Supervised machine learning tasks require training data with accurate labels. As precisely known emission rates are not available for TROPOMI methane plume observations, we use WRF-Chem version 4.1.5 to simulate plumes with known emission rates. WRF-Chem is configured with three nested, centered domains, with the innermost domain containing 99×99 grid cells at a 4km×4km spatial resolution. Vertically, this domain consists of 38 pressure levels using a sigma coordinate system. For meteorological boundary conditions, we use the Global Data Assimilation System (GDAS) dataset at 1°×1° spatial and 6-hourly temporal resolution, provided by the National Centers for Environmental Protection (NCEP) , covering the period 1 June–31 August 2019. We simulated plumes in seven different regions across the world that cover varied surface and meteorological conditions, shown in Fig. . Within each innermost domain, we initialize passive tracers at four different locations and two separate release heights (approximately 25 m and 250 m, see Fig. ). We choose these release heights to mitigate potential model overfitting to a single release height within the planetary boundary layer. Each tracer emits at a constant flux for the duration of the simulation. We sample WRF-Chem model output daily at 1400 h local time, roughly aligning with the TROPOMI overpass. To match the pixel footprints of the corresponding TROPOMI overpass, we apply an area-weighted resampling scheme to project the simulation output onto the satellite's pixel footprints, followed by a pressure-weighted vertical averaging to compute the total column density. We train our model on the resulting resampled methane plume enhancement scenes that are divided into training and validation subsets using a random 90/10 split. We show in Sect.  that this choice of split is resilient to geographic overfitting by ML-SPERE.

Data augmentation techniques, such as scaling, rotation, and translation, are crucial for training CNNs as they enhance model generalization, reduce overfitting, and, in the context of this work, improve robustness to variations in plume strength and plume orientation . To increase the diversity and size of the training and validation datasets, we apply transformations to model output sampled from WRF-Chem before we resample to TROPOMI pixel footprints. First, the methane enhancements for each scene are linearly scaled to match a randomly drawn target emission rate , sampled from a gamma distribution with location=0 th-1, scale=32.13 th-1, and shape=1.38. These parameters are chosen to match the distribution of IME-estimated emission rates from . The scaled plume is then randomly rotated by 0, 90, 180, or 270°, followed by a random horizontal or vertical flip. After resampling to TROPOMI pixel footprints, a random crop is applied to produce a 32pixel×32pixel scene, the dimensions of which match the output of the pipeline of . The pixel containing the plume source remains within the central 28pixel×28pixel region of the cropped scene, which ensures that ML-SPERE does not require plumes to be centered within input scenes after training is complete. After data augmentation, there are 94 159 scenes in the training dataset and 10 829 scenes in the validation dataset.

CNNs can be trained on multi-channel images, enabling the integration of additional meteorological data alongside methane data. While previous studies have trained CNNs on single-channel methane scenes for plume emission rate estimation, this approach has predominantly been applied to high-resolution instruments, where the fine spatial detail of the observations captures plume structures that convey information about the wind field . Some high-resolution CNN approaches still explicitly incorporate wind information . Our initial attempts to train a CNN for usage with TROPOMI observations without wind information exhibited over 30 % lower relative performance on our test dataset than the final model which incorporates wind channels. This is likely due to TROPOMI's coarser spatial resolution, which does not capture the same level of wind-related information in plumes as higher-resolution instruments. Consequently, the images in our training, validation, and test sets each contain seven channels, including data on the 10 m wind field vector, pixel area, surface pressure, and the corresponding plume mask, shown in Fig. . Channels for pixel area and surface pressure are included to provide context on methane mass contained within each pixel, which total column concentration alone does not provide. Plume masks are generated via the methodology described in . In the training and validation sets, we use the NCEP 10 m wind fields, and in the test set (see Sect. ), we use the ERA5 10 m wind fields , i.e. the meteorology used in the respective simulations. Wind information is taken at the same timestamp as the methane observation. These extra channels undergo the same data augmentation steps as the methane channel to ensure consistency with the final augmented methane scene.

