the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 13 Jul 2026
Evaluation of area-source methane-emission quantification by Uncrewed Aerial Systems using Gauss’s law
Abstract. Quantifying methane emissions from lakes and wetlands remains a persistent challenge. Existing measurement approaches commonly sample only at distinct points (chambers) or integrate over poorly defined and meteorology-dependent footprints (eddy covariance, flux-gradient methods). A different framework for methane-flux estimation from lakes and wetlands entails an aerial cylindrical mass-balance technique in which an aircraft with methane and wind sensors circumscribes a methane source. This creates a control volume, allowing for the enclosed flux to be determined with Gauss's divergence theorem. The suitability of this methodology has not been evaluated for uncrewed aerial systems (UAS). We conducted an observing system simulation experiment (OSSE) that coupled a Gaussian-plume forward model with a simulated Gaussian cylindrical-flux estimation over an idealized methane-emitting lake. Across three experiments, we tested the effects of (i) receptor (points of collocated methane and wind measurements) grid resolution, (ii) methane contamination from a nearby upwind lake, and (iii) the effects of sampling under evolving atmospheric stability, on retrieval accuracy and precision. We introduce nondimensional variables to represent the estimation error from these three effects for a broader set of system configurations. Vertical-receptor resolution was the dominant control on retrieval accuracy, while azimuthal resolution primarily affected precision relative to the vertical resolution. When a nearby lake (~0.1–10 km) with an upwind-methane source was introduced to the simulation, this induced a systematic negative bias compared to the true methane flux. Under prescribed atmospheric-stability transitions, retrieval accuracy degraded monotonically with increased mission duration, with the shortest flights (30 min) preserving the highest flux retrieval accuracy across all stability transitions tested. This is because shorter flights more closely capture a snapshot of the environment before changes in the atmosphere can occur, which can skew methane-flux estimates. However, repeating short flights and averaging the resulting source-flux retrievals improved precision over single flights even across longer (12 h) atmospheric stability transitions. Within our nondimensional framework, signal-to-noise increased retrieval accuracy, but by an amount that was determined by the geometry of the measured lake and observations. The OSSE framework presented here provides a quantitative basis for planning UAS methane-flux-measurement campaigns using cylindrical mass-balance over lakes, wetlands, and possibly other heterogeneous natural methane sources.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-3109', Anonymous Referee #1, 19 Aug 2026
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CC1: 'Comment on egusphere-2026-3109', Colin Wong, 18 Sep 2026
In the paper, the authors refer to and apply “the Conley et al. (2017) method (hereafter the cylindrical-flux method)”. However, although Conley et al. (2017) described their method as “novel”, their paper overlooked some relevant earlier publications. In 1980, Milly (US patent 4,204,121) described a “cylindrical method of quantifying fugitive emission rates from pollution sources”. In addition, Wong and Wyles (2012) and Wong & Ramkellawan (2013) described and applied a fugitive emission rate measurement method that can involve encircling a source and that can be practiced on any basic control volume shape, including cylinders. The methods described in these three earlier publications have commonalities to the method described in Conley et. al.’s (2017) paper. Therefore, it is recommended that the authors include in their paper an explanation of the features that make “the Conley et al. (2017) method” sufficiently novel that renders it unnecessary for the authors to reference these earlier publications. If the Conley et al. (2017) method is not sufficiently novel, then to preserve the integrity of the authors’ research, attribution to the relevant prior literature is necessary.
Note that the above comment is not intended to imply that Conley et al. (2017) did not provide a meaningful scientific contribution, as it is recognized that they presented a different mathematical treatment and analyzed certain influences such as the minimum number of passes. Rather the above comment refers to the physical and calculation process to obtain a fugitive emission rate measurement.Milly, G. 1980. Cylindrical method of quantifying fugitive emission rates from pollution sources, US patent 4,204,121.
Wong, C. and R. Wyles. 2012. Mapping concentrations of airborne matter to quantify the fugitive emissions discharge rate from a landfill. Greenhouse Gas Meas. Manag. 2(1):50-60.
