For the divergence method a flux is derived by multiplying TROPOMI measured SO₂ vertical column density (VCD) gradients with the horizontal 2D wind field. The divergence of this flux is related to the emissions. We use the TROPOMI COBRA (Covariance-Based Retrieval Algorithm) SO₂ VCDs with a spatial resolution of 3.5 km × 5.5 km at nadir. The COBRA SO₂ VCDs represent SO₂ within the Planetary Boundary Layer (PBL), mainly associated with anthropogenic emissions. The COBRA retrievals can detect SO₂ concentrations of small anthropogenic sources with emissions of 8.0 Gg yr⁻¹ (Theys et al., 2021). We calculate the daily SO₂ divergence and subsequently compute seasonal averages for the period December 2018 to November 2023. To ensure good data quality, we exclude retrievals with a QA value below 0.5 or a surface height above 3 km (https://data-portal.s5p-pal.com/product-docs/SO2cbr/S5P-BIRA-PRF-SO2CBR_1.0.pdf, last access: 19 January 2026). Daily wind fields are taken from the daily operational 12h forecasts of the European Centre for Medium-range Weather Forecasts (ECMWF) at 0.25° × 0.25° resolution (https://www.ecmwf.int/en/forecasts, last access: 31 July 2025). Assuming SO₂ is vertically well mixed within the PBL, we use horizontal wind fields at half of the PBL height to represent PBL wind conditions. To reduce the artifacts from the simplified 2D wind field, especially over complex terrain, we correct the 2D wind fields for the wind divergence following the method of Bryan (2022).

The monthly mean OH climatology is derived from the 5-year average from November 2018 to December 2023 using CAMS (Copernicus Atmospheric Monitoring Service) global forecast data (DOI: 10.24381/04a0b097; https://ads.atmosphere.copernicus.eu, last access: 9 September 2025) for chemical lifetime calculation. The forecast dataset is based on ECMWF's Integrated Forecast System (IFS), which assimilates and models the concentrations of more than 50 chemical species (such as SO₂ and OH), seven aerosol types, and various meteorological factors, all at a resolution of 0.4° × 0.4°. We derive the monthly mean OH climatology for the time period before the TROPOMI overpass time (13:30 local time) by averaging monthly OH concentration at 06:00 UTC (11:30 local time) within the PBL between 2018 to 2023, excluding days with extreme weather events, such as large-scale precipitation. The dry deposition lifetime is calculated by assuming a constant dry deposition velocity of 0.4 cm s⁻¹ in the atmosphere. Except for OH concentration, the SO₂ VCD within PBL and the wind field data in the mid-PBL layer from CAMS datasets are used for the method validation in Sect. 4.1.

We use two datasets for validation over India. The first dataset is from the global power plants database maintained by the World Resources Institute (https://github.com/wri/global-power-plant-database, last access: 31 July 2025). This database provides the locations and power generation of 255 coal-based thermal power plants in India and is used to assess the positional accuracy of the point sources identified in our inventory. The second dataset is the global catalog of large SO₂ point sources from the Multi-Satellite Air Quality Sulfur Dioxide (SO₂) database, Long-Term L4 Global V2 (referred to as MSAQSO₂L4) (Fioletov et al., 2023). This catalog is based on SO₂ slant column density (SCD) data from two sources: the operational version 2 OMI and OMPS Principal Component Analysis (PCA) retrieval algorithm, and the TROPOMI Covariance-Based Retrieval Algorithm (COBRA) (Theys et al., 2021). Their emission estimates are derived using an exponentially modified plume fitting model. In total, the catalog identifies 92 SO₂ point sources in India. Both datasets are used to assess whether our method detects additional new point sources.

