This paper is aimed at the retrieval of atmosphere, snow and underlying terrain properties using imaging spectroscopy. I suggest that the authors make a moderate revision of the manuscript. My comments are given below.

General comments 

1. GOSHAWK algorithm for the retrieval of snow and atmosphere properties is based on AART and libRadtran. I would suggest that the authors add a section aimed at the description of the accuracy of the algorithm for the parameters listed in Table 1. 

This is a fair consideration, especially since we are inverting for many parameters listed in Table 1. We will add a section in the discussion outlining accuracy of parameters. The atmospheric parameters (water column vapor and aerosol optical depth) are untested in our approach so far. We will discuss this as possible avenues for future work, as well as including ozone in the inversion (per response below).

1. Could you explain how to do you make the ozone correction. Do not you think that you can retrieve total ozone as well?

While it has been shown that ozone may be retrieved, which is an important feature in shorter wavelengths, our focus here is to solve for terrain. This is because retrieving terrain is more pronounced in this spectral range and is a required first step. However, we agree that more accurate ozone estimation is important, and therefore, we have included ozone estimation from Sentinel-5P NRTI O3: Near Real-Time Ozone dataset as input into libRadtran. Future work may expand upon this to also retrieve ozone.

1. The static and radiance methods give very similar results (inside the retrieval error, see Table 3). Any comment?

See response to comment “p.19, line 255 (and p.27, line 304)“ below. This is correct and will revise to clarify. The intention of showing the density histogram was to call out that this method is primarily focused on fixing outlier cases as discussed in Dozier et al. (2022). Therefore, the median and standard deviation give very similar results. Interestingly though, this should promote some amount of confidence in the radiance method, as they give similar average results, despite not using the DEM.

Minor comments

p.2, line 26, please, mention EnMAP

Will do.

p.3, line 50, degrees?

This will be revised by “Dozier et al. (2022) found errors in the cosine of the local solar illumination angles ranging from 0.048 to 0.117 (dimensionless) across several sites for Copernicus global DEMs caused by errors in slope and aspect.”

p.7, line 96, could you give Lat/Lon for all sites

Lat/long are included in Figure 2.

p.10, line 133, remove ‘TBD’

To be corrected.

p.11, line 141, ‘as PRISMA’, add a space

To be corrected.

p.13, line 159. According to the ART theory one should write alpha**f and not just alpha in Eq (2). Please, explain.

This has been corrected in our previous manuscript, and will be implemented here in this paper with the correct alpha**f. Corrected code can be found at: https://github.com/cryogars/goshawk/blob/main/scripts/snow.py

p.14, line 175. Please, check subscripts in Eq.(4).

We will remove EQs (3) and (4) and simply state that the local view angle and local phase angle are functions of terrain. The main idea we try to portray is that optimizing for terrain will impact three different geometry parameters: local view angle, local solar incidence angle, and local phase angle. 

p.16, do not you think that you need to add dust as LAPs and also O3 in Table 1?

Thank you for this comment. Instead of adding ozone to the inversion, we have elected on a static ozone derived from Sentinel-5P NRTI O3: Near Real-Time Ozone dataset. This serves as forcing into our libRadtran runs for the specific image. We have also updated our model to include dust in the inversion. The model can either solve for soot concentration or dust concentration. The dust angstrom parameter and MAE-400 are fixed based from China PM-2.5 tabulated in Caponi 2017 (in a similar fashion to TARTES).

p.17/18, lines 215, 218, 226, LWC-->liquid water

We will change all instances of LWC to say liquid water.

p.18, line 225. The accuracy of ART drops in SWIR (bands 1451-1779nm, 1951-2449nm as used by you (Kokhanovsky, Snow Optics, 2021)). Also the band 1951-2449nm is very sensitive to the upper snow layer microphysics (Kokhanovsky, Frontiers in Environmental Science, 2024). This may introduce the biases in your retrievals. You may use the  look-up table based on libRadtran to avoid this problem.

We will include the (Kokhanovsky, 2024) in the discussion and specifically point to it as a first attempt at resolving potentially sensitive upper layer microphysics. This would be especially important for areas with very heterogenous snow layering and may be quite beneficial for certain snow environments.

p.19, line 255 (and p.27, line 304)  radiance and static methods give very similar results with variation,  which is inside the retrieval error.

