the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Quantifying charger-related uncertainty in electrical mobility analysis of aerosols with MPSS-UQ 1.0
Abstract. Charging probability is the greatest source of uncertainty in electrical mobility-based measurements of aerosol size distributions, but its influence on the results is rarely quantified and reported. In bipolar charging, the charge distribution is almost universally modeled using the Wiedensohler approximation, although it has been shown to deviate significantly from the true charge distribution under many measurement conditions. The charge distribution depends, among other factors, on the mobilities of the charger ions, which are typically not precisely known. Ignoring this uncertainty can lead to biased size distribution estimates and severe underestimation of their uncertainty. In this work, we quantify the uncertainty that imprecisely known charger ion mobilities introduce into the charged particle fractions, and then propagate this uncertainty into the estimates of the particle size distributions using a modular Bayesian approach, in which the ion mobilities are treated as nuisance parameters and marginalized over their plausible range. The inversion method, which is available as the open-source Python package MPSS-UQ, is implemented with particular emphasis on computational efficiency and tested with both synthetic and real mobility particle size spectrometer data. For a month-long field dataset, marginalizing over the uncertain ion mobilities widened the posterior credible intervals of the estimated size distributions on average by a factor of 2.4, with factors up to 10 in some size classes, compared to conditioning on fixed mobility values. The wider intervals provide a more realistic assessment of uncertainties in the inferred size distributions, and quantifying the structure of this uncertainty helps identify where improvements in the characterization of charger ion properties or in the measurement setup would be most effective.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-2013', Anonymous Referee #1, 23 Aug 2026
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AC1: 'Reply on RC1', Matti Niskanen, 10 Oct 2026
Dear Reviewer,
We thank you for your comments and the time you took reviewing our manuscript. We have carefully considered all remarks and suggestions and give our responses below.
Kind regards,
Matti Niskanen
on behalf of all co-authorsREVIEWER:
- The Pfeiffer manuscript cited in support of LYF actually showed that Gatti and Kortshagen model fared better --- did you try to run that model throught your python package? On github I only see LYF and Wiedensohler as options. (Btw, list the github link itself in the acknoweldgement as well as the doi, it makes easier for people to find it)AUTHORS:
This was indeed the finding reported by Pfeifer et al. (2023), and it therefore would be interesting to experiment with the Gatti and Kortshagen model, as well as the model(s) proposed by Gopalakrishnan and co-workers. However, to keep the manuscript focused on the effects of charger ion uncertainty and the MPSS inversion methodology, we have not carried out such a comparison between different charging models here and therefore have not tested the Gatti and Kortshagen model with our Python package. We chose the LYF model mainly because it is based on the Fuchs theory and builds on the Hoppel and Frick model that the Wiedensohler approximation is based on. We note that the charging model choice and possibility of using alternative models were already discussed in the originally submitted manuscript (lines 646-650).Regarding the accessibility of the code, the GitHub repository URL is provided in the Code and data availability section, together with the DOI of the archived version used for this study. The software is also cited as Niskanen (2026) in the manuscript and included in the reference list. To our understanding, this follows the journal requirements, but we leave the final placement and formatting of these links to the editorial team.
REVIEWER:
- It would be good to compare this method against what people usually use by default (without custom inversion algorithm). For example, what would a commercial or default algorithms show for those measurements you showed in figs 9 and 10?AUTHORS:
We agree that comparison with a commonly used inversion procedure would be informative. However, to the best of our knowledge, no generally accepted "default" algorithm for MPSS inversion currently exists. The inversion algorithms used by commercial instruments are typically not openly available, and we do not have access to a commercial algorithm that we could apply to our own data to directly compare with the estimates presented in Figures 9 and 10.We have, however, done a related comparison using data from an atmospheric simulation chamber experiment measured with a commercial TSI SMPS Model 3082, with a Model 3077 neutralizer, and a Model 3081 DMA. For this experiment, we exported both the raw measurement data and the particle size distributions reported by the instrument software. We then applied MPSS-UQ to the raw data and compared the resulting estimates with the instrument-reported estimates. This comparison was mentioned in the originally submitted manuscript (lines 506-512), although the results were not presented for reasons of brevity.
We present these results here for the reviewer's consideration. To enable proper comparison with the TSI SMPS estimates, we used the Wiedensohler charging model in MPSS-UQ. Attached Figure 1 shows the size distribution estimates over the full experiment, which lasted approximately 7 hours, and attached Figure 2 presents the PSD estimates at two representative time points. The overall distribution shapes and magnitudes are similar, while the MPSS-UQ estimates are smoother and the estimates reported by the TSI SMPS show more variability from one size bin to another.
