The paper describes the comparison of the GEMS formaldehyde retrievals with those of TROPOMI and ground observations.

In addition sensitivity analyses are performed. It is a useful and complete manuscript but difficult to read sometimes, 

since it lacks precision in its formulations or because of the many grammar or style mistakes. After improving the 

writing style I would recommend it for publication.

Below I will give minor comments and several examples of grammar mistakes, but it is far from a complete grammar check.

Line 21: "...has monitored Asia." This is very vague. What has been monitored for Asia?

Line 29: "..over the latitude.." What is meant by this?

Line 30: "..between the two is.." Between the two what ?

Line 96: "by applying air mass factor" => "by applying an air mass factor"

Line 101: "Variables of GEMS HCHO Level 2 product" => "Variables of the GEMS HCHO Level 2 product"

Line 120-121: "..and Japan and could affect the background contributions to VCD" => 

    "..and Japan, which can affect the background contributions to the VCD"

    

Line 245 "who reported that cloud-free assumption" => "who reported that the cloud-free assumption"

Line 255 and 257 : what does %p mean?

Line 262-264: I think I understand the procedure you followed here for averaging the GEMS observations, 

but the description is very unclear. 

Line 264-266: This is also an unclear description. Didn't you simply apply the averaging kernel of GEMS to the MAX-DOAS profile?

Line 285: "GEMS pixel observing the MAX-DOAS station covers a much larger area, leading ..." => 

        "The GEMS pixel covering the MAX-DOAS station has a large area, leading ..."  

    

Line 290-291: ".. with the previous result from De Smedt et al. (2015), with the increasing trend.." =>

 ".. with previous results from De Smedt et al. (2015), showing an increasing trend.."

 

Line 299: "was started by" => "was made by"

Line 323: " the large pixel size dilutes an error from the problematic area". Please rewrite this sentence.

In general, I think the conclusions section is a summary with a lot of repetition. I would expect also to see

some statements about the precision and accuracy of the GEMS formaldehyde product in the conclusion.

This paper describes upgrades to GEMS HCHO retrieval, and its comparison and evaluation versus TROPOMI, FTIR and MAX-DOAS observations. The upgrades to the “baseline” formaldehyde retrieval consist in fitting polarization sensitivity vectors and constructing radiance reference spectra using clear-sky pixels. The intercomparisons between GEMS and TROPOMI shows good correlation with a small bias of 10-16%. GEMS captures seasonal variations well, showing relatively high correlations with FTIR and MAX-DOAS ground-based observations. Overall, the paper is well written, even though it could benefit from an English language edit.

The paper has a clear structure and provides important information to understand and use GEMS formaldehyde retrievals. Addressing the questions that follow before publication would help to provide a more solid description of the retrieval upgrades and the comparison with correlative measurements. Its publication is therefore more than justified, providing important reference material for anyone working with GEMS formaldehyde retrievals.

General comment regarding retrieval upgrades:

The inclusion of polarization vectors and the modification of the radiance reference affects slant column density (SCD) retrievals. The discussion about the effects of these changes in the retrievals should focus on SCD. Describing them in terms of vertical column density (VCDs) compounds the changes on SCDs with AMFs (affected by the change in the a priori profiles) and they should be analyzed separately.

Questions regarding the calculation of the radiance reference and the background correction:

• Is the background correction computed as one North/South 1D vector? It would be very interesting to compare the background columns computed for different days using the old and new radiance reference / background corrections.
• Further details regarding the radiance reference calculation would be very useful, for example: What is the minimum number of pixels used to calculate the radiance reference? Why having larger signals (over clouds) is a problem? The intuition suggests that pixels affected by clouds could result in higher signals and therefore less noise. Are radiance references time of day dependent or is one radiance reference per day calculated?
• In line 130 it is suggested that radiance reference changes affect mostly high VCDs, yet I wonder if the radiance reference only affects the high value of the retrieved SCDs or is a uniform change? Figure 2, on top of the radiance reference itself could show the retrieved SCDs for one scan using the different radiance reference options. Also, it would be very interesting to include another figure illustrating the methodology used to calculate the background correction and its latitudinal dependency.
• Another question that needs to be addressed here is the dependency of the retrieved SCDs with the radiance reference construction method. The paper does not provide enough details about how the radiance reference is constructed. For example, what is the effect of using the radiance reference from day i in day i+1? What about hour h on hour h+1?

