To form the observation dataset, we used satellite data of tropospheric NO2 vertical column densities from the TROPOMI instrument aboard the European Space Agency's (ESA) Copernicus Sentinel-5P satellite . Launched in October 2017, TROPOMI provides data at a nadir spatial resolution of 3.5 km (across-track) × 7 km (along-track), which improved to 3.5 km × 5.5 km in August 2019; pixel size increases toward the swath edges due to viewing geometry.

We downloaded raw Level-2 NO2 data in NetCDF format from the NASA Earthdata portal. Each file corresponds to a single satellite orbit (∼ 101 min), containing one Level-2 swath with 450 across-track ground pixels and thousands of along-track scanlines. For our US analysis (1 January 2019–31 December 2024), we acquired 9636 files. For the global analysis (1 May–31 December 2018), we obtained 3421 files. The data come from the v2 series of the TROPOMI L2 NO2 processor (v2.4.0–v2.8.0), spanning both the reprocessed (RPRO) and operational offline (OFFL) streams. The May 2018 start of the global window is set by the v2.4.0 NO2 full-mission reprocessing, which begins on 1 May 2018; earlier observations are only available in the v1 product line, which is not directly comparable.

Throughout this paper we use observation to refer to one TROPOMI overpass at a target power plant: the L2 NO2 retrieval at the pixel closest to the plant's center, paired with the corresponding emission record.

To generate a high-quality dataset, we processed these raw files through a multi-step filtering pipeline. For each TROPOMI observation over a power plant, the observation is kept if it contains:

a quality flag greater than 0.75, which removes data contaminated by clouds or other errors ,

After applying these quality assurance criteria, this process yielded a final dataset of 666 222 high-quality observations for the US analysis and 875 686 for the global analysis. Across the mapped facilities (US, N=500; global, N=6000), observation coverage is extensive. In the US, plants have a median of 1301 observations (10th and 90th percentiles of the per-plant distribution P10=1050 and P90=1645; we use PX to denote the Xth percentile of whichever per-plant distribution is under discussion, applied throughout to observation counts, detection counts, and detectability values). Globally, the median is 141 observations (P10=90, P90=218), with 98.8 % of plants having ≥ 50 observations (range 2–350). As illustrated in Fig. a and b, the geographic density of these final observations is highest in drier, less cloudy regions and at higher latitudes.

CAMPD, maintained by the U.S. Environmental Protection Agency (EPA), provides hourly emissions data for CO2, NOx, SO2, and mercury from individual power plants. This level of granularity is unique globally and offers a distinct opportunity to study how emission rates influence the detectability of NO2 plumes in satellite imagery. For our analysis, we downloaded hourly NOx emission data from the CAMPD API, specifically matching the times of TROPOMI satellite observations for each plant.

CEMS provide these hourly emissions data by measuring pollutant concentrations and exhaust flow rates to compute mass emission rates. These systems operate continuously, reporting hourly averaged data directly to the EPA.

The CAMPD inventory is comprehensive, containing 97.1 % of annual US power-sector NO_x emissions as of 2023 . From this inventory, we selected the 500 power plants with the largest total NOx emissions from 2019 to 2024, representing the upper tail of all US facilities, for our study; their emission distribution is shown in Fig. c. Our selection accounts for 93.6 % of the inventory's NOx emissions and 79.8 % of its CO2 emissions. By 2024, 461 of the 500 plants still reported to CAMPD, the remaining 39 having ceased reporting. Among the 461, pipeline natural gas facilities (238 plants, 52 %) and coal plants (176 plants, 38 %) dominated, followed by natural gas (13), wood (12), coal refuse (5), diesel oil (3), other gas (3), process gas (3), residual oil (2), petroleum coke (1), and one plant reporting a combined coal/natural gas primary fuel; fuel type was unreported for a further 4 plants. Over this 6-year period, this group of top emitters transitioned measurably from coal to natural gas: coal-fired plants fell from 229 to 176 (a 23.1 % decrease), while pipeline natural gas facilities grew from 225 to 238 (a 5.8 % increase). For context, the EPA's broader power sector data covered approximately 96 % of US fossil fuel-based electricity generation as of 2018 .