We evaluate our final trained model using a test set of synthetic TROPOMI methane plumes simulated with the HYSPLIT atmospheric transport model . These simulations use ERA5 global wind data for atmospheric transport, provided at a spatial resolution of 0.25°×0.25° and hourly temporal resolution. By constructing the test set using a different atmospheric transport code and meteorological inputs than those used for training, we assess the robustness of the model to changes in underlying plume transport representations. To further assess geographic generalization, we simulate test set plumes at multiple timestamps in 2019 at 224 global locations of known persistent methane emissions distinct from those used in training and validation, shown in Fig. . These “hotspot” locations are found using a wind-rotation methodology and are reported to the International Methane Emissions Observatory . The simulated plumes were scaled with emission rates matching the distribution described in Sect.  and processed identically to the training set, but without data augmentation (e.g. scaling or rotation). The final test set comprises 438 synthetic plumes.

To enhance the representativeness of the test set scenes and capture the challenges involved in estimating methane enhancements in TROPOMI data, we add a unique 32pixel×32pixel TROPOMI observation as background methane to each scene . Using TROPOMI observations as backgrounds also introduces a realistic spatial distribution of missing data in the methane scene. These background scenes are selected from TROPOMI orbits from 2023 and 2024 using the method of to ensure they are highly unlikely to contain any real plumes. After combining a simulated plume with a randomly selected TROPOMI background scene, we pass the final scene back through the plume detection pipeline of to ensure that the synthetic plume is “detectable”. An example of a synthetic methane plume observation, complete with a real TROPOMI background methane and realistic missing spatial data, is shown in Fig. a. As ML-SPERE is trained using methane plume enhancements, the background methane column must be removed from the test set scenes before being used as input. We perform background removal using the binary high-confidence plume mask that is generated as part of the plume detection pipeline of . First, the median methane value is calculated from pixels outside the plume mask and subtracted from all pixels in the plume mask. Then, pixels outside the plume mask are set to zero (Fig. b and c). We report model performance on this test set as the primary benchmark before evaluating results on real TROPOMI observations.

We develop and train ML-SPERE using TensorFlow , a widely used machine learning framework in Python. Prior to training, both the training and validation sets are standardized on a per-channel basis relative to the training set, i.e. for each channel in an input image, values are transformed to have zero mean and unit variance based on the channel-wise mean and standard deviation of the training data. For hyperparameter optimization, we employ the Keras Tuner library to perform a randomized grid search, fitting multiple models to the training data across a range of hyperparameter configurations. From this ensemble, we select the architecture and hyperparameters of the top-performing model, detailed in Sect. . The selected model architecture is relatively shallow compared to standard benchmark CNNs such as ResNet and ImageNet , which is expected given the relatively small image size of the input scenes and is consistent with findings in previous work (e.g. ), enabling efficient training that completes within a few hours on a standard desktop machine. We use the mean absolute percentage error (MAPE) as the loss function during training, chosen for its ability to reduce overfitting to high-emission scenes and provide balanced error sensitivity across the emission rate range . Training is executed for a maximum of 100 epochs, halted early under two criteria: (1) if the validation MAPE does not improve for 10 consecutive epochs, or (2) if the ratio between the validation MAPE and training MAPE exceeds 1.05 for 10 epochs, indicating potential overfitting. ML-SPERE completed training after 18 epochs.

An emission rate estimate is produced by passing a processed, seven-channel input image through the trained model, which outputs a single predicted emission rate. To estimate uncertainty in these predictions, we generate an ensemble of perturbed input images that reflect both variability in pre-processing steps known to introduce uncertainty as well as uncertainty on the input data itself. By passing this ensemble through the model and analyzing the resulting emission rate distribution, we obtain an estimate of the prediction uncertainty. Our perturbation ensemble incorporates uncertainty from three primary origins: the processing required to convert a TROPOMI methane scene into a plume abundance scene, uncertainty in the wind speed, and uncertainty associated with the trained model itself.

