The reviewer finds the manuscript hard to read and understand, due to the confusion in the terms used, the vague model description for emission estimation, and poor English in the manuscript.

1.    Confusing terms used in the manuscript.

A)    CH4

In equations (1), (2) and (3), CH4 represents methane concentration with the unit of ppm, while the in the main part of the manuscript, CH4 just means methane in English. This creates unnecessary confusion for readers.

B)    CH4 emissions

Why one term “CH4 emissions” is assigned to two different variables, one in the unit of ppm/min (E_CH4) , and another one in the unit of kg/h (E’_CH4), and E_CH4 has never been clearly defined in the manuscript: is it the methane concentration change over time at the certain point? Or average methane concentration changer over time over a controlled volume? This is the first time that the reviewer has seen such a term is used to define emissions. Please define parameters with their actual physical meaning.

C)    Temporal frequency  

Why a frequency has a unit of minute? Should it be hertz (event per time) (Lines 136, 143)

2.    The Mass Conserving Model of Measured CMM and the 2-Box model

First, the model or models used to estimate methane emissions from one or multiples coal mines are not well described. The reviewer is expecting the following information to be clearly stated in the model:

A)    Is the model dealing with one coal mine or multiple coal mines?

B)    Is the coal mine emission treated as point source or area source?

C)    Are the methane emissions from the coal mine considered stable or not?

D)    What is the control volume that the model is applying?

E)    What are the boundary conditions and initial conditions if transit process is considered?

A scientific description of a mechanism physical transport model should include the following contents:

A)    Control volume: the physical region where the model is applying. In the case of this paper, are we considering 3-dimensional box covering multiple coal mines and monitoring points with a height of boundary layer?  An illustrative figure will help the readers and authors too.

B)    Key assumptions of the model (3-dimension transport or one-dimension only? Transit or stable?) which will lead to

C)    Control equations base on mass balance and simplified by key assumptions

D)    Boundary equations and initial conditions

Secondly, the model itself is questionable. Since the model is not clearly defined in the manuscript, the reviewer cannot assess it accordingly. But in principle, the changes in methane concentration (ppm/min) downwind of a coal mine should be contributed to:

1)    Variation of coal mine methane emission rates (not the absolute emission rate, but the changes)

2)    Changes in wind speed and direction (again, not the absolute value)

3)    Noise created by the instrument itself.

In other words, the changes in methane concentration (ppm/min) at a certain downwind point is not related to the absolute methane emission rate (kg/h) upwind, how can we estimate the methane emission rate (kg/h) from the downwind methane concentration change (ppm/min)?

Consider an extreme ideal scenario: a coal mine emits 1000 kg/hr as a points source, the wind is precisely eastward at constant speed of 1 m/s. The instrument downwind measures the true in-situ methane concentration without any noise. In this case, we will observe constant methane concentration with 0 methane concentration changes, and lead to 0 methane emission rate from the model described in the current manuscript, which does not make sense. 

If a model cannot deal with simple scenarios, it cannot treat the complex situation when transit process is considered.

3.    Language and logical issues in the manuscript

A)    Lines 40, 41: CH₄ emission estimates are highly uncertain in both space and time (Brandt et 41 al., 2014; Saunois et al., 2020b). 

When people talk about the spatial and temporal variability of oil gas emissions, they are referring to the real emissions, not the emission estimates.

B)    Lines 40-45: For these reasons, new approaches to quantify, reduce uncertainty, and attribute CH4 emissions are necessary and can provide support for policies aiming to control and mitigate 45 CMM (Cao, 2017).

New approaches are necessary not because the emissions change with time and location, nor the fat tail distribution. It is because we need more accurate and economical tools.

C)    Line 54: Uncertainties are rarely assessed holistically or in detail (Cohen and Prinn, 2011; Cohen and Wang, 2014).

Be careful to make such a claim. Almost all methane measurement papers have one section addressing and reporting their measurement uncertainties.

D)    Line 55: Airborne remote sensing is a highly technical and costly approach to record CH4 fluxes from...

Where does the claim on “costly” come from? Actually, aerial approach has been widely employed due to its relative low cost comparing to other approaches. It will definitely less expensive to deploy than the method described in the current manuscript.

E)    Lines 61, 62: … but only after being calibrated by upward looking remotely sensed measurements…

Aren’t almost all instruments need to be calibrated before adoption?

F)    Lines 73-74: This work employs a high-frequency surface-based observation platform of CH4 concentration, which is portable, economical, and unaffected by most environmental factors

What is the proof for “economical”? Do not make any claims that you cannot support.

