These authors contributed equally to this work.

Differential mobility particle size spectrometers (DMPSs) are widely used to measure the aerosol number size distribution. Especially during new particle formation (NPF), the dynamics of the ultrafine size distribution determine the significance of the newly formed particles within the atmospheric system. A precision quantification of the size distribution and derived quantities such as new particle formation and growth rates is therefore essential. However, size-distribution measurements in the sub-10 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 size range. 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 40 %, 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.

Differential/scanning mobility particle size spectrometer (DMPS or SMPS) systems can be used to measure the number size distribution of ambient aerosol particles ranging in size from sub-10 nm to hundreds of nanometres (Aalto et al., 2001; Wang and Flagan, 1990). The instruments typically consist of an impactor, a charger, a DMA (differential mobility analyser), and a CPC (condensation particle counter). The impactor is used to limit the maximum particle size to enable multiple charging corrections in the inversion. The charger then brings the particles to a known charge distribution (typically steady-state bipolar charging equilibrium as described by, for example, Wiedensohler, 1988), and the charged particles are size-selected in a DMA based on their electrical mobility. Finally, the number concentration is counted by condensational growth and subsequent optical detection with a CPC. The number size distribution is then determined by stepping/scanning different voltages at the DMA and the application of an inversion process if the maximum particle size, the charging probability, all the losses, and the detection efficiency are known.

As size predominantly determines the dynamics of ultrafine aerosol
particles, measurements of the particle number size distribution are
essential for understanding the role of aerosols in the atmospheric system.
One process in which the smallest ultrafine (

The number of registered counts in the CPC is determined from the total size-dependent penetration of the DMPS/SMPS, the CPC aerosol flow rate through the optics, and the sampling interval for an individual size. Most recent advances in the sub-10 nm size distribution instrumentation have been focused on increasing the sampling time (Stolzenburg et al., 2017), size resolution (Kangasluoma et al., 2018), or inversion performance (Stolzenburg et al., 2022a). However, large advances are expected simply by using a CPC with a large aerosol flow rate, which linearly increases the number of counted particles. In addition, it remains unquantified to what extent improved counting statistics provide more reliable results on quantities typically inferred from sub-10 nm size distributions, such as the particle growth and formation rate. Solid uncertainty estimates for these size-distribution-derived quantities are rare (Dada et al., 2020; Kangasluoma and Kontkanen, 2017) or only provided via sophisticated inversion schemes (Ozon et al., 2021).

In the current work, we use a new laminar flow CPC (modified Airmodus A20)
that has 2.5 L min

The measurements were performed from 24 March–19 May 2017 at the SMEAR II
station (Station for Measuring Ecosystem–Atmosphere Relations;
Hari and Kulmala, 2005) The station is located in Hyytiälä, southern
Finland (61

Schematic of the measurement setup. Sample is taken from the
ambient air and dried to

The modified Airmodus A20 CPC is a laminar flow CPC, where the entire sample
flow is heated and saturated with butanol. The saturated sample flow goes to
a multi-tube (six tubes) condenser, where the temperature is decreased to
activate the aerosol particle growth by condensation, followed by optical
detection. The nominal cut-off diameter, using the factory settings, of the
Airmodus A20 CPC is 7 nm. The TSI 3776 CPC is also a laminar-type CPC, but
in contrast to the A20 CPC, the TSI 3776 CPC utilizes the ultrafine CPC
design, where the sample flow is introduced in the middle of the condenser
with a capillary (Stolzenburg and McMurry, 1991). The TSI 3776
CPC was operated with the high-flow setting, where the CPC draws an inlet
flow of 1.5 L min

Kangasluoma et al. (2015) showed that a
conventional, unsheathed CPC can be tuned for even sub-3 nm particle
detection by increasing the temperature difference between the saturator and
the condenser and by adjusting the inlet flow rate. With the factory
settings of the Airmodus A20 CPC, the saturator temperature is
39

The detection efficiency of the CPCs was characterized using negative silver
particles produced with a tube furnace. The test particles were charged with
a

Figure S1 in the Supplement shows the cut-off calibration curves for the CPCs. The 50 % cut-off diameters of the Airmodus A20, the modified Airmodus A20 and the TSI 3776 CPC are approximately 5.5, 2.9, and 2.0 nm, respectively. With the modifications, the modified Airmodus A20 CPC has a performance almost comparable to the TSI 3776 CPC. It should be noted that this specific device in this specific calibration performed exceptionally well, as its nominal cut-off is typically closer to 2.5–3 nm for silver test particles (Wlasits et al., 2020).