Wong, C. and J. Ramkellawan. 2013. Calibration of a fugitive emission rate measurement of an area source. J Air Waste Manag. Soc. 63 (11):1324-34.Citation: https://doi.org/10.5194/egusphere-2026-3109-CC1 -
RC2: 'Comment on egusphere-2026-3109', Anonymous Referee #2, 14 Oct 2026
This manuscript by Rozmiarek et al. presents an observing system simulation experiment (OSSE) to evaluate the performance of a cylindrical mass-balance approach for quantifying methane emissions from area sources using uncrewed aerial systems (UAS). The authors systematically investigate the effects of spatial sampling resolution, contamination from nearby sources, and atmospheric variability on flux-retrieval accuracy and precision. The study addresses a relevant methodological challenge in atmospheric methane measurements and provides potentially useful guidance for designing UAS-based emission surveys.
The manuscript is generally well structured and the topic falls within the scope of AMT. However, several methodological assumptions require further clarification and justification, particularly regarding the representation of atmospheric transience and the practical feasibility of the simulated sampling strategy. I recommend that the authors address the following general and specific comments before the manuscript can be considered for publication.
General comments
1. Experiment 3 investigates the effect of atmospheric variability on sequential UAS sampling. However, the Gaussian plume model appears to generate concentration fields based on the meteorological conditions at each receptor sampling time, without explicitly accounting for the transport history of methane emitted at earlier times. Under transient atmosphere conditions, the methane concentration at a given receptor depends not only on the instantaneous wind field and atmospheric stability but also on the preceding transport and dispersion conditions. Furthermore, changes in plume structure may introduce a non-negligible storage term within the control volume.
Could the authors clarify how these effects are represented in the current simulation framework? It would be useful to discuss to what extent the reported retrieval errors can be attributed specifically to asynchronous sampling, and how they may be influenced by the quasi-steady-state assumptions adopted in the forward and inverse models.
2. In Experiment 3, the default receptor grid consists of 96 azimuthal positions and 27 vertical levels, resulting in 2,592 receptor locations per complete profile. For a 30-minute flight, the corresponding dwell time is approximately 0.69 s per receptor. However, the simulated instrument operates at a sampling frequency of 1 Hz (i.e., one measurement per second). This implies fewer than one independent measurement per receptor on average for the shortest flight scenario.
While I understand that this study is based on an idealized simulated framework, it would be helpful if the authors could clarify how measurements are assigned to individual receptor locations when the nominal dwell time is shorter than the sampling interval. Furthermore, the authors are encouraged to discuss the potential effects of instrument response time, travel time between sampling locations, and vertical transitions between flight levels on the practical feasibility of the proposed sampling strategy. Since the 30-minute profile is identified as the most accurate configuration, further clarification of its practical implementation would strengthen the operational relevance of the study.
Technical comments
1. Figure 1: The description of the green vertical arrow appears to refer to panel (a) rather than panel (b). Please check the correspondence between the figure panels and their descriptions. In addition, It seems (c) is missing.
2. Line 236: “σfloor = 0.25 ppb is the minimum precision achievable through extended averaging”. I do not fully understand this explanation. Does this value represent an instrument-specific noise floor, a long-term stability limitation, or an empirical averaging limit? Please clarify.
3. Line 365: Equation 23: The Gaussian vertical integral is evaluated over the range from negative to positive infinity, whereas the physical control volume extends only above the ground surface. Could the authors clarify how ground reflection is accounted for in the definition of the effective lateral transport area? Please justify the integration limits used in deriving the characteristic concentration enhancement.
4. Line: 576-577: The authors state that “Across 20 repetitions of the multi-profile flights, the average standard deviation of flux retrieval improved to ±0.30 mg CH₄ m⁻² d⁻¹ for 30 min to 2 h flights.” However, each flight-duration configuration should have its own standard deviation based on the 20 independent realizations. Could the authors clarify how the reported average standard deviation of 0.30 was calculated? Does it represent an average across different flight durations, atmospheric stability transitions, or both? Reporting the standard deviation separately for each flight duration and stability-transition scenario would make the results clearer and facilitate comparison between the different sampling strategies.