There are two sources of uncertainty introduced during the processing of the methane channel: the method used to generate the plume mask, and the procedure for calculating methane enhancements above the local background (which is conditional on the definition of the plume mask). To address this, we first generate a binary plume mask following the procedure outlined in . To account for uncertainty in this masking step, the methane scene standard deviation thresholding factor (ordinarily taken to be 1.8) is drawn from the normal distribution N(1.8,0.2). Once the plume mask is defined, background removal is applied to the methane channel as described in Sect. . To incorporate uncertainty in the estimation of the local background methane level, we calculate the mean (μCH4) and standard deviation (σCH4) of methane values in pixels outside the plume mask, excluding outliers beyond 1.5 times the interquartile range. A random background value is then sampled from the distribution N(μCH4,σCH4), capturing scene-specific uncertainty in background removal. We adopt this background reduction approach because it is more conservative (i.e. it yields a larger estimate of background uncertainty) than defining background uncertainty as the standard error of the mean of background pixels or propagating the TROPOMI retrieval uncertainties on those pixels to the background mean.

To account for uncertainty in the wind speed channels, we first compute the average wind speed w‾ across all pixels within the identified plume mask. If w‾>3ms-1, we assign a fractional wind speed uncertainty of σw=1.5ms-1w‾, using the standard deviation between in-situ airfield wind speed measurements and wind data shown in . For lower wind speeds (w‾<3ms-1), we set a constant fractional uncertainty value of σw=0.5 (i.e. 50 % uncertainty). To incorporate this uncertainty into our ensemble of input images, we draw a wind scaling factor wscale from a truncated normal distribution N(1,σw), and scale all pixel values in the wind magnitude channel by this factor. The usage of a truncated normal distribution ensures that wscale is never negative.

A final source of uncertainty in our model's emission estimates stems from the model itself. To quantify this, we use Monte Carlo dropout as an approximation of Bayesian model uncertainty . For each perturbed input image in the ensemble, we perform a single forward pass with dropout activated at inference time (dropout strength as detailed in Sect. ). This introduces model-based variability into the total uncertainty estimate for methane plume emissions. We repeat the entire procedure (including random generation of the plume mask, methane background threshold, wind scaling factor, and a forward pass with Monte Carlo dropout) 5000 times per scene to ensure that the ensemble is sufficiently sampled. This yields a posterior distribution of emission estimates, from which we compute summary statistics such as the mean, median, standard deviation, and 2.5th and 97.5th percentiles. Unless otherwise indicated, we report the uncertainty on the estimate as the standard deviation of the posterior distribution of emission estimates. To assess the contribution of each uncertainty source, we also generate posterior distributions while systematically omitting one of the four error components.

We compare the performance of ML-SPERE in estimating TROPOMI methane plume emission rates with that of the IME method. In the IME method , the emission rate Q is estimated as 1Q=UeffLIMEkgs-1, where Lm is the effective plume length (typically calculated as the square root of the area of the plume mask), IMEkg is the total methane enhancement above the background summed over the plume mask, and Ueffms-1 is the effective wind speed. Effective wind speed calibrations are specific to the instrument and can also vary according to which wind data products are used in the calibration. The effective wind speed calibration for TROPOMI as calculated from a 10 m wind speed (U10) is determined in as 2Ueff=0.59U10+0.0ms-1, whereas the effective wind speed calibration for a planetary boundary layer average wind speed (UPBL) is given as 3Ueff=0.47UPBL+0.31ms-1.

calculate Q using ERA5 10 m winds as well as GEOS FP 10 m and planetary boundary layer winds . They additionally estimate uncertainties using a grid-based ensemble approach, varying input parameters such as plume masking thresholds, background methane concentration, wind magnitudes, and effective wind speed coefficient values. IME estimates (and associated uncertainties) for synthetic and real methane observations in this work follow the methods of directly, using only the ERA5 10 m wind product. We apply the IME method and Ueff parameterization from without modification, allowing us to benchmark the performance of ML-SPERE against a published and operationally used implementation of the IME method that was specifically calibrated for TROPOMI methane observations.

