General comments:

The manuscript presents the improvement in TROPOMI's methane product retrieval to tackle the effect of surface artifacts that produce anomalous retrieval values and are especially dangerous in areas with potential real methane emissions. To address the effect, the author applies a third-order polynomial in those areas with anomalous retrievals. The result is compared with the retrieval obtained from the second-order polynomial, demonstrating that the effect of the artifacts can be successfully corrected. As a routine method, the authors present the results of the validation of the retrieval obtained with the third-order polynomial.

The results presented in this manuscript are timely and highly relevant, given the importance of TROPOMI data for detecting global methane emission hot spots and sporadic ultra-emissions. The correction of anomalous values produced by surface artifacts should be applied as soon as possible to make the global methane data more accurate and to operate efficiently as soon as possible.

The paper presented here is a high-quality, clear, and well-written document. However, some minor issues need to be clarified.

Specific comments:

Lines 83-84 and in results in general: throughout the text, it is emphasized that the second-order polynomial is optimal for most surfaces, and the third-order polynomial is optimal for areas with surface artifacts even though it shows no improvement in the rest of the surfaces. After reading the text, it is not clear to me if, from now on, the operational product is the TROPOMI data processed fully with the third-order polynomial, if it is a combination of both polynomials depending on the area, or if the operational product is the data processed with the second-order polynomial and the third-order polynomial is provided separately but is not considered for the official product.

Lines 115-116: The authors point out that, in the case of Algeria, the effects do not occur in the major field of the country. However, in Figure 3, the effect of surface artifacts can be seen in the Hassi R'Mel field, west of the image, or the Illizi basin, south of the image (only the northern part of the basin is seen in the image, but the same type of surface extends over several kilometers). In these areas, the O&G production is high, and, for example, Lauvaux et al. 2022 reported ultra-emissions detected with TROPOMI in these areas. Does this imply that the quantified emissions in these areas may have erroneous estimates?

If so, in the same way that the authors mention confidence in the data from the major field in Algeria, it would be convenient to also warn about the danger in the rest of the areas affected by the artifacts.

Figure 3: I suggest adding a label on the left of each row indicating the country or region that is being represented. This is already indicated in the image caption, but I think adding the label in the figure could improve the visualization of the image.

Technical corrections:

Line2: add "a" before "few false…" => pointed to a few false

L14: add comma after "still" => but still, a posterior

L19: measurements have => has

L20: Add comma after “regional” => global, regional, and local

L22: was launch => was launched

L23: remove the second "to" => albedo measurements, update the…

L24: remove "to" before "retrieve" => and retrieve methane

L33: add s in “type” => different types

L36: add comma after "study" => In this study,

L38: asses => assess

L57: add comma after "matrix" => weighting matrix, and

L60: add comma after "algorithm" and "surfaces" => retrieval algorithm, a second order polynomial was selected (Hu et al., 2016), but for specific surfaces, this

L61: show => shows

L70: add comma after "rocks" => minerals, rocks, and

L84: add comma after "section" => In this section, we

L104: add comma after "region" => Over this particular region, the underlying

L105 ad comma after "shown)" => (not shown), which

L112: add s in “type” => different types

L114: this regions => these regions

L119: add comma after "section" => In this section, we

L120: add comma after "ratio" => their ratio, and

L121: add comma after "4c)" and "example" => plot (Fig. 4c), localized artefacts that are removed are clearly visible, for example, in several points

L122: add comma after "Siberia" => over Siberia, as discussed

L133: even the correction => even if the correction

Figure 4: add comma after "polynomial" in the second line => third order polynomial, and

Figure 5: add comma after "polynomial" in the second line => third order polynomial, and

L147: add comma after “(−5.3 ppb)” => -0.2 % (−5.3 ppb), and

L149: add comma after "stations" => the stations, and Fig. 6b

L155: add comma before and after "therefore" => artefacts and, therefore, cannot

Table 1: add "the" before "number" and comma after "bias" and "stations" in the second line => The table shows the number of collocations, mean bias, and standard deviation for each station and the mean bias for all stations, and

L157: add comma after "section" => In this section, we

L164: add comma after "average" => on average, TROPOMI XCH₄

L168: add "the" before "biggest" => that the biggest

L 174-175: add comma after "data" and "algorithms" and add "a" before "few" => TROPOMI methane data, as well as an intercomparison between different scientific retrieval algorithms, pointed to a few false methane

L188: add "to" before "oil" and add comma after "gas" => emissions due to oil, gas, and coal

L196: Asian in capital letter

L198: add comma after "still" and "if" after "even" => but still, a posterior correction needs to be applied. This implies that even if the

L200: add comma after "Finally" and replace "asses" with assess

General comments:

This manuscript documents the improved surface reflectance model that has been implemented in the SRON methane (CH₄) retrievals from the TROPOMI instrument. These changes are based on increasing from a second-order polynomial to a third-order polynomial within the surface reflectance model. The second-order scheme led to artefacts with anomalously high XCH₄ values over certain surfaces. The paper describes the changes, analyses the differences between the old scheme and the new one, and validates the new retrieval values against independent observations. The authors successfully demonstrate that the new version removes the artefacts in a number of diverse locations.

The results in the paper are clear and convincing, whilst the writing is generally succinct and coherent. The new developments to the retrievals are important, given the potential of TROPOMI CH₄ retrievals to provide comprehensive and long-running observation of global CH₄. As mentioned in the text, the artefacts that were present in the previous version of the data may have already led to misjudged conclusions in other research.

Taking this all into account, I am happy recommend publication in AMT subject to some minor changes, detailed below.

Specific comments:

Figures 1 & 3: Perhaps an inset in each row, showing the location of the zoom area in a global or at least regional context would be helpful here.

Figure 3: make it clearer that the difference plots show the 2^nd-order scheme minus the 3^rd order scheme. I think that the phrase “difference between XCH4 retrieved with second and third order polynomial” is not quite clear enough.

Line 147 and elsewhere in that paragraph: I wasn’t quite sure that the numbers in the text matched that in Table 1. For example, the text states that the average bias for the corrected XCH4 is -0.2% whereas the Table states that it is -0.3%. Then on line 149, the bias is stated as +0.3%. Otherwise, if I have misunderstood, please clarify the text.

Line 148: I was initially confused about the use of the word ‘uncorrected’ here as I assumed that it was referring to use of the second-order polynomial. The caption text above Table 1 does make the meaning clear but it would helpful if this information was included in the main text here too.

Line 167: Could you briefly state the second-order values here to aid the reader? “Similar magnitude” is a bit vague.

General throughout text: You state that the third-order polynomial scheme significantly improves results over the regions that previously had artefacts due to errors in the surface reflectance, but no improvements away from these regions. You state that a second order-polynomial is optimal elsewhere, in fact. Does this mean that the third-order scheme leads to reduced performance elsewhere and the second-order scheme should be used there – i.e. a mix of schemes is necessary? Or just that the third-order scheme is used globally but does not produce improvements in most regions? The text discussing this needs to be clearer.

Technical corrections: 

Line 19: have been -> has been

Line 22: was launch -> was launched

Line 33: type -> types

Line 38: asses -> assess

Line 133: even the -> even though the

Line 166: remove ‘as well’