Quantifying burning efficiency in megacities using the NO₂∕CO ratio from the Tropospheric Monitoring Instrument (TROPOMI)

This study investigates the use of co-located nitrogen dioxide (NO₂) and carbon monoxide (CO) retrievals from the TROPOMI satellite to improve the quantification of burning efficiency and emission factors (EFs) over the megacities of Tehran, Mexico City, Cairo, Riyadh, Lahore, and Los Angeles. Efficient combustion is characterized by high NO_x (NO+NO₂) and low CO emissions, making the NO₂∕CO ratio a useful proxy for combustion efficiency (CE). The local enhancement of CO and NO₂ above megacities is well captured by TROPOMI at short averaging times compared with previous satellite missions. In this study, the upwind background and plume rotation methods are used to investigate the accuracy of satellite-derived ΔNO₂∕ΔCO ratios. The column enhancement ratios derived using these two methods vary by 5 % to 20 % across the selected megacities. TROPOMI-derived column enhancement ratios are compared with emission ratios from the EDGAR v4.3.2 (Emission Database for Global Atmospheric Research v4.3.2) and the MACCity (Monitoring Atmospheric Chemistry and Climate and CityZen) 2018 emission inventories. TROPOMI correlates strongly (r=0.85 and 0.7) with EDGAR and MACCity, showing the highest emission ratio for Riyadh and lowest emission ratio for Lahore. However, inventory-derived emission ratios are 60 % to 85 % higher than TROPOMI column enhancement ratios across the six megacities. The short lifetime of NO₂ and the different vertical sensitivity of TROPOMI NO₂ and CO explain most of this difference. We present a method to translate TROPOMI-retrieved column enhancement ratios into corresponding emission ratios, thereby accounting for these influences. Except for Los Angeles and Lahore, TROPOMI-derived emission ratios are close (within 10 % to 25 %) to MACCity values. For EDGAR, however, emission ratios are ∼65 % higher for Cairo and 35 % higher for Riyadh. For Los Angeles, EDGAR and MACCity are a factor of 2 and 3 higher than TROPOMI respectively. The air quality monitoring networks in Los Angeles and Mexico City are used to validate the use of TROPOMI. For Mexico City and Los Angeles, these measurements are consistent with TROPOMI-derived emission ratios, demonstrating the potential of TROPOMI with respect to monitoring burning efficiency.

1 Introduction

Rapid urbanization and economic growth in developing countries has led to a strong increase in urban air pollution (Pommier et al., 2013; United Nations, 2018). In the South Asian cities of Kabul and Dhaka, for instance, nitrogen dioxide (NO₂) increases in the order of 10 % yr⁻¹ have been reported (Schneider et al., 2015). In New Delhi, emissions of carbon monoxide (CO) increased by 22.4 % from 2000 to 2008 (Jiang et al., 2017). In European countries, in contrast, the use of modern technology and other air pollution abatement measures decreased NO₂ concentrations by 10 % to 50 % between 2004 and 2010 (Castellanos and Boersma, 2012) and decreased CO concentrations by 35 % between 2002 and 2011 (Guerreiro et al., 2014). Thus, to develop effective air pollution control strategies, accurate information on local emission sources and combustion processes is important (Borsdorff et al., 2018a; Ma and van Aardenne, 2004). However, developing countries and remote areas lack the local infrastructure needed to obtain detailed information about factors such as energy consumption, fuel type, and technology. Limited process information contributes greatly to the uncertainty in emission inventories (Silva and Arellano, 2017). For example, the range of uncertainty in the Chinese NO_x and CO emissions between 2005 and 2008 has been estimated to range from −20 % to +45 % due to inadequate information about fuel consumption and uncertain emission factors (Zhao et al., 2011, 2012). In the global emission inventory EDGAR v4.3.2, uncertainties in regional emissions have been estimated to range from 17 % to 69 % for NO_x and from 25 % to 64 % for CO (Crippa et al., 2016). In this study, we investigate the use of satellite remote sensing to improve the emission quantification for these important air pollutants.

In global emission inventories, combustion-related emissions are computed as the product of the amount of fuel burned (activity data) and the composition of the emissions as represented by the emission factor (EF; Vallero, 2007). EFs depend strongly on the burning conditions (Sinha et al., 2003; Ward et al., 1996; Yokelson et al., 2003), in particular on the combustion efficiency (CE). The CE is defined as the fraction of reduced carbon in the fuel that is directly converted into CO₂ (Yokelson et al., 1996). Usually, EFs are measured in laboratories under controlled burning conditions. However, in the ambient environment, combustion conditions are highly variable (Andreae and Merlet, 2001; Korontzi et al., 2003) and, therefore, introduce large uncertainties into global emission inventories through the impact of the CE on the EF. A case study (Frey and Zheng, 2002) on NO_x emission estimates from coal-fired power plants with dry-bottom wall-fired boilers using low NO_x burners showed that the EF for NO_x can vary by a factor of 4 or more within a same technology. Thus, the application of mean EFs introduces uncertainties in the range of −29 % to +35 % with respect to mean emission estimates (Frey and Zheng, 2002). Fuel type, fuel composition, combustion practices, and technology are the main factors influencing the CE in the ambient environment (Silva and Arellano, 2017; Tang et al., 2019). To improve the accuracy of global inventories, a better quantification of the CE and EFs is needed.

In recent years, the availability of atmospheric composition measurements from Earth-orbiting satellites has strongly improved. Sensors such as the Scanning Imaging Absorption spectroMeter for Atmospheric Chartography (SCIAMACHY; Bovensmann et al., 1999) and the Tropospheric Monitoring Instrument (TROPOMI; Veefkind et al., 2012) deliver global datasets of multiple species. The satellite observations from SCIAMACHY have been used in combination with inverse modelling techniques to test and improve emission inventories (Konovalov et al., 2014; Mijling and van der A, 2012; Reuter et al., 2014; Silva et al., 2013). By combining observations of different species (e.g. CO, CO₂, and NO₂), information about common sources and, potentially, information about emission ratios is obtained (Hakkarainen et al., 2015; Miyazaki et al., 2017; Reuter et al., 2019; Silva and Arellano, 2017).

In this study, measurements from TROPOMI are used to investigate the burning efficiency in megacities. TROPOMI is a push-broom grating spectrometer on board Sentinel-5 Precursor (S5P), which was launched by ESA on 13 October 2017 (Veefkind et al., 2012). We use the ratio of the TROPOMI-retrieved tropospheric column of NO₂ and the total column of CO, which is formally not equivalent to the CE but can nevertheless serve as a useful proxy of the burning conditions (Silva and Arellano, 2017; Tang and Arellano, 2017). The reason for this is that the NO_x emission increases with combustion temperature, which is high during efficient combustion. In contrast, CO is a product of incomplete combustion and is produced when the CE is low (Flagan and Seinfeld, 1988). The combination of these effects makes the NO₂∕CO ratio highly sensitive to the CE. To correct for differences in the NO₂ and CO background concentrations, the enhancement ratio ΔNO₂∕ΔCO is used. Here ΔNO₂ and ΔCO represent concentration increases compared with their respective backgrounds.