We evaluate ML-SPERE performance using the global test set of synthetic TROPOMI methane plume observations generated with HYSPLIT (Sect. ). On this test set, ML-SPERE achieves a MAPE of 40.2 %, compared to 46.1 % for the IME method, as shown in Fig. . Notably, the median absolute percentage error (MdAPE) for IME estimates is 40.5 %, while ML-SPERE yields a substantially lower MdAPE of 29.5 %. This difference arises because ML-SPERE estimates for this test set exhibit a heavy-tailed error distribution (arising from scenes where the plume is poorly observed, see following paragraph), and metrics such as MAPE are strongly influenced by outliers. Absolute errors produced by ML-SPERE generally scale with the true emission rate of test set plumes, but this relationship breaks down at the lowest emission rates, where an approximately constant absolute error leads to inflated relative errors. Similar behavior is observed for IME estimates. Additional performance metrics such as the Pearson correlation coefficient (R), mean absolute error (MAE), median absolute error (MdAE), mean bias, and root mean squared error (RMSE) are summarized in Table . We find no significant change in bias for either method when applied only to plumes whose masks are truncated by the scene boundary. Across all metrics, ML-SPERE outperforms the IME method. In terms of computational efficiency, the IME method implementation from is faster than ML-SPERE. On a standard desktop machine, it takes approximately 15 s to generate either an ensemble estimate of 43 923 members with the IME method or an ensemble estimate of 5000 members with ML-SPERE. These timings may vary depending on hardware. The time it takes ML-SPERE to produce an ensemble estimate scales linearly with the number of ensemble members.

The construction of plume masks is complicated by missing data and high methane background variability (various examples are shown in Fig. ). We thus define a TROPOMI methane plume in the test set to be “well-observed” if the known emission source location is contained within the estimated plume mask. When filtering the test set to include only scenes where the plume is well-observed (resulting in 264 scenes), the performance gap between ML-SPERE and the IME method widens further (Table ). MAPE and MdAPE of ML-SPERE decrease to 33.3 % and 24.3 %, respectively, whereas the corresponding IME errors remain largely unchanged at 44.6 % and 42.4 % (Fig. ). Additional figures and analyses in Sect.  show that the improved performance observed when restricting the application of ML-SPERE to such plumes arises from the model's strong reliance on spatial gradients in methane abundance near the plume head or source region when inferring emission rates. This behavior lends ML-SPERE meaningful physical interpretability. Performance may degrade when the plume mask is compromised around the plume head, either by missing data or by methane enhancements that are weak relative to background variability. However, such conditions are generally visually identifiable, allowing for informed application of the model. Even when the source location is unknown, an analyst can inspect a scene to assess whether the estimated plume mask is compromised and, consequently, whether ML-SPERE is likely to provide a reliable emission estimate. For poorly-observed plumes in the test set (i.e. those that do not meet the criteria for being well-observed), ML-SPERE and the IME method exhibit broadly comparable performance. ML-SPERE performance degrades relative to its results on well-observed plumes, whereas IME performance remains similar across all subsets.

While ML-SPERE achieves a MAPE of 40.2 % on the full test set and 33.3 % on well-observed plumes, its performance on the validation set is substantially better, with a MAPE of 14.6 %. Significant differences between the validation (and training) set and the test set include the fact that the validation set contains no spatially varying backgrounds or missing data, and that the validation set was simulated using WRF-Chem with NCEP wind data, which matches the modeling framework used for training. The test set plumes are additionally simulated at a wide variety of locations around the globe which are distinct from the locations used for model training. We have already demonstrated that spatially varying backgrounds and missing data hamper the performance of ML-SPERE by complicating the estimation of accurate plume masks. In Sects.  and , we demonstrate that further performance degradation on the test set (with respect to validation set performance) arises primarily from the use of HYSPLIT to generate test plumes, which exhibit morphologies distinct from those produced by WRF-Chem and encountered during training, rather than from limitations in geographic generalization.