This full divergence calculation follows the method in Chen et al. (2025). Specifically, we use Eq. (S1) in the Supplement together with a corrected wind field to calculate SO₂ divergence. The wind is corrected using an iterative wind-divergence correction algorithm by Bryan (2022). As described in detail in Cifuentes et al. (2025) the impact of topography is clearly reduced, especially along coastal regions. We will calculate the emissions at various grid resolutions to test the effect of our sharpening: 0.1° × 0.1°, 0.05° × 0.05°, 0.025° × 0.025°, and 0.01° × 0.01°. We calculate the divergence on the TROPOMI pixels with rotated wind field following the method of Beirle et al. (2023) and then interpolate the results on the regular grid cells of 0.025° × 0.025° for the final emission estimates for the best results. See Sect. S1 for more details.

Since the spreading of emissions always takes place during the divergence calculation, we explore a sharpening method to further improve the emission resolution. We use a spreading kernel B to describe how the original true emission map X spreads to form the blurred derived emission map Y as expressed in the following equation: 1Y=B×(X+ε), where ε represents the noise on the original SO₂ emission map X. Now, we use the spreading kernel B to calculate the sharpening kernel. Kernel B can be derived from the derived emission distribution in the grid cells adjacent to the source location. Figure 1 shows the normalize derived SO₂ emissions as function of the distance from the point source location. To obtain a spreading kernel which represents the overall spreading pattern of point source emissions, we fit the emission variation around the large and isolated point sources in India using a Gaussian-shaped function. Figure 1a shows the SO₂ emissions and the corresponding Gaussian-shaped fitting functions as function of distance in kilometers. From Figs. 1a and S1 in the Supplement, we see that the emission resolution improves with finer grid cells, but gains become marginal once the grid is finer than the TROPOMI pixel size. Figure 1b shows the SO₂ emission as function of distance from the point source location, but with distance expressed in grid cells. Since we decide to derive the SO₂ emissions based on TROPOMI pixels and regrid to 0.025° afterwards, we derive the spreading pattern from the corresponded Gaussian-shaped function (red dots in Fig. 1b) over the grid cells. The SO₂ emissions of point sources approaches zero at approximately 4 grid cells (around 11.25 km) away from the point sources. Therefore, we define the spreading region (also the size of the spreading kernel) for each point source as a 9 × 9 grid cells (around 22.5 km × 22.5 km) centered on the source location. The spreading kernel B follows a Gaussian-shaped function derived from the annual emissions with a sigma of 2.21 grid cells, and derived from 5-year averaged emissions with the sigma of 1.83 grid cells. (See details in Sect. S2 in the Supplement.)

The sharpening kernel A is derived from the spreading kernel B. When requiring local mass balance, the sharpening kernel A used to reconstruct each point source emissions can be expressed by: 2A=I+I-Bb00-1, where b00 is the central element of the kernel B, and I is the identity kernel. We cannot apply this sharpening kernel to the whole map Y because this would also sharpen spread emissions and increase the noise. Therefore, we define the following “local” sharpening kernel A′ 3A′=Aat(i,j)Ielsewhere In each iteration n, we select the location (i,j) with the highest remaining emission in emission map Yn-1, which has not been selected in previous iterations. The updated emission map is then computed as: 4Yn=A′×Yn-1. Note that in typical deconvolution method, the sharpening kernel is applied to the entire region at once. However, sharpening in this way causes the point source emissions to add more noise as shown in Fig. 2b. We therefore use Eq. (4) to sharpen locations stepwise by using the local sharpening kernel of Eq. (3) for locations in a descending order of emission strength (from high to low), minimizing the risk of applying sharpening to regions dominated by the spread emissions or noise. There is total mass balance in each local area where sharpening is applied.

The step-wise process stops when the highest unsharpened value Yn-1(i,j) is below the noise level in Y. This means we only sharpen emissions above the noise level (see noise level information in Sect. S6). This approach helps focusing on real point source emissions. If values below the noise level are sharpened, it will amplify the noise, making it harder to distinguish real point source from the sharpened noise. Figure 3 compares the results of sharpening emissions above zero and above noise level. In Fig. 3a, where all above zero grids are sharpened, the noise is also amplified.