This is correct and will revise to clarify. The intention of showing the density histogram was to call out that this method is primarily focused on fixing outlier cases as discussed in Dozier et al. (2022). Therefore, the median and standard deviation give very similar results. Interestingly though, this should promote some amount of confidence in the radiance method, as they give similar average results, despite not using the DEM.

p.19, lines 257, 260, 261 - LWC units?

This was in decimal form before, but to be clearer in our next version we will include liquid water as a percentage with the “%” symbol.

p.22, could you give average values of the retrieved parameters.

This will be included in Table 3 in which SSA and broadband albedo are already listed.

An important problem in retrieval of remotely sensed variables in mountainous terrain is that the globally available digital elevation models introduce some errors into the analysis. This manuscript proposes a way to approach this issue by solving some of the radiation geometry variables instead of accepting their values calculated from the DEM. Potentially the paper makes an important contribution, but a few issues need to be addressed.

1. The effect of surface roughness on the snow BRDF is not addressed. Although no current snow reflectance model considers this, the roughness contributes to the uncertainty in the analyses and should at least be mentioned.

Please see comment (C2: 'Reply on RC2, Line 159’, Brent Wilder, 16 Jul 2024).

“I agree that expanding upon postulations made in Shape from Spectra (Carmon et al. 2023) regarding the surface roughness being potentially included in this formulation solving for topography from radiance. Similarly to their study, when I compared lidar derived µ_s to radiance derived µ_s, see attached figure, I found that radiance derived is consistently less.

I believe this may serve as further evidence that we may be getting closer at solving a solution that also is accounting ,"within-pixel topography, surface feature texture, and within-pixel shadows." (Carmon et al., 2023). We will discuss your comments in more detail and determine in which way we can assess the impact of surface roughness in this paper.

Also, interestingly when using this approach of allowing the terrain to vary, fractional shade remains very close to zero in optimization for fully snow-covered pixels and shaded snow-covered pixels. This is likely due to  µ_s having both a shape and magnitude shift which is probably found to be more helpful in numerical optimization than just fractional shade parameter. Although, fractional shade is retained in our model because it is still helpful for accounting for other features such as cloud shadows, tree shadows, and nearby terrain shading (not accounted for or missed in our ray-tracing routine).”

1. See the comment below about Line 161. A semi-infinite nonabsorbing layer of any composition will have a reflectance of 1.0. Albedo = 1-absorption-transmission. If transmission is zero (semi-infinite) and absorption is zero, then Albedo=1.

There is a better clarification of r0. I will better define the BRDF model in the next version.

1. See the comment below about Line 184. An equation that is apparently a crucial component of the analysis is missing.

We did not include our minimization routine which is described in detail in Wilder et al. (2024). We will correct this sentence and do not think it is crucial to include for the story of this paper.

Once these comments are addressed, the paper can be reconsidered for publication. Other comments are included below, along with some suggested references.

Line 13-16. This sentence is missing something, perhaps a “that” following the closing parenthesis in Line 15.

Will correct.

Line 36. Can eliminate the “off as liquid water.”

Will do.

Line 69. Figure 1 caption should indicate that aspect is measured clockwise from north, if it is. This is the most common convention, but it’s not universal and is in fact inconsistent with a right-hand coordinate system. Sellers’ Physical Climatology (1965) for example uses aspect 0° south, positive east and negative west. In either case there is a discontinuity at north.

We will indicate we are assuming aspect as north at 0&360 degrees and is disconitnious at this point.

Line 80. Influenced by viewing geometry and surface roughness, which the already cited Bair et al. (2022) show.

The revised version will include the influence of surface roughness, and introduce the idea proposed by Carmon et al. (2023) that solving for terrain in this way may include some influences from surface roughness.

Lines 107-114. You should explain why the AVIRIS-NG data are accurate enough to serve as validation of the PRISMA retrievals. The paragraph mentions the 4 m spatial resolution and 5 nm spectral resolution, but so what? You address this later in the paper by assuming that the 4 m pixels can be considered a binary (snow or no snow) assessment. But clarify this assumption and identify it as a source of uncertainty. For example, the AVIRIS-NG data in the Indian Himalaya seem to show subpixel snow at that resolution.

To address the concern of a mixed pixel at 4 m spatial resolution, we will clarify our assumption and identify it as a source of uncertainty.

