The paper provides a comparison of the Briggs plume rise parameterisations against a deep convolutional neural network for determining plume rise from imagery (DPRNet).

I felt that there was a lack of understanding of the Briggs formulae. The underlying basis of the Briggs plume rise equations are the governing conservation equations of mass, momentum and heat. Solving these governing equations under specific conditions (buoyancy or momentum dominated, or particular meteorological conditions e.g., zero crosswind, constant buoyancy frequency) leads to the Briggs formulations. The ‘dimensionless constants’ are entrainment parameters. The Briggs formulae are commonly used for predicting plume rise but there are reasons why they may not work well, for example if the assumptions made in deriving the Briggs formulae from the underlying conservation equations do not hold true (e.g., the true atmospheric meteorological profiles may differ from that assumed). Indeed, the authors do make use of a modification for the interaction with the boundary layer top. Other authors have made direct use of the underlying conservation equations, considering the true atmospheric and release conditions (Webster and Thomson, 2002) and more elaborate models do also account for latent heat release from moisture in the rising plume / entrained atmospheric air (Fathi et al., 2025).

I found the text a bit vague in places, a little repetitive and verbose in other places and with many references to supplementary information and over-/under-predictions. It is worth the authors considering what key points / results they would like to present in the main paper and being both concise and precise. In addition, there are quite a lot of typographical errors which, with more care and attention, could have been avoided. All in all, this makes the paper quite hard to follow. Some further details are given in the detailed points below. The conclusion section was, however, well written and provided a good summary.

How are the Briggs formulae for momentum and buoyancy applied to calculate plume rise for plumes with both momentum and buoyancy? Are they just added together and, if so, is this appropriate? The calculation of the proportion of the plume rise due to momentum in section 3.2.3 assumes this simple addition but I’m not sure this is true in reality. Understanding the underlying conservation equations and the derivation of the Briggs equations (and the assumptions made) may shed some light on this.

Presumably DPRNet has been trained on an earlier dataset? What dataset was this and will the trained model be applicable to the images processed here? What about uncertainties / errors in the observations? Line of sight and plume direction are mentioned. Indeed, a sensitivity analysis of the wind direction on the determined observed plume height is conducted. Two methods for obtaining the plume rise from the observations are used, but conclusions are drawn on the performance of the Briggs formulae to these observations without consideration of uncertainties in the observations. Indeed, the authors state under- or overpredictions which are small compared to the uncertainties, say, in the observed plume rise height due to the wind direction presented in section 3.5.1.

Is Figure 3 in the horizontal plane? Is this a valid assumption? I can imagine that the plume height may not be at the same height as the camera. The caption mentions a similar transformation in the vertical plane to determine the plume rise height. A reference is given but it would be helpful to give more detail here on the calculation, what is measured (presumably SP’), what is calculated (presumably SP) and how.

Minor points:

Some minor points on the text are listed here:

• Abstract: Adding a couple more words in places will make this more readable and standalone, e.g., ‘facility’ is vague – what type of facility? GEM-MACHv2 – what type of model is this?
• The Webster and Thomson (2002) paper compared ground level concentrations, not plume heights.
• Line 106: Does ‘averaging’ mean an average of the maximum (or minimum) daily temperatures or a daily average? Without clarification, I would assume daily averages (and if that is the case, I do not think any changes are required). What is “ECCC”?
• Line 216 “(highlighted by the green star in Fig. 1)” – this reads as though it applies to “the largest smokestack” rather than the Buffalo Viewpoint.
• Line 131: Repetition of ‘in total’.
• The yellow ‘plume rise’ text on Figure 2 is hard to read on screen (and impossible to read on paper).
• The notation for plume rise is confusing (lines 168 & 175, caption Figure 2). Can you use the same notation for the figure and text? Furthermore, what does the subscript “e” refer to (Figure 2 caption)? In Figure 2’s caption, the notation used for plume rise height and plume rise distance seem too similar and will easily cause confusion. Furthermore, the text adopts different notation for the plume rise obtained from each method, but Figure 2 does not. Yet on line 185, there is mention of two sets of results for Delta h_{obs}, rather than Delta h_{obs} and Delta h_{pixel}. Is one Delta h_{obs} = 0.99 Delta h_{pixel}? Would it be helpful to add notation to figures 2d and 2f? That said, I think the ‘plume rise’ in the text and figure 2 are not the same thing (lines 182 onwards) so perhaps different notation is required. In this case, I won’t deny that this might be difficult, but can this be less confusing / better explained?
• Line 217: “Using this model” – what is ‘this model’? GEM-MACHv2? (In which case there is a jump from Briggs parameterisations.) Or the ‘plume rise calculations’? (In which case, ‘model’ doesn’t seem the right word.)
• Heights (e.g., line 237) are presumably above ground level (this should be stated). What is the elevation difference between the monitoring stations and the stack location? Is this of relevance?
• Should GEM-MACH (lines 264 and 296 and other places) be GEM-MACHv2?
• Equation 7: if T_s < T_a then the plume would be negatively buoyant (i.e., dense).
• Equation 9: H_{ast} is not a convective velocity – check the units.
• Line 324: ‘vertical extent’ – this only makes sense for a ‘bent-over plume’ rather than a vertically rising plume. Indeed, the entire study probably only makes sense for such situations. I did not, however, think this was clear early in the paper. In fact, “bent-over” is not mentioned until line 366. I don’t follow either why the vertical extent is assumed to equal the plume rise height (Delta h). Where does 2/3 H come from on line 325? Also, the discussion of removal from the analysis of vertically rising plumes occurs on line 513. Similarly line 335 mentions momentum. It would be clearer to mention the focus regarding bent-over / vertically rising and buoyancy- / momentum-driven(or both) early in the paper.
• Is the limitation of the plume top by H realistic? Depending on the buoyancy of the plume and the strength of the inversion at the top of the boundary layer, it is possible that the plume could punch through into the stable atmosphere above the boundary layer.
• I do not think the use of the word ‘fumigation’ is correct. Fumigation occurs when material is trapped in a stable region (for example in the stable atmosphere above the boundary layer) and is then subsequently mixed down to ground when it is incorporated into the boundary layer, say, as the boundary layer grows in depth due to the diurnal cycle.
• Line 331: ‘and the other models’ – this is vague. What other models?
• Line 332: Can you say what the layer-based approach is? What are the layers? Or what is the purpose of it? Is it an approach to account for the true atmospheric meteorological profile?