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AC1: 'Reply on RC1', Matti Niskanen, 10 Oct 2026
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RC2: 'Review of egusphere-2026-2013, "Quantifying charger-related uncertainty in electrical mobility analysis of aerosols with MPSS-UQ 1.0"', Anonymous Referee #2, 22 Sep 2026
Niskanen, Ursin, Ylisirniö, and Lehtinen present a manuscript describing the uncertainty in inverted particle size distributions due to uncertainty in the ion mobility and charging probability during the neutralization stage of differential mobility analysis. This specific source of uncertainty is not usually explored and the authors report that after propagating some reasonable uncertainty ranges in mobility and charging probability all the way from the ion to the final reported size distribution, the uncertainty can vary by a factor of 2.4 to a factor of 10, depending on the conditions. Conditions that affect uncertainty include carrier gas properties, particle size, and other factors. Inaccuracies were magnified by a larger mismatch between the assumed charging distribution and the actual charging probability assigned during the uncertainty analysis.
The math becomes somewhat inscrutable towards the middle of the paper. Nevertheless the variables are all defined and the Bayesian framework for solving inverse problems is well-established. The code is openly available. A large number of prior uncertainty models for aerosol mobility distribution inversions, ranging in year from the 1980s to the 2010s, are reviewed here. This is a very nice paper and should be published subject to minor revisions.
MINOR COMMENTS
[1] In the sub-section headings 3.1, 3.2, 3.3, and 3.4 - could the authors include, directly in the heading, the name of the variable (i.e. its symbol/letter) so the reader can more easily connect the subsection to its equation in the first part of section 3?
[2] On lines 568-569 - is the carrier-gas uncertainty limited (in most cases) to the air pressure and the presence of water vapor? Why not state this upfront?
Citation: https://doi.org/10.5194/egusphere-2026-2013-RC2 -
AC2: 'Reply on RC2', Matti Niskanen, 10 Oct 2026
Dear Reviewer,
We thank you for your comments and the time you took reviewing our manuscript. We have carefully considered all remarks and suggestions and give our responses below.
Kind regards,
Matti Niskanen
on behalf of all co-authors
REVIEWER:
[1] In the sub-section headings 3.1, 3.2, 3.3, and 3.4 - could the authors include, directly in the heading, the name of the variable (i.e. its symbol/letter) so the reader can more easily connect the subsection to its equation in the first part of section 3?AUTHORS:
We thank the reviewer for this suggestion. We considered including mathematical symbols in the subsection headings to facilitate connections with the equations. However, the subsections do not generally correspond to individual variables: Sections 3.1 and 3.2 discuss multiple prior and likelihood distributions, respectively, while Sections 3.3 and 3.4 concern broader estimation procedures rather than a single mathematical quantity. We therefore believe that adding individual symbols to the headings could be misleading rather than clarifying. Because the relevant variables and distributions are identified in the text immediately before the corresponding equations, we have decided to retain the current subsection headings.REVIEWER:
[2] On lines 568-569 - is the carrier-gas uncertainty limited (in most cases) to the air pressure and the presence of water vapor? Why not state this upfront?AUTHORS:
We thank the reviewer for the question. The carrier-gas-related uncertainty is not necessarily limited to air pressure and the presence of water vapour. Variations in the overall gas composition and trace constituents can affect the composition and mobilities of the charger ions. In the present analysis, we account for such effects collectively through the uncertainty assigned to the positive and negative ion mobilities, rather than attributing the mobility variation to specific gas constituents. This is stated in the Introduction, where the dependence of ion mobility on carrier-gas composition and possible trace constituents is discussed (lines 34–36), and further explained in Section 2.2. We have therefore decided to keep the original text.Citation: https://doi.org/10.5194/egusphere-2026-2013-AC2
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AC2: 'Reply on RC2', Matti Niskanen, 10 Oct 2026
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I found this to be a technically rigorous manuscript that is also engaging. The authors present a Bayesian inversion approach tackling charging uncertainties for measuring aerosol particle distributions. The theoretical claims and the method all seem to be solid. I recommend prompt publication.
If there's a revision, I invite the authors to engage the following points (but no pressure if not):
- The Pfeiffer manuscript cited in support of LYF actually showed that Gatti and Kortshagen model fared better --- did you try to run that model throught your python package? On github I only see LYF and Wiedensohler as options. (Btw, list the github link itself in the acknoweldgement as well as the doi, it makes easier for people to find it)
- It would be good to compare this method against what people usually use by default (without custom inversion algorithm). For example, what would a commercial or default algorithms show for those measurements you showed in figs 9 and 10?