Because global hourly emissions are unavailable, we used annual emissions. For our global analysis, we sourced annual power plant emissions from the CoCO2 catalog . This inventory covers at least 95.9 % of total reported global power plant emissions and provides annual data for CO2, NOx, SOx, CO, and CH4. The CoCO2 catalog derived the annual emissions using a bottom-up methodology as follows:

Europe: Use each plant's official reported NOx from the European Pollutant Release and Transfer Register (E-PRTR) and the Large Combustion Plants (LCP) dataset for the year. If a plant didn't report, estimate it from other official datasets or standard country-and-fuel ratios.

These derived annual emissions provide robust annual magnitudes but do not resolve within-year variability. Plume detectability is determined at the moment of each observation; relying on annual emissions therefore limits our ability to predict per-observation detectability.

From this catalog, we selected the 6000 facilities with the largest annual NOx emissions in 2018, with emissions ranging from 219 to 44 548 tyr-1, representing the upper tail of global power plant emissions; their emission distribution is shown in Fig. d. This selection accounts for 96.1 % of the inventory's NOx and 91.5 % of its CO2 emissions, and corresponds to at least 92.1 % of global power plant NOx and 87.7 % of global power plant CO2 emissions. Coal (3023), natural gas (1810), and oil (690) plants dominate the set, which also includes facilities that burn biomass (354) and waste (123).

To avoid double-counting in our source-attribution analysis, we filtered the catalog for duplicate entries (defined as plants within 3 km sharing identical reported emissions across all five pollutants: CO2, NOx, SOx, CO, and CH4). This step removed 3320 of 16 461 candidate facilities (20 % of the catalog), with the bulk of removals concentrated in China and India (66 % combined); per-country statistics and a brief discussion of the underlying catalog-integration causes are provided in Sect. S2 in the Supplement.

Table  lists the features we selected to predict plume detectability, based on the physical processes that govern plume formation, transport, and satellite detection. These features fall into four categories: sensor characteristics, power plant attributes, meteorological conditions, and environmental context. The variables in these categories capture the complex interplay between emission sources, atmospheric conditions, and observation geometry that strongly influences plume detectability. Several variables labeled as “TROPOMI” in Table  are not direct sensor measurements but auxiliary fields packaged into the Level-2 NO2 product from external datasets (e.g., surface albedo and surface pressure).

We extracted these variables from their respective data sources using several methods:

TROPOMI features were extracted from the pixel closest to each power plant's center.

We describe the variables and their source datasets in Table , organized by category.

For each analysis, we pair every TROPOMI overpass over a selected power plant with the corresponding emission record to form the input observations used by all subsequent steps. The TROPOMI-derived input features for the model are extracted from the single pixel closest to the plant's center, not aggregated across the plume.

US. The US analysis uses 666 222 TROPOMI overpasses across our 500 selected plants. This full set of observations is used throughout the manuscript for dataset characterization and detection statistics. For the model training and feature-importance analyses (Sects.  and ), we use 189 713 observations from 171 plants, namely the subset of overpasses that have (i) no missing (NaN) values in any input feature, since TROPOMI retrieval variables can themselves contain NaNs, (ii) a paired hourly NOx record from the CAMPD database, and (iii) a target plant lying outside interference zones (Sect. ). CAMPD only catalogs regulated facilities during operating hours with valid CEMS data, so overpasses during monitoring downtime, plant shutdowns, or over facilities below reporting thresholds are excluded.

Global. The global analysis uses 875 686 TROPOMI overpasses across our 6000 selected plants. As with the US dataset, this full set of observations is used throughout the manuscript for dataset characterization and detection statistics; for the model training and feature-importance analyses (Sects.  and ), we use 161 118 observations from 1065 plants, namely the subset of overpasses with no missing (NaN) values in any input feature, a valid annual NOx record in the CoCO2 catalog, and a target plant lying outside interference zones (Sect. ).

To build a machine learning model to explain plume detectability, we first need a large labeled dataset of plume detection. Manual plume annotation is prohibitively costly and inconsistent, so labels must be generated automatically. Existing automated methods such as the Data-Driven Emission Quantification (DDEQ) toolkit detect NO2 anomalies but cannot attribute a plume to a specific source, failing to separate a target power plant from nearby cities or other industries. To fill this attribution gap, we develop a new plume-detection–with-attribution algorithm that automatically labels plumes and assigns each one to its originating power plant.

