|The authors aim at using the information contained in GOSAT XCH4 data to correct biases in in CH4 concentrations simulated by GEOS-Chem and improve the comparison with independent data such as TCCON XCH4, NOAA surface CH4 from flasks and HIPPO data.|
As already stated in the review of the frist version of the paper, the effort at assessing the errors in the (chemistry-)transport model before going into flux inversions is necessary and the issue remains too rarely treated adequately in inversion papers. It is therefore a very good idea to present a methodology to tackle this issue. The explanations of the methodology and most of the interpretations of the results, regarding mainly biases in the transport, are clear and interesting and the revisions made after the first review have lead to a still clearer description of the work. The reduced number of figures makes it more focussed and easier to read, which I appreciate a lot.
A debate on the terminology has been launched during the first review: using 4D-Var, 3D-Var or variational for the methodology. The authors wish to stick to using 4D-Var and I agree with them that this kind of paper is not the place for deciding on the exact terminology of our domain. Since the description they added makes everything clear mathematically, I think we can drop the debate on the naming of the method.
**Section 2: data and method:
- p.8 l.11 and in Eq.5: the way the equation is written is valid for $N$ the number of hourly time steps but actually, there are not N u_i (they vary over 3 days or 1 month, as stated elsewhere) or N Q_i (there is only one as it is constant). Could the equation be written in a more general way so that it would be easy to refer to it directly for any of the experiments?
- p.8 l.15 in Eq.6: same remark
- p.9 l.14: is convergence guarranted?
- p.9 l.22: "the level of noise was estimated to correspond to GOSAT XCH4 uncertainty": do you mean that the point at which the inversions stopped was afterwards found to match the 10 ppb value provided for GOSAT data?
- p.9 l.26: "R was assumed to be diagonal": and the diagonal was filled from the 13 ppb value given in the previous sentence? An explicit link between the two sentences would make it clearer.
- p.10 l.1: "50% uncertainty on CH4 emissions in each surface grid box": how much Tg/y does it lead to? Is it realistic?
- p.11 l.5-6: "to independent observations did not change noticeably": did not change when q increased?
- p.11 l.9: "the WC method was still able to significantly improve": this sentence is not very clear to me: what does the "still" refer to?
- p.11 l.29: "The bias in vertical transport and chemistry": this is for the first two OSSEs, respectively, isn't it?
- p.12 l.1: "and have the freedom to": this part of the sentence is a bit strange. Do you mean that the bias can be placed anywhere in this configuration?
- p.12 l.6-7: "We also conducted SC 4D-Var assimilation experiment for comparisons with the WC
approach in the OSSE with biased surface emissions.": no OSSE with biased surface emissions is referred to before.
- p.12 l.22-23: "Short time windows": how long?
- p.12 l.24-25: "for short temporal correlation length scales": here, all matrices are diagonal, so that there are no correlation lengths used at all, is that right?
- p.12 l.31: "above 750 hPa" = above 750 hPa only or above 750 hPa versus the rest of the atmosphere?
- p.12 l.32: does "globally" mean one term for the whole stratosphere?
**Section 3 Results
- p.13 l.15: "The state corrections capture the general horizontal and vertical structure of the a priori bias": this seems a bit optimistic when looking at the figure as a whole. Maybe some king of statistical indicator would make it clearer.
- p.13 l.25: "fewer GOSAT retrievals": a supplementary table with the number of GOSAT retrievals per region and period would be useful.
- p.13 l.26-27: what about the increase above 100 hPa?
- p.17 l.8: do the ACE-FTS data and the model always agree on what points are in the stratosphere?
**Section 4 Discussion of Model Biases
p.18 l.14: "the asymmetrically larger number of GOSAT measurements in the northern hemisphere." Same remark as above: a table with the number of GOSAt data available in regions discussed in the text would be useful.
**Section 5 Conclusions
- p.21 l.29: "artificially introduced biases in emissions, convection,": the part with biases in emissions is not shown any more.
- p.22 l.28 and 30: what so significantly and significant fraction mean here? Can you quantify?
Throughout the text, "a priori" and "a posteriori" are used: shouldn't it be "prior" and "posterior" instead? Note that I am not a native English speaker.
- p.6 l.4: "10 ppm" -> ppb?
- p.8 l.2: "surface emissions, however, because of": cut sentence in two "surface emissions. However, because of"
- p.10 l.9: "the choice of scaling parameter2 -> the choice of the scaling parameter?
- p.10 l.34: "as described in Sect. 2.3": the reference is a bit strange since we are in Sect. 2.3; maybe use sub-subsections or paragraphs?
- p.11 l.18: "to produce pseudo GOSAT XCH4 measurements" and l.26 "No noise was added to pseudo-observations": from this I understand that the statistics in R are not used to generate the pseudo-obervations. If so, maybe put all the information about the generation of the pseudo-obs together.
- p.11 l.20: "from one of the four specified sources of model bias": only three are specified above
- p.12 l.30: "results to vertical extent" -> to the vertical extent
- p.13 l.13: "lofted" -> lifted
- p.16 l.10: "a prior" -> a priori (or prior)
- p.16 l.24: "leaves a weak positive biases" -> leaves weak positive biases
- p.16 l.25: "Mean a posterior inter-station bias" -> a posteriori (or posterior)
- p.19 l.29: "forth" -> "fourth"
- p.19 l.31: "vertical transports" -> transport
- p.20 l.22: "the dimensionality of inverse problem" -> of the inverse problem
- p.22 l.10: "slowly varying biases, however, a few stations," -> biases. However, a few
- p.22 l.27: "5 o, however, the magnitude" -> 5 o. However, the magnitude
- p.23 l.2: "model transport, however shorter-lived" -> transport. However,
- p.23 l.6-7: "incorrectly attributing model errors in vertical transport" to emissions?
- Figures 1, 3: "units of ppb" -> "ppb"
- Figure 9: "set of experiment" -> experiments