5. Figure 5: The font sizes of the axis labels, annotations, and legends are relatively small and should be increased to improve readability. In addition, a full stop appears to be missing in panel (b). Please check the figure annotations and formatting.
6. Line 651: The following papers may provide useful references for the discussion of LES: https://doi.org/10.1021/acs.est.5c15941
https://doi.org/10.5194/acp-22-6489-2022.7. Line 864: The cited paper has been published in AMT rather than AMTD.
Citation: https://doi.org/10.5194/egusphere-2026-3109-RC2
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Review comments
Rozmiarek et al. :
Evaluation of area-source methane-emission quantification by Uncrewed Aerial Systems using Gauss’s law
Summary:
The paper evaluates the effect of several measurement and atmospheric parameters on the accuracy of lake CH4 flux retrieval from a simulated cylindrical UAS mass-balance survey (OSSE), which applies Gauss's divergence theorem to convert circumscribing concentration and wind measurements into an area-source flux estimate. This is done through three successive experiments: the effect of receptor grid resolution, the effect of CH4 contamination from a nearby upwind lake, and the effect of sampling under evolving atmospheric stability. They find that vertical receptor resolution is the dominant factor controlling flux-retrieval accuracy, that upwind contamination from another lake systematically biases the retrieved flux low, and that retrieval accuracy degrades with increasing flight duration as the atmosphere evolves during sampling. Overall, this is a useful first-step theoretical treatment that can help guide the design of real UAS-based lake methane flux campaigns before they are carried out in the field.
General comments:
Line by line :
Title: nothing in the title suggests that the paper is based on simulations only. I would suggest going more towards something like: "A simulation-based evaluation of methane-emission quantification by Uncrewed Aerial Systems using Gauss's law"
6: “The suitability of this methodology has not been evaluated for uncrewed aerial systems (UAS).” Most of what is discussed in this paper could also be applied to manned flight (especially at these scales)
13: “When a nearby lake (~0.1–10 km)…” check for consistency
14: “this induced a systematic negative bias compared to the true methane flux.” How much?
16: “preserving the highest flux retrieval accuracy across all stability transitions tested” by how much? also not all, as it’s not the case from the transitions tested in the supp.mat
19-20: “Within our nondimensional framework, signal-to-noise increased retrieval accuracy, but by an amount that was determined by the geometry of the measured lake and observations.” Sentence not clear to me
21-22: “using cylindrical mass-balance” use consistent names for the method
End of abstract: add a sentence about the limitations of the method and the paper
29: remove point after “extent”
43: “than” -> that
44: please refer to fluxes in similar units (at least indicate them in parenthesis)
64-79: Good paragraph, useful to frame the knowledge gap filled in by the study
83: “cylindical-flux method” -> be sure to be consistent in using that name
90-101: nice linking sentence and last paragraph of the introduction, frames the methodology of the paper well
97: “(2) contamination from downwind area sources outside the control volume” shouldn’t it be from upwind area sources?
Figure 1: There seem to be a big mismatch between the figure and the legend, a) is not top-down (Is there a part of the figure missing???), no c) part ??? please revise accordingly
one thing that is not mentionned but that also differs from real-life: a UAS will have to transition from one level to another, costing time, would an idea of a sprial measurement be realistic? Or would it bring too many complications? (I realise that defined levels make the analysis here much easier, but just something that came to mind.
140 – 141: Was the cap flux ever tested for? Especially in the most unstable conditions?
211: “treatement” -> treatment
238-240: Adding the effect of rotor-wash here would be an interesting step for further studies
253-256: to be noted that the higher resolutions here may not be realistic for a real flight becasue of battery life
275: why are the levels for Experiment 2 not the same as for ex.1?
307-308: mention the other transitions shown in supp. Mat.
311: “of the z” -> “of z”
312-314: were the different heighs taken into account, or were more “stratified” fits tested as well?
326-328: can you describe the adaptive vertical spacing a bit more?
328: “Receptors were visited in a deterministic sequence of increasing height and then increasing azimuth within each height level.” This sentence is not very clear to me: was a single height sampled first aroung the cylinder, and then the next one, or first an azimuth at all heights?
