The authors of this paper are my colleagues and friends. Thus, I am not in a good position to provide an unbiased review. Due to this obvious conflict of interest, I would have preferred to provide neither a rating of the manuscript nor a recommendation, but the system forces me to do so. On request of the editor I have, however, checked the algebra in the Appendix. My rating of the scientific quality and my recommendation refer to the Appendix only.

The goal of this paper is to present a data fusion method that needs as input only data that are provided to the public, and thus can be applied by a wider community than the retrieval scientists involved in the level-2 processing of the parent data. The Appendix provides the theoretical basis for this.

My major concern is that in some places the derivations of the equations used seem to involve the inverse of a singular matrix. Such manipulations of equations are not truth-preserving. So I am afraid that it would need a major revision of Appendix A to remedy this. I have discussed this issue with the lead author, who meanwhile has found a theoretical basis which seems robust to me. Thus, I am confident that in the revision of the manuscript this defect will be remedied.

Some further issues:

Please note that the S_x matrix in Eqs A4 and A6 has a probabilistic interpretation only if S_a^-1 is chosen as a regularization matrix. The text before A6 suggests that the authors consider also other constraint matrices. In this case, however, S_x has no probabilistic interpretation.

lines 602/603: I do agree that Kalman filtering and retrieval use the same mathematical formalism, but I do not find it so clear in the comparison between Eqs A2 and A10. Formalism A2 is based on Rodgers' n-form, while A10 is more related to Rodgers m-form; the equivalence is correct, but it is not so obvious from these equations. Note that A10 involves covariance matrices, while A2 involves inverse covariance matrices. There is nothing wrong with the algebra here, but I would suggest to change the text.

B2 is not quite correct; we need an L matrix with x-values down the diagonal, and a ^L matrix with ^x-values down the diagonal. With these B2 should read

A = ^L A^l  L^-1≈ ^L  A^l   ^L^-1

I think that the approximative character of this transformation needs to be mentioned, and the `approximately equal' sign should be used.

typo in line 661 "logarithmnic" -> "logarithmic"

B3 can cause trouble: an S^l  matrix representing a symmetric pdf in the log-space cannot be mapped on an S-matrix representing a symmetric pdf in the linear space. Thus, l661 should read "can be expressed in linear approximation in the linear scale" and the equal-sign in B3 should be replaced by an approximativly equal sign. 

Thomas von Clarmann

The authors propose to combine independent retrievals of CH4 from  TROPOMI and IASI, which are in differing orbits, using well-known optimal estimation techniques.  They compare the combined and individual L2 retrievals to a number of independent measurements while accounting for the individual sensitivities of the retrievals.  Those comparisons are interesting as they show the strengths and weaknesses of IASI and TROPOMI. 

They describe in detail the method to combine a column retrieval and a profile retrieval using optimal estimation techniques. This extends previous approaches, e.g., Luo et al, 2013, with a useful twist that could be applicable to other instrument combinations.  

The value of this combined product, however, is not entirely clear.   The theoretical analysis presented in the appendix neglects the fact that IASI is in a morning orbit and TROPOMI is in an afternoon orbit.   The coincidence criterion that they propose is reasonable for evaluating L2 products against independent data but it is not adequate for actually combining data.  

For this study, they need to directly account for the dislocation error, which could be modeled as a covariance.  This could be done in a simulation context using, for example, CAMS methane (https://atmosphere.copernicus.eu/charts/cams/methane-forecasts).  

This is important in part because the paper neglects a key question: who would want to use this data?  Most scientists aren't interested in CH4 concentrations, they are interested in the fluxes that produce them.   Given their characterization, IASI and TROPOMI can be used in this context.  Models can readily account for the differences in time of day and how winds may shift the origins of morning and afternoon air parcels.  The proposed method would improve DOFS but potentially at the expense of the anomalies that a model would exploit infer fluxes.  They need to address this issue.

The paper asserts that a linear optimal estimation combination of L2 products is equivalent to a non-linear combination of L1B products.  They never show this.  Rather they depend on the mild non-linearity assumption in Rodgers, 2000.   However, they never show that this assumption is valid for their problem.  They could demonstrate it by showing in a simulation environment where they combine the L1B data in a multi-spectral retrieval and compare it to the equivalent L2 combination.  

The authors are impressively unaware of the literature on combining satellite data for composition.  They don't discuss the landmark Landgraf and Hasekamp (2007) or Worden et al, 2007 papers.  In addition to Cuesta, there are a number of papers by Fu et al, 2013, 2018 that solve this problem with L1B data.  Luo et al, 2013 demonstrate a similar approach for combining TES and MLS L2 data for CO.  The authors are encouraged to familiarize themselves with the literature and cite appropriately.  

