The paper is very well written and organized. The results are presented clearly with a good choice of figures. The laboratory measurements are used to create an in-orbit correction for the polarization throughput sensitivity which can be larger than 2% for some viewing geometries. VLIDORT is used to create the Degree of Linearized Polarization for a correction LUT. The results with real measurement show a significant improvement over the uncorrected cases. The authors also identify areas for future improvements and deficiencies in the ground-based characterization and its implementation.

Some specific minor editorial corrections and questions:

Line 45-46 Replace

  “Before reaching ... passes through …”

with  

  “Upon reaching … interacts with …”

Line 91 This needs to be rewritten. Maybe

  the Stokes parameters (I, Q, and U) for various atmospheric conditions were calculated and the DoLPs are arranged in a LUT.

 

Line 126 The acronym SMA need to be expanded.

   Is it Scan Mechanism Assembly? Scan Mirror Angle? 

   Also, sometimes it is used as “SMA Angle: and other times as “SMA Position” or “angle at which the SMA is located”.

Line 128 Linear Polarization Sensitivity or Polarization Factor?

   The term LPS is introduced in Line 89 but is never used. The term PF is used often.

Line 296. Says that the polarization was only characterized for one North/South position at the center. Figure 1. Is the test setup used to get measurements over the in-orbit range of scan mirror viewing angles? Table 2 has 1 for SMA position. What about the East / West characterization? Was the assembly moved to vary the mirror scan angles?

Line 238 “The polarization error caused by changes in total ozone is less than those caused by other changes.”

Figure 4. Could the authors comment on why Figure 4 does not have any (or maybe very small) dependence on TOZ? I would expect that the ozone would selectively shield the shorter channels with higher ozone absorption from the surface and clouds and thus produce wavelength-dependent changes similar in magnitude to the albedo and surface pressure changes as ozone amounts increase. That is, alter the relative amounts of single scattered, multiple scattered and reflected radiances.

Figure 4 and Figure 8. Figure 4 shows errors versus SZA and SVA of 1% or more. Figure 8 does not show corrections larger than 0.1%. (Are the units in Figure 4, 8, 11 and 12 all in % error in radiances?) Was the range of cases used to construct Figure 8 much less varied than the real cases in Figures 11 and 12? Particularly in SZAs?

Overall, I think this is a good paper. Many of the sentences are too long and complicated, and as a result lose their meaning.  The authors should strive for clarity in their writing rather than attempting grammatical manipulations that are perhaps beyond their reach.  I find that the error analysis in this paper is incomplete.  The authors acknowledge that there are more errors than what has been considered here, but there should be an attempt to quantify the additional uncertainties.

Section 1, paragraph 3

The authors introduce two methods to deal with polarized light.  One requires a scrambler and the other requires a PMD.  The discussion of the two seems asymmetric because the authors state GEMS does not have a PMD but there is no mention of the scrambler.  The authors could mention that a scrambler is difficult to implement in large aperture instruments such as GEMS.

There is at least a third method for dealing with atmospheric polarization, and perhaps more.  Sensor optics can be designed in such a way that they are relatively insensitive to the polarization state of the incoming radiation.  The design can be aided by including a polarization compensator in the optical train.  The purpose of the compensator is to offset the polarization sensitivty caused by the remaining optical train in the sensor.  It is likely that such an approach was not practical or effective for the GEMS viewing conditions, but the authors should acknowledge that there are more than two approaches to reducing polarization sensitivity.

Section 1, paragraph 4

It may be clearer to say, "In terms of a similar approach the MODIS and VIIRS instruments also lack both scramblers and PMDs.  Polarization characteristics are measured during pre-launch testing ..."

Section 1, paragraph 5

The first sentence is somewhat awkward.  The authors say, "we describe a newly developed polarization correction algorithm" after summarizing the GEMS polarization correction approach in the previous paragraph.  The wording of this first sentence implies that there is yet another, new, approach that is different than the one summarized in paragraph 3.  It would be better to simply say, "we describe the polarization correction algorithm for GEMS."

In the second sentence the language is again unclear.  Are the authors trying to say that the GEMS algorithm is unique for considering clear-sky conditions, or that older approaches only considered clear-sky conditions and the GEMS algorithm now considers partly clouded conditions?  Please use a few extra words so there is no misinterpretation of what you are trying to say.

Section 2.2, line 126

Please define 'SMA'.  Is it Scan Mirror Assembly or Scan Mirror Angle? The definition should be stated explicitly the first time the abbreviation is used.