• Line 336: ‘This is the parameterization’ – what is ‘this’ here?
• Line 338: ‘both with momentum’ – what does ‘both’ refer to here? ‘both with momentum and buoyancy’?
• Line 388: ’50 pixels’. Is this in any direction (e.g., could it be vertically) or is it a horizontal distance?
• Could the authors give a summary in the main text of the conclusions of the sensitivity analysis in the supplementary sections (e.g., to the choice of the pixel box or of the wind direction cutoff). Furthermore, how does this fit in with the uncertainty analysis in section 3.5?
• There is repetition of the selection criteria (lines 366-, lines 420-, lines 449-, lines 571- (repeating 528- note also the numbers after removing images for which the start point is too far from the stack should agree but do not (lines 529 (14431) vs 572 (11431))).
• There is much mention of over- or underprediction but often the values agree within the quoted uncertainty. The authors are comparing the mean values (without considering the uncertainty) but this isn’t always clear. Furthermore, in some places the text states an underestimation when the mean is greater (i.e., if anything it should be an overestimation) (see lines 456, 459-460 (stable conditions) and 550 (stable conditions).
• Line 454: The R^2 value of 0.93 +/- 0.04 (coefficient of determination) refers to the fit between the plume midpoint and the exponential fitted curve, but this isn’t clear here. Furthermore, using the same notation (R^2) as ‘correlation’ between the DCNN and Briggs plume rise adds to the confusion.
• Line 486: ‘likely to be flatter’. On the other hand, for bent-over plumes, the maximum height of the plume is likely to be some distance downwind and therefore possibly more likely to be rejected by the distance constraint.
• The mention of with and without momentum applies just to the Briggs formulation. This is not clear (e.g., line 480 or line 507), and one could alternatively assume that some knowledge of whether the plume was buoyancy driven or had a significant momentum component was used to select examples. In particular, the captions for tables 4 & 5 (and 8 & 9) are poorly worded: ‘Average plume rise for manually selected images without plume rise due to momentum…’.
• Line 516: ‘investigated’ should be ‘investigate’, line 518: ‘given Section S1’ should be ‘given in Section S1’, line 547: ‘overpredict predict plume rise’ should be ‘overpredict plume rise’.
• The uncertainty (95% confidence interval) in the plume rise is much less in the ensemble case (section 3.3) than in manual image selection study (section 3.2). Presumably this is related to the number of data points. Is this worth a comment?
• Line 543: Would not the consideration of latent heat lead to an increase in plume rise (with condensation of plume moisture leading to a release of latent heat)? This seems contrary to the text here.
• Lines 581-582: The % values are not in agreement with Figure 8a. Similarly Figure 8b lines 594-595 % value and text.
• Line 624: ‘better agreement’ – in neutral conditions Table 6 shows better agreement.
• Line 640: ‘a larger underprediction’ – it’s an overprediction in unstable conditions
• Line 657: new sentence starts mid-way through a sentence ‘largest overall discrepancy’
• Line 710: ‘underprediction’ should be ‘overprediction’
• Line 719: ‘in Section 4’ – is this correct? Section 4 has not appeared yet and, in fact, is the conclusions.
• Is the data in Figure 10 comparable? In other words, are the same image datasets used for both the exponential fit and visible?
• Line 779: ‘dawn at dusk’ should this be ‘dawn or dusk’?
• Line 780: ‘hour.,’ should be ‘hour,’.
• Line 781: ‘Tables and 6 and 8’ should be ‘Tables 6 and 8’.
• Lines 809-810: ‘account friction velocity’ maybe ‘account for friction velocity’?
• Lines 811 and 825: What is the basis (other than fitting to your observations) for changing the constants in equations 10 and 12? Where do the original constants come from?