The ΔNO₂∕ΔCO ratio is insensitive to atmospheric transport, as NO₂ and CO emissions are dispersed in a similar manner by the wind. Therefore, the impact of transport cancels out in the ratio. Consequently, TROPOMI-observed ratios close to emissions sources can be directly related to emission ratios. The aim of this study is to investigate the local relation between TROPOMI-retrieved ΔNO₂∕ΔCO ratios and emission ratios in a quantitative manner, focusing on megacities that show significant concentration enhancements in the TROPOMI data. In past studies, NO₂ from the Ozone Monitoring Instrument (OMI) and CO from the Measurement of Pollution in the Troposphere (MOPITT) instrument have been used to derive CO∕NO₂ ratios (Silva and Arellano, 2017; Tang and Arellano, 2017). MOPITT also has a short-wave infrared (SWIR) channel (or near IR), and the multispectral (thermal infrared/near-infrared, TIR/NIR) product, with near-surface sensitivity over some land regions, was used in both Silva and Arellano (2017) and Tang and Arellano (2017). TROPOMI provides a unique opportunity to measure CO and NO₂ using the same instrument at an unprecedented high spatial resolution (7×7 km² at nadir) and daily global coverage (Borsdorff et al., 2018b; van Geffen et al., 2019), making this instrument ideally suited for the investigation of NO₂∕CO ratios from space. Additionally, TROPOMI CO retrievals make use of the SWIR, improving the sensitivity to surface emissions of CO compared with the TIR sounders, MOPITT and the Infrared Atmospheric Sounding Interferometer (IASI). However, TROPOMI NO₂ retrievals are less sensitive to the lower troposphere, causing ΔNO₂∕ΔCO to be influenced by vertical sensitivity (Eskes and Boersma, 2003). We derived a correction factor to take this influence into account, as will be explained in detail in Sect. 2.5.

This paper is organized as follows: Sect. 2 provides detailed information about the TROPOMI CO and NO₂ retrieval, the approach used to quantify the ΔNO₂∕ΔCO column enhancement ratio over megacities, and how to relate it to the corresponding emission ratio. Results comparing satellite-derived and emission inventory-derived ratios are presented in Sect. 3. Finally, Sect. 4 summarizes our findings and presents the main conclusions.

2 Data and method

2.1 TROPOMI CO retrievals

For this study, we use the TROPOMI CO scientific beta data product provided by the SRON Netherlands Institute for Space Research (ftp://ftp.sron.nl/open-access-data-2/TROPOMI/tropomi/co/7_7/, last access: 18 November 2018). The output is identical to that of operational data product provided by the European Space Agency (ESA), but it also provides the TM5 a priori profiles (http://tm5.sourceforge.net/, last access: 18 November 2018) that are used in the retrieval. The SRON CO product also supplies more data for the early months of the mission which are not included in the operational product. Total column densities of CO (molec. cm⁻²) are retrieved from spectral radiance measurements from the TROPOMI SWIR module at 2.3 µm using the SICOR algorithm (Landgraf et al., 2018). In this profile scaling algorithm, the TROPOMI-observed spectra are fitted by scaling a reference vertical profile of CO using the Tikhonov regularization technique (Borsdorff et al., 2014). The reference a priori CO profile is derived from the TM5 transport model (Krol et al., 2005), as described in Landgraf et al. (2016). The averaging kernel (A) is an essential component of the CO retrieval and quantifies the sensitivity of the retrieved CO column to a change in the true vertical profile (ρ_true) following Borsdorff et al. (2018c):

$$\begin{array}{}\text{(1)}& C_{\mathrm{retrieval}}=A\cdot {\mathit{\rho }}_{\mathrm{true}}+{\mathit{ϵ}}_{\mathrm{CO}},\end{array}$$

where ϵ_CO is the error in the retrieved CO columns.

2.2 TROPOMI NO₂ retrievals

The UV–Vis module of TROPOMI is used to retrieve NO₂ in the 405–465 nm spectral range. NO₂ slant column densities are processed using the TROPOMI NO₂ DOAS software developed at the Royal Netherlands Meteorological Institute (KNMI; van Geffen et al., 2019). The retrieval algorithm is based on the NO₂ DOMINO algorithm (Boersma et al., 2011) which has been improved further in the QA4ECV4 project (Boersma et al., 2018). The algorithm subtracts the stratospheric contribution to the slant column densities and then converts the residual tropospheric slant column density into the tropospheric vertical density via the air mass factor (AMF). The AMF is computed using co-sampled, daily NO₂ a priori vertical profiles from output of the TM5-MP chemistry transport model at a 1^∘ × 1^∘ resolution (Williams et al., 2017). The AMF depends on the surface albedo, terrain height, cloud height, and cloud fraction (Eskes et al., 2019; Lorente et al., 2017). We used the offline Level 2 NO₂ data (mol m⁻²) that are available at https://s5phub.copernicus.eu and http://www.tropomi.eu (last access: 18 November 2018). The TROPOMI NO₂ product has been successfully used in various other studies (Griffin et al., 2019; Reuter et al., 2019); however, there are indications that NO₂ is biased low by approximately 30 % in the tropospheric columns due to issues with the cloud pressure and the a priori NO₂ profile used in the AMF calculation (Boersma et al., 2004; Lorente et al., 2017).

2.3 Data selection

We used TROPOMI CO and NO₂ retrievals from June to August 2018 due to the large number of clear-sky days during this period over the megacities of interest. Megacities are strong sources of air pollution and can readily be observed in TROPOMI data (Borsdorff et al., 2018c). Since CO and NO₂ are retrieved from different instrument channels using different algorithms, the filtering criteria and spatial resolutions are also different. To facilitate data filtering, both algorithms provide a quality assurance value (q_a value). The q_a value for both products ranges from 0 (no data) to 1 (high-quality data)

For our data analysis, we selected NO₂ retrievals with q_a values equal to or larger than 0.75, indicating clear-sky conditions (Eskes and Eichmann, 2019), and CO retrievals with q_a values equal to or larger than 0.7, representing measurements under clear-sky conditions or the presence of low-level clouds (Apituley et al., 2018). The application of the SICOR algorithm to SCIAMACHY CO retrievals with low-level clouds increases the number of measurement, with a limited impact in the ability to detect CO sources (Borsdorff et al., 2018a). CO retrievals are filtered for stripes, as described in Borsdorff et al. (2018c). The CO retrieval has a spatial resolution that is a factor of 2 coarser than the NO₂ retrieval (7 × 7 km² versus 3.5 × 7 km²). To co-locate NO₂ and CO retrievals, we combine the NO₂ pixels with centres that fall within a CO pixel, selecting only those pixels for which both the NO₂ and CO retrievals pass the filtering criteria. The total CO column and tropospheric NO₂ columns are converted into the dry column mixing ratio XCO (ppb) and XNO₂ (ppb) using the dry-air column density calculated using the co-located surface pressure data included in the CO data files, as described in Borsdorff et al. (2018c).

