General comments

This manuscript by Pang et. al. presents a study into the sensitivity of aerosol’s vertical position when assimilating ground or columnar observations. Starting from the basic formulas of the Ensemble Kalman Filter, the expected results with the two observation kinds are formulated theoretically and they are subsequently studied using a standard NWP model and real observations.

Assimilation of this kind of observations still has many unanswered questions, and these kinds of sensitivity studies are highly relevant. I particularly enjoyed reading through the analytical formulation of the problems and then seeing actual real-world data to back up the conclusions. The manuscript is well written, with clear objectives and methodology. The drawn conclusion is fair considering the results. I wholeheartedly recommend publication after some relatively minor points are addressed. I hope the authors find the following comments useful for improving the quality of the manuscript.

Specific comments

1. As I understand it, when the authors are assimilating ground-based observations, they are not using a vertical localization scheme. By not doing this, you implicitly assume that a ground-based point measurement of concentration is representative of the whole atmospheric column, which might not hold in many cases (e.g., long range dust transport occurring at higher altitudes, local emissions near the ground measurements). The point of this manuscript is not to study localization schemes, but applying localization would eliminate the issue demonstrated in Fig. 2, panels b.1 and b.2. The text near line 205 describes what would happen with strong vertical correlations in your prior, but with localization they would diminish as you increased your distance from the point observation and reduce the problematic inflation of concentrations. I strongly recommend the authors add a case demonstrating what would happen if you used vertical localization or add a note explaining its absence.
2. It would increase clarity to add a brief description about the aerosol model used in the simulations. For example, which species are used, what kind of optical properties are assumed, if there are size bins and their ranges, etc. It would also be useful to describe the observational operators for AOD and PM10 in more detail (i.e., which size bins are considered for PM10).
3. In the case studies, it is mentioned that DOD is assimilated from Himawari. Does this mean that only dust is considered in the model AOD operator? Maybe it can be referred to as a “DOD operator” for clarity.
4. When comparing with CALIPSO, is the CALIOP aerosol classification checked to ensure that dust dominated the scenes? There are methods for extracting the dust-only component from lidar measurements (for example, Mamouri et. al. 2017 and Amiridis et. al. 2015), which might be useful, given that the model also only includes desert dust in the extinction profiles.
5. When comparing CALIPSO to the model, some statistics would be interesting (e.g. RMSE). Currently the comparison is “by eye”.
6. In the introduction, it would be helpful to mention uncertainties in optical properties when discussing the difficulties in assimilating aerosol-related observations (around line 50). Some of the publications mentioned in section 2.3.1 about LiDAR assimilation would fit in the introduction as well, around line 70.
7. Line 69 mentions that no instrument can provide continuous vertical information about aerosols, but both ground-based and space-borne LiDARs do that. They do not provide 3D fields, but the information is continuous.
8. Please consider providing more information about the modelling setup to aid in the reproduction of your experiments. More details could be added to section 2.1.1 about model settings and what kind of initial and boundary conditions are used. Consider uploading configuration files and IC/BC files to a public repository.

Technical Comments

1. At lines 148-149, the superscripts `a` and `f` are used, probably referring to analysis and forecast. This should be mentioned for clarity.
2. Line 176 includes the phrase “[…] to nudge the 3D states […]”. Since nudging refers to a specific family of methods, it might be clearer to use another word here.
3. In Figure 5, it would be interesting to see the ground-based LiDAR profiles as a third line in the bottom panel, for direct comparison with the model. I understand that the model plots show concentration, but they could also be extinction, since that is a required step for computing the AOD/DOD.
4. Lines 374-375, I believe the observations have ‘low/high dimensionality’
5. At various points in the manuscript, the word “fraud” is used in regard to low quality observations or information. I think this specific word implies malicious intent, which I hope is not true in any case. For example, line 70 would be clearer as “When there is incorrect/inaccurate information […]” instead of “When there is fraud information […]”. Consider replacing all instances of “fraud” with something milder.

Best of luck to the authors

The manuscript "The sensitivity of aerosol data assimilation to vertical profiles..." by Pang et al. investigates the sensitivity of assimilated vertical aerosol profile accuracy to the prior model state generated by atmospheric models. The authors perform data assimilation using the PyFitter toolbox, a stochastic Ensemble Kalman Filter (EnKF) implementation developed by the authors, using ground-based PM_{10} and Himawari-8 satellite-derived dust optical depth (DOD) data. Through several case studies of dust storms, it shows that while assimilation of accurate profiles improves the consistency of 3D aerosol states, flawed priors can exacerbate vertical structural errors. Validation using CALIPSO and LiDAR confirms these findings, emphasizing the need for precise vertical profiling. 

While the manuscript is well organized, with a clearly written methodology supplemented by appropriately captioned plots, I think there are several major areas where both the science and writing need to be revised before publication in GMD. Once these are addressed, I would be happy to review the manuscript and re-evaluate its suitability.

Major comments:

-- Please justify how the model state assimilated with DOD data in the optical wavelength (550 nm) can be compared with extinction data collected by LiDAR at a slightly lower wavelength (532 nm)

-- How is DOD calculated from the Angstrom coefficient and AOD? The authors should move the contents of the supplementary section to the main text since the former is only 1 page and contains useful information

-- Why is the validation only performed for a single time step in Figs. 3-4, 6-7? The authors should consider providing some measure of total error (average difference between observed and assimilated dust concentration profile) over a pre-defined time window

-- L58: Rephrase "fraud assumption" with false or incorrect assumption

-- The Conclusions section would be strengthened by some discussion of the physical or statistical reasons why assimilation positively impacts certain vertical profiles while negatively impacting others