Apart from their differences in activation efficiency and effective detector
flow rate, the two CPCs have different response times to a change in aerosol
concentration, which are

A random variable

In a CPC, the particles are counted in the optical unit of the CPC, where a
nozzle directs the particle stream to cross a laser beam perpendicularly.
Light is scattered from the laser beam as the particles cross it, and the
scattered light is collected by a photodiode. In typical optics with

In our setup, we can neglect the total penetration of the system since the
compared CPCs measure in parallel in the same DMPS system, and the total
penetration is the same for both. This allows us to compare the raw data
from the CPCs without an inversion and the uncertainties related to it
(Stolzenburg et al., 2022a). As our DMPS
outputs the average concentration during each voltage step, we need to
rearrange Eq. (2) for the counted particles

Uncertainty is a fundamental concept in statistics and probability, and it
occurs in all measurements. The uncertainty of a measurement can be
systematic, due to human error or resulting from the natural fluctuation of
the observed system. In most cases, the total uncertainty of the measurement
is a combination of uncertainty from multiple sources.
Ultimately, we are interested in the uncertainty of the data obtained from
an individual CPC within a DMPS setup, which could be used within
uncertainty estimates of subsequently derived variables (

Distributions of TSI 3776 counts from four example count ranges
simultaneously measured in the modified A20

We chose the following approach to obtain an uncertainty estimate of the
measurements with the DMPS using the TSI 3776 as a detector. First, only
data for particles

We are now interested in the uncertainties determining the width of these
PDFs. By selecting count ranges in the modified Airmodus A20, we select
measurements with an actual number concentration

Using these error estimates, we can derive the corresponding uncertainties
in the quantities typically derived from DMPS size-distribution data, the
growth rate (GR) and formation rate (

The formation rate can be calculated for particle size range [

We performed a Monte Carlo simulation on one of the NPF days (28 March 2017). New sets of data were generated from the original data 10 000 times, by altering the measured counts in each size channel for each
measurement time according to their underlying uncertainties. We performed
three sets of MC simulations. First and second, we use a Poisson counting
error to vary the TSI 3776 and the modified Airmodus A20 data (assuming a

We analysed the dataset by classification of the NPF event days (Dal Maso et
al., 2005) and calculated formation and growth rates for the subset of
class-I NPF event days. Figure 3 shows an example NPF day (28 March
2017) from both CPCs (modified Airmodus A20 Fig. 3a and TSI 3776 Fig. 3b).
The 28 March is chosen as the example day as it is a typical class-1
NPF event day with a strong nucleation rate but not much higher than
average GR, such that the nucleation mode persists over a long enough time in
the sub-10 nm range to investigate the effect of improved counting
statistics in full detail. We can see that the modified Airmodus A20
produces a smoother distribution in the areas of low concentrations
(blue-to-yellow colour range). Besides the lower nominal cut-off in the
laboratory calibration of the TSI 3776 (Fig. S1), the signal at the small
sizes below 5 nm is noisier in the TSI 3776-derived size distribution
compared to the modified Airmodus A20-derived size distribution.
Potentially, the overall reduced statistics counterbalance the effect of a
more efficient detection at these sizes. Moreover, it needs to be noted that
ambient cut-offs are subject to larger uncertainties due to the unknown
chemical composition of the counted particles and the composition-dependent
response of the CPCs, which can be more than 3 nm difference for the

Comparison of the inverted size distribution using the signal of
two different CPCs in the nano-DMPS (2–40 nm) for 28 March 2017,
a strong NPF day in Hyytiälä, Finland. Panel

Comparison of the total number concentration above 4 nm obtained
from integration of the inverted DMPS data and the total concentration
measurement using a TSI 3775 CPC. Panel

Next, we compare the performance of the DMPS using different detectors with respect to the number closure with a simultaneously measuring total CPC (TSI Model 3775, nominal cut-off 4 nm). The correlation of the full campaign dataset between the integrated number concentration of the DMPS system (above 4 nm) and the total concentration measurement with the CPC 3775 is shown in Fig. 4 for both detectors (Fig. 4a using the TSI 3776 in the inversion and subsequent integration and Fig. 4b using the modified Airmodus A20). Pearson's coefficient of correlation is high for both (0.992 and 0.994) but slightly better in cases when the modified Airmodus A20 is used within the DMPS inversion, which is reasonable due to the increased statistics. However, the data deviate from the 1 : 1 relation (0.89 slope for the modified Airmodus A20, which is more significant than for the TSI 3776 based DMPS data with a slope of 0.94). This could be due to a different plateau value reached in the counting efficiency curves and not correctly accounted for by the calibration. Wlasits et al. (2020) showed that plateau values of the same instrument vary slightly between different calibrations. Therefore, this could easily lead to offsets in the inversion, resulting in the observed discrepancies in the total number concentration.