Our algorithm automates this attribution through a five-step workflow, outlined in Fig. . The process integrates TROPOMI satellite measurements with power plant and city databases to systematically isolate and label a target plume. While the steps are executed sequentially, the figure illustrates the key data dependencies that connect the different stages of the process.

Beyond the per-scene masking applied within the labeling algorithm (Sect. ), we apply a plant-level filter to construct the dataset for the second-stage detectability analysis: we retain only plants that lie outside interference zones across every analyzed year, giving a cleaner dataset.

We first find that for the US Top 500 NOx emitters (2019–2024), 312/500 plants (62.4 %) were flagged as in interference zones in 2019, declining to 283 by 2024 as the number of active plants shrank from 500 to 461. Metropolitan proximity remains the primary driver of interference. Across six years, only 171 plants were never within interference zones, accounting for 45.0 % of emissions from the original 500.

Interference is even more pervasive in the global dataset of 6000 major power plants. In total, 4935 plants (82.3 %) lie within at least one interference zone; proximity to large urban centers dominates (4491 plants), while co-located power plants also contribute substantially (2719 plants). Notably, 2275 plants are simultaneously affected by both cities and other plants, underscoring the difficulty of identifying interference-free monitoring conditions at scale. In 2018, only 1065 plants remained outside interference zones, retaining just 21.1 % of the original emissions.

These contrasting retention rates, 45.0 % for US plants versus 21.1 % for global plants, reflect the higher spatial clustering of emission sources and urban areas in the global dataset.

At an observation level, requiring (i) no missing values in any input feature, (ii) a valid paired NOx record (CAMPD for the US, CoCO2 for global), and (iii) a target plant outside interference zones, the final modeling subset retains 189 713 of 666 222 US observations (71.5 % excluded across 2019–2024) and 161 118 of 875 686 global observations (81.6 % excluded). To support the per-emission-magnitude analyses described later (Sect. ), we also consider three subsets defined by the highest-emitting plants within each region: the Top 100, Top 50, and Top 20 by total NOx emissions. Table  reports removal rates for these smaller US subsets, which are similarly large.

While this filtering is stringent, it is necessary to ensure interpretability and causal attribution. Our goal is to analyze how meteorology, emission rate, and environmental factors affect plume visibility, not to model column enhancements that may arise from overlapping sources. Without isolating interference-free scenes, plume detections could be driven by emissions from neighboring plants or urban NO2 backgrounds, obscuring the true relationships between plant-level conditions and observed plume visibility. Thus, the reduced sample size reflects a trade-off: a smaller but cleaner dataset that supports robust inference about the mechanisms underlying visible plumes in satellite imagery.

Using the dataset constructed in Sect. , we train a machine learning model to predict plume detectability from the input features. We frame plume detectability as a binary classification task. For each TROPOMI observation, which our algorithm labels as either “plume detected” or “no plume,” we extract a comprehensive set of meteorological, sensor, environmental, and power-plant features to use as classifier inputs.

We use a Multi-Layer Perceptron (MLP) for this binary classification task. The MLP is a fully-connected feedforward network with four hidden layers (256, 128, 64, and 32 neurons) using ReLU activation functions. To mitigate overfitting, we apply dropout (p=0.3) after the first three hidden layers. The network takes 25 input features (24 numeric features plus the integer-encoded primary fuel type) and produces a binary classification output, giving 49 921 learnable parameters. This architecture is used for all US and global analyses.

To understand how performance varies with emission magnitude, we trained separate models on four datasets: “All” (the full modeling subset of Sect. 3.3) and the three highest-emitter subsets (“Top 100”, “Top 50”, and “Top 20”) defined in Sect. . For each dataset, we partitioned observations into training (60 %), validation (20 %), and test (20 %) sets.