Section 2.2, line 130

The sentence beginning "However, since the signal ..." is difficult to understand.  I recommend defining central position in a separate sentence to make this sentence easier to understand.

Section 2.2

The authors treat the results of Figure 2 as the true polarization characteristic for GEMS.  Yet these results may include the characteristics of the polarizer response as a function of wavelength.  I do not expect the authors to know the details of the analysis performed by Ball, but they should acknowledge that the imperfect polarization of the source may not be fully accounted for in these results.

It is not clear if the authors are saying the mirror coating and stray light represent features in the PF spectrum that have been captured or errors in that spectrum.  The authors should clarify this.  This is also a useful point in the paper to discuss why these features are so important.  It is in fact the spectral dependence of the PF rather than the absolute level that affects the final science products.  If the PF was a flat line at 1% or 2% the authors may not be considering a polarization correction at all.  Are the retrieval algorithms not immune to wavelength-indpendent polarization sensitivity?

Section 3.1, line 156

It would help the reader if they could see a figure showing the meridian plane and the instrument plane together.  It is hard to visualize these angles and their coordinate frames based simply on the verbal description.

Section 3.1, final paragraph

This paragraph raises some questions about the GEMS polarization correction.  If the LUTs require as independent parameters surface pressure, albedo, and trace gas concentrations, how are these derived at Level 1B since this product generally does not have such information?  Some of these parameters are discussed in the next section, but it is worth noting in this paragraph that the polarization correction uses preliminary estimates for these parameters rather than final retrieved quantities.

A single sentence is devoted to derivation of the surface pressure.  This deserves as much or more discussion than the derivation of ozone or terrain height, and I recommend expanding the LER discussion in Section 3.3.2 to include characterization of the reflecting surface.

Section 3.3.1, paragraph 2

It is useful to cite the DOI for the OMI data.  In this way you need not discuss the details of exactly which product you used (for instance, that it is from Collection 3).  The DOI can be obtained from the GES DISC.

Section 3.3.3, line 310

Simply say that the correction algorithm is not very sensitive to the reflecting pressure under cloud-free conditions and that use of a terrain height pressure results in a negligible error.

Section 4.1

The second largest source of error in the polarization correction (after the GEMS characterization) is probably the VLIDORT simulation of TOA radiances.  The authors provide no estimation of this error.  Instead they assume the dominant error comes from simplifications in the model assumptions (used to generate the LUT).  The LUT errors may be significant, but that does not mean the full VLIDORT simulation errors are negligible.  Clearly, the results shown in the right hand side of Figure 7 represent an underestimation of these errors.  I view this as a major flaw in this paper.  Can the authors provide an independent estimation of the missing error?  How much larger could the true errors be?  There is a brief mention of aerosol errors toward the end of Section 4.1, and there is a limited discussion of model deficiencies in Section 5, paragraph 2.  This is the kind of discussion I am talking about, and it needs to be expanded.

Figure 8 caption

It will be clearer to label these as polarization error rather than radiance difference.  Using the term radiance difference leaves the reader asking: difference between what and what?

Figure 9 caption

The left vs. right description in the figure caption is reversed.

Section 4.1, last sentence

I am not familiar with the term "dump point."  Please choose different terminology or explain what is meant by this phrase.

Section 4.2, first paragraph

Please consider rewriting or removing this paragraph.  It lacks a point and seems out of place.  The first problem is that it is not obvious to the average reader why SNR and shift/squeeze (not shist/squeeze) should be a consideration for the polarization effect.  You do eventually explain the problem of wavelength registration, but in a complicated way.  Please use simple statements such as, "The polarization and polarization corrections affect the spectral structure of radiances.  Since the wavelength registration of each Earth scene relies on radiance spectral structure these results can be affected."  Also, please explain the effect on SNR.  The second issue with this paragraph is that the authors raise the problems but do not resolve them.  How large are the errors in wavelength registration?  How much is SNR affected?  Is there anything that can be done to reduce the uncertainty?  If the authors simply wish to say that these are problems to be considered then this discussion best belongs in Section 5 as 'future work'.

Figure 12 caption

To be clear, these are polarization errors prior to correction.

Section 4.2, second paragraph

This is an important discussion about how the polarization error can alias into diurnal variation in the data products.  It starts off well, but ends up in the wrong place.  The authors' conclusion is that it is important to apply the polarization correction properly.  That is stating the obvious.  It will be a more useful discussion if the authors can estimate the residual diurnal errors (after correction).  For example, Figure 12 could instead be a plot of the radiometric uncertainty as a function of time-of-day.  This requires the authors to have some idea of the uncertainties in the combined ground characterization + VLIDORT correction.  As I have stated previously, the lack of such uncertainty is a major omission in this paper.

