the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 23 Jun 2025
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 preprint. The responsibility to include appropriate place names lies with the authors.- Preprint
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Status: open (until 04 Aug 2025)
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RC1: 'Comment on ar-2025-19', Anonymous Referee #1, 12 Jul 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:
- The authors show in this manuscript that the new maximum cross-correlation method performs similar (providing the same medians and variance) to other methods when applied to a dataset from Hyytiälä, Finland. What is missing from this manuscript (and what should be part of an introduction into any new method) is the testing of its performance against data where the true GR is known! The central point of this manuscript is not only to show that the new approach reproduces probably the same errors than the other methods have but to show that it probably can also retrieve the actual GR of an NPF event. Inclusion of a synthesized dataset (with instrumental uncertainties imposed) and the application of the new method to it should be the number 1 point of the results. I am 100% confident, that this group of authors has access to such synthesized NPF event data and it is therefore not too much additional work to include.
- The second major point relates to the fact that the authors analyze 14 years of Hyytiälä data, but then do not make use of the already existing analyses of these datasets. As far as I know, already analyzed Hyytiälä NPF event classification and GR data should be available to that set of authors for the same 14 years they now present as being analyzed by the maximum cross-correlation method. It is unclear to my why Figure 5, only contains randomly selected days where the GR is re-analyzed with the maximum concentration method, while there should be the entire GR dataset for 14 years be available. There are two specific things I’d like to see in a revised manuscript: 1) Correlation plots of the full 14-year dataset for all instruments (ion-GR, particle-GR NAIS, particle-GR DMPS) between all GRs calculated from the maximum cross-correlation method and GRs calculated from other methods, whenever both methods returned a value. 2) The background/signal differentiation histograms when only data from manually classified NPF events (or use the ranking method or whatever) are used. Does the background population completely vanish if we only use values from “classified” NPF events (should be Appendix Figure).
Minor comments:
- Line 35-42: Stolzenburg et al., 2023, Rev. Mod. Phsy. is the most recent and complete review on particle growth and also compares different methods with each other. It should be included here.
- Line 37: In the above mentioned review, there is a long discussion about a third approach using the full evolution of the PNSD combined with the general dynamics equations. These methods do disentangle the different contributions to GR but suffer from other challenges. They should be mentioned here, because especially those methods would have the chance to also be fully automated (in an ideal world)
- Line 63: What is the difference between these methods to the one presented in Lehtipalo et al., 2014. This should be clarified here.
- Line 67: I would also add that one of the advantages of the size channel based methods is that they do not require perfect knowledge on the absolute concentrations of the PNSD (i.e. the inversion correctness). In fact, they sometimes can even be run on raw data. The same applies to the new maximum cross-correlation method and should be mentioned here.
- Line 100-101: I’d prefer N_1 (with bar above) for the mean notation, as this is far more common.
- Line 109: To judge the robustness of the method, it would also be interesting how the results change when a different averaging is applied. Especially if the method is transferred to other environments, this parameter might need to change. In addition, it is known that rolling averages can skew the results of the appearance time method, so it would be interesting to see what changes when a static, time resolution reduction (i.e. block averages) is used.
- Line 123-131: It is not fully clear to me how the approach in creating more size increments is facilitated. Is the PNSD first inverted for all data and then somehow resized? I.e. how many original channels are e.g. in that window between 2-3 nm and how many increments are later used? I.e. do you obtain a higher size-resolution than the original data with that approach?
- Line 133: In my opinion the method should be called maximum cross-correlation method throughout the manuscript as maximum correlation method could be misleading/ doesn’t describe exactly what the method does.
- Line 147-149: That sentence seems to be broken. “To ensure” what?
- Line 149-151: Again, how many original size channels are in these ranges?
- Line 173-178 and 183-184: As said in the major comment: Here should be a comparison to the classical NPF event day characterization.
- Line 189-192: Again, how many original size channels are in these ranges?
- Line 192-194: Probably the right argument. But assuming these fast GRs are really there, would it make sense to then probably just tolerate e.g. one of the tau_max,i to be below zero to still capture some of these?
- Line 211-214: As the new method can calculate GR on more days, it would be very interesting to see how this corresponds to a event classification scheme (major comment 2)
- Line 216-218, Figure 5: It is important to see this comparison across different instruments and also probably different methods. Moreover, as said in major comment 2, the authors should make use of the full Hyytiälä datasets available to them.
- Line 240-241: Again Stolzenburg et al. (2023) probably provides the to-date most complete overview of GR datasets and should be referenced here.
- Line 245-250: Feels a bit off here, as this more or less is Figure 8, but Figure 6 is not yet discussed here. Should that be later in the manuscript?
- Line 253-255, Figure 6: My honest opinion: This Figure is not very interesting as it doesn’t provide any new insights (except that the new method can perform across different seasons). If the authors want to save space as they need to include the comparisons with synthesized data or the full Hyytiälä dataset, they can remove it. In addition, the caption is too short and should explain more what is in that Figure.
- Line 260-268, Figure 7: I would love to see the median days also for the “edges” of the GR distribution, i.e. the very fast and very slow growth cases, as these might be the most interesting, where deviations from the classical “banana-type” picture might appear.
- Line 296-297: Why only ion GR from Gonzalez-Carracedo? The DMA train data are especially useful in the sub 3 nm range, where other instruments often perform worse. This comparison should be shown, as this is one of the cases where the method might reach its limits (I don’t think so, but it needs to be included).
Citation: https://doi.org/10.5194/ar-2025-19-RC1
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Dataset for "A Cross-Correlation-Based Method for Determining Size-Resolved Particle Growth Rates" Janne Lampilahti, Pauli Paasonen, Santeri Tuovinen, Katrianne Lehtipalo, Veli-Matti Kerminen, Markku Kulmala https://doi.org/10.5281/zenodo.15648698
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