Understanding the influence of combustion on atmospheric CO2 over Europe by using satellite observations of CO2 and reactive trace gases

We assess how nitrogen oxides (NOx=NO+NO2), carbon monoxide (CO) and formaldehyde (HCHO) can be used as proxies to determine the combustion contribution to atmospheric carbon dioxide (CO2) using satellite observations. We focus our analysis on 2018 when there is a full complement of column data from the TROPOspheric Monitoring Instrument (NO2, CO, and HCHO) and the Orbiting Carbon Observatory-2 (CO2). We use the nested GEOS-Chem atmospheric chemistry model to relate high-resolution emission inventories over Europe to these atmospheric data, taking into account scene-dependent 5 averaging kernels. We find that that NO2 and CO are the better candidates to identify incomplete combustion and fingerprints of different combustion sectors, but both have their own challenges associated with properly describing their atmospheric chemistry. The secondary source of HCHO from oxidation of biogenic volatile organic compounds, particularly over southern European countries, compromises its use as a proxy for combustion emissions. We find a weak positive correlation between the CO:CO2 inventory ratio and observed column enhancements of ∆CO:∆CO2 (R<0.2), suggesting some consistency and 10 linearity in CO chemistry and transport. However, we find a stronger negative correlation between the NOx:CO2 inventory ratio and observed column enhancements of ∆NO2:∆CO2 (R<0.5), driven by non-linear photochemistry. Both of these observed ratios are described well by the GEOS-Chem atmospheric chemistry transport model, providing confidence of the quality of the emission inventory and that the model is a useful tool for interpreting these tracer-tracer ratios. Our results also provide some confidence in our ability to develop a robust method to infer combustion CO2 emission estimates using satellite observations 15 of reactive trace gases that have up until now mostly been used to study surface air quality.


Introduction
Mitigating the worst effects of future climate relies on our ability to reduce rapidly increasing atmospheric levels of gases emitted by human activities that effectively absorb outgoing infra-red radiation, and subsequently influence the warming of Earth's surface. Atmospheric carbon dioxide (CO 2 ) is the predominant trace gas that continues to affect Earth's contemporary 20 global climate. Inventories of CO 2 that describe human activities, primarily derived from national-scale information about fuel Finch et al. (2021) who used a deep learning method to identify every NO 2 plumes observed by the TROPOspheric Monitoring Instrument (TROPOMI) over a two-year period. They showed these plumes effectively mapped out most of the expected hotspots across the world, including large urban centres, oil and gas production, major power plants, and shipping routes.
Researchers have used CO as a proxy for incomplete combustion, e.g. (Kasibhatla et al., 2002;Palmer et al., 2006;Wang 60 et al., 2009;Konovalov et al., 2014Konovalov et al., , 2016, which has similar advantages to using NO 2 but has a longer e-folding lifetime (weeks to months depending on season and latitude) and a large, seasonally varying secondary source from the oxidation of volatile organic compounds (VOCs). Some of these shortcomings will be overcome as measurements progressively have the capability to resolve smaller spatial scales that are closer to the scale of the responsible point sources. Formaldehyde (HCHO) is another proxy for incomplete combustion (e.g., Fu et al. (2007a); Gonzi et al. (2011)) but the secondary source of HCHO and its uncertainty from the oxidation of biogenic VOCs, particularly over southern Europe (Curci et al., 2010), is sufficiently large to compromise this measurement from being used effectively to isolate combustion.
Recent studies have used satellite observations and emission inventories to analyze enhancements of atmospheric CO 2 and co-emitted species (CO and NO x ) over individual megacities (Hakkarainen et al., 2019;Berezin et al., 2013;Silva et al., 2013) and large urban areas (Silva and Arellano, 2017;Labzovskii et al., 2019;Lama et al., 2020;Park et al., 2021) but have not 70 critically assessed the efficacy of using these data together to isolate the combustion contribution to CO 2 , which will eventually be needed to support more formal Bayesian inference methods. In this study, we explore the agreement between model and observed ratios of NO 2 , CO, and HCHO with CO 2 by taking advantage of a new, high-resolution self-consistent European emission inventory for these gases (Super et al., 2020), a high-resolution chemistry transport model centred over Europe, and co-located satellite column measurements of CO 2 , NO 2 , CO, and HCHO. We combine this information to interpret model and 75 observed ratios at the model grid-scale resolution and at the national scale over Europe.
In the next section, we describe the nested version of GEOS-Chem that we use to study the relationships between emissions and corresponding atmospheric ratios of CO 2 and NO 2 and CO over Europe. We also describe the satellite data we use to evaluate these model relationships. In Sect. 3 we present our analysis and critically assess the efficacy of these ratios to isolate the combustion contribution of CO 2 . We conclude the paper in Sect. 4.

