This paper describes and evaluates a new feature of the RemoTAP algorithm that is used to estimate atmospheric aerosols and surface reflectance properties from multi-angular remote sensing observations : A new kernel for the surface reflectance is added to allow estimates over snow covered surface.  The analysis is done both using synthetic data and actual observations from the POLDER/Parasol spaceborne instrument.  It confirms the necessity of adding such surface reflectance kernel to process data acquired over snow cover (or partially covered) surfaces.

The paper is very well written.  The objectives are clear; the analysis is well suited, and the conclusions follow the results.  It can be of interest for the remote sensing community.  The paper could then be published “as is”.  I nevertheless make below a few comments that the authors could considered to further clarify the paper and broaden its perspective :

Line 58 : Make it clear the e is not only the measurement error, but also contain the modeling error.

Line 63 : I understand that the RemoTAP algorithm uses the degree of polarization to quantify this piece of information.  In my opinion, it would have been better to use the Stokes parameter Q (normalized similarly to I) with the plane of scattering as a reference.  Indeed, Q then contains both the intensity of the polarized reflectance and some information about the direction (perpendicular versus parallel to the scattering plane).

Table 1 : I am a bit surprised to see so many aerosol parameters that are retrieved.  In particular, I doubt that there is sufficient information in the data to estimate the aerosol height for three different modes.  Is there any value in the retrieved aerosol height properties ?

Also, there is no height for mode 3, opposite to mode 1 and 2.  Any reason for that ?

I understand that the modeling assumes that the surface reflectance BRDF shape does not vary with wavelength.  This a strong assumption.  Indeed, the surface reflectance amplitude varies strongly with wavelength and high albedos tend to generate more isotropic reflectance than low albedos.  Would it be possible to add some freedom in the spectral variation of the BRDF modeling?

Line 165 : In the real world, the measurement of DoLP is more noisy in case of low reflectances than with high reflectances.  It is then unfortunate to use a fixed DoLP uncertainty that does not depend on the scene

Table 3 : What are the rationale for setting these min and max ?  Why some values are missing ?

Figure 3 and 4 : Explain color coding

An excellent structured work, proving the necessity of introducing the BRDF in the RemoTAP algorithm for accurate aerosol retrievals over snow surfaces. The newly developed extended RemoTAP algorithm is tested against both synthetic and real PARASOL retrievals showing promising performance.

Line 83: Snow kernel function is given below the equations (6-7).  I would say it is better to refer it and show its equation only on 87^th line as it is.

Line 68: It’s unclear to me if with the term z_aer you mean the top or the bottom of the aerosol layer. Other retrievals separate these two terms so here it’s a bit confusing.

Table 1: For the 3^rd Mode add the fixed z_aer as it is noted on line 74, so the reader doesn’t have to search for this information in the text.

3.5 Data pre-processing

AERONET utilized for collocation purposes is introduced in the previous paragraph, but I think it would be better if you add AND here something like “in terms of AOT, SSA, AE” because I had to look up to the AERONET data to remember this.

Table 3: The minimum and maximum values give the range of the randomly generated input parameters? Is there a reason you choose these limits?

Figure 2: The general better performance of extended RemoTAP is clear. If you changed the χ2 limit for the filtering do you think it would have better results for SSA (maybe a sensitivity test)? The difference of 0.008 (RMSE) between baseline and extended RemoTAP over snow_domi surfaces appears small but in terms of % relative difference it is not insignificant. I’m thinking if it would be more proper using the baseline RemoTAP for SSA.

Figure 3: Why x-axis is labeled as Truth and not AERONET and y-axis as Retrieval and not Extended RemoTAP? I had to read the caption to understand the figure.