General comments:

In general, I think this paper is very well written and represents an interesting contribution to the field. The authors describe a modified version of the optimal estimation retrieval called “Optimal Retrieval of Aerosol and Cloud” (ORAC), which they apply to Himawari-8/AHI measurements. The methodological improvements include a better treatment of measurement noise, considering multi-layer cloud structures, the usage of additional spectral channels leading to a better effective radius retrieval, and a better handling of ambiguities of ash clouds in the upper troposphere/lower stratosphere. The improved ORAC version was applied to the eruption of Raikoke in 2019, providing estimates of volcanic ash cloud height, optical depth and effective radius. The height retrieval was validated with GOES-17 side view height estimations and CALIOP observations. After some minor changes to improve the understandability (listed below) I recommend this manuscript for publication. Well done!

Specific comments:

• Line 63: There are newer contributions to the question of ash composition variability and its influence on the radiative transfer, which you might want to mention here, e.g., Prata et al. (2019, 10.1029/2018JD028679), Deguine et al. (2020, 10.1364/AO.59.000884), Piontek et al. (2021, 10.1016/j.jvolgeores.2021.107174)
• Line 144: Why do you use the cloud instead of the aerosol implementation of the radiative transfer forward model for volcanic ash?
• Lines 145-146: Why do you focus on the thermal channels in the measurement vector?
• Line 186: It would be interesting to know which bulk silica contents the three used volcanic ash samples had, as well as which silica content the Raikoke ash had (if corresponding measurements are available in the literature). You found that the Eyjafjallajökull ash refractive index lead to the best retrieval results. Do Eyjafjallajökull ash and Raikoke ash have similar silica contents or are they otherwise comparable in composition?
• Lines 214-215: Why do you not retrieve the cloud fraction f as well? The assumption of f being equal to one is certainly true well inside the volcanic ash cloud, but what about the edges of the ash cloud?
• Line 271: Is there a specific reason for setting the a priori uncertainties of τ and r_e to 10⁸, or is this just an arbitrary high number?
• Lines 276-277: It would be interesting to actually see the impact of considering five different setups with single and multi layer cloud structures. Maybe you can quantify the retrieval improvement of your setup compared to just considering a single volcanic ash layer without underlying water clouds, or maybe you can show an example plot indicating which retrieval configuration was used for which pixel?
• Line 285: Can you give a motivation for your choice of the ash particle density of 2300 kg m^-1?
• Lines 301-303: Can you give a motivation for the thresholds? Were they chosen upon manual inspection of the satellite data?
• Lines 314-320: How many gaps did you observe? Were they just single pixels? Can you quantify the amount of ash-contaminated pixels in the final data set that resulted from gap filling compared to the amount that directly resulted from the optimal estimation retrieval? Again it might be nice to see an example image to get a better impression on the importance/significance of this processing step.
• Line 526: The formulation “exponential decay rate of 20 h” is a bit misunderstandable, as rate rather refers to a change per time. Better give a “half-life time” or “e-folding time” or similar.
• Figure 10: Panel (f) is hard to understand, but there is probably no better way to visualize this.
• Line 538: Can you quantify the expression “wider range of effective radii sizes”?
• Line 545: If possible, can you give recommendations which visible channels to use?
• Line 547: Machine learning was already used for the volcanic ash detection flag, e.g., Picchiani et al. (2011, 10.5194/amt-4-2619-2011 ), Gray and Bennartz (2015, 10.5194/amt-8-5089-2015), Piontek et al. (2021, 10.3390/rs13163112)

Technical corrections:

• Lines 28-29: Change order of a and b in “Pavolonis et al., 2015b, a”.
• Lines 43-44: The formulation “absorption properties act in opposite directions across the thermal IR window” is a bit unclear, consider to reformulate it.
• Line 45: Mention at which wavelength the optical depth is considered, here and everywhere else in the manuscript. Different retrievals consider different optical depths of volcanic ash, e.g., Piscini et al. (2014, 10.5194/amt-7-4023-2014) consider the aerosol optical depth at 11 µm.
• Line 60: I suggest writing “radius ≤ 15 μm”.
• Lines 119-120: I suggest to note the band’s central wavelength instead of the band number for better understanding if the reader is unfamiliar with the instrument.
• Line 124: “This correspondS to one week of observations […]”
• Lines 127-128: Add the longitude position of GOES-17 as you did for Himawari-8.
• Line 135: Is the minus sign in “-0.5 km” correct?
• Line 140: “The Deutscher Wetterdienst (DWD) HAS developed the code […]”
• Line 231: Write out abbreviation “SO2“ when first mentioned.
• Table 1: In the a priori column, does the first number correspond to the pressure level of ash and the second to the water cloud? If yes, mention this in the caption.
• Figure 4: Add description of the blue line in the plots in the corresponding caption.
• Line 382: “e.g. 1.1 ± 7 Tg IN Muser et al., 2020“
• Line 530: Comma: „[…] complex, meaning […]“
• Lines 531-532: The sentence would be better understandable if you move “due to the numerous pauses and variations in height during this eruption sequence” to the end.
• Line 534: Wrong spelling: “stratoSPhere”