Previous studies have shown the effectiveness of the divergence method in estimating emissions. We expect a further improvement combining the divergence method with our sharpening algorithm. To evaluate the performance of the combined approach, we implement it within a closed-loop validation process. Specifically, we apply the divergence method together with the algorithm to derive SO₂ emissions based on simulation results from the CAMS model, including SO₂ column densities, OH concentrations and IFS model-output wind fields. Since the input emissions used to drive the CAMS model is known, we can assess the accuracy of our method by comparing the derived top-down emissions with the original model input. Here we use as input the emission inventory CAMS Global Anthropogenic Emissions Inventory Version 4.2 (CAMS-GLOB-ANT v4.2) (Soulie et al., 2023; Copernicus Atmosphere Monitoring Service (CAMS), 2020) with the original spatial resolution of 0.1° × 0.1°, and the corresponding CAMS composition forecasts driven by this inventory from December 2019 to November 2020 as output in this closed-loop validation. Figure 4 shows the comparison between the input SO₂ emissions and the derived SO₂ emissions. There is a noticeable difference in distribution between the model input emissions (Fig. 4a) and the emissions derived from the divergence method (CDM) (Fig. 4b). The latter emission map appears more dispersed, with the point source emissions spreading into adjacent grid cells. This spreading effect also leads to a lower emission peak at the point source location, for example, the maximum value is much lower in Fig. 4b than in Fig 4a. In contrast, the model input emissions in Fig. 4a are more concentrated, showing higher values at the point source locations. To reduce this discrepancy, we sharpen Fig. 4b with the model-based 5 × 5 sharpening kernel. The size and the shape of this kernel are derived from the spreading pattern (Fig. S4) of “blurry” emissions (Fig. 4b) using Eq. (2). The emissions after sharpening in Fig. 4c prove that the algorithm effectively improves the emission estimates. The total emissions shown in Fig. 4b and c are the same and comparable to Fig. 4a, but the point-source emissions in Fig. 4c are no longer spread. Additionally, Fig. 5 compares the SO₂ emissions of point sources for the different methods. As shown in Fig. 5a, a clear underestimation is shown for SO₂ emissions derived only with the divergence method. But the underestimation is efficiently reduced after applying the sharpening as seen in Fig. 5b. It is important to note that the CAMS model resolution is relatively coarse (0.4° × 0.4°). At this resolution, some individual emissions are not well recovered during sharpening, because the spreading regions of the 5 × 5 kernels can overlap with several nearby point sources. Applying this combined approach to real measurements with finer spatial resolution will lead to a better performance, which will be shown in the following sections.

After the model-based evaluation, we apply the sharpening algorithm to satellite-based top-down SO₂ emissions at a resolution of 0.025° × 0.025°. At this high resolution, the emission signals of point sources are not easily visible on the large map over India. To better illustrate the improvement, we use all Indian coal power plants with annual power generation larger than 1500 MW and check their emission distribution at surrounding areas (9 × 9 grid cell areas) before and after sharpening. In total, 38 such power plants (Table S2) are included, and all of them are detected in our 1-year emission result (from December 2022 to November 2023). We average the emission distributions centered on these 38 point sources for each surrounding grid cell, with the results shown in Fig. S5. We see that the actual emission distribution before sharpening closely follows a 2D Gaussian pattern (Fig. S5a). This supports the Gaussian-shaped spreading pattern derived earlier from Fig. 1b. After sharpening the emission spread is removed and the point source emissions are enhanced by up to 28 times compared to the unsharpened case, while ensuring mass conservation (Fig. S5b). The emission signal becomes more concentrated into a single grid cell, effectively increasing the emission resolution to match the grid cell resolution. In addition to this averaged analysis, we also check the emission distribution of several individual point sources. In Fig. 6, four examples are given to show the effect of the sharpening in individual cases, the left figure shows the original distribution and the right figure after sharpening for an area of 9 × 9 grid cells. In Fig. 6a, the emissions of two sources are mixed before sharpening, but they are clearly separated in Fig. 6b. In Fig. 6c–f, a strong signal appears at the main source location, while smaller sources nearby are also visible. The small point source in Fig. 6d is and are newly detected power plant in our inventory. In Fig. 6g and h, the point source emissions are lower than the large point sources, the emission distribution before sharpening shows less of the characteristics of a Gaussian shape, making it more difficult to identify. However, after applying the sharpening algorithm the emission source is clearly localized and quantified.