We addressed class imbalance in the training set using random oversampling and then standardized all input features to have zero mean and unit variance, based on the resampled training data statistics. We trained each model to maximize the Area Under the Curve (AUC) on the validation set. To account for training stochasticity, we repeated each experiment five times and reported the mean and standard deviation of the results. Full training details are in Sect. S3 in the Supplement.

We evaluate two complementary splits: an item split, in which observations are randomly assigned to train, validation, and test sets (in-distribution generalization), and a power plant split, in which entire plants are held out for testing (out-of-distribution generalization to unseen facilities). For each model we report six standard classification metrics (Accuracy, Precision, Recall, F1, AUC, and Cohen's κ); item-split results are presented in Sect.  and power-plant-split results in Sect. S5 in the Supplement.

After interference filtering (Sect. ), the analyzed set consists of 171 US plants outside interference zones (retaining 45.0 % of the original NOx emissions from the Top 500 selection) and 1065 global plants outside interference zones (retaining 21.1 % of the original NOx emissions from the Top 6000 selection); 189 713 of 666 222 US observations and 161 118 of 875 686 global observations remain. All detectability results in the following subsections refer to this filtered set.

With power plants near interfering emitters removed, we proceeded with a clean set of observations in which emissions can be attributed to the target power plant. We apply the pipeline to 500 US plants (January 2019–December 2024) and 6000 global plants (May–December 2018), excluding power plants within interference zones. Detection frequency varies dramatically across sites.

In the United States (171 after filtering with full 6-year availability), detections range from 11 to 258 per plant on average each year, with a median of 48. This range is highly uneven: plants at P90 (154 detectionsyr-1) record about 8.6× more detections per year than those at P10 (18 detectionsyr-1). When adjusted for the number of satellite overpasses, the per-plant detectability spans from 6.0 % to 85.2 % (median 20.4 %; P10 = 10.0 %, P90 = 63.7 %).

Globally (1065 plants after filtering), detections over the eight-month period in 2018 range from 0 to 251, with a median of 38. Plants at P90 (141 detections) record about 11.8× more detections than those at P10 (12 detections). When adjusted for the number of satellite overpasses, the per-plant detectability spans from 0 % to 100 % (median 27.8 %; P10 = 10.5 %, P90 = 81.8 %).

Detection frequency is strongly correlated with empirical detectability across plants (Pearson r=0.96 for the US and r=0.89 for the global dataset), as expected since detection frequency is the product of detectability and the number of valid overpasses.

These per-plant detectability estimates are consistent between the two independently configured pipelines: on the 160 plants present in both runs (matched within < 10 m), the US and global per-plant detectabilities agree closely (Pearson r=0.96; Fig. ), despite differences in emission temporal resolution (hourly CAMPD vs. annual CoCO2) and observation period (2019–2024 vs. 2018). The small residual offset (mean +0.036; US mean 0.163 vs. global 0.199) likely reflects the temporal gap, since US NOx emissions have continued to decline over 2019–2024.

These disparities have a clear geographical distribution: detectability is higher in arid and semi-arid regions (e.g., the US interior West and Great Plains, Iberia, North Africa, Greece/Turkey, central Brazil/Argentina, eastern Australia) and lower in humid regions. Notably, the detectability of plants with the same level of emissions varies across different geographical regions, highlighting that emissions alone are insufficient to predict detectability. Regional meteorology and surface properties also strongly affect plume detectability, as visible in Fig. a and c; we revisit these geographic patterns in Sect.  in light of the feature-importance results.

Despite this aggressive filtering, satellite detection frequencies remain remarkably high, as shown in Fig. . All 171 US plants exhibit detection frequencies exceeding 10 observations per year, with 87.7 % detected more than 20 times annually and nearly half (46.2 %) detected more than 50 times per year. The global dataset shows similarly strong performance, with 93.3 % of plants detected more than 10 times and three-quarters (75.1 %) detected more than 20 times during the eight-month observation period. Figure  further shows that 24.6 % of US plants exceed 100 positive detections per year and 19.8 % of global plants exceed 100 positive detections over the eight-month period, demonstrating TROPOMI's capability for frequent monitoring even after conservative spatial filtering. Detection frequency generally increases with emission magnitude, though substantial variability exists within emission bins, likely reflecting differences in meteorological and environmental conditions across facilities.

