General Comments

This manuscript presents an aerosol layer height (ALH) retrieval algorithm based on PACE/HARP2 multi-angle polarimetric observations using an optimal estimation framework. The authors first investigate the information content of multi-angle polarization measurements for ALH retrieval using Degrees of Freedom for Signal (DFS) analysis and subsequently develop an ALH retrieval scheme based on HARP2 observations at 441 nm. The retrieval results are validated against EarthCARE/ATLID lidar observations and further compared with the TROPOMI ALH product.

Overall, the topic is scientifically important and timely. With the advent of next-generation multi-angle polarimetric satellite missions, such as PACE and 3MI, retrieving aerosol vertical structure from multi-angle polarization measurements has become an active and important research area in atmospheric remote sensing. The manuscript is generally well organized, and the results demonstrate that polarization measurements can effectively improve ALH retrieval capability. However, several aspects of the manuscript require further clarification and improvement, particularly regarding the algorithm description, uncertainty characterization, validation strategy, and discussion of the results. In particular, the retrieval framework strongly relies on externally provided AOD products and prescribed aerosol models, while the impacts of these assumptions on the retrieved ALH are not sufficiently discussed. Therefore, I recommend that the manuscript undergoes minor revision before it can be considered for publication.

Major Comments / Suggestions for Improvement

1. Please clarify whether any quality control procedures or filtering criteria were applied to the ATLID lidar observations used for validation. Since ATLID retrieval quality may vary under different atmospheric conditions, it is important to describe how the ATLID data were screened prior to the intercomparison analysis.
2. The collocation strategy among HARP2, TROPOMI, and ATLID observations is not sufficiently described. The manuscript should clearly specify: the maximum spatial collocation distance; the temporal collocation window; the spatial averaging strategy; the quality control criteria applied to each dataset. These details are essential for reproducibility and for properly interpreting the validation results.
3. The retrieval algorithm relies on externally supplied VIIRS AOD products. Since AOD is a key parameter governing atmospheric radiative transfer, uncertainties in AOD are expected to propagate into the retrieved ALH. It is suggested that the authors clarify: the sensitivity of ALH retrievals to AOD uncertainties; whether retrieval errors increase significantly under low-AOD conditions. A simple sensitivity analysis would greatly strengthen the robustness assessment of the proposed method.
4. The authors selected the 441 nm channel for ALH retrieval. Although shorter wavelengths generally exhibit stronger sensitivity to aerosol vertical distribution due to enhanced molecular scattering, it remains unclear why 441 nm was ultimately chosen instead of other available HARP2 wavelengths. It would be beneficial if the authors could provide quantitative evidence supporting this choice, for instance by conducting ALH sensitivity analyses at different wavelengths, comparing DFS across channels, and examining Jacobians with respect to ALH. These analyses would strengthen the justification for selecting the 441 nm channel.
5. Only six case studies are used for validation in this manuscript. Although these cases appear to be representative, the sample size is relatively limited. Please clarify: the criteria used to select these six cases; whether only favorable observational conditions were considered. In addition, the authors should discuss the extent to which these selected cases are representative of global aerosol conditions.
6. The forward simulations in this study assume a single aerosol layer. However, multilayer aerosol structures are frequently observed in real atmospheric conditions, especially during biomass burning and dust transport events, where elevated aerosol layers often coexist with boundary-layer aerosols. It is recommended that the authors clarify: what physical quantity is actually retrieved under multilayer aerosol conditions; whether the retrieved ALH is more representative of an extinction-weighted height, centroid height, or dominant aerosol layer height; the potential biases introduced by multilayer aerosol structures. Furthermore, this limitation should be explicitly discussed in the Conclusions or Discussion section.
7. Additional literature must elaborate on the issue of: (i) aerosol particle size spectra collected at 2.5-min time resolution with a Scanning Mobility Particle Sizer at various height levels. See, for example: https://doi.org/10.1016/j.atmosenv.2012.05.015; (ii) the fact that the aerosol vertical distribution plays a crucial role in shaping the ozone vertical profile and strongly influences the biologically effective radiation that reaches the Earth’s surface. See for example: Journal of Geophysical Research: Atmospheres 106.D14 (2001): 14843-14854. 

Minor Comments / Typographical / Formatting

1. Page 2, line 64: "CALIOP provide" should be "CALIOP provides".
2. Suggest clearly and consistently define ALH throughout the manuscript. Different studies may define ALH as extinction-weighted height, aerosol centroid height, or aerosol layer top height. In addition, it should be clearly stated whether all ALH values reported in this study are referenced to mean sea level or to the local surface.
3. Suggest carefully check all equations and ensure that every symbol and variable is explicitly defined when first introduced.

This manuscript investigates theoretically the information content of multi-angle polarimetric  measurements for ALH retrievals in the UV, using a Degrees of Freedom for Signal (DFS) analysis. It demonstrates that polarisation measurements adds information, especially at geometries that are relevant for satellite observations. Subsequently, an ALH retrieval algorithm is applied to multi-angle polarimetric PACE/HARP2 observations at 441 nm and compared to independent ALH retrievals from EarthCARE/ATLID, using active lidar measurements, and TROPOMI ALH using the O2-A band.  