Figure  illustrates a systematic bias where ML-SPERE tends to underestimate emission rates for plumes with large emission rates above the mean of the training dataset, and overestimate emission rates for plumes with small emission rates below the mean. The IME method also tends to underestimate emissions for plumes with large emission rates, despite the fact that the IME method is not a mean-biased method. The tendency for ML-based predictions to regress toward the mean of the training dataset labels is a common issue reported in similar studies . This regression dilution for ML-SPERE is reduced by 1/3 when we restrict application to well-observed plumes (Fig. d), though no such improvement in estimate biases is found for the IME method (Fig. c). For scenes with wind speeds below 2 ms-1, residuals between ML-SPERE emission rate estimates and true plume emission rates show no correlation with scene wind speed. In contrast, residuals of IME estimates in this wind speed regime exhibit a strong positive correlation, with the IME method significantly underestimating emissions for these plumes. Although low wind speeds aid in plume detection (48 % of the detections reported by are found at wind speeds below 2 ms-1), they complicate emission rate quantifications for mass-balance based approaches such as the IME method and the cross-sectional flux (CSF) method . Under such conditions, plumes often exhibit blob-like structures or irregularly rotated morphologies , which complicate emission rate estimation. Equation () in conjunction with the 10 m effective wind speed calibration from Eq. () implies that as U10 approaches zero, the IME-estimated emission rate Q must also approach zero. As a result, the IME method may be biased low and underestimate emissions from methane plumes detected by TROPOMI in low-wind-speed environments, for which the uncertainty on the wind speed is also relatively large. Figure  shows this trend clearly, and displays that the IME method systematically underestimates the emission rates for test set plumes with average wind speeds of less than 2 ms-1. By contrast, ML-SPERE is an unbiased estimator for plumes at low wind speeds, despite utilizing the same input data as the IME method.

Ideally, a model that accurately estimates uncertainty would capture about 95 % of true emission values within the 2.5th–97.5th percentile range of its posterior distribution for each emission-rate estimate. Across the full test set, 61 % of true values fall within this interval for IME estimates, compared to 81 % for ML-SPERE. These results indicate that both methods underestimate predictive uncertainty, although ML-SPERE provides more reliable uncertainty estimates than the IME method. We retain the hyperparameters specified in the error ensemble described in Sect.  (i.e. the assumed uncertainties in wind speeds, methane backgrounds, and plume masking strength) which are drawn from literature or informed by expert judgment. While increasing these values could widen the estimated uncertainty ranges (and thereby increase the proportion of true emission rates captured within them), doing so would risk masking model misspecification by attributing errors to input uncertainty alone. In Sect.  and Fig. , we apply the probability integral transform to show that the ML-SPERE error ensemble generalizes better across simulated plume datasets than the IME approach.

In 2023, a well blowout took place in Kazakhstan's Karaturun East oilfield which lasted for more than 200 d (days) . This event was observed with multiple methane-sensing satellites, including TROPOMI and high-resolution (25–60 m) satellite instruments such as GHGSat , EMIT , EnMAP , and PRISMA . For TROPOMI methane observations, inverse analysis estimates of emission rates were produced on a daily basis when observing conditions allowed. Separate IME estimates were also made using the observations of the point-source imagers when available. These quantifications showed that the daily estimated emission rate varied between 20–50 th-1 over the duration of the blowout, emitting an estimated total of 131±34 kt of methane . For dates during this blowout where a methane plume is detected in the TROPOMI data following the procedure of , we compare ML-SPERE emission rate estimates with those from as well as to IME emission rates estimates that we have produced using the TROPOMI data.

