Evaluation of plume rise parameterizations in GEM-MACHv2 with analysis of image data using a deep convolutional neural network

Axelrod, Kevin M.; Gordon, Mark; Koushafar, Mohammad; Hao, Jingliang; Makar, Paul A.; Fathi, Sepehr; Sohn, Gunho

doi:10.5194/egusphere-2025-4582

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https://doi.org/10.5194/egusphere-2025-4582

Preprints

15 Oct 2025

| 15 Oct 2025

Status: this preprint is open for discussion and under review for Geoscientific Model Development (GMD).

Evaluation of plume rise parameterizations in GEM-MACHv2 with analysis of image data using a deep convolutional neural network

Kevin M. Axelrod, Mark Gordon, Mohammad Koushafar, Jingliang Hao, Paul A. Makar, Sepehr Fathi, and Gunho Sohn

Abstract. The study of plume rise from smokestacks and other pollutant point sources is extremely important for the estimation and modelling of the dispersion of pollutants on regional scales via atmospheric modelling platforms. However, the algorithms which have been used to represent plume rise were based on observations conducted nearly 50 years ago (the semi-empirical dimensional modelling framework of Briggs, 1984), and more recent measurement techniques are available which can be used to generate new data, against which pollutant plume rise theories may be evaluated. A key result of the theoretical formulations based on these past observations is the height reached by the plumes (the process by which they reach that height is known as plume rise). In this work, a previously developed deep convolutional neural network (Deep Plume Rise Network, DPRNet) for determining plume rise from visible RGB images was applied to images taken of a facility in the Athabasca oil sands and compared to the theoretical estimates of Briggs parameterizations as formulated in GEM-MACHv2. On average, the Briggs parameterizations tend to predict plume rise in stable and neutral conditions within 30 %, but consistently overpredict plume rise during unstable conditions by more than 100 %. Further, while Briggs parameterizations predicted diurnal variations in plume rise, no such variation was observed by the image analysis. The parameterizations could be improved reducing dimensionless constants by factors of 2 and 6 in neutral and unstable conditions, respectively. The plume height data have been shown to provide a significant resource for plume rise theory evaluation and development.

Received: 17 Sep 2025 – Discussion started: 15 Oct 2025

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Kevin M. Axelrod, Mark Gordon, Mohammad Koushafar, Jingliang Hao, Paul A. Makar, Sepehr Fathi, and Gunho Sohn

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RC1:
'Comment on egusphere-2025-4582', Anonymous Referee #1, 21 Nov 2025 reply
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?

Reply
Citation: https://doi.org/10.5194/egusphere-2025-4582-RC1
CEC1:
'Comment on egusphere-2025-4582 - No compliance with the policy of the journal', Juan Antonio Añel, 07 Dec 2025 reply

Dear authors,

Unfortunately, after checking your manuscript, it has come to our attention that it does not comply with our "Code and Data Policy".

https://www.geoscientific-model-development.net/policies/code_and_data_policy.html
First, one of the links that you provide to store part of the assets necessary to replicate your work does not correspond to an acceptable repository according to our policy. This is the case of Borealis.
Second, you have not provided the code for the deep convolutional neural network that you use in your manuscript, which is mandatory according to our policy.
Therefore, the current situation with your manuscript is irregular. Please, publish your code and data in one of the appropriate repositories according to our policy and reply to this comment with the relevant information (link and a permanent identifier for it (e.g. DOI)) as soon as possible, as we can not accept manuscripts in Discussions that do not comply with our policy, and given the no compliance of your manuscript, it should not be accepted for Discussions or review in our journal.
I must note that if you do not fix this problem, we cannot continue with the peer-review process or accept your manuscript for publication in our journal.
Juan A. Añel

Geosci. Model Dev. Executive Editor

Reply

Citation: https://doi.org/10.5194/egusphere-2025-4582-CEC1
- AC1:
  'Reply on CEC1', Mark Gordon, 09 Jan 2026 reply
  
  We thank the editor for noting the omission of the required code and the use of a non-compliant repository. We have addressed these points as follows…
  The Borealis dataset has been duplicated with an exact copy on Zenodo. To avoid confusion and to make the duplication as transparent as possible, the same DOI is used for the new Zenodo dataset: https://doi.org/10.5683/SP3/WZVZBV. Currently this DOI links to the Borealis site. In the Borealis metadata, there is a link to the Zenodo dataset: https://zenodo.org/records/18087309 and there is an explanation of the duplication on both the Borealis and Zenodo sites. [As an aside: The Borealis repository is working to guarantee long-term preservation for future publications.]
  The Neural Network (DCNN) code has been added to the FRDR dataset in Version 2 which has the following DOI: https://doi.org/10.20383/103.01559.
  We hope that this satisfies the requirements. Please let us know if further modifications are needed.
  
  Reply
  
  Citation: https://doi.org/10.5194/egusphere-2025-4582-AC1
  - CEC2: 'Reply on AC1', Juan Antonio Añel, 11 Jan 2026 reply
    
    Dear authors,
    Many thanks for your reply. We can consider now the current version of your manuscript in compliance with the Code and Data policy of the journal. Please, if eventually the Topical Editor decides request further review of your manuscript or accept it for publication, modify the "Code and Data Accessibility" section in your manuscript and replace the link and information for Borealis with the information for the Zenodo repository.
    Juan A. Añel
    Geosci. Model Dev. Executive Editor
    
    Reply
    
    Citation: https://doi.org/10.5194/egusphere-2025-4582-CEC2
RC2:
'Comment on egusphere-2025-4582', Anonymous Referee #2, 09 Feb 2026 reply
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:
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.

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.

Section 2.2 would benefit from a brief summary of the DCNN-based framework to help readers better understand the methodology.

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.

In Figures 9 and 10, why are the data for Manual/Visible/Unstable and Manual/Exp Fit/Unstable not shown?

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.

Reply
Citation: https://doi.org/10.5194/egusphere-2025-4582-RC2

Kevin M. Axelrod, Mark Gordon, Mohammad Koushafar, Jingliang Hao, Paul A. Makar, Sepehr Fathi, and Gunho Sohn

Data sets

Smokestack Plume Images and Plume Identification Masks M. Gordon et al. https://doi.org/10.20383/103.01448

Model code and software

Code and data for the calculation of plume rise M. Gordon et al. https://doi.org/10.5683/SP3/WZVZBV

Kevin M. Axelrod, Mark Gordon, Mohammad Koushafar, Jingliang Hao, Paul A. Makar, Sepehr Fathi, and Gunho Sohn

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Short summary

The is a study of the plumes that rise from smokestacks. Knowing how these plume behave helps predict downwind pollutant concentrations. We use photos over a 2-year period to investigate how these plumes rise under different conditions and compare this to a commonly used model parameterization. It is found that the equations used to model plume rise in current models do well for some condition, but these equations can over-predict the plume rise, typically during the day when it is hot.


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