In Fig. 5, we compare the calculated GR

Comparison of the GR

Results from the Monte Carlo simulations testing the influence of a
pure counting error on the size-distribution-derived quantities

In Fig. 6 we present the results from our Monte Carlo analysis of
28 March 2017, comparing the performance of the modified Airmodus A20
with the TSI3776, assuming the measured signal is only subject to a counting
uncertainty. Figure 6a and b present the results of the 10 000 GR

This directly translates into the significantly larger variance of the
GR

Overview of the results of the Monte Carlo simulations for all 3
investigated days. Formation and growth rate as obtained from the initial
data are given together with the relative uncertainty (1

Results from the Monte Carlo simulations testing the influence of
a pure counting error and an additional measurement error on the size-distribution-derived quantities

In addition, it needs to be noted that 28 March 2017 was one of
the days with the highest formation rate (

We now aim to estimate the total error in a CPC measurement based on our
dual setup. As described by Eq. (6), we can obtain an upper estimate of the
total error in the TSI 3776 measurement by selecting small count ranges in
the modified Airmodus A20 and estimating the width of the resulting count
distribution in the TSI 3776 at simultaneous measurements. In Fig. 8a we
show the upper relative error estimate together with the pure counting error
(

Total uncertainty estimate for the TSI 3776 by selecting narrow
count ranges in the modified Airmodus A20. Panel

Results from the Monte Carlo simulations testing the influence of a
total measurement error in the TSI 3776 on the size-distribution-derived
quantities

To estimate the influence of such additional uncertainties in CPC
measurements on the size-distribution-derived quantities GR

Our limited dataset does not allow for the reverse procedure due to a lack
of statistics (i.e. selecting narrow count ranges in the TSI 3776 and
obtaining the PDF for the simultaneous measurements of the modified Airmodus A20), and hence we do not provide a detailed Monte Carlo analysis on the effects on the growth and formation rate. However, as the relative counting error is so much lower in the modified Airmodus A20, we suspect that this additional source of uncertainty would dominate the formation and growth
uncertainties in that case by the following simple reasoning: the relative
counting uncertainty scales with

The strength and importance of NPF with respect to the climate system is often characterized by formation and growth rates, which are commonly derived from the evolution of measured particle number size distributions obtained from DMPS/SMPS systems. However, the uncertainties in the DMPS measurements and their effect on the size-distribution-derived quantities are not well quantified. As the CPC counting process can be considered a Poisson process, the resulting uncertainty from the counting process can be non-negligible at the low count rates and might dominate the uncertainty in the derived size distribution and formation and growth rates.

Here, we deploy a DMPS system with a modified Airmodus A20 CPC providing a
factor 50 higher counting statistics compared to the commonly used TSI 3776
ultrafine CPC. We found that the modified Airmodus A20 provides smoother
number size distributions, especially in the case of low concentrations of
ultrafine particles and achieves very good correlation with simultaneous
absolute number concentration measurements. The difference between the
counting statistics of the CPCs is propagated to the values derived from the
measured number size distribution, resulting in significantly reduced
uncertainties for GR

This study shows significant improvement in the determination of the formation and growth rate during NPF by the deployment of a DMPS with improved counting statistics. The wide deployment of such instrumentation which is optimized for sub-10 nm measurements could significantly reduce our uncertainties in formation and growth rate determination or even allow for the application of better analysis tools due to the increased statistics (Pichelstorfer et al., 2018; Ozon et al., 2021) and hence boost our understanding of NPF; for example, they provide better mass closure in aerosol growth (Stolzenburg et al., 2022b). However, this study also shows that other sources of uncertainty are typically present in DMPS measurements, which also need to be understood and potentially be reduced or at least be well quantified, which requires future work on CPC techniques.

The software code for performing the Monte Carlo analysis is available under

Raw particle number size distribution data and retrieved growth and formation rates are available under

The supplement related to this article is available online at:

TL, PA, JV, and JK performed the measurements; DS and TL analysed the data and performed the simulations; DS, TL, TP, and JK were involved in the scientific discussion and interpretation of the results; DS and TL wrote the manuscript; and all co-authors commented on the manuscript.

Joonas Vanhanen is the Chief Technology Officer of Airmodus Ltd., the company producing and selling the A20 CPC. The remaining authors have no conflicts of interest to declare. This study was independently performed and was not co-funded by Airmodus Ltd.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We thank Lubna Dada for her support in nucleation rate calculations.

This work was funded by the Academy of Finland Flagship via the Atmosphere and Climate Competence Center (ACCC; grant no. 337549) and the Academy of Finland (grant nos. 1325656, 346370, and 79999129). It also received funding from the University of Helsinki 3-year grant (grant no. 75284132) and the University of Helsinki ACTRIS-HY. It also received support from the European Union's Horizon 2020 Research and Innovation programme under a Marie Skłodowska–Curie Action (grant agreement no. 895875) (NPF-PANDA), from the European Commission through Research Infrastructures Services Reinforcing Air Quality Monitoring Capacities in European Urban & Industrial AreaS (RI-URBANS; grant no. 101036245) and through ACTRIS-CF (329274) and ACTRIS-Suomi (328616).Open-access funding was provided by the Helsinki University Library.

This paper was edited by Hang Su and reviewed by two anonymous referees.