Figure a shows a time series of the daily emission rate estimates from and the ML-SPERE estimates. In general, ML-SPERE estimates tend to be higher than the TROPOMI inverse modeling results presented in , although they typically agree within uncertainty and show slightly closer agreement than that between the TROPOMI inverse modeling and IME estimates. For three of the four dates in the time series where we have an IME emission rate estimate from a high-spatial resolution satellite, we find greater agreement with ML-SPERE estimates than we do with TROPOMI IME estimates. We also find general agreement between ML-SPERE estimates and TROPOMI IME estimates. Error bars in Fig.  for ML-SPERE estimates span from the 16th to the 84th percentile of the posterior distribution of emission rates, in order to show the skew of posterior estimates (e.g. see Fig. a). These error bars are typically skewed with a heavy tail toward higher emission values, since ML-SPERE will not produce estimates below zero but has no upper bound. For most days in the time series, the uncertainty in ML-SPERE predictions is dominated by uncertainty in the input wind data. The next largest contribution to the overall uncertainty arises from uncertainty in estimating the methane background level within each scene. In contrast, uncertainties associated with plume masking and the model itself contribute comparatively little to the total uncertainty (Table ).

In Fig. b and c, we compare ML-SPERE estimates and TROPOMI IME estimates with the corresponding TROPOMI inverse modeling estimates. The ML-SPERE estimates exhibit a reduction in bias relative to the TROPOMI IME estimates when compared against the inverse modeling results, along with an improved R correlation and reduced chi-squared χν2 (though the scatter between inverse analysis estimates and both ML-SPERE and TROPOMI IME estimates remains large). To investigate potential sources of bias between ML-SPERE and the inverse modeling estimates for these scenes, we apply ML-SPERE directly to the resampled simulated plumes from that were identified as the best matches to the observations. Using these simulated plumes (without missing data or background methane) and their corresponding meteorology as inputs, ML-SPERE shows improved agreement with the simulated emission rates (i.e. the results shown in ), achieving a Pearson correlation of R=0.91 and a substantially reduced mean bias of 15.4 th-1. In contrast, IME estimates applied to the same simulated plumes remain largely unchanged relative to the metrics shown in Fig. c. The remaining positive bias of 15.4 th-1 in the ML-SPERE estimates could be attributable to plume morphologies resulting from complicated wind fields or conditions which violate the steady-state emission assumptions represented in the training dataset. This interpretation is supported by the fact that the IME method (which assumes steady-state emission scenarios) produces estimates that are twice as large as those of the ML-based estimates when applied to the same simulated plumes from . Furthermore, ML-SPERE does not show similar positive biases when applied to other simulated plume datasets with steady-state emissions (e.g. Figs. , , , and ). Applying ML-SPERE to the same simulated plumes while masking the abundances to reproduce the spatial pattern of missing data in the TROPOMI observations does not degrade performance. This robustness arises because the well blowout source remains clearly visible, and the absence of a spatially variable methane background allows the automatically generated plume masks in the ML-SPERE ensemble to reliably capture the source region. These results suggest that the remaining scatter between ML-SPERE and inverse modeling estimates for the real TROPOMI observations is likely driven by a combination of highly variable coastal methane backgrounds that complicate plume masking on certain dates, discrepancies between meteorological reanalysis products and true wind vectors, and conservative inverse modeling estimates where the forward modeled plume does not closely reproduce the TROPOMI observation. Although the actual underlying emission rates are not known for this super-emitting blowout, the improved agreement between ML-SPERE and inverse modeling estimates (compared to IME method vs. inverse modeling agreement) is notable as inverse modeling is a far more information-rich method, incorporating three-dimensional wind fields and atmospheric transport processes to produce plume emission rate estimates (albeit at a substantially higher computational cost than other methods).