Section 5, paragraph 2

The discussion here of areas of uncertainty in the polarization correction is very important.  These uncertainties deserve to be quantified rather than simply listed.  The reader cannot assess the validity of the polarization correction without some estimation of these uncertainties.  I understand it is a lot of work to come up with reasonable uncertainties, but that does not mean the authors can ignore the issue.  The lack of PF information as a function of SMA angle is a good example.  The authors offer a plausible approach to improving the characterization, and it is understandable they do not include such improvements in this paper.  But they should include estimates of the uncertainties as a result of the SMA spatial dependence.  Even though the authors do not have access to the original test data, there are ways of estimating the degree of S and P polarization from a reflecting aluminum surface given the incidence and view angles.  It's true that we do not know exactly how the scan mirror is coated, but the goal here is to bound the error rather than to improve the characterization.

Section 5, paragraph 3

I cannot understand what the authors are saying here.  Please rewrite this paragraph and simplify the sentences.  

• This work describes a polarization correction scheme for GEMS to reduce the impact of the instrument’s polarization sensitivity on the observed radiance. The paper is an important step in this development by illustrating its impacts through synthetic data. Further validation using observed data could build on this work.
  
  
  
  

General comments:

• Including a discussion on the potential for validation the polarization correction with GEMS observational data would strengthen the discussion. For instance, would it be possible to compare the L1 data with and without corrections to other reference satellites? (Perhaps solar/view geometries could be chosen where the polarization effect is largest). Or could derived L2 products based on the corrected and uncorrected L1 could be compared with ground measurements.
• Given the limitations in the pre-launch characterization, such as only measuring the center position, and other complexities, were L2-based correction methods considered?
• Please clarify what was demonstrated with the actual GEMS data (see related specific comments below)
• Please include more details on the reference frame transformation methodology (see below for detailed comments)

Specific comments:

• 35: “high peak of curvature of polarization error”: Do you mean in the spectral region with a sharp spectral feature in the polarization sensitivity? Please clarify.
• 38: “diurnal variation for the spatial distribution of polarization error confirmed.”  My understanding is that the diurnal variation is based on the calculated Stokes combined with the pre-launch measurement parameters, not the GEMS observations.
• 58: Could include the spectral sampling here (although I realize it is included in Table 1).
• 62: I think along with accuracy, stability should be emphasized as well, since, with a polarization-sensitive instrument, the diurnal signal can change as the solar/view angles change throughout the day.
• 93: This statement makes it sound like VLIDORT is the only RTM that can perform RTM in this spectral range. Perhaps more justification can be offered by citing some associated validation work for the model.
• 131: Aside from a lower signal from off-nadir positions, could the polarization sensitivity vary as well depending on scan mirror angle?
• 133: “ideal state” is a bit confusing. I recommend removing this sentence.
• 160: Please provide more description on reference frame transformation methodology. For instance, it is not clear to me what the difference is between the instrument and boresight reference frame. Some suggestions:
• A figure showing the geometry including definitions of the various reference frames.
• A working example (maybe as an appendix if the authors feel this breaks up the flow too much)
• 200: “with assumed cloud albedo to be 0.8” to “with an assumed cloud albedo of 0.8”
• Figure 3: spectral range is slightly different than the GEMS spectral range. Perhaps make them consistent or explain the discrepancy.
• 244: These statements are a bit confusing to me. In the previous section, the sensitivity of TOA radiance to ozone was shown to be smaller than the other parameters considered. Here, the authors state that polarization sensitivity plays a crucial role for ozone. Can you clarify?
• 276: Perhaps change “ideal” to “complete” or “comprehensive”
• 322: Figure S1 and S2 seem to be missing.
• Fig. 6: The degree of linear polarization used seems low. Was the solar geometry limited to around noon? Please add more details about the times of day/solar angle ranges, since this would greatly impact these values.
• 323: What RTM input parameters were used to simulate the clouds?
• 330: “exhibit sharp curvature in PF.” Can you explain the significance of your choice of wavelengths. Do you expect larger errors due to the instrument’s spectral sampling over these features?
• 354: What are “dump points”?
• 358: It would be interesting to understand the impact of the pre-launch measurement uncertainty on the polarization correction. Perhaps the authors could mention that this was not considered or that it will be considered in the future if that is the case.
• Fig. 11, 365: Perhaps it would be helpful to clarify that you are plotting the ratio in Eq 1 as a percent difference (if that is the case). 

