Characterizing model errors in chemical transport modeling of methane: using GOSAT XCH<sub>4</sub> data with weak-constraint four-dimensional variational data assimilation

Stanevich, Ilya; Jones, Dylan B. A.; Strong, Kimberly; Keller, Martin; Henze, Daven K.; Parker, Robert J.; Boesch, Hartmut; Wunch, Debra; Notholt, Justus; Petri, Christof; Warneke, Thorsten; Sussmann, Ralf; Schneider, Matthias; Hase, Frank; Kivi, Rigel; Deutscher, Nicholas M.; Velazco, Voltaire A.; Walker, Kaley A.; Deng, Feng

doi:https://doi.org/10.5194/acp-21-9545-2021

Articles | Volume 21, issue 12

https://doi.org/10.5194/acp-21-9545-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/acp-21-9545-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 21, issue 12

Research article

|

24 Jun 2021

Research article |

| 24 Jun 2021

Characterizing model errors in chemical transport modeling of methane: using GOSAT XCH₄ data with weak-constraint four-dimensional variational data assimilation

Ilya Stanevich, Dylan B. A. Jones, Kimberly Strong, Martin Keller, Daven K. Henze, Robert J. Parker, Hartmut Boesch, Debra Wunch, Justus Notholt, Christof Petri, Thorsten Warneke, Ralf Sussmann, Matthias Schneider, Frank Hase, Rigel Kivi, Nicholas M. Deutscher, Voltaire A. Velazco, Kaley A. Walker, and Feng Deng

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Final revised paper (published on 24 Jun 2021)
Preprint (discussion started on 15 Nov 2019)

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AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC1: 'RC on "Characterizing model errors in chemical transport modelling of methane: Using GOSAT XCH4 data with weak constraint four-dimensional variational data assimilation"', Anonymous Referee #3, 12 Dec 2019
RC2: 'Reviews to acp-2019-786', Anonymous Referee #2, 12 Dec 2019
RC3: 'Manuscript Review from Anonymous Referee #1', Anonymous Referee #4, 10 Jan 2020
AC1: 'Comment on "Characterizing model errors in chemical transport modelling of methane: Using GOSAT XCH4 data with weak constraint four-dimensional variational data assimilation" by Stanevich et al.', Dylan Jones, 03 Dec 2020

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Dylan Jones on behalf of the Authors (03 Dec 2020) Author's response Manuscript

ED: Referee Nomination & Report Request started (04 Jan 2021) by Patrick Jöckel

RR by Anonymous Referee #3 (15 Jan 2021)

Suggestions for revision or reasons for rejection

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.

General comments:
--------------------------
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.

Specific comments:
--------------------------
**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?

Technical corrections:
-----------------------------
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

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RR by Anonymous Referee #2 (18 Jan 2021)

ED: Publish subject to minor revisions (review by editor) (18 Jan 2021) by Patrick Jöckel

AR by Dylan Jones on behalf of the Authors (01 Feb 2021) Author's response Author's tracked changes Manuscript

ED: Publish as is (02 Feb 2021) by Patrick Jöckel

AR by Dylan Jones on behalf of the Authors (12 Feb 2021)

Short summary

We explore the utility of a weak-constraint (WC) four-dimensional variational (4D-Var) data assimilation scheme for mitigating systematic errors in methane simulation in the GEOS-Chem model. We use data from the Greenhouse Gases Observing Satellite (GOSAT) and show that, compared to the traditional 4D-Var approach, the WC scheme improves the agreement between the model and independent observations. We find that the WC corrections to the model provide insight into the source of the errors.

Characterizing model errors in chemical transport modeling of methane: using GOSAT XCH4 data with weak-constraint four-dimensional variational data assimilation

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Characterizing model errors in chemical transport modeling of methane: using GOSAT XCH₄ data with weak-constraint four-dimensional variational data assimilation