We report results from the two split designs introduced in Sect. . Table  reports the item-split results for both US and global datasets; the power-plant-split results are reported in Table S2 in the Supplement (Sect. S5). The tables organize performance by region, emission data resolution (annual vs. hourly NOx), and dataset scope (All vs. Top X emitters). Of the six classification metrics reported, we focus discussion on Precision, Recall, and the F1 score, which together quantify the reliability of positive predictions, the ability to capture all true events, and the balance between these competing objectives in operational monitoring.

Our model predicts plume detectability from meteorological and emissions features with high accuracy. As reported in Table , across US and global datasets, the multi-layer perceptron reaches 0.75–0.78 accuracy, 0.65–0.67 F1 score and achieves AUCs above 0.80; the underlying receiver operating characteristic (ROC) curves for the “All” subset are shown in Fig. S1 in the Supplement (Sect. S4.1). These metrics show that sensor, power plant, meteorological, and environmental variables can predict plume detectability, though imperfectly. The residual errors suggest that key drivers are either unmeasured or captured too coarsely, limiting the separability between detectable and undetectable plumes.

Model performance improves when focusing on high-magnitude emitters, as seen by comparing the “All”, “Top 100”, “Top 50”, and “Top 20” rows of Table , where each row corresponds to a separate model trained and evaluated on the indicated subset (Sect. ). As the subset is restricted to higher emitters, Precision, Recall, and the F1 score all rise, with Precision showing the largest improvement. This trend suggests that on these subsets the model makes fewer false positive errors, since stronger emitters tend to produce less ambiguous plume signals.

We note that the slight decrease in accuracy in the US when focusing on high emitters is caused by a significant shift in class balance. The full dataset contains a large number of “undetectable” cases (true negatives), and the model correctly identifies them, boosting the overall accuracy score. When the dataset is filtered to only the top emitters, these easier-to-classify negative cases are removed.

Though the global dataset uses coarser temporal emission data, the model trained on it matches or exceeds the model trained on the US dataset across all subsets, with the gap widening for the highest emitters (e.g., on Top 20, Global F1 = 0.935 vs. US hourly F1 = 0.825). This may initially appear surprising; we speculate that the broader variability in environmental variables and emissions in the global dataset sharpens the boundary between detectable and undetectable cases, helping the global-trained model generalize better.

To understand how model performance varies across the world, we performed a spatial analysis of F1 scores for individual power plants. Figure  shows the geographic distribution and reveals distinct regional patterns in model accuracy. For the US-trained model (Fig. a), performance is strongest in the Midwest and parts of the Western US, where the model achieves F1 scores consistently above 0.8 for major emitters. The globally trained model (Fig. b) demonstrates robust performance across industrialized regions including North America, Europe, and the Arabian Peninsula, with F1 scores often reaching 0.8–1.0 for large point sources. Performance degrades in parts of Asia, South America, and Africa, where F1 scores show greater variability and often drop below 0.5, likely because training data are sparser and emissions are lower in these regions. The sparser training data in these regions are themselves partly a consequence of factors that make satellite retrievals more difficult there, including high aerosol load, water vapor, and persistent cloud cover, which reduce the number of high-quality TROPOMI observations available for analysis. Across all regions, a clear positive relationship exists between emission magnitude (point size) and model performance: larger NOx emitters are detected with higher accuracy, likely because stronger plume signals exceed detection thresholds more reliably; this relationship is verified in Fig. S3 in the Supplement.

One notable outlier appears in the northeastern US. The global model shows poor performance for what appears to be the largest emitter in the US after interference zone filtering in the CoCO2 dataset, yet this facility is absent from the US analysis. This facility, Domtar Paper Company, LLC, reports 2018 NOx emissions of only 35.57 t in the EPA dataset but 29 652 t in CoCO2, an ∼ 830-fold discrepancy. If the EPA data are correct, the facility's small actual size explains the poor detectability. In other words, the CoCO2 dataset is likely incorrect about Domtar Paper Company's emissions.

