the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A Cross-Correlation Based Method for Determining Size-Resolved Particle Growth Rates
Abstract. The particle growth rate (GR) is a key parameter in aerosol dynamics and plays a crucial role in understanding atmospheric new particle formation and its effects. A fast, robust and reproducible calculation of GRs from aerosol number-size distribution data remains a challenge. In this study, we introduce a new method that we call the maximum correlation method for calculating particle and ion GRs from number-size distributions. We employed this novel method to calculate GRs from Hyytiälä, Finland using 14 years of ion and total particle size distribution data and compared our results against previous studies that used conventional methods for calculating the GRs. We found that our method compares well against the published data and reproduces the seasonal variability and size-dependent trends in the GRs. The maximum correlation method enables fast and repeatable GR calculations from large aerosol datasets, which facilitates the systematic incorporation of GR analysis into new particle formation studies.
Competing interests: Markku Kulmala is a member of the editorial board of Aerosol Research.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: final response (author comments only)
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RC1: 'Comment on ar-2025-19', Anonymous Referee #1, 12 Jul 2025
- AC1: 'Reply on RC1', Janne Lampilahti, 26 Sep 2025
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RC2: 'Comment on ar-2025-19', Anonymous Referee #2, 19 Jul 2025
The work of Lampilahti et al. introduces a novel, fully automatic method for calculating particle growth rates (GRs) during new particle formation (NPF) events, using a maximum correlation approach applied to particle number size distribution data (both ions and particles). The accurate determination of GRs is essential for understanding NPF mechanisms and for quantifying the influence of NPF on climate, particularly in relation to the formation of CCN. Automating this calculation is a crucial, but challenging step and I consider the current manuscript a valuable addition to the NPF community. However, in its current form, the manuscript presents a few methodological and conceptual issues that need to be addressed to ensure the robustness, transparency, and comparability of the proposed method. I therefore recommend the manuscript for publication in AR after the authors have adequately addressed the major and minor comments outlined below.
Major comment:
The GRs calculated with the maximum correlation method are compared with GRs calculated with other methods, for the corresponding time periods, in Hyytiälä. However, the various studies used for comparison have utilized an event classification algorithm (either manual or automatic) before calculating the GRs. These are usually calculated only for clear/strong (Class I) NPF events but sometimes even for Class II events (Manninen et al., 2009). The new method seems to include days not typically classified as clear events (maybe sometimes undefined but also non-events due to quiet NPF). While I agree that most “Signal Days” are indeed clear NPF events, I have concerns about the comparability of the results, because of lack of classification prior to GR calculation. The absence of a pre-classification step introduces uncertainty; for example, your method may exclude days previously identified as Class I events or include days that would not typically qualify. What was the mean clear event (Class I) frequency in Hyytiälä during the periods of interest? Is it comparable with the signal % you find in Fig. 4? How many days were previously classified as Class I but were excluded by your method (and vice versa)?
Furthermore, as pointed out in lines 167-172 (and elsewhere) the early morning/late evening concentrations leading to erroneous and small GRs (background) seems to be a small weakness of the method (especially if one wants to use it in environments with increased local sources etc.), which is of course expected for automatic methods. However, my greatest concern is the possibility of getting GRs that appear reasonable, but for the wrong reasons, for example by having similar concentration and diameter increases from different sources (and not NPF) which can “trick” the method into calculating a “fake” GR higher than β, resulting in “signal” and not in “background”. Figure 7 helps illustrate that most of these days are NPF, but because it is averaged and normalized, days that do not follow this behavior can be averaged out. Have you observed such discrepancies in Hyytiälä?
General comment:
- I suggest that the “Results” section should be reorganized into clearly defined subsections. At present, the narrative lacks coherence, and transitions between paragraphs are abrupt, making the analysis difficult to follow. For instance, the paragraph starting on line 260 appears disconnected from the preceding discussion and could logically belong to a separate subsection.
Minor comments:
- Lines 54-67: I would suggest commenting a bit more about how these existing methods compare with each other. When each method is preferred (for example type of data, available sizes etc.).
- Line 63: A related approach to what? Related to the size channel-based methods? Please clarify.
- Lines 70-72: Please elaborate a little bit more. GR calculation and especially fitting-based methods are extremely sensitive to concentration spikes (e.g. from local sources), noisy data and even meteorological conditions that can alter the number concentration for a while.
- Lines 73-74: Additionally, there is not a “universal” GR calculation method, and some (older) studies do not even mention how GR was calculated exactly.
- Lines 96-97: What was the temporal resolution of your dataset? It would help to specify it here.
- Lines 109-110: Isn’t that a high averaging time for such a dynamic phenomenon as the growth rate? I get that in Hyytiälä the GRs are generally small compared to other environments, but still when calculating it for the size range of 2-3 nm (or even the 3-7 nm) as you do later, major changes can happen even within 1 hour. Also, I’m certain that during the 14 years, there should be NPF days with high GRs. Is the method/ averaging/ smoothing time-sensitive enough to catch these dynamic changes and calculate a trustworthy GR? What happens if you have more than one NPF events on the same day?
- Figure 1: What is the data time resolution you use in general with this method? From Fig 1a it seems it’s 1 hour. However, you have said that you use 3 hour rolling mean smoothing to run the method. Why not apply it in these graphs?
- Line 167-168: How was the local minimum, β ranging between the different diameter classes? In other words, what was the minimum growth rate above which you considered to have an NPF event (signal)?
- Line 171-172: I understand that, but it is not very clear to me why this happens. Please elaborate on this.
- Line 177: Please replace “of” with “or”.
- Line 181: How many days were the outliers? What was different in these days? Increased local sources?