present an automated, ML–based algorithm for detecting large methane emission plumes in TROPOMI satellite data, with a corresponding catalog of detections for all of 2021 published in . This dataset comprises 2974 plume detections distributed globally, with all but 30 linked to dominant anthropogenic sources such as urban areas/landfills, oil, gas, or coal mining operations based on bottom-up inventories. We use this 2021 detection catalog as a benchmark dataset to compare the performance of ML-SPERE to the traditional IME approach. ML-SPERE and IME estimates exhibit a strong correlation (R=0.79, Fig. a) and agree within errors (χν2=0.94, Fig. a). ML-SPERE estimates tend to exceed those of the IME method at low IME-estimated emission rates (i.e. below 10 th-1). This behavior may reflect the regression dilution discussed in Sect.  and shown in Fig. c. Additionally, it may indicate underestimation by the IME method for these plumes due to the wind-speed bias described in Sect. , as discussed further below. Emission estimates for TROPOMI plumes below 10 th-1 should be interpreted with caution, as this lies near the conventional detection threshold.

As shown in Sect.  and Fig. , ML-SPERE produced unbiased estimates with no correlation with wind speed for low-wind plumes in the synthetic test set, while the IME method showed increasing negative bias with decreasing wind speed. The residuals between the IME estimates and those of ML-SPERE for the real 2021 plume dataset exhibit a similar trend at lower wind speeds (Fig. b), which is consistent with the findings from Sect. . As nearly half of plumes are detected at wind speeds below 2 ms-1, ML-SPERE may therefore provide less biased emission rate estimates than the IME method for these commonly detected plumes.

A global comparison of ML-SPERE and IME emission rate estimates for the full 2021 TROPOMI detection catalog reveals that although the two methods generally agree (Fig. a), there are few regions where systematic differences emerge. These differences are statistically significant only in northern Russia and southwestern Australia, where ML-SPERE yields higher estimates than the IME method, and in the Congo Basin, where ML-SPERE yields lower estimates. A full analysis is given in Sect.  (with Figs.  and ) and summarized below.

In northern Russia, the largest discrepancies correspond to extremely compact, high-enhancement signals that coincide spatially with major gas pipeline infrastructure. These features resemble short-duration, transient emissions rather than the steady-state plumes on which ML-SPERE was trained, and their out-of-sample elevated methane enhancements likely contribute to the elevated emission estimates. Such transient, non steady-state emissions may also not be well estimated by the IME method (especially if the plume has detached from the source and is being transported downwind, as this violates the steady-state assumptions underlying the method). For these plumes, the total plume mass may provide a more relevant characterization than estimated instantaneous emission rate as emissions are no longer ongoing . For ongoing or persistent events, the observed mass only provides a lower boundary for the total emitted mass, as mass is still being emitted at the time of observation. In contrast to pipeline emissions in northern Russia, methane enhancements in the Congo Basin have very large spatial extents and may be more representative of area-source emissions than (TROPOMI-scale) point-source emissions on which ML-SPERE was trained and the IME method was calibrated. Finally, for plumes in southeastern Australia, ML-SPERE estimates are systematically higher than IME estimates in a low–wind-speed regime, where we have already demonstrated that IME estimates exhibit a negative bias. Although transient emission events and spatially extended plumes can occur globally, analysis of this dataset suggests that temporal averaging limits statistically significant differences between total emissions estimated by the two methods to a small number of regions. These regional diagnostics highlight that ML-SPERE likely performs most accurately when the observed plume exhibits a coherent head and well-defined downwind structure, and that applying either method can benefit from human oversight in cases involving transient, discontinuous emissions or spatially fragmented plumes.

In Fig. c, we compare average estimated emissions for the 2021 TROPOMI plume detections grouped by estimated source sector . Sectoral emissions estimated for this dataset using the IME method and ML-SPERE largely agree, with the exception of those attributed to wetland emissions, which are underrepresented in this dataset. These plumes are spatially concentrated in the Congo Basin and, as discussed in the previous paragraph, have large spatial extents that may lead to overestimation by the IME method. The agreement across the remaining sectors likely reflects averaging over a broad distribution of wind speeds, which can mitigate wind-speed–dependent biases in the IME method. Taken together, the consistency between ML-SPERE and IME across most sectors supports the robustness of the sectoral emission estimates for this plume dataset.