Table 1 Selected megacities and specifications used for emission ratio quantification.

2.4 Calculation of NO₂∕CO

This study focuses on the following megacities (with populations exceeding 5 million): Mexico City, Tehran, Riyadh, Cairo, Lahore, and Los Angeles. These six megacities are well isolated from surrounding sources and frequently experience cloud-free conditions, allowing for the retrieval of a large number of XCO and XNO₂ data from TROPOMI. Los Angeles and Mexico City have automated air quality monitoring networks that measure CO and NO₂ at different locations in the city. These measurements are used in Sect. 3.3 to validate the results obtained using TROPOMI. In addition, these megacities are expected to span a sizable range of burning efficiencies, as they include urban centres in developed (Los Angeles, USA) and developing countries (Mexico City, Mexico; Cairo, Egypt; Riyadh, Saudi Arabia; and Lahore, Pakistan).

The concentration gradient between the background and the city centre is used to determine the ΔXNO₂∕ΔXCO enhancement ratio. To determine this ratio, we divide each city into a core city area and a background area. Every city has a different size and different neighbouring CO and NO₂ emission sources; therefore, the appropriate choice of radii for the background and outskirts varies between cities (see Sect. S1 in the Supplement for details). Since the same regional definition is used for NO₂ and CO, the enhancement ratio is not sensitive to the details of the selection of the region. Thus, capturing the local enhancement in CO and NO₂ to its full extent is most important for the choice of radii in order to optimize the signal over noise and, in turn, the detection limit for urban emissions. To maximize the size of the city enhancement, we exclude the diffuse outskirts between the city centre and the background. For the location of the city centre, we use the weighted average emission centre of NO₂ derived from the EDGAR emission database (Dekker et al., 2017). The derived centre coordinates as well as the radii of the city core and background area are listed in Table 1. We test the robustness of the satellite-derived emission ratio using two different methods, which are explained in detail below.

2.4.1 Upwind background

To determine the upwind background (UB) column mixing ratio, we select a section of the background region that is upwind from the city centre using the average wind direction over the core city area (see Figs. 1 and S7 for further details). Generally, more than 75 % of all pollutants are emitted between the surface and an altitude of 200 m (Bieser et al., 2011). Therefore, the average wind speed and direction from the surface to an altitude of 200 m are derived from the ERA-Interim reanalysis data, which are provided at a 0.75^∘ × 0.75^∘ spatial and 3-hourly temporal resolution. The wind vector components of ERA-Interim are spatially and temporally interpolated to the central coordinate of TROPOMI pixels. Using this information, daily enhancement ratios are calculated as follows:

$$\begin{array}{}\text{(2)}& {\displaystyle }\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}={{\mathrm{XNO}}_{\mathrm{2}}}_{\mathrm{city}}-{{\mathrm{XNO}}_{\mathrm{2}}}_{\mathrm{background}}\text{(3)}& {\displaystyle }\mathrm{\Delta }\mathrm{XCO}={\mathrm{XCO}}_{\mathrm{city}}-{\mathrm{XCO}}_{\mathrm{background}}\text{(4)}& {\displaystyle }\mathrm{Ratio}={\displaystyle \frac{\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}{\mathrm{\Delta }\mathrm{XCO}}}\end{array}$$

The background area might contain free tropospheric NO₂ from lightning and convectively lofted surface NO₂ from elsewhere. However, these contributions vary on scales that are usually large compared with the scale of a city. Therefore, the calculated ΔXNO₂ and ΔXCO enhancements are predominantly caused by emissions from the city.

Figure 1 Average wind speed and direction from the surface to 200 m from ERA-Interim at the TROPOMI overpass time (a), and the TROPOMI-derived total column CO over Mexico City (b) for 4 June 2018. The black star represents the centre of the city. In the right panel, the white circle is the background area for Mexico City, and the blue section represents the upwind background area that we selected depending upon the wind direction (θ) in the core city area. P0, P1, P2, and P3 are the points where the northern, eastern, western, and southern wind directions intersect with the background area. P0_new is the new point generated by rotating P0 with θ in reference to the city centre.

2.4.2 Plume rotation

The daily TROPOMI-observed city images are rotated in the direction of the wind using the city centre as the rotation point to align each CO and NO₂ plume in the upwind–downwind direction (Pommier et al., 2013). Rotated images for June to August 2018 are averaged together (see Fig. S8). ΔXNO₂ and ΔXCO are determined by subtracting the average of the first quartile XNO₂, XCO values in a 100 km × 20 km region upwind from the city centre from the average of the fourth quartile XNO₂, XCO values in a 100 km × 20 km region downwind from the city centre. Finally, the enhancement of XNO₂ and XCO is calculated as described in Eq. (5), and the enhancement ratio is derived using Eq. (4).

$$\begin{array}{}\text{(5)}& \begin{array}{rl}& \mathrm{The}\mathrm{downwind}\text{–}\mathrm{upwind}\mathrm{difference}=V_{\mathrm{d}}-V_{\mathrm{u}}\\ & ={\displaystyle \frac{\sum _{i=\mathrm{1}}^{n_{\mathrm{downwind}}}(X\ge \mathrm{75}\mathrm{th}\mathrm{percentile})}{n_{\mathrm{downwind}}}}\\ & -{\displaystyle \frac{\sum _{i=\mathrm{1}}^{n_{\mathrm{upwind}}}\left(X\le \mathrm{25}\mathrm{th}\mathrm{percentile}\right)}{n_{\mathrm{upwind}}}},\end{array}\end{array}$$

where n_downwind refers to the number of observations ≥75th percentile, and n_upwind refers to the number of observations ≤25th percentile

2.5 NO₂∕CO emission ratio

Local TROPOMI-derived ratios in column abundance are compared with emission ratios derived from the Emission Database for Global Atmospheric Research (EDGAR v4.3.2) at a 0.1^∘ × 0.1^∘ spatial resolution for the most recent year of 2012 and the database provided by Monitoring Atmospheric Chemistry and Climate and CityZen (MACCity) for 2018 that is available at a 0.5^∘ × 0.5^∘ resolution (Granier et al., 2011). MACCity has been re-gridded to a spatial resolution of 0.1^∘ × 0.1^∘, assuming a uniform distribution of the emissions within each 0.5^∘ × 0.5^∘ grid box. Both emission inventories contain total emissions of NO_x and CO. NO_x emissions are converted into NO₂ by dividing NO_x by the conversion factor of 1.32. This conversion factor is based on Seinfeld and Pandis (2006) and represents urban plumes at 13:30 local time (LT). The emission ratios of NO₂ and CO ($E_{{\mathrm{NO}}_{\mathrm{2}}}/E_{\mathrm{CO}}$) are calculated from total emissions (the sum of all processes) within the core city area for the EDGAR and MACCity emission inventories.