The paper is relevant and interesting, and the analysis is generally of good quality. However, for publication a number of issues need to be addressed, mainly to better explain what has been done and provide concise information. 

Details are listed below:

l64-67

"Specifically, more photons are scattered back to space at higher altitudes, thereby reducing their probability of penetrating into the lower atmosphere and being absorbed by O₂. As a result, higher aerosol layers lead to stronger Top-of-Atmosphere (TOA) reflectance within the absorption bands."

suggest to reformulate something like:

Specifically, for scattering layers at higher altitudes, the probability for photons to penetrate into the lower atmosphere and be absorbed by O₂ reduces, leading to shallower absorption lines in within the absorption bands for higher altitude aerosol layers.

l77

It has shown -> It has been shown

l107-108

Moreover, the quantitative contributions of multi-dimensional observations to ALH retrieval have not yet been systematically assessed, highlighting the need for further investigation.

I do not agree here. There is a large body in literature, some of which are already ilisted.  

The GRASP consortium has shown quite systematically that they can use multi-dimensional observation to improve the ALH and other aerosol parameters. 

Another reference is 

Hasekamp, O. P., P. Litvinov, and A. Butz (2011), Aerosol properties over the ocean from PARASOL multiangle photopolarimetric measurements, J. Geophys. Res., 116, D14204, doi:10.1029/2010JD015469.

l170

"which further improves the reliability of the data."

This is a rather empty statement. The ALH product is for cloud-screened pixels only. Period.

Section 3. 

The theoretical treatment needs improvement. The relationship between eq (1) and (2) is not given. S_epsilon (3) is diagonal, which means that the errors are assumed to be independent, this needs to be mentioned. 

The Stokes parameters were mentioned in section 2, but only here treated formally. Better to remove the introduction in section 2, and treat it here properly. Same for DoLP (change all DOLP to DoLP). 

l244 "radiance III" is unclear. 

I also suggest to move eq (13) and its discussion on l632 to section 3. The extinction-weighted height is used in the text before it is defined. 

l250 Mie scattering is proper for small and/or spherical particles only. 

Table 1: Where are the numbers coming from? The table lists 3 references, the text says Lee et al (2015). Please, be concise and consistent.

l271 MCD43A1 product is a MODIS product, which is not described. Please add.

l287 

"Under typical aerosol loading conditions (AOD = 0.3–1)"

It is unclear what aerosol type is used in Fig 1 and what the AOD is, since it wavelength-dependent. This should be specified properly and consistently throughout the text. Also see next item.

Fig 1. 

The AOD is a wavelength-dependent parameter. In Fig.1 the AOD ranges from 0-5 for all wavelengths, representing markedly different ranges, since the AOD at 441 is 2-3 times higher that at 873 for smoke. It is not clear what is used and the figures should be scaled to the same ranges to be compared as they are in the text now. 

l336

Same as before: aerosol optical depth (AOD = 0.3) is ambiguous. Please, describe exactly how Fig. 2-6 were produced.

Fig. 2-6. The captions should describe what's in the figures: I guess relative azimuth from 0-180 degrees? The axis from 0-10 is unexplained.

l370

"DFS exhibits a pronounced enhancement with viewing geometry. "

I do not understand this. Viewing geometry in this sense is ambiguous. Please rephrase. 

l372-274:

Under large viewing angles, the intensity-only observations are not so bad. I think the conclusion is that for small viewing angles the additional information form polarisation measurements is largest. 

l428-430: Repetition, move theoretical treatments to section 3. 

l475. 

The reference Fromm et al from 2010 is a strange reference to describe the transport of a 2025 smoke plume. Please, rephrase. I guess the idea is that this happens more often or happened before.

The vertical distribution of aerosols plays significant roles in solar radiation transfer and climate change. The authors use a vector radiative transfer model and information content analysis and evaluate the contributions from key factors, including multiangle and polarimetric information to ALH retrieval. The authors also do some case and sensitivity studies and found that multiangle polarimetric measurements substantially increase the degrees of freedom for signal and improve ALH accuracy. An optimal estimation method is developed. Retrieved ALH values are validated against observations and showed reasonable estimations, such as HARP2 retrievals achieve a root mean square error of 1.03 km. Generally, this manuscript is well organized, written and explained. Some minor comments and suggestions are given.

L143, please explain I, Q, and U.

L145, please rewrite “I represents total radiance intensity ……”.

L149-150, “while Q and U denote the linear polarization components that characterize the polarization state of the scattering field” could be removed to L143.

L237, “Conversely” could be improved by using another word.

L286-287, “the information content of ALH shows a clear decreasing trend with increasing wavelength, i.e., 441 nm > 549 nm > 669 nm > 873 nm”, more explanations about the information content of ALH and the mechanism of this sentence are suggested.

L465, “This study selects three representative smoke transport events over North America on May 28, May 30, and June 1, 2025” can be removed and combined to L444-445. Please explain why the selected 3 and 6 events is representative.

6 Conclusion, is a little longer and should be shortened. Please report the key conclusions.

 The authors revised the manuscript. Now, it is much improved.