend analysis and its implications.
3. Lines 75-83: Have the two instruments been intercompared? More details (manufacturer etc) should be provided for the UB DMPS. Some details or references on measurement quality should be provided. Were the sample streams dried in both instruments?
4. Line 85: More detail on the operation of the ACSM or relevant references should be provided. Was it calibrated? Was the sample dried? Were the data quality controlled? Was a chemical composition dependent collection efficiency used?
5. Lines 136-138: Couldn’t the fact that the dataset was treated to its entirety, be a source of uncertainty, given that there can be substantial seasonal variability in observed sources? Did the authors perform any seasonal tests and establish that the number of factors remain invariable from season to season, or that their profiles were comparable to the whole period PMF?
6. Lines 168-169: A quantitative metric of the authors’ choice, describing the comparison with the dispersion corrected PMF, should be provided. Furthermore, details on how the input data were treated for this dispersion corrected PMF run, how was the solution presented selected, along with relevant references should be added.
7. Line 180: Please correct the typos, “Then-Seil” at the beginning of the sentence and “Thei-Sen” further on.
8. Line 240: What about the afternoon? TRA1 exhibits a peak during the afternoon rush hour. Given that TRA2 is a product of primary traffic particles’ atmospheric processing, shouldn’t a TRA2 afternoon peak be expected? Is all the processing assumed to be linked with photochemistry? In that case would there be a summer-winter difference?
9. Line 244: If BL dynamics could be part of the explanation for such pronounced seasonal variability for TRA2, shouldn’t it also affect the other traffic related factor (TRA1)?
10. Line 259: This suggestion, that m/z 60 OA might be related to traffic, needs a citation or some more analysis to back it up. The diurnal pattern especially when not season specific, cannot support something like that on its own.
11. Line 268: How come the SecA factor correlates with ORG₄₃, that can be considered a primary OA marker? Could it be that such correlation is driven by specific reoccurring events during wintertime? What about ORG₄₄, is there some correlation there? Could it be that the SecA factor has different origins when moving from wintertime to summertime? Does the selected PMF method allow such an assessment?
12. Lines 270-271: This statement seems a bit speculative since the authors don’t provide any information on the BC mixing state. How much of the BC measured is fresh at the SC site and how much at the UB. How long would it take for a shell to form? Is there a consistent time shift between concentration peaks in BC and SecA?
13. Lines 273-283: Any comment on the LRT factor seasonal variability, where an enhancement during the Jan – Mar period is observed? Moreover, in Table 3 the highest correlation calculated for the organics concentration at m/z 60 was with the LRT factor. Did the authors exclude somehow that there is some factor mixing here?
14. Lines 326-327: I don’t understand what the authors mean with these two sentences. Please rephrase to make the message clear.
15. Lines 328-329: I believe that the authors here use a previous speculation as a fact in order to develop their argument based on decreasing BC concentrations. In fact, a “somewhat” correlation can’t act as a solid basis for such a discussion. Please rephrase.

Figures

• Figure 1: Not so sure that this figure is necessary in the main text. It could be moved to the supplement.
• Figure 4: Tick marks every 6 or 4 hours would greatly improve the readability of the diurnal contributions presented.
• Figures 7 & 8: These two figures are not actually discussed in the text. The relevant discussion could apply to some pie charts alone. More discussion should be provided in case the authors believe that the monthly variation reveals important information.

References

Pandolfi, M., Mooibroek, D., Hopke, P., van Pinxteren, D., Querol, X., Herrmann, H., Alastuey, A., Favez, O., Hüglin, C., Perdrix, E., Riffault, V., Sauvage, S., van der Swaluw, E., Tarasova, O., and Colette, A.: Long-range and local air pollution: what can we learn from chemical speciation of particulate matter at paired sites? Atmos. Chem. Phys., 20, 409–429, https://doi.org/10.5194/acp-20-409-2020, 2020.

Van Pinxteren D, Fomba KW, Spindler G, Müller K, Poulain L, Iinuma Y, Löschau G, Hausmann A, Herrmann H. Regional air quality in Leipzig, Germany: detailed source apportionment of size-resolved aerosol particles and comparison with the year 2000. Faraday Discussions. 2016;189:291-315, DOI: 10.1039/C5FD00228A.