To compare TROPOMI to inventory-derived ratios, the NO₂ tropospheric column has to be corrected for its limited atmospheric residence time. The CO lifetime is long enough compared with the transport time out of the city domain to be neglected. In addition, we need to account for differences in the vertical sensitivity of TROPOMI to NO₂ and CO, as quantified by their respective averaging kernels (A) shown in Fig. 2. To compare TROPOMI to EDGAR and MACCity, we formulate a relationship between the emission ratio ($E_{{\mathrm{NO}}_{\mathrm{2}}}/E_{\mathrm{CO}}$) and the column enhancement ratio (ΔXNO₂∕ΔXCO) taking the combined effect of atmospheric transport, chemical loss, and the averaging kernel into account. This relationship is as follows (see Appendix A for its derivation):

$$\begin{array}{}\text{(6)}& {\displaystyle \frac{E_{{\mathrm{NO}}_{\mathrm{2}}}}{E_{\mathrm{CO}}}}={\displaystyle \frac{\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}{\mathrm{\Delta }\mathrm{XCO}}}{\displaystyle \frac{\left(\frac{U}{l_x}+K\left[\mathrm{OH}\right]\right)}{\frac{U}{l_x}}}{\displaystyle \frac{\mathrm{1}}{(\mathrm{1}-A_{\mathrm{influence}})}},\end{array}$$

where U is the is the 200 m wind speed (m s⁻¹), l_x is the diameter of the city centre (m), and K is the rate constant of the reaction of NO₂ with OH of $\mathrm{2.8}\times {\mathrm{10}}^{-\mathrm{11}}{\left(\frac{T}{\mathrm{300}}\right)}^{-\mathrm{1.3}}$ cm³ molec.⁻¹ s⁻¹ (Burkholder et al., 2015). T (K) and OH (molec. cm⁻³) are the boundary layer average temperature and OH concentration respectively, and A_influence is the influence of the averaging kernel on ΔXNO₂∕ΔXCO (see Sect. 3.2).

Figure 2 TROPOMI averaging kernels (A) for CO total column and tropospheric NO₂ over Mexico City on 1 June 2018. The error bars represent the standard deviation of the mean A at each vertical level.

Copernicus Atmospheric Monitoring Service (CAMS) real-time OH, CO, and NO₂ fields are used to account for the impacts of chemical loss and the averaging kernel. The CAMS data, at a 0.1^∘ × 0.1^∘ and 3-hourly resolution, are spatially and temporally interpolated to the TROPOMI footprints. The CAMS CO and NO₂ vertical mixing ratio profiles are converted into vertical column densities using the ERA-Interim reanalysis surface pressure. For CO, the TROPOMI data provide column A values from the surface to the top of atmosphere. For NO₂, tropospheric A is derived using the AMF for the troposphere as fraction of the total column (Boersma et al., 2016). For further details, see Appendix B.

2.6 Uncertainty

To quantify the uncertainty in TROPOMI-derived ΔXNO₂∕ΔXCO ratios for the plume rotation method, we use the error propagation method of Pommier et al. (2013) and bootstrap for the upwind background, as explained further in the following.

2.6.1 Bootstrapping

The bootstrapping method is a statistical resampling method that is used here to calculate the uncertainty in the daily enhancement ratio of $\frac{\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}{\mathrm{\Delta }\mathrm{XCO}}$. The first step is to generate a new set of samples by drawing a random subset with replacement from the full dataset of N daily $\frac{\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}{\mathrm{\Delta }\mathrm{XCO}}$ ratios. The subset has the same number of samples as the full dataset, from which a mean ratio is calculated. This procedure is repeated 1000 times for each city. Finally, the standard deviation of the resulting ratios is taken and used to represent the uncertainty in the daily $\frac{\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}{\mathrm{\Delta }\mathrm{XCO}}$.

2.6.2 Error propagation

To calculate the uncertainty in $\frac{\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}{\mathrm{\Delta }\mathrm{XCO}}$ by error propagation, we first determine the uncertainty in the enhancements ΔXNO₂ and ΔXCO, which are derived from the uncertainty in the mixing ratios upwind and downwind of the source as follows:

$$\begin{array}{}\text{(7)}& {\mathit{\sigma }}_{\mathrm{\Delta }X}=\sqrt{{\left({\displaystyle \frac{{\mathit{\sigma }}_{\mathrm{upwind}}}{\sqrt{n_{\mathrm{upwind}}}}}\right)}^{\mathrm{2}}+{\left({\displaystyle \frac{{\mathit{\sigma }}_{\mathrm{downwind}}}{\sqrt{n_{\mathrm{downwind}}}}}\right)}^{\mathrm{2}}},\end{array}$$

where X is XNO₂ or XCO.

Here, we assume that the upwind and downwind uncertainties are independent. The uncertainty for the column enhancement is

$$\begin{array}{}\text{(8)}& {\mathit{\sigma }}_{\mathrm{ratio}}=\left(\sqrt{{\left({\displaystyle \frac{{\mathit{\sigma }}_{\mathrm{\Delta }{\mathrm{NO}}_{\mathrm{2}}}}{\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}}\right)}^{\mathrm{2}}+{\left({\displaystyle \frac{{\mathit{\sigma }}_{\mathrm{\Delta }\mathrm{CO}}}{\mathrm{\Delta }\mathrm{XCO}}}\right)}^{\mathrm{2}}}\right)\cdot {\displaystyle \frac{\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}{\mathrm{\Delta }\mathrm{XCO}}}\end{array}$$

