The Orbiting Carbon Observatory-2 (OCO-2) launched in July 2014 collects high-resolution spectra of reflected sunlight in the bands centered near 0.765, 1.61 and 2.06 µm (Crisp et al., 2017). OCO-2 flies on a near-polar sun-synchronous orbit and crosses the Equator at a fixed local time (LT) near 13:36 with a repeat cycle of 16 d. About 10 % of the approximately 1 million daily CO2 observations are cloudless and can be used to retrieve the column-averaged dry-air mole fraction of carbon dioxide (XCO2) with the Atmospheric CO2 Observations from Space (ACOS) algorithm at a spatial resolution of about 1.29 × 2.25 km2 across swaths which are up to 10 km wide (O'Dell et al., 2018). The Orbiting Carbon Observatory-3 (OCO-3) launched in May 2019 is mounted on the Japanese Experiment Module – Exposed Facility (JEM-EF) of the International Space Station (ISS) and views the Earth at all latitudes less than about 52∘ with a footprint size of about 1.6 × 2.2 km2. In addition to the same three observation modes (nadir, glint and target) as OCO-2, OCO-3 also collects nearly adjacent swaths of data using a new pointing mirror assembly (PMA), resulting in a snapshot area map (SAM) scan of approximately 80 × 80 km2. Since all the power plants in this study are located on land, we only exploit OCO-2 and OCO-3 measurements over land surfaces (i.e., surface type = 1 in the OCO data). For the observations of OCO-3 SAM mode, we only analyze data on the same scan line (i.e., similar PMA elevation angles). We use good-quality retrievals (XCO2_quality_flag = 0) of version 10r of the OCO-2 bias-corrected XCO2 retrievals from January 2018 to December 2021 and version 10.4r of the OCO-3 bias-corrected XCO2 retrievals from August 2019 to November 2021 provided by NASA's Goddard Earth Sciences Data and Information Services Center (https://oco2.gesdisc.eosdis.nasa.gov/data/s4pa/OCO2_DATA/OCO2_L2_Lite_FP.10r/, last access: 1 March 2022, https://oco2.gesdisc.eosdis.nasa.gov/data/s4pa/OCO3_DATA/OCO3_L2_Lite_FP.10.4r/, last access: 24 March 2022).

The passive-sensing hyperspectral nadir-viewing instrument TROPOMI on the Copernicus Sentinel-5 Precursor satellite provides daily global coverage of tropospheric NO2 vertical column densities (NO2 TVCDs) with a spatial resolution of 3.5 × 7 km2 initially and 3.5 × 5.5 km2 since 6 August 2019. TROPOMI flies on a sun-synchronous orbit with an overpass time of 13:30 LT, the same as OCO-2. Global daily NO2 TVCD maps were gridded to a regular latitude–longitude grid with 0.025∘ resolution using pixels with a cloud fraction less than 30 %. In order to keep as many pixels as possible to observe as much of the plume as possible, data quality (i.e., “qa value”) filtering is not used. The NO2 data we obtained are consistent with the OCO-2 and OCO-3 data of the same day in this study (https://s5phub.copernicus.eu/, last access: 19 October 2021).

We collected reported hourly CO2 emission data for US power plants from the US Environmental Protection Agency (EPA) from 2018 to 2021 (https://www.epa.gov/airmarkets/power-sector-emissions-data, last access: 5 March 2022) as truth to validate the satellite-estimated emission. We sorted out the list from EPA for all 1631 power plants operated during this period.

The publicly available Global Power Plant Database (GPPD, v1.3.0) from the World Resources Institute was used to automatically identify CO2 emission signals from power plants upwind of satellite tracks (Yin et al., 2021). The GPPD includes 34 936 power plants (https://datasets.wri.org/dataset/globalpowerplantdatabase, last access: 2 June 2021) with 15 fuel types, such as biomass, geothermal, hydro, nuclear and solar. In this study, we selected power plants using gas, coal, oil and pet coke as primary fuel to a subset. The resulting subset of the GPPD comprises 8660 power plants of which 3998, 2330, 2320 and 12 use gas, coal, oil and pet coke as primary fuel, respectively. In order to see emission signals from as many power plants as possible, we did not delete power plants with a low generation capacity as was done in other studies (Nassar et al., 2017; Beirle et al., 2021). The reason is that if a power plant with a small capacity is located in an area with less background interference - such as an area far away from cities and with low vegetation coverage – its emissions may still be detectable by satellites.

