the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Improved Counting Statistics of an Ultrafine DMPS System
Dominik Stolzenburg
Tiia Laurila
Pasi Aalto
Joonas Vanhanen
Tuukka Petäjä
Juha Kangasluoma
Abstract. Differential mobility particle size spectrometers (DMPS) are widely used to measure the aerosol number sizedistribution. Especially during new particle formation (NPF) the dynamics of the ultrafine sizedistribution determine the significance of the newly formed particles within the atmospheric system. A precision quantification of the sizedistribution and derived quantities such as new particle formation and growth rates is therefore essential. However, sizedistribution measurements in the sub10 nm range suffer from high particle losses and are often derived from only a few counts in the DMPS system, making them subject to very high counting uncertainties. Here we show that a CPC (modified Airmodus A20) with a significantly higher aerosol optics flow rate compared to conventional ultrafine CPCs can greatly enhance the counting statistics in that sizerange. Using Monte Carlo uncertainty estimates, we show that the uncertainties of the derived formation and growth rates can be reduced from 10–20 % down to 1 % by deployment of the high statistics CPC on a strong NPF event day. For weaker events and hence lower number concentrations, the counting statistics can result in a complete breakdown of the growth rate estimate with relative uncertainties as high as 75 %, while the improved DMPS still provides reasonable results at 10 % relative accuracy. In addition, we show that other sources of uncertainty are present in CPC measurements, which might become more important when the uncertainty from the counting statistics is less dominant. Altogether, our study shows that the analysis of NPF events could be greatly improved by the availability of higher counting statistics in the used aerosol detector of DMPS systems.
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Dominik Stolzenburg et al.
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RC1: 'Comment on amt2022270', Anonymous Referee #1, 30 Jan 2023
The comment was uploaded in the form of a supplement: https://amt.copernicus.org/preprints/amt2022270/amt2022270RC1supplement.pdf
 AC1: 'Reply on RC1', Dominik Stolzenburg, 02 Mar 2023

RC2: 'Comment on amt2022270', Anonymous Referee #2, 12 Feb 2023
I congratulate the authors for the nice manuscript, and I would like to start by offering my sincere apologies for the delay in providing this review. The authors compared a standard ultrafine CPC with a modified Airmodus A20 CPC to investigate the effect of poor counting statistics on the calculation of growth and formation rates. Uncertainties on these quantities are often neglected and this work offers new and interesting results. The manuscript is wellwritten and fits the scope of the journal. The analysis is sound, and the results are presented clearly and concisely. However, some minor comments need to be addressed, and the manuscript's clarity can also be improved in a few places.
Minor comments:
Lines 4244: This sentence about technological development can probably be used for every measurement system. Consider removing or rephrasing it.
Line 44: “a large fraction” can you provide more quantitative information? Losses will clearly depend on the instrumental setup but please mention what the typical range is.
Line 48: The “PI” parameter is not used in the rest of the manuscript, and I do not see the reason for mentioning it here in the introduction. The only relevant information is that a system with lower losses, higher flow rate and sampling time will have better counting statistics. You already explained this in lines 4748, so you can remove this part on the PI parameter.
Line 51: “the PI parameter … describes the instrument sensitivity towards low number concentrations” instrument sensitivity represents the smallest absolute amount of change that can be detected. So, sensitivity should be the same at low and high number concentrations. I think speaking of the signaltonoise ratio is more meaningful in this context.
Line 54: Is there any drawback in using a CPC with a higher aerosol flow? I guess there must be an optimum range; otherwise, why not use a 10lpm flow rate or higher? I could think of coincidence (probably not a big issue when the CPC is used behind a DMA), a higher DMA sheath flow is required to keep the same resolution, and probably some other technical issues with the CPC construction itself. Adding a short sentence on the cons/problems of having a larger flow would be useful.
Section 2.2:
 did you also intercompare the counting efficiency of the two CPCs? From Figure S1, it seems there is a ~5% difference; if not corrected, can this affect your results?
 What about the response time of the two CPCs? This is a relevant parameter for your analysis, so it would be important to report it here (CPC3776 response time is well characterized, but I don’t know if it is the same for the modified A20).