This study uses a deep convolutional neural network framework developed by Koushafar et al. (2023) to analyse images of smoke plumes from an industrial site, comparing the plume rise estimates against theoretical predictions using Briggs parameterisation. The authors concluded that Briggs consistently overpredicts plume rise during unstable conditions with high wind speeds, and that neural network-based plume rise estimates show no diurnal variability compared to those from Briggs parameterisation.

The application of deep convolutional neural networks to plume image analysis represents a methodological advancement for estimating plume height over extended time series compared to previous studies relying on in-situ or flight measurements. Based on their results, the authors proposed revised values for the Briggs parameterization to improve plume height estimation accuracy. Overall, this is an interesting study that advances the methodology for estimating plume rise through the application of deep convolutional neural network. However, the manuscript would benefit from improvements in language clarity and revision of several figures to enhance readability and accessibility.

Major Comments:

1. The paper would benefit from more precise language to improve readability and flow. The text contains repetitive wording in several sections. Additionally, the citation style is inconsistent throughout the manuscript. I have identified some of the specific citation issues in the minor comments below, but the authors should conduct a thorough review of all in-text citations.
2. In the introduction, the authors reference several previous studies that estimated plume rise and compared results to Briggs parameterization (e.g., Gordon et al., 2015; Akingunola et al., 2018; Gordon et al., 2018; Fathi et al., 2025). However, the distinctions between these approaches are not clearly articulated. What are the potential reasons for the over- or under-estimation of plume heights compared to observations? Furthermore, the paper lacks substantive comparison with these previous studies. The limited comparisons provided (e.g., Lines 542-545) would be strengthened by incorporating more quantitative analysis.
3. Section 2.2 would benefit from a brief summary of the DCNN-based framework to help readers better understand the methodology.
4. Several figures are not colorblind-friendly, including Figures 1, 2, 9, and 10. The authors should revise the color schemes to avoid using red and green simultaneously in the same plot. The resolution in Figure 2 is very low and the annotations are not easy to read because of the colour scheme chosen.
5. In Figures 9 and 10, why are the data for Manual/Visible/Unstable and Manual/Exp Fit/Unstable not shown?
6. The authors can highlight the newly fitted dimensionless constant values in the conclusion, as these values could be valuable for future studies applying this parameterisation.
   
   
   
   

Minor comments:

• Line 33, be more specific about the dimensionless constants
• Line 34 and 37, repetitive about the observations made 
• Line 40, missing citation for Moore
• Line 48, what kind of surface concentrations measurements?
• Line 52-55 used very similar wordings to Koushafar et al. (2023). The authors should consider paraphrasing the sentences.
• Line 56, missing comma in citation
• Line 60, check citation style
• Line 65, the authors commented that the studies referenced are relatively short in duration. Is it on the scale of hours to days? The authors can be more specific about “long term data collection” here, and mention seasonal variations in atmospheric conditions that may affect plume rise theory.
• Line 68, since the main stack is already defined here, suggest keeping the terminology throughout the manuscript
• Line 73, check citation style
• Line 73-74, subscripts for CO2, and also elsewhere throughout the paper (e.g., SO2)
• Line 77-78, “most of the emission” is a bit vague. What’s the percentage of emission from the main stack?
• Line 78, it is unclear what is ordinary operating condition
• Line 80, this paragraph is disconnected from the previous paragraph. 
• Line 83, what are traditional methods?
• Line 83, check citation style
• Line 90, I find the wordings “determine plume rise” not very clear in this sentence. 
• Line 91, the authors mentioned that Koushafar et al. (2023) used the same initial dataset to evaluate DPRNet. Is the image data used in this paper part of the training dataset or validating dataset? 
• Line 99, to compare with the parametrisation -> to compare with the Briggs’ parametrisation
• Line 103-108, a lot of the description of the research site is not relevant to the analysis. The authors should consider revising this paragraph.
• Line 108, missing fullstops.
• Line 132, main stack already defined earlier
• Line 133, not necessary to mention 600 feet
• Line 151, move the sentence out of the bracket.
• Line 168, missing comma
• Line 223, main stack
• Line 236, Figure 1 instead of Figure 2
• Line 455, The numbers look comparable between DCNN-analysed and Briggs-predicted plume rise for the average values and the numbers are also within uncertainty. Why does it indicate Briggs underestimate plume rise on average?
• Line 458-459, From Table 3, Briggs under predicts the plume rise for neutral condition and over predicts the plume height for stable conditions. It is unclear why the authors concluded that Briggs generally under predicted plume rise.

This study highlights that the Briggs plume rise equations struggle with high-resolution imagery and parameterisation. The authors use a Deep Convolutional Neural Network to generate masks from visible-wavelengths images and compare the obtained geometrical parameters with theoretical calculations from Briggs equations. Their contribution represents a good advancement in the study of this kind of plumes which are usually analysed through more classical in industrial applications. Their manuscript is to be considered close to publication standard once a couple of concerns are addressed.