To identify the key predictors of NO2 plume detectability, we performed a permutation importance analysis on our best-performing models from Table . Figure  (left) shows the ranked feature importance, sorted by the combined US and global importance. The top 5 features are NOx emission rate, surface altitude, surface albedo (NO2 window), sensor zenith angle, and primary fuel type, with wind speed close behind at rank 6. Our SHAP score analysis yielded similar results, which are shown in Sect. S4.2 in the Supplement. A complete list of permutation-importance values appears in Table S3 in the Supplement (Sect. S6). Cloud fraction appears low in this ranking, but still shapes detectability within the post-quality-assurance range (quality flag >0.75); we show this in Sect. S6.2 in the Supplement.

To examine how these features shape detectability, we employ a quantile-based binning strategy, using data between the 1st and 99th percentiles. This approach ensures a balanced distribution of observations across bins while mitigating the influence of extreme outliers. We grouped the data into 20 quantile bins for each feature (≈ 7900 observations/bin globally; ≈ 9300 in the US) and computed the detectability within each bin. While we acknowledge that these variables can be correlated, we find the trends persist when we parse the data to isolate each feature's effect (e.g., by holding other variables roughly constant). The resulting curves, plotted against the corresponding feature values, are shown in the right panel of Fig. .

Detectability increases with both emission rate and surface albedo. As expected, higher emissions increase NO2 concentration and therefore the detectable signal, while brighter surfaces increase scene radiance, improving signal-to-noise ratio (SNR). This albedo dependence is consistent with the geographic patterns reported in Sect. : arid and semi-arid regions have higher detectability partly because of their elevated surface albedo, while humid regions are penalized by both lower albedo and more frequent cloud cover. Our analysis finds that for US power plants, an average hourly emission rate of ≈ 400 kgh-1 corresponds to a ∼ 50 % detectability. The result for global power plants is similar, although the global P(detect) versus NOx emission curve is slightly above the US curve. To compare US and global performances in Fig. , we align their emission axes to share the same numerical scale, despite the different units (kgh-1 for the US, tyr-1 for global). We align the x-axis for US emissions (kgh-1) and global emissions (tyr-1) by converting the US hourly rates to annual values using 24 × 365/1000, allowing direct comparison with the global annual rates. The US curve consistently falling below the global curve suggests that the premise of continuous operation is often invalid, as many US plants run intermittently, leading to lower detectability.

By contrast, the sensor zenith angle (VZA) shows a hump-shaped dependence, with mean peak plume detectability near 20° VZA globally and 35° in the US. Two effects can possibly explain the rising flank. First, retrievals measure NO2 slant column density along the line of sight and convert it to vertical column density by dividing by the AMF; at higher VZA the longer slant path yields a larger AMF , so the same slant-column noise translates into a smaller vertical-column noise. Lower background noise raises detection probability at fixed plume signal. Second, for the US analysis period our 25 km² flagged-area threshold introduces a pixel-quantization step: TROPOMI pixel area grows from ∼20 km² at nadir to ∼25 km² near VZA =26° for the 3.5 km × 5.5 km pixels available from August 2019 onwards (Fig. S7 in the Supplement), so detection requires ≥2 contiguous flagged pixels below 26° but only one above, producing a step increase in detectability. At larger VZA, detectability falls as radiance drops, multiple scattering grows, the larger pixel size dilutes the plume signal more strongly, and retrieval uncertainty increases under oblique geometry .

Finally, wind speed is negatively correlated with detectability. Stronger winds advect and dilute plumes, lowering column contrast and thus detectability. We note that this is different from the ideal wind speeds for quantifying emissions, which prior literature shows to occur at moderate wind speeds (2–4 ms-1) . Very low wind speeds make it difficult to quantify the rate of emission due to the high relative uncertainty in the wind measurement itself, while the same plume dilution that hinders detection at very high wind speeds also introduces large errors into the quantification algorithm . These two relationships are not in conflict because detection and quantification address different tasks: quantification requires a coherent plume structure that the retrieval can fit, which breaks down at very low wind (no advection); detection only asks whether any NO2 enhancement is present at the source, which is favored by low wind because NO2 accumulates near the source.

