The authors present a very novel ground-based observational study to estimate power plant CO2 emissions. Passive plume-mapping hyperspectral instruments have been deployed from many suborbital and orbital platforms, but utilizing a ground-based spectrometer for this plume-mapping use-case is quite new and exciting. The manuscript itself is very clear and all steps from observation to emission quantification are clearly described. The manuscript should proceed to publication, though I have a few minor comments, which I detail below.

1. Is the dimension of your covariance matrix sufficient to constrain (i.e., not underestimate) CO2 concentration in the CMF algorithm? Reading from the text, it appears that a the dimension of your data cube is 286 x 384 x 288 - with 286 being the number of frames. How many active bands do you use in your retrieval? If it's 6-7nm spectral sampling between 1900-2100, that would roughly 30 bands, so a 30x30 dimension covariance matrix. Are 286 elements sufficient? Previous studies have found that too few pixels (aerial hyperspectral imagers) in the along-track direction can result in concentration enhancements that are biased low. 

2. How much of the uncertainty comes from your fit mask? An attractiveness of your approach is that you only need a statistically representative sample of pixels within the plume to make an assumption about emission rates. Why consider the mask from the simulation? Looking through the plume masks in the main manuscript and the SI, seems like many of the masks incorporate areas of null enhancement within the observation. Is this biasing any of your results? Is there much of a difference if you use an observation only plume mask?

3. Figure S22 - you speak in the manuscript of the inability to get a good emission estimate on 2022-05-13 and point to problems with the width scaling factor. Curious however if you think another quantification approach could be well suited for this problem - many plume-mapping aerial/satellite algorithms use the integrated mass enhancement method, which is mostly concerned with getting the mass of the plume correct and less the transport, rise, etc. Could this be an option for this problem, or not given the nature of the observation?

GENERAL COMMENTS

Estimating the emission amounts is more challenging than detecting the enhancement　due to large uncertainty in wind speed and direction. Retrieving plume heights, wind height and direction is difficult from a snapshot of satellite data.  The measurement technique and analytical method described here are unique. The authors are measuring the plume structure with an imaging spectrometer and a wind lidar and then comparing with a model. The paper demonstrates the difficulty and importance of field measurements. 5-day data set with various weather condition are very valuable for scientific community. Minor revisions will help readers’ understanding. I recommend publication after revisions.

SPECIFIC COMMENTS

(1) Page 2, Line 33, analogue techniques

An additional explanation on “analogue techniques” is helpful.

(2) Page 4, Figure 1

Descriptions such as the height of the chimney, distance between three chimneys, and distance between spectrometers and the chimneys in the figure or the figure caption will helpful.

(3) Page 8, Line 185, “sparsity constraint on enhancement”

A brief description will help readers without referring the paper.

(4) Page 25, Line 507 “Favorable observation condition”

Disadvantage of this observation is a weak scattered light as a light source. Scattering depends on the geometry of the sun, target, and observer.  Is the back-scattered geometry such as “the sun is behind the observer” favorable?

(5) Supplement P2, Figure 2 the right panel

Do colors in the right panel mean something?

TECHNICAL CORRECTIONS

No specific comments.