The improved emission resolution makes it easier to precisely locate the SO₂ point sources in the top-down emission inventory. To evaluate the location accuracy of the SO₂ point sources in our emission inventory, we compare the detected locations using one-year emission results (December 2022 to November 2023) with the actual locations of 82 known coal power plants with annual power generation larger than 1000 MW as shown in Fig. 7. The locations of the selected point sources are shown in Table S3. Among them, 51 power plants are detected within the same grid cell as their actual location, and 26 power plants are detected in the grid cells directly adjacent to the actual locations. If we consider the average TROPOMI pixel size (6.0 km × 6.0 km) as the resolution for detecting point sources, then 80 out of 82 power plants (approximately 97.5 %) are successfully located within this range using emissions derived from TROPOMI measurements. The remaining 2 power plants are detected two grid cells away from their actual locations, which is the result of the influence from nearby sources, e.g. other closely located point sources or large urban areas, may cause the peak VCD and resulting emissions shift away from the point source location.

Since the point source emission signals have been enhanced, we expect more emission signals to be visible on our satellite-based emission map. Coal-based power plants are the largest sector for SO₂ emissions in India. To assess our results, we compare both annual and 5-year averaged emission signals with the actual locations of all coal-based power plants across the country. These plants have annual capacities ranging from 10 MW to 4760 MW. Because some sources may have low emissions in certain years and the emission peaks may not align exactly with plant locations, we define a power plant as “detected” if the annual emission signal above the annual detection threshold 10 Gg yr⁻¹ or the 5-year averaged emission signal above the corresponded detection threshold 3.4 Gg yr⁻¹ within 6.0 km of the plant (see Sect. S6 for more details on noise levels and detection thresholds). As summarized in Table 1, long-term averaged emissions allow more power plants to be detected. All large power plants with annual power generation larger than 1500 MW are identified in both annual and 5-year results. In addition, approximately 80 % of power plants with capacities larger than 100 MW yr⁻¹ are successfully detected using 5-year averages, while the emissions of the remaining 20 % of power plants are lower than the noise level or 6.0 km further away from the actual location. These detected plants represent 99 % of India's total coal-based power generation. For large power plants with annual capacities above 1000 MW, contributing 77 % of the total generation, the detection rate reaches 95 %. The higher the output, the more coal is burned, making emissions more likely to be detected.

We find some new operating SO₂ point sources using both annual and 5-year averaged SO₂ emission inventories. These emissions are absent in the Indian power plant database and are also not identified by the top-down SO₂ catalogue MSAQSO₂L4. These new point sources include not only coal-based power plants, but also cement factories, crude oil production facilities, a chemical fertilizer factory, and copper, steel, and aluminum industries. Table 2 provides the list and locations of these sources. Many newly detected sources are small and located close to known large point sources, but their weaker signals are distinguishable in our inventory. The annual emission inventory better distinguishes small point sources located near large ones, whereas the long-term averaged inventory provides more precise source locations. Most operating point sources show persistent SO₂ emission signal over five years. However, Rashtriya Chemicals Fertilizers (RCF) complex involving a sulfuric acid plant located in Trombay, Maharashtra is detected only for the year 2021. RCF reported that sulfur consumption in the financial year March 2021–March 2022 was 2.7 times higher than in 2020-2021 (https://www.rcfltd.com/public/storage/investers/1669721755.pdf, last access: 20 February 2026), indicating substantially higher potential SO₂ emissions in 2021. This indicates that applying the sharpening algorithm to short-term emission results enables the analysis of temporal variability, including emission changes and possible commissioning or shutdown events. In contrast, the Phil Coal Beneficiation and Sponge Iron Cluster is only detected in the 5-year averaged inventory, but not in any individual annual result. This is because long-term averaging results reduces noises, allowing the sharpening algorithm to better detect small but stable emitters.