Since the preprint is technical, it may be better suited for the "Atmospheric Measurement Techniques" journal.

The study of Galkowski et al. addresses the challenges of quantifying emissions from single plume images  from airborne or space-borne remote sensing instruments in the presence of turbulence. The problem arises from the stochastic nature of turbulence, which adds uncertainty to flux estimates that is very difficult to mitigate. Even the most realistic and highest-resolution model can only reproduce the statistics of turbulence, but not the exact state of turbulence at any given time as observed during a satellite or aircraft overpass.

Several previous studies have taken note of this issue but have not addressed it systematically. The study presented here is therefore a very valuable and timely contribution to the topic.

However, the study has a few issues described below under "major points" that need to be addressed before it can be considered for publication.

Major points

• The introduction is too long and not well tailored to the study. It explains at length the process of national inventories and the usefulness of top-down methods, but it falls short in explaining the fundamental issue associated with the turbulent nature of plumes and what this study exactly contributes to the problem. I see little value of sentences like those on lines 21-24 or 37-45 for the scope of this study.
  
  There is also quite a few unnecessary filler words like "moreover" or "nevertheless" and awkward formulations like "multiple adverse effects across numerous domains" or "the availability of accurate data is insufficient to provide estimates with low enough uncertainty". Low enough for what? What are "robust studies" (line 54)? Do space-borne platforms really provide "accurate information" (line 50)?
• Section 2.3 introduces the tagged tracers, but it is not explained at this point why they are used and what additional information can be obtained from them. Only stating that they are used "to study the effects of atmospheric turbulence on source estimation inference" is not enough. The purpose of these tracers becomes clear only later, but it should already be motivated here or in the introduction.
• The utility of wind speed at emission point and time introduced in Section 2.8.2 is not clear and not sufficiently well motivated. The apparent emission at location x_i is determined by the total mass of the tracer at this cross-section and the effective wind speed (Eq. 3). Why should this quantity be related to the wind speed at the emission point? This is not explained at all.
  
  Deviations of the wind at the emission point from u_eff could simply be used to describe the magnitude of turbulent fluctuations. Approximately the same turbulence should be present at all downstream locations x_i where the apparent emission is determined. This fluctuation could thus be used as a measure for the variations in the estimates of apparent emissions. However, with increasing distance downstream, the plume becomes wider and thus the flux is no longer determined by the wind at a single location but by the winds along the whole cross-section (which may extend over multiple turbulent eddies).
  
  What could potentially be interesting is to link the wind speed at the emission point to the mean transport speed of the puffs from their release to the locations x_i. Initially, they are identical but with increasing distance the correlation will likely be lost.
• An aspect that would have been useful to explore is whether the impact of turbulence diminishes with increasing distance from the source. This is to be expected because the dispersion of the plume reduces spatial gradients (which reduces turbulent cross-gradient fluxes) and because the lateral extent of the plume increases with distance, such that the plume extends over multiple eddies in across-plume direction. As a consequence, it might be beneficial to estimate emissions only from cross-sections at larger distances. On the other hand, a lower number of cross-sections reduces the advantage of averaging.

Minor points and corrections

Line 3: delete "status of the" (repetition of "status")

Line 7: "Realistic assessment" not "Realistically assessment"

Line 8: Suggestion: use ".. the impact of the stochastic nature of .." instead of "stochastic impact"

Line 9: "on the estimation" not "estimations"

Line 11: turbulent structures in a plume are not "persistent"

Line 12: "… method, on the order of " (replace . by ,)

Line 14: These are just temporally tagged tracers. I don't see the novelty. This is by far not the first study using tracers tagged by the time of emission.

Line 15: ".. and TO explain why"

Line 20: "represented by A 1.5°C temperature increase"

Line 28: Is "accurate" not enough instead of "accurate, precise .."?

Line 45: Unclear what you mean by "have also been recognized"

Line 47: Delete "accurately", not necessary.

Line 50: Delete "accurate". It is clear that they aim to provide accurate information, but they do not necessarily achieve that, and it remains unclear what "accurate" means without a definition.

Line 58: Another important reference for urban mass balance approaches is Cambaliza et al. (2013, https://doi.org/10.5194/acp-14-9029-2014)

Line 61: Not very clear what is meant by "some instrumentation", and "applied" is not the right verb. There are important airborne remote sensing instruments used for emission quantification missing in the references, notably AVIRIS-NG and MethaneAir. Furthermore, it's not clear that by "orbiting platforms" you mean satellites.

Line 63: "In fact" unnecessary.

Line 64: Change to "OCO-2/3 observations were used"

Line 68: CarbonSat was planned as an Earth explorer mission, not an operational mission.

Line 70: Maenhout et al. (2020, https://journals.ametsoc.org/view/journals/bams/101/8/bamsD190017.xml) would be the better reference

Line 75: "applications IN the past". And change to "more recent developments"

Line 81: Why does variability stem from the "estimation method"? Please be more specific.

Lines 85-86: Gerbig et al. and Lin et al. are good references for some problems of transport uncertainty (PBL height, uncertainties in wind speed and direction (not turbulence!), but they are not good references for addressing issues related to the stochastic nature of turbulence.

Line 87: Similar to what? Similar to Gerbig et al. or similar to the present study?

Line 92: Change to "insight into the mechanisms". What is a "detailed mechanism"? Also change to "to shed light".

Line 93: "are using … simulations" (not simulation)

Line 97: Again "detailed" is unnecessary.

Line 100: "on the planet" is enough.

Line 119: change to "at scales ranging from global to local"

Line 121: "Employed" rather than "deployed" the WRF model.

