Review of Bauerova et al. ACP

The topic of the manuscript is both interesting and relevant to ACP readers. However, significant revisions to the presentation of the methods and results are necessary before the validity of the findings can be assessed and their relevance fully evaluated.

Abstract is somewhat confusing, more like a list of unrelated sentences and not a concise overview. Please rewrite.

Basics of MARS method (why, how, the elements of the model, meaning of splines) should be described as it cannot be considered as commonly known method.

The method description lacks sufficient detail to allow for replication of the analysis, which should be the standard level of detail. Conversely, the methods section includes numerical information that would be better suited to the results section. This misplacement makes the methods section harder to read. When transferring these details to the results section, explain the significance of the numbers (e.g., CVs, R²) and the narrative they convey.

It should be discussed whether linearity can be assumed in the data and whether the linear regression model is therefore appropriate. If linearity can be assumed I would recommend considering more robust fitting methods, as the ordinary least squares has been shown to be ill-suited for many types of atmospheric data (see e.g. Cantrell, 2008 and Mikkonen et al. 2019).

Section 2.3.2 could also be improved by adding subtitles or breaking it into smaller, thematically organized segments for better readability.

Describe clearly in the main text what are the COR and COR2 methods as your results are strongly dependent on them. Show an example of a correction model in the main text and justify the form of the model. The meaning of the equations in Table S14 is not fully clear even for experienced statistician, let alone the average reader of the ACP.

The manuscript leans too heavily on the massive Supplement. Reconsider which result tables and figures you are showing in the main text. If important results are shown only in 51-page supplement, it will not be found by readers.

Minor remarks

There are two sections numbered as 2.3.2

Section 4.1.2: Comparing R2 values from different studies is not meaningful as the value can be calculated in numerous ways which are not necessary comparable.

As different calibration methods are discussed in the manuscript, it would also be interesting to hear what the authors think on use of dynamic models, like in Zaidan et al. (2020), which are able to account for evident autoregression in the data.

Lines 737-738: stating that transport is not the main source of PM10 and PM2.5 in European cities needs reference.

References

Cantrell, C. A.: Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems, Atmos. Chem. Phys., 8, 5477–5487, https://doi.org/10.5194/acp-8-5477-2008, 2008.

Mikkonen, S., Pitkänen, M. R. A., Nieminen, T., Lipponen, A., Isokääntä, S., Arola, A., and Lehtinen, K. E. J.: Technical note: Effects of uncertainties and number of data points on line fitting – a case study on new particle formation, Atmos. Chem. Phys., 19, 12531–12543, https://doi.org/10.5194/acp-19-12531-2019, 2019.

Zaidan, M. A.  et al., "Intelligent Calibration and Virtual Sensing for Integrated Low-Cost Air Quality Sensors," in IEEE Sensors Journal, vol. 20, no. 22, pp. 13638-13652, 15 Nov.15, 2020, doi: 10.1109/JSEN.2020.3010316.