348-349: why only focus on the lateral extent of the plume, and not take into account the vertical as well (to defend)? especially seeing the emphasis placed on atmospheric stability in one of the experiment
Eq.23: domain extends here over infinity, is this compatible with the limited height domain you actually use?
408-409: Maybe I am missing something here, but wouldnt it be interesting to vary the analysis resolution as well, as this is one of the main findings (that measurement resolution impacts flux estimation accuracy)?
438: -29.17% is quite large, more than “slightly”
439-444: nice explanation for the midpoint rule
Figure 2: maybe it would be less cluttered to use a lower receptor resolution as an example?
Legend: change heights to levels for consistency, true CH4 as dashed line not clear in legend (make dash visible in legend)
446-447: “increasing” should be “decreasing”
Figure 3: I would maybe inverse the direction of wind in figure a, as in all other figures, the wind is shown coming from the left…help with quick interpretation (also put a wind arrow)
Figure 4: maybe replace the arrows on the ‘0’ sides, as there is neither a out or in- flow there
504-506: “In our simulations, wind direction was aligned to maximize intersection with the control volume. In contrast, a wind direction that causes the plume to partially intersect with the control volume would have a fractional effect.” This means that the contamination values presented here are upper bounds, would be nice to emphasise this
517-518: “the upwind source increasingly resembles a spatially uniform background field as it passes through the control volume. For an upwind-contaminant source area that is infinitely large, the diffusion gradient vanishes entirely.” Seems reasonable, but was this actually tested?
545: “Note that for any flight duration (i.e., 30 min, 1 h, etc.), the flight starts at the beginning of the 12-hour period” what would happen if flights were started mid-transition, how would the main results change? As implication for real world-flights?
559-560: “The loss in accuracy (-12.30% for B–D, -5.65% for C–D, and -13.74% for C–F) scaled with the magnitude of the change in φ of the underlying stability transition. “ is scaled the right word here? B-D and C-D are pretty similar, but their deltaZ are different…
Figure 5: text too small (also valid for the other figures, but especially here), not sure how useful a) is… or maybe I don’t understand it, it is an average of multiple flights over 12h, right? I would maybe remove it
576: “relative to a single flight that began at the start of the 12-hour period.” Of what duration?
577-581: please check these numbers, they seem strange (numbers seem to repeat, but maybe its true)
Table 1: Could the ΠS<1 bin be influenced by the low F0 values, causing huge relative errors? Does absolute flux units values show the same behaviour?
602: “…downwind like shown…” -> “…downwind as shown…”
612-614: “The F–D case presented in Supplementary Fig. S6, showed substantially larger negative bias and higher error even within the higher ”S region, with RMSE of approximately 112% and only 53% of scenarios within 25% of the true methane flux.” shows that the non-dimensional variables are not that robust, and this point should be better conveyed, also, any potential explanation as to why?
619-620: “Restricting to the nominal favorable region with ”S > 10 and ”G < 1 increased this fraction to 69.7% and reduced the median absolute error from 15.1% to 9.6%” this is a relatively modest improvement
Figure 6: legend line 3: “bines” -> bins
669-671: “The methane analyzer (LI-COR LI-7810) used as the basis for our simulated sensor has a mass of approximately 10.5 kg, which exceeds the lift capacity of many types of UAS” yes, I think this would be very interesting to investigate in a follow up study, how would a more realistic UAS setup would behave.
669-677: Good paragraph, mentions most of the questioning I had previously. One other thing could be the question of possible flight duration, regarding typical battery life of UAS, and/or the compatibility of using fixed-wind drones with the flight speed required
680-682: I’m not quite convinced of a real-life practicality of such a setup… but maybe at a dedicated station…
689: would remove the hyphen in “natural-methane”, natural applies here to “methane sources”
718-720: Around here should also be acknowledged that receptor resolution is not a term in either ΠS nor ΠG
730-731: “Significant gaps remain in our understanding of how real-world emission heterogeneity and turbulent transport affect flux retrieval fidelity under more complex conditions.” Which is also visible in the fact that the F-D and D-B transitions do not follow the same pattern as the other transitions