Line 140: 6 km is outside the grey zone. The upper limit is rather around 2 km, which I think would also better correspond to the cited publication of Honnert et al.

Line 150: It would make things clearer if you write "time-varying Cartesian coordinate system"

Line 159: "single point source" rather than "single-point source". How many sources are there in reality, and why is it justified to treat them as a single source at 400 m resolution?

Line 165: Change "are and" to "are"

Section 2.4: Why is the period 9 – 10 April 2020 used in this study? This should be better motivated.

Line 178: On line 148 it was stated that output is saved at 5 minute resolution, but here it is 1 minute.

Section 2.5: Column average dry mole fractions are frequently used because they are NOT proportional to the total mass of the tracer. Variations in surface pressure and topography are largely eliminated when using dry air mole fractions, whereas they affect the total mass of the tracer.

Line 190: To make clear that n_d is not a density (moles m-3), it should be explained that n_d is the number of moles of dry air in the grid cell at x_i, y_j, z_k. Otherwise Equation 4, which divides by the grid cell area A would be wrong.

Line 192: change to "with THE x-axis .."

Line 194: replace "all the way to orbit" by "to the top of the atmosphere".

Line 197: I don't agree that it is not necessary to extend beyond the model top at 50 hPa, because the total number N_d of dry moles in the vertical column is about 5% larger when extending beyond 50 hPa, which has the effect that the mole fraction enhancements calculated following Eq. 1 become 5% lower (because the weights are proportional to 1/N_d, see Eq. 2).

Equation (3): This equation is only correct if turbulent flux along the x-axis is negligible compared to the advective flux represented by u_eff. Section 3.4 in Conley et al. (https://doi.org/10.5194/amt-10-3345-2017) provides an excellent description of turbulent flux terms versus advection. In case of low wind-speeds, the contribution of turbulent fluxes may not be negligible. Furthermore, it should be more clearly explained that Eq. 3 describes the flux through a plane perpendicular to the wind direction, and therefore integrates along the y-axis.

Line 205: I would call DeltaOmega(x,y) the column-integrated enhancement of CO2 rather than column-averaged. Note that this quantity is not "integrated along the y-axis" (only Phi(x) is).

Line 206: "mimic" is probably the more appropriate term than "reproduce"

Line 208: What formula did Varon et al. use for u_eff? Actually, the way u_eff is calculated is described in more detail on lines 227-230, and I doubt that Varon et al. did it exactly in the same way.

Equation 4: This equation results in units of g/m2, not kg/m2.

Line 215: change to "Applying the above to Eq. 3". Change x to x_i

Line 216: No need to state again that "other symbols are as before".

Line 226: Not clear to me what is meant by "Gaussian plume assumptions". This assumption doesn't seem to be necessary to simply compute a plume centreline.

Line 228: Change to "affecting u_eff"

Line 231: It is unclear at this point what quantities will be correlated against what other quantities and thus why the definition in Eq. 6 is useful. Why do you "also" make use of the apparent emission anomaly? What other things are you using?

Line 238: Change to "dependent on the effective number"

Line 249: Change to "along THE x-axis"

Line 251: This sentence is not quite correct and should be deleted. A particle in a Lagrangian particle dispersion model is not similar to a plume centroid. Particles rather span the whole plume.

Equation 9: Why do you use lower case "c" rather than upper case "C" as in Eq. 4.? Is "c" a different quantity? Is it concentration rather than dry mole fraction. To describe a real center of mass, c_i,j,k in Eq. 9 should actually be the mass of the tracer in grid cell i,j,k rather than the concentration or dry mole fraction.

Lines 257-261: What do you mean by "density function of puff-centroids"? I did not understand these sentences at all. I could only guess what they mean after having read the rest of the paper.

Line 279: "of each" puff?

Line 282: Why Xc and not XC as in Equation 1?

Line 288: Why "also" and not simply "we correlate"?

Line 294: The simulations alone cannot demonstrate that the day was typical, because they extended over 2 days only.

Line 300: Delete "orbiting"

Figure 3: The vertical dispersion (lower left panel) would be better visible when integrating the tracer in across-plume direction rather than showing it only along the centerline.

Line 332: Change to "due to THE moderate sample size"

Line 360: What characteristics should one expect?

Lines 360 – 361: The sentence "The estimated cross-section emissions show typical features" makes little sense to me.

Line 367: Change to "is remarkably similar to that"

Line 371: The result that independent estimates are obtained only every 3.6 km is very relevant in the context of satellite observations. Satellites with coarser resolution will loose useful information that could have been exploited at higher resolution. How do the 3.6 km relate to actual satellite missions?

Line 374: The realism of the WRF-Chem simulations was also evaluated in the Brunner et al. study. What was the conclusion in that study?

Line 377: Change to "section of THE plume"

Line 379: The factor four has little importance, because it entirely depends on the number of cross-sections taken, which in the present study is determined by the model resolution. Here this factor is presented like a general uncertainty amplification factor.

Line 383: change to "using THE GPI method"

Line 392: Unclear what is meant by "same subset". Same as what?

Line 400: A systematic comparison between CSF, GPI and IME methods was recently presented by Santaren et al. (2025, https://doi.org/10.5194/amt-18-211-2025).

Line 404: What about ".. as generally fewer observations over shorter distances are available"?

Line 413: Not quite clear whether vertical or horizontal advection is meant here by "atmospheric advection".

Line 454: Use "can only be higher" rather than "increased". Another source of uncertainty is errors in the observations.

Line 459: Turbulent structures are (usually) not persistent.