the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 28 May 2026
A deep learning-driven emission estimator utilizing a mixture of experts for local wind speed situations applied to high-resolution methane imagery
Abstract. Methane (CH4) is the anthropogenic greenhouse gas with the second-highest impact on the Earth's radiative budget since pre-industrial times. A substantial amount of CH4 emissions are from the fossil fuel industry and are emitted from point-like sources that can be measured using airborne or space-based spectrometers. The precise quantification of point-source emissions has proven to be difficult, with uncertainties driven by the lack of local wind speed measurements and the task of estimating the effective wind speed of the plume. Here, we continue the development of deep learning-based methods using convolutional neural networks (CNN) to estimate emissions without the need for auxiliary wind speed information. We use a library of plumes obtained from large-eddy-simulations (LES) and realistic background noise scenes from the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS-NG), used in previous studies, to generate realistic synthetic data. We suggest a mixture of experts (MoE) architecture, that is able to extract the wind speed forcing used in the LES and to estimate emission rates conditional on the wind speed present in the scenes. This allows us to integrate the concept of different wind speed scenarios into the network architecture, making the performance of the network more transparent and explainable and, while still being independent of external wind speed information, makes it possible to use external wind speed information to validate or improve emission estimates. The MoE-based network, without any external wind speed information, provides a mean absolute percentage error (MAPE) of 5.65 % for scenes with CH4 emission rates exceeding 100 kg h-1, which is a 40 % improvement compared to previous implementations. The proposed network is also able to address biases at high wind speed situations, leading to almost unbiased estimates over the entire emission and wind speed domain.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Atmospheric Measurement Techniques.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-2572', Anonymous Referee #1, 01 Jul 2026
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RC2: 'Comment on egusphere-2026-2572', Anonymous Referee #2, 27 Jul 2026
This manuscript addresses an important and timely problem: automated quantification of methane point-source emissions from high-resolution plume imagery without relying entirely on uncertain auxiliary wind information. The central advance over Plewa et al. (2025) is to make the wind-speed dependence explicit through a mixture-of-experts (MoE) architecture: a router first classifies the LES wind-speed forcing and the selected expert then estimates the emission rate and uncertainty. It is scientifically interesting that the model attempts to separate wind information implicitly encoded in plume morphology and uses this estimate both for emission quantification.
The reported improvement over the authors' previous model is promising. However, the present evidence is largely based on a synthetic benchmark constructed from LES plumes. The exceptionally tight agreement in Figure 3 is therefore not yet sufficient to establish comparable performance under the more complex conditions of real airborne or satellite observations. In addition, the current availability and validation descriptions do not yet permit robust reproduction or assessment of transferability.
- The abstract and conclusion state that the MoE network achieves a MAPE of 5.65% above 100 kg h-1 and a 40% improvement over the previous implementation. This is a clear improvement relative to Plewa et al. (2025), which reported MAPE values of 10.29% above 40 kg h-1 and 9.48% above 100 kg h-1. However, the present evaluation uses the same synthetic data. They do not yet support broader claims such as “new state-of-the-art emission estimation” or robust applicability across a wide range of real-world settings. The authors should either narrow this language or add other validation.
- Figure 3 shows predictions and ground truth strikingly close to the 1:1 line. While encouraging, this result is also likely to raise concerns that the model is evaluated within the assumptions of the LES simulator and augmentation pipeline. Real methane plume quantification is affected by retrieval noise and bias, plume masking, heterogeneous surfaces, and so on. I strongly recommend adding a controlled-release test set, ideally including a Stanford-organized controlled-release experiment such as the TADI/AVIRIS-4 campaign, or another appropriate airborne imaging dataset. Even a limited blind external evaluation would substantially strengthen the manuscript for both academic and operational audiences. The key question is whether the router and the emission experts remain informative when the plume originates in the real atmosphere rather than in the same simulation used for training.
- Release code, models, and reproducibility materials. This is the most important practical revision. The manuscript proposes a machine-learning estimator whose value depends on independent reproduction and comparison. The data-availability statement currently says only that data are available upon request, and I did not find a code-availability statement. The authors should release public code, trained model weights, inference and training scripts, configuration files, and enough synthetic-data generation information to reproduce the principal figures and tables.
Citation: https://doi.org/10.5194/egusphere-2026-2572-RC2
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- 1
Plewa et al. presented a mixture of experts (MoE) model for estimating methane point source emissions trained using simulated methane plumes and hyperspectral aircraft imagery. The model achieved 40% improvement over previous end-to-end approaches in emission rate estimation accuracy, while not requiring external wind speed information. The paper is overall well written, and I only have a few comments listed below for the authors to address.
Major comments:
Minor comments:
Page 3 Line 80: “explicit” -> “explicitly”
Page 5 Table 1: Please capitalize the first letter of the table title and column/row headers
Page 6 Figure 1: The presentation of plume images is not immediately clear to me. Particularly, it is not obvious to me that the four images in the bottom-right panel all correspond to resulting scenes. I’d suggest adding colored or bordered panels for each image group (simulated plumes, background, resulting scenes with plumes) to highlight visual separation.
Page 8 Figure 2: Please add the full name of FFN and explanations of the nodes with the plus sign and times sign in the caption.
Page 8 Line 180 & Line 192: Why use a wind speed value range (+- 1m/s) instead of a percentage range? For example, I’d assume that it is much more likely for a 10 m/s wind speed estimate to be assigned to 8 m/s (-20%) than a 1 m/s to be assigned to 3 m/s (+200%).
Page 10 Line 248: “the performance” -> “the performance of wind speed classification”, since there are two types of performance in discussion, it’d be better to clarify explicitly. I’d also recommend carefully reviewing the Results section to change any unambiguous terminology.
Page 10 Line 248-257: Back to my previous point, wouldn’t a percentage range of surrounding wind speeds help mitigate the bias? For example, by providing a +-20% range you are telling the model that a 10 m/s wind speed estimate could possibly be 8 m/s in reality.
Page 11 Figure 3: The red 1:1 line is not mentioned in the caption. It would also be useful to add a fitted line with R2 marked in the plot.
Page 13 Line 282: I think here the author meant MAPE rather than MPE? It’s claimed that MAPE represents “the spread of our data”; and in Table 2 only MAPE in the filtered model is lower than the unfiltered one for all the three emission rates.
Page 16 Line 303: A difference of 1 m/s between the correct wind speed and the external wind speed seems too optimistic to me. How was it determined?
Page 17 Line 325: It would be helpful to explicitly clarify that, the comparison between the unfiltered and filtered models is intended as a diagnostic analysis to separate errors from wind misclassification from those related to emission estimation under different scene conditions, rather than as an indication that the filtered model would be preferable in operational settings, since we never know the true wind speed in practice. The same clarification applies to the “correct” and “corrected” configurations.