Line 133. The Bohn et al. (2024) paper is available as a preprint and should be in the bibliography. The URL is https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4671920.

Thank you for providing the reference to this paper. We will include this in the revision.

Line 159. The formulation does not address surface roughness. Does the solution for µ_s perhaps account for mean of that value over a pixel? Or does fractional shade (Table 1) account?

Please see (C2: 'Reply on RC2, Line 159’, Brent Wilder, 16 Jul 2024), or Major Point#1 above.

Line 161. Isn’t the reflectance of a “semi-infinite nonabsorbing snow layer” 1.0? Or is there a better clarification of r0?

There is a better clarification of r0 and will be included in the revision.

Line 168. I don’t know if the Van Rossum citation is necessary. The atan2 function has been available for decades in most computer languages, before most Python coders were born.

That’s a fair point, and so we will change it so that atan2 function is not cited here.

Line 170. What does “circular” mean in this context? Aspect is discontinuous at north.

Thank you for the clarification and this will be revised.

Line 184. The “following equation” seems to be missing.

See above comment. Not a critical piece of this paper, and it was just showing our minimization problem we solve (see Wilder et al. (2024)).

Table 1. The caption does not explain the meaning of the three colors in the table. The range of LAP concentration (ng/g) ranges from 0 to 0.5e-5. This can’t be correct; the maximum dimensionless mass concentration would be 0.5e-14.

The colors will be removed for the final paper as per the editor’s comments. The range of soot concentration was incorrect in our table and was not scaled properly after optimization. Per the other reviewer we will remove soot concentration and instead model as dust. We will put units in terms of PPM (parts per million).

Line 208. Rob Green and I agree that “higher” spatial resolution is ambiguous and suggest “finer” instead.

Thank you for the insight and we will use this term “finer” instead here.

Line 227. The citation to a 43-year-old thesis (Segelstein, 1981) is unusual. Unless there’s an important, peer-reviewed, published update, I suggest citing Hale and Querry (1973).

We will cite Hale and Querry (1973) instead as recommended by the reviewer.

Line 398. The correct year is 2018.

Thank you for providing the correct references below. We will use these in the revised draft.

Line 410. The Dozier-Frew (1981) paper does not address the view factor. I think you mean Dozier and Frew (1990), but I would recommend instead Dozier (2022) which addresses the issue where the pixel slope itself is a significant part of the view factor calculation. That code is available on the MATLAB file exchange (https://www.mathworks.com/matlabcentral/fileexchange/94800-topographic-horizons).

See, “CC3: 'Reply on RC2, Line 410', Brent Wilder, 18 Jul 2024”. In short, we have adapted the Dozier (2022) method to include impacts from pixel itself. We apologize for mistakenly referencing the Dozier-Frew (1981) paper, we intended to reference the 1990 paper. However, now we will reference the 2022 paper.

Line 471. “Chime” should be in all upper case, “CHIME.”

Typo will be fixed.

Line 449. The references should include their DOIs, mostly available and making the citation much easier to find if the reader wants to.

All citations and DOI will be reviewed and included as available.

Line 457. The “author” of this publication is “National Academies of Science, Engineering, and Medicine.” The correct citation is shown below, including the DOI.

Thank you!

Lines 503 & 529. The citation to “McKenzie Skiles, S.” should instead be “Skiles, S.M.” as is correct in other citations in the bibliography.

Indeed it should. We will fix this, as well as ensure other citations are correct.

References mentioned in the Review

Dozier, J.: Revisiting topographic horizons in the era of big data and parallel computing, IEEE Geoscience and Remote Sensing Letters, 19, 8024605, doi: 10.1109/LGRS.2021.3125278, 2022.

Dozier, J. and Frew, J.: Rapid calculation of terrain parameters for radiation modeling from digital elevation data, IEEE Transactions on Geoscience and Remote Sensing, 28, 963-969, doi: 10.1109/36.58986, 1990.

Hale, G. M. and Querry, M. R.: Optical constants of water in the 200-nm to 200-µm wavelength region, Applied Optics, 12, 555-563, doi: 10.1364/AO.12.000555, 1973.

National Academies of Sciences, Engineering, and Medicine: Thriving on Our Changing Planet: A Decadal Strategy for Earth Observation from Space, National Academies Press, Washington, DC, 716 pp., doi: 10.17226/24938, 2018.