Recovery of sparse urban greenhouse gas emissions

Zanger, Benjamin; Chen, Jia; Sun, Man; Dietrich, Florian

doi:https://doi.org/10.5194/gmd-15-7533-2022

Articles | Volume 15, issue 20

https://doi.org/10.5194/gmd-15-7533-2022

© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/gmd-15-7533-2022

© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 15, issue 20

Methods for assessment of models

|

17 Oct 2022

Methods for assessment of models |

| 17 Oct 2022

Recovery of sparse urban greenhouse gas emissions

Benjamin Zanger, Jia Chen, Man Sun, and Florian Dietrich

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Final revised paper (published on 17 Oct 2022)
Supplement to the final revised paper
Preprint (discussion started on 21 Feb 2022)
Supplement to the preprint

Interactive discussion

Status: closed

RC1:
'Comment on gmd-2021-438', Anonymous Referee #1, 04 Mar 2022
The paper investigates whether GHG emissions from urban areas are sparse (in physical or wavelet space) and whether they could be estimated from concentration measurements via sparse recovery. The authors find that the Gini index is a measure of the sparse nature of the emissions (as found in bottom-up inventories) and sparse reconstruction can indeed reconstruction them. They prove this with synthetic data . They find that emissions that have to be reconstructed in wavelet space are not very robust to noise in the measurements. They provide the code and data used in this study, so reproducibility is possible.

The work is good and I would recommend that it be published provided that the issues I mention below are addressed. They are minor, except for the language used in the text. Sections 1, 2 and 6 are well-written. The technical sections 3, 4 and 5 have grammatical errors and have to examined carefully. I will provide some examples below.

Line 57: What is a 3rd-level wavelet transform? If emissions on a N x N grid are subjected to Haar transform, one gets a transform hierarchy of log2(N) levels. In a 3rd-level transform, do you ignore all levels finer than 3 (which would give a very rough emission field) or do you only keep level 3?

Line 390: "SR is good at localization and SR-in-wavelet-domain is not robust to noise". I see that empirically from the results, but can you explain why? Does it have anything to do with the 3rd-level transform? Or Haar wavelets, which are oscillatory? Or because you do not impose non-negativity on the estimated emissions?

In Sec 4.2.2, 4.2.3 and 4.2.4, what are the wind coverage in the cities? Are the wind velocities the same or are the footprints stretched to cover the cities which are of different sizes?

Fig 7 and Fig. D1: The x-axis has bins called "0 - 0.4%" ; the label on the x-axis is "Highest emission in inventory". What does it mean? Do you rank-order the gridded emissions, and bin them in unequal bins? How were the bin cutoffs decided? Should that be cast in terms of percentiles of the gridded emissions? Or is it the percentiles of teir ranks? Some explanation of what this axis is, in the text or captions, would be helpful

The English in Sec 3, 4 and 5 needs to be improved.

The is a lot of use of the emissions being "good compressible" or "well compressible". I think one could simply use "compressible"

Also, in the text and tables, one sees emissions "not good compressible" or "not well compressible" . What about non-compressible?

The is also use of the terms "amount of measurements" and "less measurements". Measurements in this paper are counts. What about using "number of measurements" and "fewer measurements"?

Line 332: The authors talk about estimating the measurement counts needed to achieve "descent results". That is rather casual. What about "acceptable results"? Also, what would constitute an "acceptable result"? Please clarify

Fig 7: The caption mentions "how many percents ...." This is hard to decipher. What about explaining the figure in the text where there is no shortage of space?

On the whole, a rather nice and innovative paper.
Citation: https://doi.org/10.5194/gmd-2021-438-RC1
- AC1: 'Reply from the authors to reviewer 1', Benjamin Zanger, 26 Jun 2022
  
  Please see the attached PDF
  
  Citation: https://doi.org/10.5194/gmd-2021-438-AC1
RC2:
'Comment on gmd-2021-438', Anonymous Referee #2, 09 Mar 2022

Comment attached as a .pdf

Citation: https://doi.org/10.5194/gmd-2021-438-RC2
- AC2: 'Reply from the authors to reviewer 2', Benjamin Zanger, 26 Jun 2022
  
  Please see the attached PDF
  
  Citation: https://doi.org/10.5194/gmd-2021-438-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Benjamin Zanger on behalf of the Authors (26 Jun 2022) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (29 Jun 2022) by Jinkyu Hong

RR by Anonymous Referee #1 (05 Jul 2022)

RR by Anonymous Referee #3 (26 Jul 2022)

Suggestions for revision or reasons for rejection

Overall, I think the authors have done a great job of responding to the reviews. I think the manuscript is excellent, and I recommend publication.

