Review of "Cancellation of cloud shadow effects in the absorbing aerosol index retrieval algorithm of TROPOMI" by Trees et al.

The manuscript describes the findings of the systematic investigation of the effect that cloud shadows have on the AAI. The investigation was performed on an observational data set and compared with results from radiative transfer model (RTM) calculations using a newly developed Monte Carlo model. The authors conclude that cloud shadow effects on AAI are (1) difficult to correct, and (2) can mostly be ignored (due to the cancellation occurring within the AAI definition). The manuscript addresses a topic that could be neglected when the AAI was originally developed, but has become of importance with the advent of TROPOMI, which has a footprint on the same order of magnitude as cloud effects.

The investigation is well performed, the manuscript reads well and figures are illustrative and appropriate. Nevertheless, I have a number of serious concerns that I believe should be addressed before the manuscript can be published.

First: the advantages of using a Monte Carlo RTM to aid the understanding of cloud shadows and their effects on AAI can be clearly seen in the Figures 7 and 10, as the atmosphere's extinction profile can be studied. However, the model is not described in any detail (not even the acronym is explained) and the reader is expected to rely solely on the authors' statement that the RTM ''shows an excellent agreement'' with DAK (line 177). To lend credibility to the results shown in the manuscript, at least part of the analysis should be performed with DAK and the results compared.

Second: a number of RTM results are presented and explained, but the explanations are not always easy to follow. A schematic diagram of the phenomena involved, combined with a conceptual explanation, would greatly improve the understanding. The diagram could show, in a more simple way than Figs. 7 and 10, what the effects of surface, atmosphere, and clouds are on the reflectance and how this results in the observed (and modelled) blueing effect. This would particularly aid the understanding of ''second-order effects'', which I had trouble with.

Third: the discussion of the manuscript is very limited. The authors argue at length why a shadow-effect correction to the AAI is not feasible (or necessary), a minor aspect of the manuscript, whilst ignoring a number of important aspects. The following points need to be added:

(1) statistics as to how often serious AAI deviations (greater than, say, 1 unit) due to high thick clouds, high surface albedo, and/or low AMF_geo are encountered in observations. This would provide a more objective basis on which to build the argument that the correction is or is not necessary.

(2) A discussion of the effects of aerosols on the studied shadow effects --- AAI is an aerosol index, after all --- and

(3) the opposite: the effect of blueing on TROPOMI aerosol retrievals. Even if a detailed discussion is out of scope, the issue should be mentioned in your discussion.

(4) A discussion on how the choice of first and second neighbours influences the observational analysis: E.g., Fig. 10 shows that pixels between the cloud and the shadow have a larger AAI deviation than those in the shadow. And what happens if neighbouring pixels with a strongly deviating surface albedo are selected for comparison?

All in all, the manuscript contains the description of a number of interesting observations and calculations, but in its present form does not advance the field. A more in-depth analysis of the results, coupled with sufficient evidence that MONKI is an appropriate tool for the study, would greatly improve the impact of the research.

Please find a few other comments and suggestions below:

l. 69: ''extraterrestrial solar irradiance perpendicular to the beam'' - change to ''solar irradiance''

ll. 109-110: ''As shown in Figure 1, (...) overlap each other.'' - change to ''The area of interest in Europe was covered by TROPOMI during three successive, partially overlapping overpasses on November 11, 2020, as shown in Fig. 1.''

ll. 110-112: ''For each day (...) from the data set.'' - insert the sentence before ''The selected'' on line 106

ll. 116-117: ''the already available effective cloud fraction in the TROPOMI NO2 product'' - Which cloud algorithm does that come from - FRESCO?

l. 130 - ''SCSFs are a better extimate of the cloud shadows thn the PCSFs.'' - In which sense are they better: more accurate? Less or more strict? Where is the evidence? The next sentence refers the reader to the right panel of Fig. 1 ''as an example'', but it is not clear what one should see there.

l. 141: '' potential neighbour pixels of two TROPOMI pixels'' - change to ''potential neighbour pixels within a two-pixel radius''.

l. 143: '' Because we require (...) shadow free,'' - redundant, can be removed

l. 198: '' (2) increased shadow darkness due to the longer slant path length of the incoming direct light through the clouds.'' - Is this hypothesis based on calculations? Intuitively, I'd say that there is a larger amount of indirect (Rayleigh-scattered) radiation as well, maybe counter-acting this effect. Also, the light-path length effect is only valid for relatively thin clouds, as thick clouds will not let any radiation through anyhow.

Fig. 4, upper right panel: please shrink the x-axis to -/+ 2.5 units to make out more details.

Fig. 4, middle and lower right panels: is the secondary peak visible at Delta(R340/R380)= 0 real? Where does it come from?

Section 3.2.2: This section is hard to follow without a conceptual diagram, as suggested above

l. 273 and further: ''gas'' - change to ''atmosphere''

l. 278: ''gas pressure (...) is largest.'' - change to: ''atmosphere is most dense.''

l. 280: ''of the gas'' - remove

ll. 296-297: '' Apparently, all photons were scattered away from the direct beam'' - this is not surprising in view of the cloud droplets' Mie phase function, which features a strong forward-scattering peak

Fig. 7, lower left panel: please change the color scale to a more appropriate range, like -2.5 to 2.5; it would make the effects more apparent to the reader

Fig. 7, lower center panel: the shadow is very difficult to pick out in the figure; it might be helpful to change the color range

Fig. 8: what do the histograms show? The number of counts is appreciably higher than the number of scenes.

Fig. 9: these plots would make more sense as AAI contours plots with h_c and tau_c on the x- and y-axis, resp. Then these plots can disappear into the appendix. It's the AAI you're interested in, not the blueness per se.

Section 3.3.2.: This section contains a lot of interesting results that probably form the key to understanding the investigated effects --- but I fail to understand it completely. Particularly the paragraph starting on line 378 is difficult to follow without a schematic.

ll. 409-410: ''the cloud height obtained with FRESCO is in fact the cloud centroid height'' - this is a rather lazy argument, as the correction could simply be made to depend on the cloud centroid height.

l. 414: ''the ~4 km spatial resolution'' - is this not sufficient for such a correction?

l. 422: ''the positive AAI increases'': please note that we have observed and modeled the same effect for a high-altitude non-absorbing aerosol plume in the past as well [Penning de Vries et al., 2014].

Reference:

Penning de Vries, M. J. M., Dörner, S., Puķīte, J., Hörmann, C., Fromm, M. D., and Wagner, T.: Characterisation of a stratospheric sulfate plume from the Nabro volcano using a combination of passive satellite measurements in nadir and limb geometry, Atmospheric Chemistry and Physics, 14, 8149–8163, https://doi.org/10.5194/acp-14-8149-2014, 2014.