Questions regarding the inclusion of polarization vectors in the fitting:

• It will be very interesting to see the value of the polarization vector fitting parameter for a given scan? Does it have a bigger impact on some SZA/surfaces than others? What is the optical depth associated with the polarization vector pseudo absorption? As mentioned above, the fitting of the polarization vector affects the retrieved differential columns not the VCD. To avoid convolution of new fitting approach with AMF calculations and changes in the cloud algorithms the analysis of results affecting the spectral fit should look at dSCDs only. This comment applies to figures 6, 7, 8...
• What about the correlation between the retrieved polarization parameter and HCHO fitting?

Questions associated with the discussion of the sensitivity tests:

• Line 179 and figure 8: The paper should compare dSCDs with SCDs, since the VCD contains information about the AMF, imposing a priori information that most likely increases the correlation between both retrievals above the one expected if only dSCD and SCDs where considered.
• What is the behavior below 40N? Looking at figure 8 looks like if the bias is gradual?
• The higher RMS using irradiances points towards unaccounted spectral signals in the model of the fit (as expected) that are accounted for when using the radiance reference.
• Line 183: Results using radiance and irradiance are almost not identical. The differences are significant and, depending on the location, important. Please review this statement.

Questions regarding the comparison with TROPOMI observations:

• It will be very interesting to break down the comparison between TROPOMI and GEMS in terms of SCDs, AMFs and VCDs to try to understand the performance of those two retrieval steps separately. Even more interesting would be to compare VCDs pre and post reference sector background correction.
• Line 250: this is an interesting discussion if done with care. First it is important to establish how much of the latitudinal variability comes from the background correction for GEMS (for TROPOMI there is no dependency on the background correction but there is also a bias correction, is that considered?). Second, it is necessary to understand which percentage of the reported VCD is coming from the background correction? Finally, how large is GEMS background correction variability as function of SZA and day of year/season.
• Line 192: Please add detail about the filtering criteria associated with QA<0.5 (particularly for what it refers to cloud fraction and SZA) since those two parameters are used to filter out GEMS. What does it mean FinalAlgorithmFlag=0 in GEMS?
• Line 194: Does this mean that only GEMS pixels with LT of 13:30 are used? I guess the answer is not since TROPOMI overpass time off nadir is different from 13:30 LT. Please provide further details.

Questions regarding the comparison with FTIR and MAX-DOAS

• Are there plans to make comparisons in other locations?
• Line 282: Please, place the results of this GEMS comparison with FTIR and MAX-DOAS in the context of Vigouroux et al., 2020 and de Smedt et al., 2021 with TROPOMI information. Are correlations and biases similar? Please quantify. This would be useful since given the preceding discussion regarding GEMS and TROPOMI comparisons.
• Line 285: Does Xianghe have a forested area that could explain large biogenic emissions of isoprene; are they of anthropogenic origin? It would be great to provide some context.
• Line 290: Is the diurnal evolution of GEMS columns linked to increased formaldehyde or does it has to do with the development of the boundary layer during the day? In the early hours of the day, even if there is a large HCHO column it would be near the surface. GEMS sensitivity to that early morning shallow boundary layer is very limited. Most variability of the columns (spatial) at those hours I would assume is associated with a priori information of the AMF calculation unless proven otherwise by showing heterogeneity in the slant columns. What is the correlation at different hours of the day?

Minor/specific comments:

Abstract. The description of the comparison between GEMS and TROPOMI is interrupted by two sentences introducing the use of polarization vectors and reference spectrum calculations. Maybe it would be more logical to move these two sentences at the end of the discussion concerning GEMS and TROPOMI comparisons.

Line 57: “adopted” implies the instrument could have chosen the resolution. Maybe “have much finer” is a better description if combined with “allowing to observe” (“have adopted much finer… allowing to observe local pollution plumes…”

Line 63: ”the presence of clouds”

Line 76: What is the definition of “co-added” pixels (how many)?

Line 91: “consisting of a three steps”, remove processes.