Primary Fuel Type is a significantly less important feature in the US model (feature importance: 0.005) compared to the global model (feature importance: 0.049). This difference likely stems from the relative homogeneity of the US power sector in both its fuel sources and emission controls. First, the Top 500 US emitters are dominated by gas- and coal-fired plants: of the 461 plants still reporting in 2024, ≈ 56 % burn gas (pipeline natural gas, natural gas, other gas, or process gas) and ≈ 39 % burn coal or coal refuse, leaving ≈ 4 % on other fuels and ≈ 1 % with no reported fuel type. This low fuel variability is in stark contrast to the global dataset. While also led by coal (≈ 50 %) and natural gas (≈ 30 %), the global mix is far more diverse, including substantial shares of facilities running on oil (≈ 12 %), biomass (≈ 6 %), and waste (≈ 2 %). Second, this effect is compounded by emission controls. In the US, power plants are subject to relatively uniform and stringent environmental regulations, such as the Clean Air Act, often requiring technologies like Selective Catalytic Reduction to control NOx emissions. Globally, however, the presence and effectiveness of these technologies vary drastically by country. In that context, fuel type can serve as a stronger proxy for a facility's overall emission profile.

While the feature importance analysis identifies the key predictors and their marginal effects, real-world plume detectability emerges from the combined influence of multiple interacting factors. To illustrate how emission rates, albedo, and wind speed operate in concert at individual facilities, we examine in Fig.  five representative power plants that span the range of conditions observed in our dataset. Marion, with low NOx emissions (∼ 83 kgh-1) and low albedo (0.04), has the lowest detectability (P(detect)=0.18). Ottumwa shows higher NOx (∼ 180 kgh-1) but experiences high wind speeds (5.74 ms-1) and a low but highly variable albedo (mean ≈ 0.07, with a long tail from winter snow cover), yielding P(detect)=0.25.

Comparing Marion and Independence directly demonstrates the dominant effect of emission rate: Independence's high NOx (∼ 670 kgh-1) achieves P(detect)=0.57 despite similarly low albedo (0.05). Among the three high-emitting plants (Independence, Dave Johnston, Huntington), surface characteristics and wind become the limiting factors. Independence's low albedo constrains detectability to 0.57, while Dave Johnston (high wind, 6.69 ms-1; albedo 0.09) reaches 0.61, and Huntington (low wind, 3.81 ms-1; high albedo, 0.12) achieves the highest detectability at 0.64. These examples demonstrate that high surface albedo and low wind enhance NO2 retrieval sensitivity even when emission rates are comparable.

Our results empirically confirm several theoretical expectations from satellite trace-gas retrieval physics while quantifying their combined effects on plume visibility at global scale. Viewing geometry exerts a strong nonlinear influence: moderate off-nadir angles enhance detectability by increasing the optical path length through the lower troposphere, consistent with established AMF and averaging-kernel theory . At larger angles, detectability declines as scene radiance decreases and multiple scattering increases . Surface reflectance also plays a major role, with higher albedo increasing scene radiance and retrieval SNR, improving the contrast between a plume and its background, consistent with TROPOMI characterization studies .

Our analysis extends these theoretical principles by quantifying their global impact empirically. Across thousands of facilities, detectability peaks at intermediate sensor zenith angles (near 20° globally and 35° in the US) and increases monotonically with both emission rate and surface brightness. For the US subset, an average hourly NOx emission rate of roughly 400 kgh-1 corresponds to a ∼ 50 % detectability. These results provide the first global observational confirmation of how viewing geometry, surface brightness, meteorology, and emission strength jointly control satellite plume visibility.

The same meteorological, environmental, sensor, and power-plant variables that determine whether a plume is detectable also shape how it appears in satellite imagery. Wind speed controls plume width and dispersion, solar and sensor geometry set the radiative contrast and effective path length, and surface albedo defines the background brightness against which NO2 enhancements are retrieved. If these factors affect visibility, then they also influence the quantitative mapping between observed plume morphology/enhancement and underlying emissions. Consequently, emission-retrieval frameworks, whether physics-based inversions or machine-learning models, are likely to benefit by explicitly incorporating these variables. In inverse modeling, detectability probabilities or their underlying covariates could serve as weights or priors, emphasizing scenes with favorable observing conditions and reducing biases introduced by low-sensitivity observations. In machine-learning-based retrievals, including features such as wind speed, solar/sensor angles, and surface albedo alongside the imagery would allow models to learn how identical plume appearances can correspond to different true emissions under different conditions. This contextual information should improve generalization across power plants and climates, reduce bias in data-poor regions, and produce more physically consistent emission estimates.