3 Results and discussion

3.1 Detection of NO₂ and CO pollution over megacities

The co-located TROPOMI XNO₂ and XCO data have been averaged for June to August 2018 for domains of 500 × 500 km² centred around the selected megacities, as described in Sect. 2. The results for Mexico City and Cairo are shown in Fig. 3. The enhancements of XCO and XNO₂ over Mexico City and Cairo are clearly separated from the surrounding background areas and are prominent in several overpasses of TROPOMI (Fig. S9). This demonstrates that a relatively short data averaging period is sufficient for TROPOMI to detect hotspots of CO pollution at the scale of large cities, compared with instruments such as IASI and MOPITT. The orography surrounding Mexico City causes pollutants to become trapped, thereby facilitating detection by TROPOMI. The longer lifetime of CO compared with NO₂ causes the urban influence of CO to be propagated further in the westward direction. As can be seen in Fig. 3, the retrieved XCO and XNO₂ signals of emissions from Mexico City and Cairo correlate quite well with each other, confirming that it should be possible to obtain useful information about burning efficiency by studying $\frac{\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}{\mathrm{\Delta }\mathrm{XCO}}$. An industrial area is located to the east of Cairo (29.797351^∘ N, 32.148266^∘ E), showing a clear enhancement in XNO₂ but not in XCO (Fig. 3c, d). It demonstrates that variations in the column enhancement ratio can already be seen by eye when comparing TROPOMI-retrieved XCO and XNO₂ images.

Figure 3 Co-located TROPOMI-retrieved XNO₂ (a, c) and XCO (b, d) data over Mexico (a, b) and Cairo (c, d) averaged for June to August 2018. De-striping is applied to CO total columns (Borsdorff et al., 2018b), and CO and NO₂ retrievals have been re-gridded to 0.1^∘ × 0.1^∘. The white stars represent the centres of Mexico City and Cairo respectively. The red circle in (c) and (d) points to an industrial area east of Cairo.

3.2 Comparison of TROPOMI- and inventory-derived ratios

Here, we attempt to compare TROPOMI-derived NO₂∕CO column enhancement ratios to emission ratios from EDGAR and MACCity for the six selected megacities (see Fig. 4). As explained in Sect. 2, column enhancement ratios from TROPOMI are obtained using the upwind background (UB) and plume rotation (PR) methods. These estimates differ by 5 % to 20 % across the six cities, providing an initial estimate of the accuracy with which the column enhancement ratio can be derived (see Table S1 in the Supplement for details). The EDGAR and MACCity inventories show a substantial variation in emission ratios between cities, with relatively high emission ratios for Riyadh and the lowest emission ratios for Lahore. TROPOMI-derived ΔXNO₂∕ΔXCO column enhancement ratios for the UB and PR methods show similar patterns to EDGAR and MACCity, with Pearson correlation coefficients of 0.85 and 0.7 respectively (Fig. S10 in the Supplement). However, inventory-derived emission ratios are clearly 60 % to 85 % larger than TROPOMI-derived column enhancement ratios, which is largely explained by the impact of the limited NO₂ lifetime and the averaging kernel, as will be discussed further after an explanation of the differences between EDGAR and MACCity. Emission ratios from MACCity are 10 % to 75 % lower than those from EDGAR. To understand the differences in emission ratios between MACCity and EDGAR, we selected two cities, Cairo and Mexico City, which present the largest and smallest differences in the emission ratio. The CO and NO₂ emissions are categorized into seven sectors: agriculture, residential, energy, industrial, transportation, shipping, and waste treatment. Sectors that contribute most to the total emission are compared. In the case of Cairo and Mexico City, these are the transportation, industrial, energy, and residential sectors (Fig. S11a, b). For Cairo, the total CO emission is a factor of 2 lower in EDGAR than in MACCity, whereas the total NO₂ emission is 10 % higher in EDGAR. This results in an emission ratio that is a factor of 3 higher. The largest discrepancy between EDGAR and MACCity CO emission is due to the residential sector, followed by energy. For NO₂, the energy, transportation, and residential sectors explain most of the difference between EDGAR and MACCity. In Mexico City, EDGAR total CO and NO₂ emissions are both a factor of 2 higher than MACCity values; thus, the total emission values cancel out in the ratio, leading to the best agreement of all selected megacities. However, it is complicated to identify the main factors explaining the differences between EDGAR and MACCity at the sector level due to the combined influence of differences in activity data, EFs, and the methods used to disaggregate country totals. To understand the disaggregation of emission in EDGAR and MACCity, we compared the country total CO and NO₂ of Mexico City (Mexico) and Cairo (Egypt). The comparison shows that the EDGAR and MACCity country CO total and the NO₂ total for Mexico show a small difference (∼12 %), whereas the difference is about factor of 2 in Mexico City (Fig. S11c). For Egypt, the EDGAR and MACCity CO total shows a similar difference to Cairo, whereas the EDGAR NO₂ country total emission value is a factor of 2 lower (Fig. S11d). This shows that EDGAR attributes CO and NO₂ emissions to the city, whereas MACCity smears them out over the country.

Figure 4 Comparison of TROPOMI-derived ΔNO₂∕ΔCO enhancement ratios, calculated using the different methods shown in shades of blue, with the corresponding emission ratios from the EDGAR (shown using shades of red) and MACCity (shown using shades yellow) emission inventories for six megacities. Dark solid shades for emission inventories represent the annual average inventory-derived ratio, whereas the lighter shades represent the June to August averaged inventory-derived ratios. The upwind background-corrected emission ratio (UBCER) and the plume rotation-corrected emission ratio (PRCER) account for the impact of photochemical NO₂ removal and the averaging kernel. Error bars for the TROPOMI-derived ΔNO₂∕ΔCO enhancement ratios represent 1σ uncertainties calculated using bootstrapping (upwind background) and error propagation (plume rotation method). The error bars for UBCER and PRCER account for the uncertainty in the methodology and TROPOMI data (for details, see Table S3).

The difference between satellite-derived column enhancement ratios and inventory-based emission ratios can be explained in part by the relatively short lifetime of NO₂ that reduces columnar NO₂∕CO ratios compared with the emissions. In addition, the sensitivity to the planetary boundary layer is lower for NO₂ than for CO TROPOMI measurements, further reducing the satellite-observed column enhancement ratio. Taking these influences into account using Eq. (6) leads to the upwind background-corrected emission ratio (UBCER) and the plume rotation-corrected emission ratio (PRCER) in Fig. 4, which have been calculated on a daily basis before averaging over the full period. Due to the short lifetime of OH, its concentration depends strongly on the local photochemical conditions (de Gouw et al., 2019). Therefore, to account for the local lifetime of NO₂, we need an estimate of the OH that is representative for the photochemical conditions inside cities. Figure 5 shows the boundary layer OH concentration at the TROPOMI overpass time from CAMS for Mexico City, averaged over June–August 2018. Figure 5 shows a clear enhancement of OH in the city centre, confirming that the spatial resolution of CAMS is sufficient to resolve the urban influences on OH in megacities. The UB and PR column enhancement ratios increase by 60 % to 85 % when accounting for the NO₂ lifetime (see Table S1). The boundary layer OH concentrations and mean wind speeds for the six cities are listed in Table 2.

Figure 5 The boundary layer average OH concentration at the TROPOMI overpass time during June to August 2018 over Mexico City. The white star represents the centre of Mexico City.

The impact of differences between the XNO₂ and XCO averaging kernels is calculated using vertical profiles of NO₂ and CO taken from CAMS. These profiles were used to calculate XNO₂ and XCO using either the TROPOMI A values or A values replaced by identity matrices. The relative difference $A_{\mathrm{influence}}=\frac{(\mathrm{Without}A-\mathrm{With}A)}{\mathrm{Without}A}\cdot \mathrm{100}$ % quantifies the impact of differences between the averaging kernels (see Appendix C for the derivation). The CAMS-simulated city enhancements for CO from June to August 2018 did not compare well with TROPOMI for Tehran, Cairo, Riyadh, and Lahore, which was possibly due to the coarse resolution of CAMS (see Figs. S14, S15, S16, and S17). Therefore, A_influence has been determined for Mexico City and Los Angeles to calculate the averaging kernel impact (Figs. S12, S13). To test the accuracy of A_influence, a few days were selected for Tehran, Cairo, Riyadh, and Lahore when CAMS CO and NO₂ enhancements compared relatively well with TROPOMI. For the six megacities, TROPOMI-derived ΔNO₂∕ΔCO ratios are 10 % to 15 % lower than the “ideal” ΔNO₂∕ΔCO ratio that would be measured if both retrievals had uniform vertical sensitivities, i.e. every molecule in the column received equal weight. Details about the selected days and the corrections calculated for each city are listed in Table S2.

After correction, UBCER and PRCER for Tehran and Mexico City are close to EDGAR and MACCity (10 % to 25 %). This confirms that the EFs for these cities are well represented in the EDGAR and MACCity emission inventories. The difference between corrected and uncorrected ratios in Fig. 4 highlights the importance of the correction, in particular the influence of OH, for assessing emission ratios using TROPOMI. For Cairo the correction also reduces the difference between TROPOMI and the emission inventories, although the EDGAR ratios remain about 65 % higher for Cairo than UBCER and PRCER. For MACCity, the emission ratios are close to the TROPOMI-derived UBCER and PRCER for Cairo (within 20 %), pointing to a more accurate representation of emission ratios in MACCity than in EDGAR. For Riyadh, UBCER and PRCER are close to MACCity (∼10 % to 20 %), whereas EDGAR is 35 % higher. However, for Lahore, PRCER is close to the EDGAR ratio, whereas MACCity is a factor of 2.5 lower. For Los Angeles, the ratios from EDGAR and MACCity are 55 % and 70 % higher than UBCER and PRCER after correction respectively, suggesting poorer burning conditions than represented by the emission inventories. To further investigate this discrepancy for Los Angeles, we included the Hemispheric Transport of Air pollution version 2 (HTAP-v2) emission inventories for 2010 in the comparison. HTAP-v2 has a resolution of 0.1^∘ × 0.1^∘ and makes use of emission estimates from the Environmental Protection Agency (EPA) for the USA (Janssens-Maenhout et al., 2015). The HTAP-v2-derived emission ratio over Los Angeles is 0.074, which is close to UBCER and PRCER (within 20 %). This result provides further confidence in the TROPOMI-derived emission ratio. However, different sources of uncertainty play a role, as discussed further below.

Seasonal variations in EFs may influence our comparison between the seasonal averaged TROPOMI data and annual average EDGAR emissions. To account for the influence of seasonally varying EFs, we compute a seasonal correction factor based on EDGAR v4.3.2 2010, as monthly data are not available for EDGAR 2012 (see Fig. 4). Except for Lahore, the June to August (JJA) EDGAR ratio is 5 % to 12.5 % lower than the annual average EDGAR ratio. The MACCity ratio for JJA, however, is 10 % to 71 % higher than the annual average, indicating that EDGAR and MACCity disagree on the seasonality of the NO₂∕CO emission ratio. For MACCity, the agreement with TROPOMI improves the most when seasonality is taken into account (see Fig. 4).

Table 2 Average wind speed and boundary layer CAMS OH concentration for June–August 2018 that was used to correct for the limited lifetime of NO₂. The errors presented represent the 1σ uncertainty calculated by the bootstrapping method.

The ozone concentration and the photolysis rate impact the partitioning of NO and NO₂ (Jacob, 1999), thereby influencing the applied conversion factor of 1.32. To further investigate the uncertainty introduced by this factor, we analysed CAMS surface NO and NO₂ at the TROPOMI overpass time (see Table 2). The CAMS-derived conversion factor varies by less than 10 % compared with the standard value of 1.32, introducing an uncertainty of less than 10 % in the inventory-derived emission ratio. However, given the uncertainty in the CAMS-simulated urban NO, NO₂, and OH concentrations (Huijnen et al., 2019), the actual uncertainty is probably higher. Additionally, TROPOMI underestimates the NO₂ column by 7 % to 29.7 % relative to MAX-DOAS ground-based measurement in European cities (Lambert, et al., 2019). However, as we currently do not know how representative this estimate is for the cities studied, the impact of this bias has been accounted for as an additional source of uncertainty of 30 % in the TROPOMI-inferred NO₂∕CO ratio (see Table S3). Compared with this number, other sources of uncertainty, such as the wind direction and speed (Figs. S18, S19), the boundary layer OH concentration (Table 2), the A_influence correction (Table S2), and the predefined background setting (Fig. S20), only make small contributions to the TROPOMI-derived emission ratio. The total uncertainty in the TROPOMI-derived emission ratio is calculated using error propagation (see Table S3) and ranges between 33 % and 35.6 %.

We also acknowledge that our treatment of the photochemical removal of NO₂ is simplified. In reality, NO₂ is influenced by several other factors including meteorological parameters, such as temperature, wind speed, and radiation (Lang et al., 2015; Romer et al., 2018), causing the formation and loss of NO₂ to vary spatially and temporally. In the corrected ratio, we only consider the first-order loss of NO₂ by OH forming HNO₃. Several studies show that the loss of NO₂ via the formation of alkyl and multifunctional nitrates (RONO₂) can play a more important role than nitric acid production in cities surrounded by forested areas (Browne et al., 2013; Farmer et al., 2011; Romer Present et al., 2020; Sobanski et al., 2017). In addition, the secondary production of CO from volatile organic compound (VOC) oxidation may play a role. However, this only affects our ratios if it changes the CO gradient between the city and the background. Hence, to further improve the accuracy of the TROPOMI-supported evaluation of emission ratios, a more sophisticated treatment of urban photochemistry is required.

3.3 Validation using ground-based measurements

To further evaluate TROPOMI's ability to quantify burning efficiencies, TROPOMI-derived ΔXNO₂∕ΔXCO ratios have been compared with ground-based measurements from Mexico City and Los Angeles. For this purpose, 20 ground-based stations in Mexico City with hourly measurements of CO and NO₂ have been selected from the AIRE CDMX network (http://www.aire.cdmx.gob.mx/, last access: 17 July 2019). Similarly, 12 ground-based stations from the South Coast Air Quality Management District (AQMD) monitoring network (http://www.aqmd.gov/, last access: 20 July 2019) have been selected for Los Angeles. For details (names and locations) on these sites, see Table S4. For Mexico City, data were only available for June 2018. For Los Angeles, data for the June to August 2018 period were used, but the periods from 25 July to 11 August and from 17 to 26 August were excluded to avoid the influence of wild fires on the observed urban pollution level.

The validation results are presented in Fig. 6 for spatially averaged, hourly CO and NO₂ measurements for Mexico City and Los Angeles collected during the noon hours (12:00 to 14:00 LT). To determine the enhancement in CO and NO₂ due to local emissions for each ground-based station, the fifth percentile of hourly CO and NO₂ measurements is used as background. ΔCO and ΔNO₂ enhancements for individual monitoring stations are calculated as $\mathrm{\Delta }X=X_{\mathrm{individual}}-X_{\mathrm{background}}$. For comparison with TROPOMI, all measurement sites are spatially averaged.

Figure 6 The relation between ΔNO₂ and ΔCO in surface measurements from Mexico (a) and Los Angeles (b). The red dots represent spatially averaged hourly measurements collected during the day (12:00 to 14:00 LT).

Ground-based ΔCO and ΔNO₂ at Mexico City and Los Angeles are strongly correlated, with a Pearson correlation coefficient of r=0.95 and 0.80 respectively, confirming that the observed signals reflect NO₂ and CO emissions from common sources. The slope of the regression line for Mexico City is 0.048, which is 45 % higher than the TROPOMI-derived column enhancement ratios using the UB and PR methods. The ΔNO₂∕ΔCO ratio that is observed at ground level is likely less influenced by the photochemical removal of NO₂ than the TROPOMI-retrieved columns and is, therefore, closer to the inventory-derived ratio, which is consistent with our results. This comparison suggests that the removal of NO₂ reduces the ratio for ground-based measurements by 35 % compared with EDGAR and MACCity. Overall, the emission ratios in EDGAR and MACCity for Mexico City are consistent with both the ground-based measurements and TROPOMI, i.e. within the uncertainty introduced by the chemical removal of NO₂.

For Los Angeles, the regression slope is 0.042, which is 10 % to 20 % larger than the TROPOMI-derived column enhancement ratios using the UB and PR methods. However, the EDGAR and MACCity ratios are a factor of 5 higher than the ΔNO₂∕ΔCO ratio observed at ground level. The ground-based measurements point to similar ratios for Mexico City and Los Angeles, confirming the HTAP-v2-supported TROPOMI finding that the emission ratios in EDGAR and MACCity are too high for Los Angeles. Therefore, the ground-based measurements for Los Angeles provide independent support for the TROPOMI-derived ratios, pointing to poorer burning conditions in Los Angeles than indicated by the emission inventories, and confirm the value of TROPOMI with respect to monitoring the burning efficiency of megacities.

4 Conclusions

In this study, we investigate the use of TROPOMI XCO and XNO₂ retrievals for monitoring the burning efficiency of fossil fuel use in megacities. To improve the accuracy of the global emission inventories, the burning efficiency and the EF are quantified using co-located XCO and XNO₂ enhancements over the megacities of Tehran, Mexico City, Cairo, Riyadh, Lahore, and Los Angeles. TROPOMI is very capable of detecting XCO and XNO₂ enhancements over these megacities with a relatively short averaging time and shows the expected spatial correlation.

TROPOMI-derived column enhancement ratios have been compared with emission ratios from EDGAR and MACCity. The TROPOMI-derived column enhancement ratios are strongly correlated with the EDGAR and MACCity inventory-derived emission ratios (r=0.85 and 0.7 respectively), showing the highest emission ratio for Riyadh and the lowest emission ratio for Lahore. This shows that Lahore has the poorest burning efficiency, whereas fossil fuel burning is the most efficient over Riyadh (of all megacities that were analysed). The impact of the short NO₂ lifetime and differences in the vertical sensitivity of the TROPOMI XCO and XNO₂ retrieval on the ΔNO₂∕ΔCO enhancement ratio has been quantified. Correcting for these factors significantly improves the agreement between ratios derived from TROPOMI and emission inventories. The comparison indicates that the emission ratios in MACCity and EDGAR are well represented for Mexico City and Tehran. For Lahore, the EDGAR emission ratio agrees better with TROPOMI, whereas the MACCity emission ratios are closest to the TROPOMI-derived emission ratios for Cairo and Riyadh. Emission ratios in EDGAR and MACCity are significantly higher (by 55 % to 70 %) than TROPOMI for Los Angeles. The total uncertainty on TROPOMI-derived emission ratios ranges from 33 % to 35.6 %. The bias in S5P TROPOMI NO₂ retrievals has the most important contribution to the uncertainty in the TROPOMI-derived emission ratio.

TROPOMI-derived ΔXNO₂∕ΔXCO column enhancement ratios for Mexico City and Los Angeles have been validated using ground-based measurement from local air quality monitoring networks. For Mexico City, the enhancement ratio derived from ground-based measurements is consistent with EDGAR, MACCity, and the TROPOMI-derived emission ratio. For Los Angeles, TROPOMI-derived enhancement ratios are consistent with the ground-based measurements as well as the HTAP-v2 inventory based on EPA statistics, whereas EDGAR- and MACCity-derived emission ratios appear to be overestimated by a factor of 5 compared with ground-based measurements. This demonstrates the potential of TROPOMI data for monitoring burning efficiency and evaluating emission inventories.

Appendix A

A1 Derivation of Eq. (6) for CO

The mass balance equation for CO is as follows:

$$\begin{array}{c}{\displaystyle \frac{\mathrm{d}\mathrm{\Delta }\mathrm{XCO}}{\mathrm{d}t}}=\mathrm{emission}-\mathrm{loss}\mathrm{by}\mathrm{transport}\\ {\displaystyle \frac{\mathrm{d}\mathrm{\Delta }\mathrm{XCO}}{\mathrm{d}t}}=E_{\mathrm{CO}}-{\displaystyle \frac{U}{l_x}}\mathrm{\Delta }\mathrm{XCO}\end{array}$$

In the steady state, $\frac{\mathrm{d}\mathrm{\Delta }\mathrm{XCO}}{\mathrm{d}t}$ is zero.

$$E_{\mathrm{CO}}={\displaystyle \frac{U}{l_x}}\mathrm{\Delta }\mathrm{XCO},$$

where ΔXCO is the enhancement of CO in the city (in ppb), U is the wind speed (in m s⁻¹), and l_x is the diameter of the city (in m).

A2 Derivation of Eq. (6) for NO₂

The mass balance equation for NO₂ is as follows:

$$\begin{array}{c}{\displaystyle }\begin{array}{rl}{\displaystyle \frac{\mathrm{d}\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}{\mathrm{d}t}}& =\mathrm{emission}-\mathrm{loss}\mathrm{by}\mathrm{the}\mathrm{transport}\\ & -\mathrm{chemical}\mathrm{loss}\end{array}\\ {\displaystyle \frac{\mathrm{d}\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}{\mathrm{d}t}}=E_{{\mathrm{NO}}_{\mathrm{2}}}-{\displaystyle \frac{U}{l_x}}\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}-{\displaystyle \frac{\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}{\mathit{\tau }}}\end{array}$$

In the steady state, $\frac{\mathrm{d}\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}{\mathrm{d}t}$ is zero and τ is $\frac{\mathrm{1}}{K\left[\mathrm{OH}\right]}$, K is the rate constant reaction of NO₂ with OH of $\mathrm{2.8}\times {\mathrm{10}}^{-\mathrm{11}}{\left(\frac{T}{\mathrm{300}}\right)}^{-\mathrm{1.3}}$ cm³ molec.⁻¹ s⁻¹ (Burkholder et al., 2015), T (K) and OH (molec. cm⁻³) are the boundary layer average temperature and OH concentration respectively.

$$E_{{\mathrm{NO}}_{\mathrm{2}}}=\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}\left({\displaystyle \frac{U}{l_x}}+{\displaystyle \frac{\mathrm{1}}{\frac{\mathrm{1}}{K\left[\mathrm{OH}\right]}}}\right),$$

where ΔXNO₂ is the enhancement of NO₂ in the city (in ppb), U is the wind speed (in m s⁻¹), and l_x is the diameter of the city (in m).

A3 Derivation of ratio in Eq. (6)

$${\displaystyle \frac{E_{{\mathrm{NO}}_{\mathrm{2}}}}{E_{\mathrm{CO}}}}={\displaystyle \frac{\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}{\mathrm{\Delta }\mathrm{XCO}}}.\left({\displaystyle \frac{\frac{U}{l_x}+K\left[\mathrm{OH}\right]}{\frac{U}{l_x}}}\right)$$

The influence of averaging kernel is calculated as follows:

$${\displaystyle \frac{E_{{\mathrm{NO}}_{\mathrm{2}}}}{E_{\mathrm{CO}}}}={\displaystyle \frac{\mathrm{\Delta }{\mathrm{XNO}}_{\mathrm{2}}}{\mathrm{\Delta }\mathrm{XCO}}}{\displaystyle \frac{\left(\frac{U}{l_x}+K\left[\mathrm{OH}\right]\right)}{\frac{U}{l_x}}}{\displaystyle \frac{\mathrm{1}}{(\mathrm{1}-A_{\mathrm{influence}})}},$$

where A_influence is the influence of the averaging kernel on ΔXNO₂∕ΔXCO.

Appendix B

The derivation of the tropospheric averaging kernel (A) for NO₂, as described by Eskes et al. (2019), is as follows:

$$\begin{array}{ll}{A}_{\mathrm{trop}}=\left(\frac{M}{M_{\mathrm{trop}}}\right)\cdot A_{\mathrm{total}}& \left(\mathrm{l}\le l_{\mathrm{tp}}^{\mathrm{TM}\mathrm{5}}\right)\\ A_{\mathrm{trop}}=\mathrm{0},& \left(l>l_{\mathrm{tp}}^{\mathrm{TM}\mathrm{5}}\right),\end{array}$$

where M is the total mass factor, M_trop is the AMF for the troposphere, and $l_{\mathrm{tp}}^{\mathrm{TM}\mathrm{5}}$ is the TM5 tropopause layer index.

Appendix C

$$\begin{array}{c}{\displaystyle }\mathrm{Without}A={\displaystyle \frac{\mathrm{\Delta }{{\mathrm{NO}}_{\mathrm{2}}}_{\mathrm{CAMS}}}{\mathrm{\Delta }{\mathrm{CO}}_{\mathrm{CAMS}}}}\\ {\displaystyle }{{\mathrm{NO}}_{\mathrm{2}}}_{\mathrm{new}\mathrm{CAMS}}={{\mathrm{NO}}_{\mathrm{2}}}_{\mathrm{CAMS}}\cdot A_{{\mathrm{NO}}_{\mathrm{2}}\mathrm{TROPOMI}}\\ {\displaystyle }{\mathrm{CO}}_{\mathrm{new}\mathrm{CAMS}}={\mathrm{CO}}_{\mathrm{CAMS}}\cdot A_{\mathrm{CO}\mathrm{TROPOMI}}\\ {\displaystyle }\mathrm{With}A={\displaystyle \frac{\mathrm{\Delta }{{\mathrm{NO}}_{\mathrm{2}}}_{\mathrm{new}\mathrm{CAMS}}}{\mathrm{\Delta }{\mathrm{CO}}_{\mathrm{new}\mathrm{CAMS}}}}\\ {\displaystyle }{A}_{\mathrm{influence}}={\displaystyle \frac{(\mathrm{Without}A-\mathrm{With}A)}{\mathrm{Without}A}}\cdot \mathrm{100}\mathit{\%}\end{array}$$

Here, ${{\mathrm{NO}}_{\mathrm{2}}}_{\mathrm{CAMS}}$ and CO_CAMS are the CAMS column densities derived for NO₂ and CO respectively, whereas $\mathrm{\Delta }{{\mathrm{NO}}_{\mathrm{2}}}_{\mathrm{CAMS}}$ and ΔCO_CAMS are the city enhancement of NO₂ and CO respectively. $A_{{\mathrm{NO}}_{\mathrm{2}}\mathrm{TROPOMI}}$ and A_CO TROPOMI are the TROPOMI averaging kernel for NO₂ and CO respectively.