G)    Lines 78-79: Continuous 79 observations were made around known coal mines, unknown sources, and of background conditions.

Delete “of”?

H)    Lines 80-90: High-frequency emissions calculated using these data were used to drive a 2-box model to attribute 81 emissions to the known mine and a second low production mine previously thought insignificant.

The model used the data to derive … not the data is used to derive the model.

Please revise.

I)    Lines 86-89. While the authors are talking about Changzi basin, why do we claim “province-wide” background are high?

J)    Line 92: Observations were positioned along concentric…

Should be “instruments” be positioned, not observations

There are so many similar issues in the manuscript, and the reviewer will stop here at Page 5. The reviewer recommends having somebody proofread the English in the manuscript.

This paper discusses a method of estimating methane emissions from coal mines in China using in situ measurements at sites in all directions surrounding the facility at various distances.  The authors also use a model for source attribution to determine which of the coal mines is impacting the measurement sites in cases where this is ambiguous.

The reviewer found this paper difficult to follow and much of the methodology was not as well described as it could be.  Aspects of the measurements, uncertainty analyses and modelling are not well detailed which makes it difficult to assess the validity.  The authors show a strong understanding of satellite work in the field of emissions and thus compare their results to this but there are very few references to other measurement work done, of which there is a significant amount.  Based on my understanding of what was done I would not expect this to be as accurate a method of assessing emissions as other measurement based studies involving more continuous measurements or using aircraft or mobile measurement methods.  Some of the assertions in the results of the paper are not sufficiently supported in this work though they may be accurate.  There are several grammatical and spelling errors throughout the paper that should be corrected.  I would recommend that this paper requires major revisions before being accepted to ACP.

Major comments:

Section 2.2: This section needs more detail on the operation of the instrumentation. How were the systems calibrated? How did you ensure measurements were consistent when the location of an instrument was changed?  The sampling periods are very short, how did you ensure these are representative?

L55: I disagree with the statement that uncertainties are rarely assessed.  There are many publications in the literature where uncertainties are thoroughly assessed for top-down emissions estimates.  The two papers cited to support the claim that uncertainties are not assessed are over 10 years old.

L123-126: This assumption is not commonly made in other papers using in situ measurements to do mass balance emissions estimates.  Typically, measurements are taken upwind or out of a plume to determine a background concentration.  All the citations in this section are for satellite-based emissions assessments, which this paper is not, so they are not the most appropriate comparison for this work.

Section 2.4: The citations for the mass conserving approach proposed here all direct to previous satellite analyses but more information could be provided in this paper about how the approach is also applicable to in situ emissions that are not column based.

Section 2.5: Further details of the uncertainty analysis should be added.  The section only states that uncertainty analysis was done and that the results assigned less than 5% to the input variables but does not describe how this was determined.

L400: Which emissions are considered in this average? All north and west sites, some subset?  How can we equate the emissions calculated from the measurements at sites 1km from the site with those made at a site 5km away?  Though both may be downwind, the site further away will experience more dilution and thus will always have a lower emission rate calculated from this point unless you measure along a track downwind of the site rather than at a single point to ensure you are capturing all emissions.  From the descriptions provided in the paper I do not understand how the rationale for combining emissions calculated from measurements at all the sites into one average.

L418: I’m not sure it is fair to say this represents higher sampling diversity. The sampling frequency is higher but all measurements took place over just a 2 week period where satellites have a wider variety of measurements seasonally and annually.

Minor Comments:

L35: Should be reworded to say “Emissions from fossil fuel are one of the largest sources of anthropogenic methane”

L37: Should be reworded to say “Coal mines contribute up to X% of China’s CH4 emissions”

Figure 3: Line plots are not ideal for wind direction, would recommend using something else

L135: Recommend showing the meteorological stations that were used on the map in Figure 2

L138-139: Were all wind directions used to calculate the statistics?  Wind directions are often unreliable when wind speeds are very low.

L142: Please provide more information on how temperature and pressure were measured

L181: What is u? (lower case u has not been defined)

L184: Would recommend a more recent reference

Figure 6: Wind speeds are quite low here, what is the uncertainty in these wind directions due to the low wind speed?

L249-251: Sentence is confusing

L296: Figure 10 does not have letters labelling the panels

L402: Suggest showing a figure of the fat tail distribution

L419-421: Not really supported that this is the only likely reason why you did not see the expected distribution for the 2^nd mine.

L422-424: Only 2 coal mines were measured in this study. That’s not enough data to make this claim.

L508: Recommend citing the chapter so people can easily find this information as it is the basis for the paper.