I only have a couple small suggestions on the framing of the abstract and introduction.

In the abstract, the authors state, "A common top-down approach for solving this problem is Bayesian inversion that uses a given Gaussian distributed prior emission field. However, such an approach has drawbacks when the assumed spatial emission distribution is incorrect." I worry that this statement could be misinterpreted by readers. Technically speaking, traditional Bayesian inverse models can be used to correct the spatial (and/or temporal) distribution of emissions. Rather, this approach typically assumes that the correction follows a multivariate normal distribution, and this assumption may not be appropriate for all inverse problems, like the urban applications discussed in this paper.

Line 26: Numerous inverse modeling studies also enforce temporal correlation.

Line 41: The description of Hase et al. (2017) could be confusing to some readers. E.g., it's not clear what "limitations" are being referred to or what "multiple parameterizations" refers to. Hase et al. (2017) use a dictionary that includes different types of spatial patterns or basis functions. As a result, they can represent a diversity of spatial patterns in the emissions field. (I'm not sure if my description is any less confusing, but I think it's another way to describe the important features of their work.)

Lines 86-89: This description of maximum likelihood could be confusing to some readers. E.g., "From this posteriori distribution a parameter estimation can be made using a maximum likelihood (ML) detector on the a posteriori." It's not clear what parameters this sentence is referring to. The word "detector" here also feels a bit confusing to me (i.e., it implies that ML is being used to detect something). Here's how I think of this process: inverse modelers estimate emissions by maximizing a likelihood function or equivalently, minimizing the negative log of this function. The resulting estimate is often referred to as the ML estimate of the emissions. This likelihood function is based on Bayes Theorem (which leads into Eq. 2).

Hide

ED: Publish subject to minor revisions (review by editor) (05 Aug 2022) by Jinkyu Hong

Please check the minor corrections below.

1) On line 298, in the sentence "Even though, for both domains ...", the comma is not needed.

2) Throughout the text, the word "relative" has been abbreviated as a rel. I think it should be spelled out (the typesetter might do that anyway before the paper appears in print).

3) In the abstract, the authors state, "A common top-down approach for solving this problem is Bayesian inversion that uses a given Gaussian distributed prior emission field. However, such an approach has drawbacks when the assumed spatial emission distribution is incorrect." I worry that this statement could be misinterpreted by readers. Technically speaking, traditional Bayesian inverse models can be used to correct the spatial (and/or temporal) distribution of emissions. Rather, this approach typically assumes that the correction follows a multivariate normal distribution, and this assumption may not be appropriate for all inverse problems, like the urban applications discussed in this paper.

4) Line 26: Numerous inverse modeling studies also enforce temporal correlation.

5) Line 41: The description of Hase et al. (2017) could be confusing to some readers. E.g., it's not clear what "limitations" are being referred to or what "multiple parameterizations" refers to. Hase et al. (2017) use a dictionary that includes different types of spatial patterns or basis functions. As a result, they can represent a diversity of spatial patterns in the emissions field. (I'm not sure if my description is any less confusing, but I think it's another way to describe the important features of their work.)

6) Lines 86-89: This description of maximum likelihood could be confusing to some readers. E.g., "From this posteriori distribution a parameter estimation can be made using a maximum likelihood (ML) detector on the a posteriori." It's not clear what parameters this sentence is referring to. The word "detector" here also feels a bit confusing to me (i.e., it implies that ML is being used to detect something). Here's how I think of this process: inverse modelers estimate emissions by maximizing a likelihood function or equivalently, minimizing the negative log of this function. The resulting estimate is often referred to as the ML estimate of the emissions. This likelihood function is based on Bayes Theorem (which leads into Eq. 2).

Hide

AR by Benjamin Zanger on behalf of the Authors (26 Aug 2022) Author's response Author's tracked changes Manuscript

ED: Publish as is (31 Aug 2022) by Jinkyu Hong

AR by Benjamin Zanger on behalf of the Authors (07 Sep 2022) Manuscript

Short summary

Gaussian priors (GPs) used in least squares inversion do not reflect the true distributions of greenhouse gas emissions well. A method that does not rely on GPs is sparse reconstruction (SR). We show that necessary conditions for SR are satisfied for cities and that the application of a wavelet transform can further enhance sparsity. We apply the theory of compressed sensing to SR. Our results show that SR needs fewer measurements and is superior for assessing unknown emitters compared to GPs.