- Fig A1 and A3 and A5 (and also lines 175-178): It is related to my major comment. You say that “the background days mostly days that would be classified as non-event or undefined days”. I agree, but also the signal days contain days that would not be necessarily classified as “Class I” days (which are the class typically used for GR calculations in most studies). In fact, from Figs A1, A3, A5 I see days that I would classify as non-events (Fig. A1 middle, and second line to the left) or undefined (Fig. A3 in the middle, and the one bottom right) (and also some are close to Class II). Even if a growth pattern exists in these cases (which is not clear in this color scale) how do these GRs compare to the actual NPF observations of the previous studies that use only Class I (and sometimes also Class II) events to calculate the GR?
- Lines 189-196: How did you decide the 0.1 log difference for the size increments? Was it a trial-error approach? With this approach, how many high-GR days do you think were discarded because of τmax=0? Could lowering the data averaging time help for these days?
- Lines 212-214: I suspect that the higher percentages of your method are mostly because of the so-called “quiet NPF” (Kulmala et al., 2022). Since you normalize the number concentrations, the algorithm detects growth patterns not detected by previous manual methods. Is that correct? Can you elaborate on that? If this is true, this can actually be a good feature about this method (meaning to calculate GR of days that would be otherwise not included manually).
- Lines 215-219: As Reviewer #1 pointed out, I would like to see a more comprehensive comparison of the new method with previous calculations of the GRs in Hyytiälä. Maybe you could utilize a GR database and include more days in Fig. 5.
- Lines 245-246 and 249-250: Why is that? Please elaborate.
- Figure 6: This Figure is not adequately described in both the main text and the figure’s caption. Furthermore, it is not connected to the previous analyses of the paper, and I believe it is of small value in the current paper (at least in the main text) since it focuses on the GR calculation method and not its general variability in the atmosphere of Hyytiälä. Maybe you could move it to the Supplement or try to connect it better to the rest of the text.
- Lines 260-268: I’m not sure what the conclusion of this paragraph is. That the days included automatically by the method indeed represent NPF days? Why don’t you first use an automatic classification method (Aliaga et al., 2023) to make sure that you have NPF events only? Because Fig. 6 is the median normalized diurnal, the days that are not typical NPF events but are included in the GR calculation are averaged out.
- Lines 267-268: Isn’t that self-evident?
- Lines 275-303: Relates to major comment. The studies you are comparing with have used only the clear NPF events (usually classified as Class I but some use also the Class II) to calculate the GRs, so their averages may include less days than the ones included in the new method. I think it is important to clarify this here and elsewhere in the text. Additionally, in Figure 8, consider annotating each bar with the number of days included in the corresponding average (maybe above the bars).
- Lines 311-312: This statement can be misleading, since the method was tested and validated only for Hyytiälä and no other environments yet. Please rephrase.
- Lines 339-342: That is a good idea, to combine the method with the automatic classification. From my point of view, the classification of the events should always come before the GR calculation, which is something the authors do not do directly. Have the authors tried this combination? It could increase the efficiency and the comparability of the method, since days not typically classified as NPF will not be included in the GR calculation.
References
Aliaga, D., Tuovinen, S., Zhang, T., Lampilahti, J., Li, X., Ahonen, L., Kokkonen, T., Nieminen, T., Hakala, S., Paasonen, P., Bianchi, F., Worsnop, D., Kerminen, V.-M., and Kulmala, M.: Nanoparticle ranking analysis: determining new particle formation (NPF) event occurrence and intensity based on the concentration spectrum of formed (sub-5 nm) particles, Aerosol Research, 1, 81–92, https://doi.org/10.5194/ar-1-81-2023, 2023.
Kulmala, M., Junninen, H., Dada, L., Salma, I., Weidinger, T., Thén, W., Vörösmarty, M., Komsaare, K., Stolzenburg, D., Cai, R., Yan, C., Li, X., Deng, C., Jiang, J., Petäjä, T., Nieminen, T., and Kerminen, V. M.: Quiet New Particle Formation in the Atmosphere, Frontiers in Environmental Science, 10, https://doi.org/10.3389/fenvs.2022.912385, 2022.
Manninen, H. E., Nieminen, T., Riipinen, I., Yli-Juuti, T., Gagné, S., Asmi, E., Aalto, P. P., Petäjä, T., Kerminen, V.-M., and Kulmala, M.: Charged and total particle formation and growth rates during EUCAARI 2007 campaign in Hyytiälä, Atmospheric Chemistry and Physics, 9, 4077–4089, https://doi.org/10.5194/acp-9-4077-2009, 2009.
Citation: https://doi.org/10.5194/ar-2025-19-RC2 - AC2: 'Reply on RC2', Janne Lampilahti, 26 Sep 2025
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This manuscript by Lampilahti et al. presents a new method to calculate the particle growth rate (GR) during new particle formation (NPF). The particle GR is a key metric to understand the gas-to-particle conversion during NPF and the calculation from the particle number size distribution (PNSD) is still a considerable source of uncertainty when mechanistic insights into NPF are inferred from ambient aerosol data. This has two reasons: 1) considerable instrumental uncertainties in the sub-10 nm size range 2) the usage of GR calculation methods which highly depend on the user or are sensitive to the measurement uncertainties. In that sense, this manuscript presents a considerable step forward for the community working on analyzing NPF as no fully automated method to infer the GR from the PNSD has been presented so far. The introduced maximum cross-calculation method is shown to be robust compared to the other methods when a comparing the results for Hyytiälä Finland. However, the manuscript in its current form has some shortcomings, which should be addressed such that this paper encourages the involved community to use that new method in the future and therefore I can only recommend publication in AR after the following points have been addressed:
Major comments:
Minor comments: