2.2.1 Coal-fired power plants without post-combustion NO_x control systems

We initially limited our analysis to $E_{{\mathrm{NO}}_x}^{\mathrm{CEMS}}$ and $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{CEMS}}$ from coal-fired power plants without post-combustion NO_x control systems in operation in a given year (Table 1). We find that $E_{{\mathrm{NO}}_x}^{\mathrm{CEMS}}$ and $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{CEMS}}$ have a strong linear relationship (Fig. 4). In Fig. 4a, we compare $E_{{\mathrm{NO}}_x}^{\mathrm{CEMS}}$ and $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{CEMS}}$ from power plants (using bituminous coal) by boiler firing type in 2005. We use bituminous coal-fired plants for illustration, as bituminous coal is the most widely used coal in US power plants. We analyzed power plants that use cyclone or cell burner boilers separately and exclude them in Fig. 4 because they typically produce higher NO_x emissions than other boiler types (USEPA, 2009; available at: https://www3.epa.gov/ttn/chief/ap42/ch01/index.html, last access: 1 April 2019). A strong linear relationship between $E_{{\mathrm{NO}}_x}^{\mathrm{CEMS}}$ and $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{CEMS}}$ is evident with excellent correlation (R²=0.93, N=278), regardless of boiler firing type. Similar linear relationships exist for other years (e.g., year 2016 in Fig. 4b) and other types of coal (Table 1). The slope of the regression of $E_{{\mathrm{NO}}_x}^{\mathrm{CEMS}}$ and $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{CEMS}}$, ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$, is assumed by setting the intercept to zero. Table 1 shows ${\mathrm{ratio}}_{\mathrm{regressed},i,y}^{\mathrm{CEMS}}$ by coal type and year. In Sect. 3.1, ${\mathrm{ratio}}_{\mathrm{regressed},i,y}^{\mathrm{CEMS}}$ will be applied to approximate ${\mathrm{ratio}}_{i,y}^{\mathrm{CEMS}}$ when estimating $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{Sat}}$ from $E_{{\mathrm{NO}}_x}^{\mathrm{Sat}}$ for the eight plants (Fig. 1) for years before post-combustion control systems were in operation.

Figure 4Scatterplots of $E_{{\mathrm{NO}}_x}^{\mathrm{CEMS}}$ versus $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{CEMS}}$ for all the US bituminous coal-fired electric generating units for (a) 2005 and (b) 2016. Values are color coded by firing type. (c) Scatterplot of $E_{{\mathrm{NO}}_x}^{\mathrm{CEMS}}$ versus electricity generation of the same units for years 2005 (triangle) and 2016 (square). Only plants without post-combustion NO_x control devices within a given year are used. The electricity generation data are also from eGRID. The lines in all three panels represent the computed linear regressions.

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The ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ value for power plants using bituminous coal decreased from 2005 (Fig. 4a) to 2016 (Fig. 4b) by 31 % on average because of reductions in NO_x emission factors associated with improvements in boiler operations, such as by optimizing furnace design and operating conditions. The NO_x emissions factors, defined as NO_x emission rates per net electricity generation (Gg TW h⁻¹), declined by 33 % from 2005 to 2016 (Fig. 4c). We interpolated ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ to get year-specific ratios by coal type for the entire study period, as eGRID data are only available for some years (i.e., 2005, 2007, 2009, 2010, 2012, 2014, and 2016).

In addition, ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ shows significant variation by coal type and year (Fig. 5). The ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ value is 1.7, 1.3, and 0.91 Gg NO_x∕TgCO₂ for bituminous, subbituminous, and lignite coal types in 2005, respectively. A reduction over time in ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ is observed for all coal types (Fig. 5). The ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ value displays a large decrease of 31 %, 36 % and 20 % from 2005 to 2016 for bituminous, subbituminous, and lignite coal types, respectively.

Figure 5Interannual trends of ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ for power plants using bituminous, subbituminous, and lignite coal types and without post-combustion NO_x control devices in a given year. Error bars show the standard deviations for ratios of $E_{{\mathrm{NO}}_x}^{\mathrm{CEMS}}$ to $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{CEMS}}$ for individual power plants.

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2.2.2 Coal-fired power plants with post-combustion NO_x control systems

Here, we describe how we estimated ratio^CEMS for the entire study period for plants that had post-combustion NO_x control systems installed at some time during our study period, 2005–2017. The estimation is based on ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ derived in Sect. 2.2.1 for plants without post-combustion control systems in operation. We introduce a NO_x removal efficiency parameter, f, to adjust ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ for years after the installation of post-combustion control systems, ratio^{CEMS-estimated}:

f is commonly measured for individual power plants to describe the performance of their post-combustion NO_x control systems. It is directly reported by some power plant databases, such as the China coal-fired Power plant Emissions Database (CPED; Liu et al., 2015). For databases that do not report f, like eGRID used in this study, one can estimate it for an individual power plant by first estimating the unabated emissions per electricity generation, e_unabated, which is the emission factor before the flue gas enters the post-combustion control system:

where e_CEMS denotes the actual emission factor in terms of CEMS NO_x emissions per net electricity generation (Gg TW h⁻¹).

e_unabated for a given year, e_unabated,y, is estimated based on the emission per electricity generation for years prior, p, to the installation of the post-combustion control system, e_unabated,p:

where the scaling factor, k_y, is used to account for the change over time in e_unabated associated with improvements in boiler operations discussed in Sect. 2.2.1. k_y is calculated as the ratio of the averaged e_unabated (i.e., the slope of the regression of NO_x emissions on electricity generation) in year t to that in year p.

To assess the reliability of ratio^{CEMS-estimated}, we selected all power plants that had post-combustion devices installed between 2005 and 2016. Figure 6 shows a scatterplot of ratio^CEMS (i.e., the ratio of $E_{{\mathrm{NO}}_x}^{\mathrm{CEMS}}$ to $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{CEMS}}$ for individual plants) and ratio^{CEMS-estimated}. We used the NO_x emissions factor in 2005, e_{unabated,2005}, to predict the unabated emission factor in 2016, e_{unabated,2016}, following Eqs. (3) and (4) in order to quantify the removal efficiencies for 2016, f₂₀₁₆. The ${\mathrm{ratio}}_{\mathrm{2016}}^{\text{CEMS-estimated}}$ value is based on the estimated f₂₀₁₆ and ${\mathrm{ratio}}_{\mathrm{regressed},\mathrm{2016}}^{\mathrm{CEMS}}$ from Sect. 2.2.1. ratio^CEMS and ratio^{CEMS-estimated} show good correlation (R²=0.64), which increases our confidence that the estimated removal efficiencies approximate the actual efficiencies. The slight underestimation suggested by the slope of 0.85 arises from uncertainties in estimating unabated NO_x emission factors (e_unabated,y) using Eq. (4) and thus removal efficiencies (f), which is a major source of error of $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{Sat}}$ for power plants that install post-combustion NO_x control systems (see details in Sect. 3.2).

Table 2Summary of effective NO_x lifetimes, satellite-derived NO_x emissions ($E_{{\mathrm{NO}}_x}^{\mathrm{Sat}}$) and CO₂ emissions ($E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{Sat}}$), bottom-up NO_x emissions ($E_{{\mathrm{NO}}_x}^{\mathrm{CEMS}}$), and CO₂ emissions ($E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{CEMS}}$) for eight US power plants during May to September from 2005 to 2017. The 3-year periods are represented by the middle year with an asterisk.

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Figure 6Scatterplot of ratio^{CEMS-estimated} as compared to ratio^CEMS for 2016. All 44 coal-fired power plants that operated post-combustion devices after 2005 and before 2016 (including 2016) are used in the plot. The sizes of the circles denote the magnitude of the NO_x reduction efficiency of post-combustion control devices estimated in this study. The line represents the linear regression of ratio^CEMS to ratio^{CEMS-estimated}.

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3.2.1  $E_{{\mathrm{NO}}_x}^{\mathrm{Sat}}$

The uncertainty of $E_{{\mathrm{NO}}_x}^{\mathrm{Sat}}$ is quantified following the method described in Liu et al. (2017), accounting for errors arising from the fit procedure, the NO_x∕NO₂ ratio, and OMI NO₂ VCD observations (Liu et al., 2016). The number 1.32, used for scaling the NO_x∕NO₂ ratio, is based on assumptions presented in Sect. 6.5.1 of Seinfeld and Pandis (2006) for “typical urban conditions and noontime sun”. Note that conditions are quite similar in this study because of the overpass time of OMI close to noon, the selection of cloud-free observations, the focus on the ozone season, and the focus on polluted regions. A case study of chemical transport model (CTM) simulations shows an identical value of 1.32 for Paris in summer (Shaiganfar et al., 2017). The simulated NO_x∕NO₂ ratio at the OMI overpass time within the boundary layer (up to 2 km) in a chemistry–climate model, European Centre for Medium-Range Weather Forecasts – Hamburg (ECHAM)/Modular Earth Submodel System (MESSy) Atmospheric Chemistry (EMAC)(Jöckel et al., 2016), was 1.28±0.08 for polluted (NO_x > 1×10¹⁵ molec cm⁻²) regions for the 1 July 2005, and 1.32±0.06 on average for the ozone season. However, the coarse grid of EMAC ($\mathrm{2.8}{}^{\circ }\times \mathrm{2.8}{}^{\circ }$ in latitude and longitude) may not capture the true range of variation in the NO_x∕NO₂ ratio. Therefore, we assumed an uncertainty of 20 % arising from the NO_x∕NO₂ ratio, double the standard deviation of the EMAC ratio.

Additionally, the tropospheric air mass factors (AMFs) used in NO₂ retrievals are based on relatively coarsely resolved surface albedo data and a priori NO₂ vertical profile shapes, likely causing low-biased VCDs over strong emission sources (e.g., Russell et al., 2011; McLinden et al., 2014; Griffin et al., 2019). The average AMF uncertainty of ∼30 % (see Table 2 in Boersma et al., 2007) likely contributes to the underestimation of emissions from some power plants in this study. Both random and systematic (bias) uncertainties in VCDs directly propagate into the uncertainty of $E_{{\mathrm{NO}}_x}^{\mathrm{Sat}}$ (see details in the Supplement of Liu et al., 2016 and Sect. 3.4 of Liu et al., 2017).

The overall uncertainties of $E_{{\mathrm{NO}}_x}^{\mathrm{Sat}}$ range from 57 % to 64 % for all power plants in our analysis, which is comparable with the level of differences between $E_{{\mathrm{NO}}_x}^{\mathrm{Sat}}$ and $E_{{\mathrm{NO}}_x}^{\mathrm{CEMS}}$. We expect this uncertainty to be less for new (e.g., TROPOMI) and upcoming (e.g., NASA Tropospheric Emissions: Monitoring Pollution, TEMPO) OMI-like sensors, which have enhanced capabilities relative to OMI. Further details are provided in Sect. S1 of the Supplement.

3.2.2  ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$

For power plants without post-combustion devices, ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ derived from the regression (Fig. 4a and b) and the plant-specific CEMS measurements are within 15 %, which is assumed as the uncertainty of the ratio for all power plants.

3.2.3  f

For power plants with post-combustion devices, an additional uncertainty of 20 % is applied to reflect the difference between the predicted and the true removal efficiency as suggested by Fig. 6.

We assume that their contributions to the overall uncertainty are independent. We then define the total uncertainty, expressed as a 95 % confidence interval, as the sum of the root of the quadratic sum of the aforementioned contribution. The overall uncertainties of $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{Sat}}$ are ∼60 % for all power plants in our analysis.

3.2.4 Summary of uncertainties

However, it is worth noting that this uncertainty estimate is rather conservative. The mean and the standard deviation of the relative differences between $E_{{\mathrm{NO}}_x}^{\mathrm{CEMS}}$ and $E_{{\mathrm{NO}}_x}^{\mathrm{Sat}}$, and $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{CEMS}}$ and $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{Sat}}$ for all eight power plants provide a good alternative measure of uncertainties (Table 3). The relative differences are rather small, which are 0 %±33 % and 8 %±41 % (mean ± standard deviation) for NO_x and CO₂, respectively. We additionally calculate the geometric standard deviations (GSDs) of the difference between $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{CEMS}}$ and $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{Sat}}$ from 2006^* to 2016^* for individual power plants in Table S2. The small values of GSDs ranging from 1.07 to 1.31 further improve our confidence in the accuracy of the derived emissions in this study.

3.3.1 Comparison with bottom-up ratios

Figure 8 shows the NO_x to CO₂ emission ratios for 2010 from the global power emissions database (GPED; Tong et al., 2018a), which is the only publicly available bottom-up emission database that reports both NO_x and CO₂ emissions for individual power plants for every country. All countries with over 30 coal-fired power plants in the GPED are shown in Fig. 8. Not surprisingly, countries with more strict standards in place for NO_x emissions from power plants (i.e., NO_x emission limit value, ELV, < 200 mg m⁻³; hereafter referred to as “more strict countries”) have smaller NO_x to CO₂ ratios (i.e., 1.0 versus 2.5 on average) than countries with less strict standards (i.e., NO_x ELV > 200 mg m⁻³; hereafter referred to as “less strict countries”). Additionally, the correlation coefficients are smaller for more strict countries (i.e., 0.82 on average) as compared to less strict countries (i.e., 0.96 on average) because power plants in more strict countries are more likely to have installed post-combustion NO_x control systems, which likely lowered ${\mathrm{ratio}}_y^{\mathrm{CEMS}}$, similar to what occurred in the US over our analysis period (Sect. 2.2.2).

Figure 8Comparison of the regressed NO_x to CO₂ emission ratios derived from the global power emissions database (GPED) for different regions versus the correlation coefficient of the regression. The blue and red circles denote regions that are subject to more strict standards for NO_x emissions from power plants (i.e., a NO_x ELV of 200 mg m⁻³ or less) and other regions, respectively. The y axis is the slope of the regression of the NO_x to CO₂ emissions with an assumed y-intercept of zero. Error bars show the standard deviations for the NO_x to CO₂ emission ratios for individual power plants. The x axis is correlation coefficient of the regression. The dashed line represents 2005 US ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ for bituminous coal derived in this study. The grey shadow represents 2005 US ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ ± standard deviation. ^* China switched from being a less strict country to a more strict country in 2014, when most coal-fired power plants in China were required to comply with its new emission standards (GB13223-2011).

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We further compare the 2005 US ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ in Table 1 with the GPED NO_x to CO₂ emission ratios for less strict countries. We chose the 2005 value for comparison based on the following considerations. In 2005, the US EPA issued the Clean Air Interstate Rule (CAIR) to address the interstate transport of ozone and fine particulate matter pollution for eastern US states, which reduced NO_x emissions and thus NO_x to CO₂ ratios (${\mathrm{ratio}}_y^{\mathrm{CEMS}}$). However, similar comprehensive control strategies have not been adopted in less strict countries. In this way, the 2005 values are expected to show better consistency with the NO_x to CO₂ ratios of less strict countries than values for more recent years. Note that the GPED database does not give information on ratios by coal type. Therefore, we use ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ for bituminous coal, which is the most widely used coal type in coal-fired power plants in most countries.

The ratios for individual power plants in less strict countries tend to be larger than the US ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ for 2005, considering that power plants in those countries may not be equipped with any NO_x control devices or even low-NO_x burners, a technology which is widely installed in US power plants with and without post-combustion NO_x control devices. Most ratios range from US 2005 ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ to 2005 ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}+$ standard deviation (Fig. 8). It is no surprise that some less strict countries have ratios higher than this range, which also occurs for some US power plants without post-combustion emission controls (Fig. 4). However, there are considerable uncertainties in the GPED database given the scarcity of reliable emissions information in less strict countries. For example, the GPED NO_x and CO₂ emissions estimates for Turkey and Russia, which are outliers in Fig. 8, are subject to more assumptions and thus larger uncertainties than countries with high-quality country-specific emission data, such as China, which has a high-resolution emissions database (CPED; Liu et al., 2015), and India, which has a database developed by Argonne National Laboratory (Lu et al., 2012).

Figure 9Schematic of our methodology to estimate the NO_x to CO₂ emission ratios for power plants outside the US. ^* China switched from being a less strict country to a more strict country in 2014, when most coal-fired power plants in China were required to comply with its new emission standards (GB13223-2011).

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Figure 9 shows a schematic of our methodology to estimate the NO_x to CO₂ emission ratios for power plants outside the US. We adopt different approaches for more and less strict countries. More strict countries, including Canada, European Union (EU) member states, Japan, South Korea, and, more recently, China, usually use CEMS to monitor emissions, particularly from the largest emitters. For power plants with CEMS measurements for both NO_x and CO₂ emissions, it is straightforward to use the measured ratios. However, there is still a significant number of power plants in those countries without CEMS technology, particularly for CO₂ measurements. For example, EU member states do not require power plants to use CEMS for CO₂ reporting and the majority of plants in the EU therefore reports CO₂ emissions based on emission factors (Sloss, 2011). Therefore, we recommend applying our method described in Sect. 2.2 to infer region-specific ratios for those power plants. The US ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ could be a less accurate but reasonable approximation when no CEMS data are available, considering those countries share NO_x ELVs for power plants that are similar to the US. For less strict countries, we recommend using the 2005 US values by coal type when ratios from countries with similar NO_x emission standards are not available. We also recommend assigning a range from 2005 ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ to 2005 ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}+$ standard deviation, instead of a fixed value, to the ratio for inferring CO₂ emissions, considering the knowledge about ratios from those regions is too low to narrow the constraint.

As demonstrated in Sect. 2.2, our method presented in this study provides a reasonable estimate of the ratio for power plants without post-combustion NO_x control devices with only knowing coal type. Even for regions without reliable emission information, the information on coal type, particularly for large power plants, are very likely publicly available. For power plants that install post-combustion NO_x control technology, we additionally require the removal efficiency of the device to derive the ratio. The removal efficiency of post-combustion NO_x control devices is usually directly reported, as the operation of such devices is very expensive and is expected to be subject to strict quality control and assurance standards. In contrast to bottom-up approaches, many details are required for calculating NO_x and CO₂ emissions, including coal type, coal quality, boiler firing type, NO_x emission control device type, and operating condition of boiler and emission control device.

Figure 10Mean OMI NO₂ tropospheric VCDs around the Matimba power plant (Lephalale, South Africa) for (a) calm, (b) southwesterly wind conditions, and (c) their difference (southwesterly minus calm) for the period of 2005–2017. The location of Matimba is represented by a black dot.

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3.3.2 Application to Matimba power plant in South Africa

We apply the methodology shown in Fig. 9 to estimate CO₂ emissions from a South African power plant, Matimba, which is a strong isolated NO_x point source (Fig. 10). It is a well-studied power plant, having had its emissions estimated using several different methods as reported in the literature. We estimate $E_{{\mathrm{NO}}_x}^{\mathrm{Sat}}$ for Matimba from 2005 to 2017 based on OMI NO₂ observations following the approach in Sect. 2.1. Matimba uses subbituminous coal with a calorific value of ∼20 MJ kg⁻¹ (Makgato and Chirwa, 2017). We apply the ratio ranging from 2005 ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ to 2005 ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}+$ standard deviation to Matimba, following the methodology in Fig. 9, considering that South Africa is a less strict country without any post-combustion NO_x control devices (Pretorius et al., 2015). Our derived $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{Sat}}$ is shown in Fig. 11 and fluctuates over time. The growth after 2008^* is most likely caused by the increased unit operating hours driven by the desire to meet fully the demand for electricity in South Africa after a period of rolling blackouts (2007–2008) (Duncan et al., 2016). The decline afterwards may be associated with the tripping of generating units at the Matimba because of overload and shortage of coal as reported by South African government news agency (available at: https://www.sanews.gov.za/south-africa/eskom-alone-cannot-solve-our-energy-challenges, last access: 1 March 2019). The increase in 2016^* may be associated with a newly built power plant, Medupi, which began limited operations in 2015. Note that the range of $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{Sat}}$ (grey band) in Fig. 11 represents the emissions based on a range of NO_x-to-CO₂ ratios and not the uncertainty. We calculate the uncertainty of $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{Sat}}$ for Matimba following Sect. 3.2 with an additional uncertainty of ∼50 % to reflect the fact that the ratio may range from ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ to ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}+$ standard deviation. The overall uncertainty of $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{Sat}}$ for Matimba is 81 %, as shown by the error bars in Fig. 11.

Figure 11Comparison of $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{Sat}}$ (Gg h⁻¹) derived in this study, with existing estimates for the Matimba power plant during 2005 to 2017. $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{Sat}}$ is inferred based on the NO_x to CO₂ emissions ratio ranging from ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ to ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}+$ standard deviation of ratio. The upper and lower grey bands denote the emissions inferred from ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}$ and ${\mathrm{ratio}}_{\mathrm{regressed}}^{\mathrm{CEMS}}+$ standard deviation of ratio, respectively. The grey dots and error bars show the mean of the upper and lower grey bands and their uncertainties, respectively. ^a Emissions are estimated for 2009 by Wheeler and Ummel (2008), for 2010 by Tong et al. (2018a), for 2014 and 2016 by Nassar et al. (2017), for 2016 by Reuter et al. (2019), and for 2012 and 2016 by Oda et al. (2018).

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Figure 11 shows $E_{{\mathrm{CO}}_{\mathrm{2}}}^{\mathrm{Sat}}$ derived in this study and other independent estimates reported in the literature, including two top-down (Nassar et al., 2017; Reuter et al., 2019) and three bottom-up estimates (Wheeler and Ummel, 2008; Tong et al., 2018a; Oda et al., 2018). Despite the uncertainties associated with each of these methods, the CO₂ emissions estimates agree reasonably well, but we do not have sufficient information to understand the differences between these estimates. However, Tong et al. (2018a) present in their CPED database both CO₂ and NO_x emissions, which allows us to determine that the difference between $E_{{\mathrm{NO}}_x}^{\mathrm{Sat}}$ and the CPED bottom-up estimate contributes significantly to the difference in CO₂ estimates from the two methods. $E_{{\mathrm{NO}}_x}^{\mathrm{Sat}}$ for Matimba is 3.8 Mg h⁻¹ for 2010^*, which is 65 % smaller than the estimate by Tong et al. (2018a) for 2010. It is not surprising to see such differences considering the uncertainties of satellite-derived NO_x emissions and bottom-up estimates for power plants without reliable CEMS measurements. For instance, $E_{{\mathrm{NO}}_x}^{\mathrm{Sat}}$ is potentially underestimated because of the bias in the OMI NO₂ standard product (version 3.1) associated with a low-resolution static climatology of surface Lambert-Equivalent Reflectivity (OMLER) (Kleipool et al., 2008). We perform a sensitivity analysis by using the preliminary new version of the OMI NO₂ product, which uses new geometry-dependent Moderate Resolution Imaging Spectroradiometer (MODIS)-based surface reflectivity. The inferred $E_{{\mathrm{NO}}_x}^{\mathrm{Sat}}$ based on the new product is over 10 % higher than version 3.1. The bottom-up estimates for Matimba are subject to significant uncertainties as well. For example, Tong et al. (2018a) used national total fuel consumption of the power sector for South Africa as reported by the International Energy Agency to estimate fuel consumption at the plant level, as detailed fuel consumption for each plant is not currently available. Additionally, they used default NO_x emission factors obtained from the literature because of the absence of country-specific measurement data.