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:

- 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.

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.