Line 95: suggested change “by” to “using” “…corrections using model columns from unpolluted clear areas”

Line 111: suggested change “is to” to “…the background correction adds slant…”

Line 117: suggested change “ …GEMS cannot sufficiently obtain clean…” to “…GEMS cannot obtain sufficient clean…”

Line 136: Are these residuals and fitting uncertainties characteristic of retrievals at any time of the day/location or there is a diurnal dependency of the uncertainties with SZA and the brightness of the scene?

Line 142: This sentence is confusing. Is the LUT of scattering weights recalculated using GEOS-Chem at higher resolution? Which profiles (ozone, temperature...). What I think is going on here is that the HCHO a priori profiles have been updated but the LUT remains the same. It could be interesting to briefly remind the reader the parameters of the LUT table.

Line 170: Would it be possible to quantify the change in the retrieved SCDs between the pre-launch and "optimized" fitting window? Adding a plot showing the SCDs for one scan using both fitting windows and their difference would be interesting.

Line 178: What is the meaning of "with background correction"? If I'm not mistaken the use of the irradiance instead of a radiance makes the background correction unnecessary.

Line 208: What does it mean that the value of cloud fraction increases exponentially for SZA? Is the cloud fraction proportional to e^SZA?

Line 215: Figure 9, could the authors shows the effect of using two different radiance references (one calculated with FW the other one with the nominal scan)?

Line 222: This is not the only source of difference in the AMF calculations? A detail analysis should breakdown the contributions from surface properties, clouds, a priori profiles and scattering weight LUT. Lorente et al., 2016 paper could be very illustrative of the different contributions and guide further analysis.

Line 240: Adding information about collocation statistics for each city and month would be helpful to understand the significance of the comparison.

Line 320: Problems associated with scene heterogeneity are first mentioned in the conclusions of the paper and not discussed in its body. Either no mention it at all or please add a section explaining how it affects the retrievals, when and where?

Table 1:

• I understand that the paper does not discuss the construction and use of a common mode (mean residual) so maybe this question is outside the scope of this paper, but I wonder what is the dependency of the common mode with time of the day.
• Are the scattering weights precalculated for each 2x2.5 grid? What is the point of doing so, accounting for different ozone and aerosol profiles? The surface albedo is one of the parameters so don't see the benefit? What is the number of the LUT vertical layers?

Figure 1: Which fitting window is used by TROPOMI retrievals (the only one relevant for this study)? Why show the others? Second, cutting the formaldehyde feature at 330 nm by starting at 329.3nm instead of 328.5 nm is counter intuitive. Showing correlation with other fitting parameters is crucial to understand the benefit of starting at 329.3 nm. What is the point of showing a normalized solar spectrum here? Likewise with the ring spectrum. This figure would be more useful if broken into panels showing the typical optical depth of each parameter within the fitting window. This figure is quite misleading giving the impression of very strong formaldehyde signals when it is the weakest signal fitted in this fitting window together with O4.

Figure 2: As mentioned before this figure would give a better understanding of the impact of the radiance reference if it included an example of the SCDs retrieved for one scan using different radiance references (old vs clear sky).

Figure 3 could be more interesting if it showed the optical depth of other parameters considered in the fitting (such as o3, Ring, BrO, and o2-o2). Not a very important change. As it stands now, if doesn’t bring much information to the analysis.

Figure 5 suggestion; plotting some fitting residuals (including the polarization vector vs. not) would be very convincing if the dramatic signal around 350 nm shows clearly.

Figure 6: Is the white area in the southern part of the plot moving towards the west as the day progresses the glint cone? As expected, the effect of the polarization depends greatly on the geometry of the retrieval. It seems that backward scattering results in higher polarization signal. Is that correct? Is the fitting window used in the top and middle row retrievals the same?

Table S1:

• While the cross-track and along-track jargon is meaningful to those familiar with LEO instruments similar, it does not really apply to GEO satellites since they are not moving on a orbit with a pre-determine track. Don't know if there is a better terminology to better describe GEO observations.
• Is there some other documentation explaining the contents of these variables? Particularly important to use the product would be to specify the meaning of the different flags. If so, it could be very useful to provide a link to the document or the page where this "file document format" document resides.
• What are the different degrees of convergence in the fit?

Figure S1: Where is the eastern boundary of the full central scan (pink)? Maybe it could be useful to use a discontinuous line on the eastern edge to show where it is, since I assume it overlaps with full western or half Korea eastern edges?