We emphasize that detectability as defined here is necessary but not sufficient for emission quantification: it characterizes the upstream observational limit (whether any NO2 enhancement attributable to the plant is present in the scene), whereas quantification additionally requires that the plume's structure be sufficiently coherent to recover an emission rate. The conditions favorable for detection and for quantification therefore overlap but are not identical; for example, low wind favors detection (because NO2 accumulates near the source) but is unfavorable for quantification methods that require a clearly advected plume.

A natural concern is that the reported emission rates used as a predictor are themselves uncertain. Reported inventories disagree both with satellite-derived estimates (e.g., ) and among themselves (e.g., EDGAR vs. E-PRTR ). Within the global subset we use CoCO2 annual emissions , while the US subset uses hourly emissions .

Two factors degrade the signal the model can extract from the reported emissions: noise in the reported inventories, and the use of annual emissions for the global subset (the only data available at global scale), which is a less faithful proxy of the emissions at each observation.

To make the first factor concrete: because NOx emission rate is the model's most important predictor (Sect. ), a plant that over-reports its emissions is presented to the model with a high emission value, leading it to predict high detectability; yet TROPOMI detects the plume less often than expected because the true emissions are lower, so the prediction overshoots. A plant that under-reports produces the opposite error.

These errors propagate in two ways. First, the reported F1 and AUC values should be read as lower bounds on the model performance achievable under cleaner inputs. Second, the same noise feeds into our feature-importance estimate, so that NOx emission rate appears less important than it truly is. Its top SHAP ranking is therefore a conservative lower bound, and access to cleaner inventories, including global hourly data, would only strengthen this ranking.

Several new and forthcoming satellite missions are moving point-source plume sensing toward spatial resolutions finer than TROPOMI's 3.5–7 km pixels. GOSAT-GW/TANSO-3 targets 1–3 km footprints in Focus Mode , CO2M will provide collocated CO2, CH4, and NO2 through CO2I/NO2I at ∼ 4 km2 , and TANGO-Nitro targets facility-scale NO2 imaging at ∼ 300 m . How do the TROPOMI-scale relationships quantified here translate to sensors with smaller footprints? We discuss implications for plume detectability and feature importance in turn.

Spatial resolution affects detectability through competing mechanisms. First, a smaller instantaneous field of view reduces mixing between the plume and background, so a point-source enhancement may be less diluted within a pixel. Second, finer pixels can reduce interference from neighboring power plants and cities. This is particularly relevant for our study because interference filtering excludes a large fraction of plants from the second-stage detectability analysis. Higher-resolution sensors could therefore allow more power plants, and a larger fraction of global emissions, to be characterized. Third, for a fixed instrument design, smaller pixels collect fewer photons, which can increase retrieval noise and background variability. Thus finer spatial resolution should improve plume detection when TROPOMI is limited by plume dilution or source interference, but this gain depends on maintaining sufficient SNR and retrieval quality.

How feature importance changes at finer spatial resolution is harder to predict. The important features identified in Fig.  should be interpreted as properties of the TROPOMI retrieval, TROPOMI pixel size, the detection algorithm, and the sampled observation conditions, rather than as feature rankings that transfer unchanged across sensors. Surface albedo and surface altitude are especially important examples. In our TROPOMI-based model, these variables may influence detectability both by affecting retrieval and by acting as proxies for systematic bias associated with unresolved surface heterogeneity. Recent work on CO2M-like retrievals shows that correlated subpixel variations in surface reflectance and altitude can produce retrieval biases, and that improved subpixel surface characterization can reduce those biases . At finer resolution, some of the apparent importance of albedo or altitude could therefore decrease if it currently reflects unresolved subpixel bias. Repeating our analysis for higher-resolution sensors would show which predictors remain dominant across instruments and which are specific to TROPOMI-scale retrieval and resolution. We leave this comparison to future work.