General comments

Tirpitz et. al 2021 present an extensive and interesting study on possible improvements of aerosol and trace gas parameter retrievals from ground-based MAX-DOAS measurements when multispectral polarimetry data is included. A novel approach is shown to retrieve aerosol microphysical properties from MAX-DOAS measurements. Clear advantages for the retrieval of aerosol parameters were found!

The results are promising and aim at the general lack of knowledge of an accurate aerosol characterization when ancillary data sets are not available. However, the advantages for the retrieval of trace gas vertical profiles are either small or not existing showing a clear benefit for aerosols only. This analysis was made on synthetic data leaving it open if the approach will also show clear advantages for measured data and unfavorable conditions as temporal and spatial inhomogeneities and larger measurement uncertainties. These points have been discussed shortly but a second study including validation data sets would be interesting to assess the actual importance for the community.

This paper is well written, the figures are presented in a clear and structured way and the analyses have been performed thoroughly and consistently. Therefore, I suggest publication in AMT but please consider some minor comments:

Specific comments



P1, L2: "analysis ultra-violet" ) "analysis of ultra-violet"

P1, L7 & L8: "measurement" ) "measurements"

P1, L12: "retrieval aerosol" ) "retrieval of aerosol"

P8, L234: The aim of inverse model ) inverse modeling

Table 1: Since 360nm and 477nm are used to cover the O4 absorption and 343nm and 460nm are more or less central wavelengths for HCHO and NO2 respectively, I was wondering why did you use 415nm and 532nm? What is the benefit and how would the neglection of these wavelengths deteriorate the results?

P13, L337: Why did you decide for an exponential grid? Most retrieval algorithms use an

equidistant spacing in all retrieval altitudes.

P17, L401: DOFS in table S2 are larger so I would write larger instead of smaller here.

Table 6: I was wondering if e.g. the UV only mode means that for the trace gases only one wavelength is used but for aerosols both? If yes, how large is the DOFS for individual parameters of aerosols at different O4 absorption bands? I would assume that the aerosol information content of the absorption band at 343nm is extremely small and the benefit of including this wavelength is insignificant.

Fig. 3: What do the thick vertical lines mean? Please add also rows for Vis. Why do trace gases show double peaks for Multi-S-P-A and Multi-S-P-A-I? Do we see different results for HCHO and NO2 here? Please discuss!

Fig. 4: This is the first time you show box-whisker plots. Please give a short explanation in the caption of this figure.

P21, L444-L445: Could you please explain more about where the sensitivity for the surface albedo comes from? You do not look to the surface so photons must be scattered into line of sight mainly due to multiple scattering. Would a negative elevation angle increase the sensitivity?

Fig. 9 and 10: It would be interesting to compare with what the normal uv and vis mode would retrieve since this is what the community is mostly doing. Could you please add this as well or are results similar to UV-S? Could you please change the noiseless lines in a different way? It is hard to identify them. What does the shaded area around the a priori mean? The caption indicates that this is the uncertainty of a priori? I thought one fix a priori is used? Please explain!

Fig. 11: I am surprised by the VCD results. In general, common MAX-DOAS profiling algorithms perform strongly for integrated quantities but might have larger deviations for certain profile features. If possible, please add a discussion and maybe another column to Table 6 for VCDs.

Section 11: This section is interesting but I would assume even larger uncertainties for real data. Especially when thinking about measurements of elevation scans at different azimuthal directions and subsequent Almucantar scans, temporal changes in the atmospheric composition might vary strongly. Which part of Kreher et al. 2020 supports 5% and why do you assume that this is enough based on the study of synthetic data by Frieß et al. 2019?

Fig. S14: Please change color and name of "Multi-S-P-A-I" mode in legend. And add the description of random noise magnitudes for the x-axis in the caption.

Table 7: Please add another column and discussion of the data presented in section 11 for 6% because this analysis is most likely closest to real measurements.