Technical corrections

• 358: typo: change “shist” to “shift” 
• 91: Recommend changing “comprised” to “included” 

This study describes a polarization correction algorithm for GEMS, the first environmental geostationary satellite. The algorithm uses the instrument’s polarization sensitivity and a radiative transfer model. Improving the quality of L2 products relies on a thorough understanding of polarization sensitivity and the ability to correct polarization effects on L1B radiance data. Therefore, the contents are important to obtain a better quality of GEMS products and are appropriate for the scope of AMT. However, I would recommend considering the following comments before publication in AMT.

General comments:

1. This paper discusses both atmospheric and instrumental polarizations, but some sentences are confusing. Please clarify throughout the paper.
2. This study used the pre-flight instrumental polarization sensitivity on the central point of the GEMS instrument. However, it is important to note that the polarization sensitivity can vary with different angles and over time due to different solar and viewing zenith angles. Although estimating the changes in the polarization sensitivity is challenging, it is important to assess whether the algorithm effectively corrects polarization effects on the radiance in real. If it is not easy to do so, it is recommended to provide quantitative values by showing the improvement of GEMS L1B and L2 products after polarization corrections or doing a sensitivity test. Additionally, the limitations of the algorithm should be discussed more when the algorithm is applied to real GEMS data.
3. The polarization correction algorithm utilizes spectra calculated by one of the radiative transfer models (RTMs), VLIDORT. Since a model is not perfect, it is important for the authors to ensure that VLIDORT simulates Stokes parameters well by providing references. To address this, the author should describe VLIDORT in an independent chapter of Section 3 or somewhere.
4. It is necessary to ensure that the sentences and terms are clear and unambiguous to avoid any confusion for the readers.

Specific comments:

Line 29: Is it the polarization axis, not angle?

47: Please provide specific a wavelength region to describe the polarization effects.

48: Typo Mischenko -> Mishchenko. Please check all references.

52: There are TROPOMI and OMPS nadir mappers with the same objectives.

62-78: Please clarify whether instrumental or atmospheric polarization is referred to here and throughout the paper. For example, the PMD is a device to measure instrumental polarization? However, the authors explained that GEMS does not have a PMD to measure atmospheric polarization states.

126: What does SMA stand for? Regarding one of the general comments, polarization effects with different SMA angles should be discussed.

128: Please describe the physical meaning of PA like PF.

150-154: Chi is the polarization axis, but chi_LMP is the polarization angle? Also, please explain how the polarization angle (chi_LMP) is calculated by Eq (2).

175-185: Define all notations and their meanings. The quaternion matrix and multiplication might be unfamiliar to many readers. It would be helpful to provide an overall explanation of the quaternion matrix and multiplication in the Appendix.

189: Figure 3 just shows the overall flow of processes from original GEMS L1B to corrected GEMS L1B, but it does not present the algorithm flow chart. It would be more helpful to show how parameters in Eq (1) are derived using input data in Figure 3. In addition, please provide the meanings of box shapes in Figure 3.

192: In the re-process, the authors use GEMS L2 products for polarization correction, but satellite products have large uncertainty. It is worth considering if the method of using GEMS L2 products can achieve the same performance compared to polarization correction using climatological data.

202: How well does a radiative transfer model including VLIDORT simulate atmospheric polarization effects? Regarding the general comment, it would be helpful to provide a basic description of the model with references.

218: The light could be polarized by liquid water and water vapor, which are abundant in climate and weather conditions. Why are they not considered?

229: Can the GEMS slit function be assumed as a Gaussian function? Is there any error resulting from a different shape of the slit function?

233: Please define what I_obs and I_true represent.

283: GOME-2 already has a coarse spatial pixel size of 80 km x 40 km, and it is difficult to achieve a finer resolution than its own spatial resolution. Therefore, despite interpolation to a finer spatial resolution, it does not make the surface LER more accurate.

322 The normalized radiance is not shown anywhere in this paper, and Figure S2 seems to only show Q and U components without cloud. The authors should clarify a sentence and provide supporting figures.

327: It is difficult to distinguish clouds in the figures. Therefore, it is hard to understand cloud effects on polarization. It would be helpful to show clouds in figures.

Figure 10: The difference is mainly related to interpolation? Rather than interpolation, it seems to be other reasons because the difference is too large.

372: Figure 5 just showed climatological ozone, not diurnal variation.

Table 1: Please correct a unit of the spatial resolution (not km).