The authors describe a new aerosol retrieval from SCIAMACHY as well as new retrievals of various aerosol PSD parameters and compare them with other ground- and space-based measurements and retrieved parameters. Knowledge of both the amount and size distribution of aerosols is of key importance not only for climate modeling but also the retrievals of both aerosols and trace gases from many different instruments. PSD parameters are particularly important for many satellite retrievals as most instruments rely upon assumptions, rather than measurements, of these parameters for their retrieval algorithms. This paper is well organized and presented and I would recommend it for publication. The following comments are minor and only offer up suggestions for improvement or clarifications.

Pg 07, Ln 197: “For the public, we also calculate the aerosol extinction coefficient at 525 and 1020 nm to enable a comparison with other satellite aerosol products”

            How is this done exactly? Is this done using the measurements at 750 nm and 1020 nm to compute the Angstrom exponent to then relate 525 nm to one of those channels?

Pg 07, Ln 209: “0% relative humidity”

            Does this assumption impact the data quality at the bottom of the profiles?

Pg 07, Ln 210: “They are specified as a mixture of 75% sulphuric acid and 25% water.”

            How does this assumption impact the results seeing as how recent measured estimates of this parameter from ACE-FTS show variability in this concentration?

Pg 08, Ln 216: If N remains fixed, how is the value determined? Is a single value retrieved somewhere else for each measurement or is a single value used for all retrievals?

Pg 08, Ln 240: “The noise covariance matrix is assumed to be diagonal, i. e., the noise is spectrally and spatially uncorrelated.”

            If there is known stray light, should this be the case? Or is the stray light sufficiently small as to ignore it completely? I am guessing there is some transition region near the upper end of the retrieval range.

Pg 16, Ln 430: “Therefore, the SAGE II and SAGE III extinction coefficients are converted to 750 nm via the Ångstrom exponent”

            If you use the ~750 nm SAGE III channel for the TWE method of computing Reff, why not also use the extinction data from that channel instead of converting from the other two?

Pg 18, Ln 471: “Discrepancies are slightly higher in the tropics at altitudes below 22 km due to cloud effects”

            Why not apply some rudimentary cloud filtering (or omit all data below just above [e.g., 1 km] the tropopause)?

Pg 20, Ln 500: “However, SCIAMACHY v2.0 and the SAGE II DWE approach rely on different assumptions …”

            What about the SAGE II NASA approach? It appeared that the SCIAMACHY v2.0 Reff matched those better than the DWE approach.

Pg 20, Ln 509: “… the differences in rg and σg correlate with the differences between SCIAMACHY-assumed and SAGE III-retrieved number densities …”

            They correlate, but do their magnitudes align with the sensitivity tests shown in Fig. 2?

Pg 23, Ln 532: “Note that effective radii from SAGE III increase slightly but significantly over time. It is due an increasing median radius with a simultaneously decreasing geometric standard deviation. Such an evolution of the aerosol particle size is not observed in SCIAMACHY and both SAGE II (v7.0 NASA, DWE) data sets. This might be because in those three retrieval algorithms one of the PSD parameters is assumed to be constant.”

            Is there another referenceable source that definitively shows mean radius/geometric SD systematically increasing/decreasing over this time period to show that the SAGE III data is correct and the SAGE II / SCIAMACHY data is incorrect?

Pg 26, Ln 615: “Thomason et al. (2010) have reported on an impact of the etalon effect on the water vapor retrieval. An additional influence of this effect on the extinction coefficient retrieval cannot be excluded.”

            It is unlikely that the etalon impacts either the 520 or the 1020 nm channels in a meaningful way. An etalon is a spectral interference pattern that can change with the thickness (correlated to temperature) of the attenuator. This interference pattern will be most influential when attempting to resolve fine spectral absorption features such as with the water vapor or oxygen A-band retrievals, particularly because the temperature of the attenuator will change during an occultation. The measurement of aerosol through the 520 and 1020 nm channels does not depend on resolving any spectral features and is effectively broadband thus likely averaging out any interference patterns.

Pg 26, Ln 628: “The retrieved median radii and geometric standard deviations should therefore be considered with caution in areas with high aerosol loading.”

            This is unfortunate as these scenarios tend to be of greater interest to the scientific community. Is there any way to iterate the retrieval and update the assumptions based on other retrieved parameters such as extinction and/or effective radius?

The paper is dedicated to improved retrievals of aerosol characteristics from  SCIAMACHY limb observations. Compared to the previous version of (Malinina et al., 2018), the algorithm has been improved, and implemented to measurements not only in the tropics, but also on the entire globe.

The measurements that allow retrieval of information about aerosol particle size distributions are limited, while this information is important both for evaluation of climate response and also for retrievals from satellite measurements. This paper provides a valuable contribution to this topic.

The paper is well-structured and well-written. I recommend it for publications. Please find my minor comments below.

COMMENTS.

About assumption of fixed number density. While further in the text it becomes clear what you mean by “fixed number density”, the first mentioning of this creates many questions (for example, P.3). It is worth to add something like “details are provided below ” with the first mentioning the fixed number density assumption.

A related question: have you tried a maximum a posteriori inversion with three parameters retrieved (Bayesian approach with a priori information)? After obtaining the estimates of the parameters with your two-parameter retrievals, this might be a working approach.

Line 78. “ …on the entire globe, here”.  “here” is not needed

Line 190 “Either”  -> “either”

Line 245: It is better to use  the word “data” instead of “products”

Figure 3. It would be useful to add  letters near the triangle indicating volcanic eruptions, and to provide a table listing them.

Figure 8. Please indicate dates of volcanic eruptions in the figure, for example, by adding vertical lines.

Line 693: Please provide the link to the dataset.