References



Frieß, Udo, Steffen Beirle, Leonardo Alvarado Bonilla, Tim B¨osch, Martina M. Friedrich, Francois Hendrick, Ankie Piters, u. a. "Intercomparison of MAX-DOAS Vertical Profile Retrieval

Algorithms: Studies Using Synthetic Data". Atmospheric Measurement Techniques 12, Nr. 4

(10. April 2019): 2155{81. https://doi.org/10/ghx39n.



Kreher, Karin, Michel Van Roozendael, Francois Hendrick, Arnoud Apituley, Ermioni Dimitropoulou, Udo Frieß, Andreas Richter, u. a. "Intercomparison of NO2, O4, O3 and HCHO

Slant Column Measurements by MAX-DOAS and Zenith-Sky UV{Visible Spectrometers during CINDI-2". Atmospheric Measurement Techniques 13, Nr. 5 (6. Mai 2020): 2169{2208.

https://doi.org/10/gm4xsg.

The article "Enhancing MAX-DOAS atmospheric state retrievals by multispectral polarimetry - studies using synthetic data" by Tirpitz et al. explores the potential benefit of including information about the polarisation state of scattered sunlight in the retrieval of vertical profiles of trace gas concentrations and of aerosol properties and abundances. This topic has until now been largely overlooked in the MAX-DOAS literature, partly because of the challenges it poses on the forward model, on the inverse modelling and perhaps also because of technical challenges in the development of a multispectral sensor capable of taking such measurements. It is however highly relevant to make such an assessment for the MAX-DOAS technique because from other applications in atmospheric composition research (e.g. with ground-based or satellite radiometers) it is well-known that making use of polarization enhances the information content and accuracy of aerosol retrievals. 

Other noteworthy aspects of this study are (1) the implementation of a combined aerosol and trace gas retrieval in a single optimisation step, allowing for optimal propagation of errors in the measurements and in the a-priori assumptions into the uncertainty estimates of the many parameters that are retrieved and (2) the retrieval of micro-physical properties as described by the Mie model, which is more sophisticated in its description of aerosol properties compared to the more simple aerosol models used in MAX-DOAS studies until now.

I find the manuscript very well written, thorough and despite the high level of complexity of this subject certainly understandable for the target audience. The impact of different measurement modes (S,P,I,A) on the retrieval accuracy is quantified and interpreted in great detail. Questions such as on the impact of high aerosol abundances and the impact of spatio-temporal variability are addressed and provide relevant insights, for instance to those who will use MAX-DOAS data for comparison studies.

Some important conclusions are: (1) including polarisation affects mostly the accuracy of the aerosol-related quantities, (2) the impact on trace gas VCDs is limited (almost negligible) and (3) the impact is highest for the surface layer (both aerosols and trace gases). 

It could be considered a limitation of this study (by itself) that it is based solely on simulations, making it difficult to judge the real impact of these algorithmic developments in practice. From this perspective, the summary of the main findings of a complementary study on field data (Tirpitz 2021) in the Outlook section adds a realistic perspective to the challenges met when implementing (and validating) these methods in practice. This is a valuable addition to the present study.

I recommend the manuscript to be published as is, after the following minor issues have been addressed:

• p. 11, l.309 The approach to model the aerosol bulk extinction efficiency to be constant with altitude limits the possibility to retrieve vertical aerosol profiles with different aerosol types at different altitudes (e.g. a mixture of soot, nitrate aerosols and sea salt in the lower part of the atmosphere and desert dust at higher altitudes). This is a limitation that could be mentioned in the manuscript.   
• Fig. 3. Please add to the legend the meaning of the horizontal lines corresponding to each histogram (e.g. median)
• p. 23, l.485 ".... if measurements are performed a only two ... " please rewrite "a", e.g. "at" / "for".
• p. 27, l.546-547 It could be considered to leave out the last part of this sentence because of redundancy: "(the effective ... polarimetric measurements)"