We used three types of wind field data in the CO2 emission estimation procedures described in Sect. 3. Hourly horizontal wind fields u and v at 10 m are taken from the European Centre for Medium-Range Weather Forecasts (ECMWF) next-generation reanalysis ERA5 dataset (0.25∘ × 0.25∘) and the Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2) dataset (0.5∘ × 0.625∘). The effective wind speed proposed by Varon et al. (2018) and used by Reuter et al. (2019) and Hakkarainen et al. (2021) was calculated from the 10 m wind by applying the empirical scaling factor 1.4. Varon et al. (2018) derived this scaling factor from a linear fit between effective wind speed and 10 m wind speed. The effective wind speeds from ERA5 (WERA) and MERRA-2 (WMERRA) are derived using factor 1.4 for this study. In addition, the wind field (0.25∘ × 0.25∘) at half the height of the planetary boundary layer (WPBL) is derived from the 3D hourly wind fields, and PBL heights are derived from the twice daily (0 and 12 h) operational high-resolution forecasts of ECMWF. We use the wind vector of the model layer, which contains the altitude equal to the PBL height divided by 2. These three wind field choices are used to explore the robustness of the emission estimates.

The first step towards estimating CO2 emissions from power plants is to extract plume XCO2 anomalies, i.e., XCO2 local enhancement. We use power plants with hourly reported emissions from the US EPA as research objects, search for all adjacent XCO2 observations as candidate cases and choose XCO2 enhancement cases linked to isolated power plant emission plumes by the wind direction. The search range is limited to a 0.25∘ radius around each power plant. The selection is based on the visual identification of a plume in the downwind direction of the power plant. Power plants located in urban areas are excluded because their emission plumes are compounded by urban emissions. This selection of cases for isolated US power plants allows us to verify the accuracy of estimated emissions using hourly reported emission data from EPA. For global XCO2 data, we provide a semi-automatic detection algorithm described in Sect. 3.3.

In this study, we use the following steps to extract XCO2 anomalies of global power plants for the estimation of their CO2 emissions:

We detect all satellite overpass data within a 0.25∘ radius around each power plant and intercept all observations within the latitude range of ± 0.5∘ around the nearest observation from the power plant as potential cases.

Figure 1a shows an example of a power plant emission plume in the satellite observations. The Jeffrey Energy Center power plant in Kansas was in operation at about 01:30 local time on 30 October 2020, and its CO2 plume was captured by the downwind track of OCO-2. The local enhancement appears as a peak in a latitude direction, the cross-section of which is well approximated by a Gaussian (Fig. 1b). For the entire US, we analyzed the 1284 plants reported by the EPA, of which 347 were excluded because of nearby city emissions. A total of 9950 OCO-2 and 13 427 OCO-3 tracks were recorded within a 0.25∘ radius of these power plants. We used observations in the latitude range of ±0.5∘ around the XCO2 maximum for all tracks (the range shown in Fig. 1a) and performed a visual selection to identify cases of enhancement from plumes of isolated power plants like in Fig. 1. The screening criterion is able to select a clear plume profile in the XCO2 observations downwind of the power plant, such as in Fig. 1e–h, while other cases are rejected due to insignificant XCO2 enhancement, missing data and emission source cluster interference, such as in Fig. S10. In the end, we arrived at 50 cases where the power plant was operating and the emission plume crossed the satellite track, including 30 cases from OCO-2 and 20 cases from OCO-3. When the distance between two adjacent power plants did not exceed the range of 1 pixel of the satellite, it was regarded as a single isolated emission source, and their names were connected with commas (Table 1).