Specific comments:

1. The authors should clearly state at the beginning that they are correcting the heights they measure for the wind direction. Moreover, they only refer to Koushafar et al. (2023) for the wind correction, without explaining the precess with any equations. Also in that paper, if used as reference for the wind correction, there is a lack of information. I would suggest to check that the equations used by the authors correspond to those published in Snee et al. (2023; 10.30909/vol.06.02.447458), a paper in which the wind correction is applied to correct height and width measurements of volcanic plumes. For example, in lines 200-201 the authors stated that only the wind direction and the camera-smokestack distance are necessary for the wind correction, but normally also field of view, inclination and camera orientation are normally required to perform a complete wind correction. Also, at lines 686-688, a bent-over plume with wind blowing towards the camera normally gives a plume height calculated in the wind-corrected plane that is smaller than that calculated in the image plane (see Snee et al., 2023, for a description of the wind correction applied to plume-shaped objects and for some examples). Also, I am not sure to understand the purpose of lines 682-686.
2. I would not use the wording "real-life" referred to the position (lines 199, ). It is more a corrected projection on a plane corresponding to the wind direction than its actual position (as the wind direction can have uncertainties and the reconstruction is still in 2D). Moreover, I think Figure 3 might be misleading in this sense, as the plume is represented in 2D in birds-eye view, but this is not a real information obtained from the camera.
3. Lines 463-464: If my understanding is correct, you are not comparing the same dataset (60 plumes vs only 26 plumes). I guess this might also play a role on this lower heights determined with exponential curve fitting. This needs at least to be stated, or, better, the comparison should be made between the same dataset.
4. Lines 811-812 and 825-830: Dimensionless constants usually represent physical relationships. Reducing them by a factor of 2 or 6 implies that there is an important change in the dynamics. Also, this parameterisation is site-specific. All this might be at least stated in the manuscript, but has strong physical implications.

Minor comments:

1. Line 79: I suggest to describe better the composition of these plumes. Are they only water vapour plumes? Do they contain other species?
2. Lines 126-129: The sentence is maybe unnecessary, as it seems the authors are not correcting the plume rise measurements for the wind direction, which they are actually doing. I would consider erasing the sentence or already specify that the values are actually wind-corrected.
3. Lines 183-184: I would use "plume position in the image plane to plume position in a wind-corrected plane", as this is still a planar correction (not a 3D reconstruction)
4. Figure 2: I suggest adding the notations for plume rise height and distance on the images, as well as a white/black buffer around words to improve readability. In the caption, the notation of plume rise height seems to be wrong, while that of the distance is not in math format.
5. Line 221: I would use "physical units" instead of "real-life distances", as it is about the conversion from pixel units to physical units (i.e., meters)
6. Equation 4: Is dividing by L correct? Or is it just the notation that is misleading?
7. Lines 287-288: Why data points are only available every three hours? What ERA5 product has been used? Also, ERA5 datasets normally have a citation.
8. Lines 306-317: Could the authors motivate why they chose these particular formulations? Do other formulations exist for smoke plume rise and why they were not chosen?
9. Line 357: Is it worth adding the variation for hour of day to the supplementary materials?
10. Figure 5: I would add the camera orientation value on the figure, maybe also with a small arrow pointing towards that direction to show it effectively
11. Line 395: I would change "plumes that are perpendicular to the camera orientation" for "having propagation axis that are close to the perpendicular to the camera orientation", as the plume has an extension and because also plumes twith axis hat are close to the perpendicular are used in the study.
12. My general feeling is that a lot of tables could be merged (for example tables 2-5 and 6-9) to improve readability.

Technical corrections:

• Line 108: Missing point at the end of the sentence
• Lines 338-340: Maybe change the structure of the sentence for readability
• Lines 341, 343, 345: I would move "plume rise becuase of momentum" before the bullet point for clarity
• Lines 448-451: This sentence is redundant, as it is the same processing applied in section 3.2.1, consider removing it
• Lines 572-576: This sentence is unnecessary, as you could just mention that with the applicaiton of the plume rise distance the remaining images are 1514 (from the 3785 obtained in section 3.3.1 with the other filters)
• Line 647: missing comma after "average"
• Line 779: Missing "and" between "dawn" and "dusk"?
• Line 780: There is an extra point after "hour"