Line 110: here, you define ‘time t’ but in equation (1) it is defined as tau; please use the same definition.
Lines 118125: this part is confusing because you provide the Poissonian distribution before saying what a Poissonian process is. Additionally, you are mixing the general description of a Poissonian process with its applicability to an optical counting system. For example, coincidence applies to certain types of measurement systems but not to a general Poissonian process. My suggestion is first to define a general Poissonian process, then describe the Poissonian distribution and conclude with the applicability of Poissonian statistics to a counting system like a CPC.
Lines 126129: when reading this part, I was confused about the applicability of Poissonian statistics to your problem because N during an NPF event is a function of time and is not Poissonian. It is easy to see this if you think that for Poisson P(t1) = P(t2) for any t1 and t2 but for NPF P(t1)<P(t2) if t2>t1 (the particle number increases with time during NPF). After reading the manuscript, I understood that this is probably not a concern because you are working with narrow concentration intervals where the time dynamics likely do not play a role. However, I think it is necessary to comment on this and on the general applicability of Poissonian statistics to describe NPF events.
Line 132: Any observed system is characterized by random fluctuations leading to some sort of inherent variability, but I would not classify this as ‘random uncertainty’. I attribute random uncertainty to fluctuations in the measuring system (e.g., small changes in the flow rate, laser current,…).
Lines 142145, a few comments regarding this approach:
 As mentioned before, what is the effect of the instrument response time? I would expect that if the response time is substantially different, then, with this approach, you would amplify the error. However, this is not a real error because of the different instrument transfer functions. Ideally, you should account for it before performing this analysis (especially considering that you are working with narrow time intervals).
 Instead of considering a narrow interval, why didn’t you select a single count value (e.g. pick 300 counts per unit time in the A20 and compare it with the corresponding distribution in the 3776 CPC)? This would remove the uncertainty related to the finite interval selection in the A20.
 Mention explicitly that a gaussian distribution is a good approximation of a Poissonian when mu*tau is sufficiently large (>~10), which is why you are using a gaussian PDF to fit the data.
Line 188: Did you use the square root of N as underlying uncertainty? If so, please mention it explicitly.
Line 192: Replace the second “using” with a different verb and the correct form (e.g. considers).
Lines 219222: You could make the same scatter plot for periods with no NPF to exclude the sizing effect. It should be an easy check with your dataset and would probably resolve this open question (Fig. S1 already shows a difference in the counting efficiency).
Figure 5: to what extent can the Poissonian statistics explain the observed discrepancies in GR and J? I guess that for a quantitative answer, you would have to run the MC simulation for all events, which is not what I am asking for, but a comment on this aspect would be useful for the paper.
Figure 6 and Figure 7: is the GR and J distribution centered around the “real” value? It would be useful to report the value measured for the real event (or mention that is the same as the distribution mean if this is the case).
Line 263: is the statistical uncertainty defined as one standard deviation? Please report which type of statistical uncertainty was used.
Line 281: “with” instead of “which”.
Line 295: “the” instead of “that”
Section 5.3: This part is interesting because it shows that counting statistics is the main source of uncertainty for GR and J determination. You show that other CPC measurement errors can be neglected even with your upperlimit approach (you are essentially attributing all A20 measurement errors to the TSI CPC). However, this message is not very explicit, my suggestion is to restructure this section to clarify this point. I think this is an important conclusion and should be highlighted better.
Line 338: I would remove ‘sub10 nm range’, your findings regarding Poissonian statistics apply to any size range, and absolute counts are often lower for larger particle sizes.
Lines 349351: I would rephrase this because, for most practical applications (the majority of NPF studies are performed with UCPC having a small flow rate), this additional source of error seems negligible, as you have shown in the previous section. So, I would say that the additional measurement error becomes important only when using a system with high counting statistics, as in the case of the A20 CPC.
Citation: https://doi.org/10.5194/amt2022270RC2  AC2: 'Reply on RC2', Dominik Stolzenburg, 02 Mar 2023
Dominik Stolzenburg et al.
Dominik Stolzenburg et al.
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