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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'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?

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Citation: https://doi.org/10.5194/egusphere-2025-4582-RC1

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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