As noted by the authors, the value of this approach will be better realized with Sentinel 5, rather than IASI and TROPOMI.  I would suggest orienting the paper more towards a proof-of-concept for S5 or similar configurations, e.g, the A-Train.  Whether this approach is as good as a combined L1B retrieval with coincident measurements or separately assimilating L2 products remains to be seen.  But, the current strategy with IASI and TROPOMI is not clear.

Additional comments are embedded in the supplement.  

The paper by Schneider et al. presents an interesting approach to derive tropospheric methane retrievals by synergism of IASI and TROPOMI level 2 products. The presented method is an a posteriori combination of the two level 2 products, using methane total columns from TROPOMI and profiles from IASI. The theoretical basis of the synergism is presented as well as comparisons with in situ measurements and ground-based retrievals. While previous work on fusion or synergism of level 2 products have been done, the present study shows an application of this kind of approach for methane retrievals, including the application and comparison with real data.

However, major revisions are needed in order to make the paper publishable. The present manuscript lacks some key elements to demonstrate the real contribution and validity of the combined retrieval and in some cases of criticism. Moreover, I disagree that the authors demonstrate the equivalency between this combination of level 2 products and a synergism of level 1 measurements. I strongly recommend modifying the manuscript with respect to the following major issues:

• Performance of the TROPOMI only approach vs the combined product: figure 3, 4 and 5 show that the TROPOMI total column retrievals are more sensitive (between 5 and 15 km), have less contribution of the a priori and less error than the combined product. How is this possible that the combination degrades the total column retrieval, both in sensitivity and the error? How is it possible that the IASI product does not really provide additional information according to the averaging kernels (except for a small change between 2-3 km of altitude, which is much smaller than the loss above) and it even slightly increase the error? Other synergetic satellite approaches show a very clear gain in total column retrievals, for example in total column degrees of freedom, as compared to single-instrument products. Why in the case of the combined product shown in this paper we do not see such gain and we even remark a small degradation? It is important to clarify the reason for this degradation and clearly indicate it in the manuscript. The manuscript should also point out limitations of the combined approach.
• Since the gain of the combination for the total column retrieval is not clear (even a small degradation is seen), what is the actual information provided by IASI measurements? And what would the advantage of the combined product as compared with a profile retrieval using TROPOMI measurements only?
• In Lines 8, 63-64 and 491-492, the authors strongly claim an equivalence between the level 2 combination and a level 1 synergism. I disagree that this statement is demonstrated in the paper. Such a strong statement can not only be based in theoretical estimations of appendix A2, but a practical comparison with real data should be given. The only way to demonstrate it is to fully develop and implement a full synergism of level 1 measurements of TROPOMI and IASI and then compare its performance with that of the a posteriori combination of level 2 products. However, the authors do not show such level 1 synergism product in their paper. I strongly suggest removing these statements, unless such thorough practical demonstration is provided.
• Global daily maps: The authors claim their product enables the generation of global daily maps of combined data (line 60), however the manuscript does not provide any map of the combined product. The validation of a satellite product in specific locations (figure 6) does not imply the capability to derive global daily maps with a satellite product. In order to provide such a general statement, it should be demonstrated by showing the capacity of this approach to map tropospheric methane distribution.
• Co-location of TROPOMI and IASI products: the authors arbitrary propose co-location criteria in section 2.2. Such criteria should be geophysical justified by comparison between the time-space variability of methane. What is the influence of the difference in the overpass time? How does it compare with the diurnal evolution of methane? The same in terms of space variability. It should also be clearly specified the horizontal resolution of the combined product and the coarser resolution of this product as compared to TROPOMI should be explicitly indicated as a limitation. Moreover, section 4.2 on data inconsistency should also deal with heterogeneity and time evolution of methane as observed by IASI and TROPOMI, and in addition to their biases.
• Title: “Synergetic use of IASI and TROPOMI space borne sensors ..” calls for ambiguity when it comes for the use of the IASI and TROPOMI spaceborne sensors measurements. I recommend to clearly indicate in the title “level 2 products” or “level 2 retrievals” instead of only the sensors.
• The authors claim that the major contribution of the combined product is a tropospheric column of methane that is not obtained with the individual single-instrument product. However, this statement should be more moderate since Figure 12 only show an increase in correlation R2 from 0.245 (IASI only) to 0.346 (combined product), which remains a rather moderate gain.

Other important points:

• A UTLS partial column retrieval from TROPOMI: in Figure 5c, black marks are drawn that would correspond to a TROPOMI retrieval. Does this partial column retrieval exist?
• The “correlation plots” or scatter plots of figures 7, 10 and 11 are very difficult to understand visually (biases and slopes) due to the change in the scales (vertical and horizontal). I recommend changing them to have the same range in both axes.  
• The use of % for correlation coefficient is not the most common practice. I recommend expressing correlation coefficients as values between -1 and 1.