Previous studies used various choices of wind information to approximately account for the plume spreading, such as the wind speed at the assumed height of the chimney plus an assumed 250 m for typical plume rise above the stack height (Nassar et al., 2021) or 31 m (Chevallier et al., 2020), the average wind speed of the pressure layer near the ground (Zheng et al., 2020a; Hakkarainen et al., 2021), or a calculation of an effective wind (Varon et al., 2018; Reuter et al., 2019; Hakkarainen et al., 2021). In this study, we compared the estimated CO2 emission results driven by WERA5 (Fig. S3), WMERRA (Fig. S4) and WPBL used for the GPM method. The correlation coefficient R of the estimated emission and time-corrected reported US EPA emission of the 50 cases of isolated power plants are 0.35, 0.28 and 0.14 for WPBL, WERA and WMERRA, respectively (Figs. 2a, S3a, S4a). The results show that the emission estimates obtained using WPBL give better results than the other two wind options, which suggests that it represents the spreading of CO2 plumes in the vertical direction more accurately (Figs. 2, S3, S4). The results using MERRA-2 were worse (Fig. S4) due to its low resolution (GMAO, 2015), which cannot provide precise wind information for emission sources. These 50 cases contain multiple observations of 22 isolated power plants. For some power plants, we have multiple observation days. For these cases we have averaged the results. As shown in Fig. 2b, the correlation coefficient R of the averaged estimated emission and the reported emission is 0.63, 0.44 and 0.22, corresponding to WPBL, WERA and WMERRA, respectively (Figs. 2b, S3b, S4b). We also tested the weighted average considering the uncertainty of the estimates and reached the same conclusion that WPBL has the best performance. The improved correlation illustrates the large fraction of randomness in the emission retrieval uncertainty (Chevallier et al., 2022). For the sum of the estimates of the repetitive cases of each power plant, we obtained a better correlation of 0.93, 0.89 and 0.73, corresponding to WPBL, WERA and WMERRA, respectively (Figs. 2c, S3c, S4c). Therefore, we decided to use WPBL for the estimation of power plant emissions. In this study, the background for the cross-sectional flux method is determined by fitting of Eq. (3), while the background for the Gaussian plume model (GPM) method is determined by the 90th percentile showing the lowest error for all cases in Fig. S2a. The difference in background obtained by these two methods is on average small (Fig. S11a) but with a maximum difference of 0.86 ppm and a minimum of 0.004 ppm (Fig. S11b). Under the two background calculation methods, the GPM method has good consistency in the estimation results driven by three wind fields (Fig. S11c–e). With the background computing by Eq. (3), the conclusion that estimated emissions have better accuracy using the WPBL is still valid (Fig. S12).

In Fig. 3, we compare the GPM method and the cross-sectional flux method driven by WPBL. Among them were two cases without a result from the cross-sectional flux method because of invalid fitting. It shows that the estimates from the cross-sectional flux method fluctuate much more than the estimates from the GPM method. This is mainly because the orbits of the OCO-2 and OCO-3 satellites are not perpendicular to the plume, and the final step of the cross-sectional flux method uses the wind field component normal to the orbit multiplied by the line density to estimate the flux, while the GPM method derives the posteriori emission by a linear least-squares fit between observed and simulated enhancements. Moreover, the OCO-2 and OCO-3 observations do not sample the entire emission plume, as shown in Fig. 1f, but just the part of the plume cross-section within the narrow width along the orbit. Hakkarainen et al. (2021) also found that the estimates from the cross-sectional flux method fluctuated greatly. Therefore, we decided to use the GPM method for the estimation of global power plant emissions. When comparing plant-level estimated emission with reported emission by the US Energy Information Administration (EIA) from fuel consumption records (https://www.eia.gov/electricity/data/emissions/, last access: 21 March 2022), Fig. S6 shows that the correlation between estimated emission and reported annual emission from EIA (R=0.39) is lower than that from EPA, although the reported annual emissions from EPA and EIA reveal a good correlation (R=0.80). Figure 4 shows that, due to strong hourly variations in the power plant emission, the satellite overpass time is not always representative of the annual emission of a power plant. Note that EIA reports the yearly mean emission based on the annual fuel consumption of the power plant, which will differ from the emission at the satellite overpass time.

Table 1 lists the average estimated emissions for 22 power plants and the estimated uncertainty caused by the background, XCO2 and wind field. The deviation of the estimated emissions and reported emissions varies between 0.47 and 22.11 kt d-1, and the total uncertainty varies between 1.65 and 28.32 kt d-1. The total uncertainty is comparable to the uncertainty of power plant emissions in previous studies, which ranged from 3.42 to 19.2 kt d-1 (Nassar et al., 2017, 2022). The uncertainty of wind speed is between 0.08 and 1.4 m s-1, and the uncertainty of background varies between 0.03 and 0.1 ppm (Table S1 in the Supplement). Among the three uncertainty components, the uncertainty caused by the wind field is the highest. From 2018 to 2021, for the XCO2 archived data, there are six cases found for the Jeffrey Energy Center power plant (KS) and four cases for the Prairie State Generating Station (IL), Colstrip (MT), Cumberland (TN) and Oak Grove (TX) power plants. For a few power plants, we found that the time variability of estimated and time-corrected hourly EPA-reported emissions from multiple observation cases of power plants displays a good consistency (Fig. S5), such as the Gibson (IN) and Labadie power plants (MO). Excluding the two power plants whose uncertainties are greater than the estimated emissions, the uncertainties of the other cases are within 8 % to 51 % of the reported emissions.