Data and Methods
Here we describe the nested GEOS-Chem atmospheric chemistry transport model and the satellite data we use to explore the relationships between CO 2 , NO 2 , and CO. For the purposes of this study, we focus on contrasting summer (July) and winter (December) months during 2018 when there are data from all relevant satellite instruments.
2.1 GEOS-Chem atmospheric chemistry transport model 85 We use v12.6.1 of the GEOS-Chem 3-D atmospheric chemistry transport model (www.geos-chem.org) to describe the relationship between surface fluxes and atmospheric concentrations of CO, NO 2 , and CO 2 . We drive the GEOS-Chem model with Goddard Earth Observing System, forward processing (GEOS-FP) meteorological analyses from the Global Modeling and Assimilation Office (GMAO) at NASA Goddard Space Flight Center.
For the experiments presented here, we use the nested version of GEOS-Chem to study atmospheric CO, NO 2 , and CO 2 over 90 Europe (broadly defined as 15 • W-40 • E, 30 • -70 • N, taking into account a buffer zone that helps to absorb any discontinuities associated with the coarser lateral boundary conditions), driven by the GEOS-FP meteorological analysis at its native spatial resolution of 0.25 • (latitude) × 0.3125 • (longitude). To provide time-dependent lateral boundary conditions for the nested model, we use a self-consistent version of GEOS-Chem at a coarser resolution of 4 • (latitude) × 5 • (longitude). For both models we use 47 hybrid-sigma levels from the surface to 0.01 hPa, of which 30 lie below the dynamical troposphere. 95 We use a GEOS-Chem simulation that includes HO x -NO x -VOC-ozone-halogen-aerosol tropospheric chemistry, which is coupled with stratospheric chemistry via the unified tropospheric-stratospheric Chemistry eXtension (Eastham et al., 2014).
For our global run, we use anthropogenic emissions of chemically reactive gases (CO,CH 4 ,NH 3 , NO x , SO 2 , non-methane volative organic compounds (VOCs)), carbonaceous aerosols (including black carbon and organic carbon), and CO 2 , from the Community Emission Data System (CEDS) global emission inventory (Hoesly et al., 2018). Offline dust aerosol, lightning and 100 soil NO x , biogenic VOCs and sea salt aerosols emissions (Weng et al., 2020) are used in both global and regional simulations.
We use Global Fire Emissions Database version 4 (GFED4, http://globalfiredata.org) to describe pyrogenic emissions. The GFED inventory provides monthly dry matter emissions based on satellite observations of fire activity and vegetation coverage from MODIS (Moderate Resolution Imaging Spectroradiometer, van Marle et al. (2017)). The GEOS-Chem model calculates biomass burning emissions of trace gases and aerosols by applying vegetation-specific emission factors (Akagi et al., 2011) to 105 the dry matter burned data.
For our nested European domain, we replace our global inventory anthropogenic emissions of CO, NO x , CO 2 with the TNO-GHGco inventory (Netherlands Organization for Applied Scientific Research (TNO), greenhouse gas and co-emitted species emission database, Super et al. (2020)). This inventory is based on national emissions submitted to the United Nations Framework Convention on Climate Change for CO 2 and to the European Monitoring and Evaluation Programme/Centre on 110 Emission Inventories and Projections for NO x and CO. National totals are distributed across individual countries on a 0.05°l atitude × 0.1°longitude grid by using proxies such as the location of large industrial point sources, industrial area land cover maps for industrial emissions, and road networks derived from Open street map and Open transport map for road transport emissions (Super et al., 2020). Annual emissions are distributed in time using temporal emission profiles according to month, day of the week, and the hour of day for every GNFR (Gridded Nomenclature For Reporting) sector code, based on the sector 115 specific emission data reported by each country, and long-term mean activity data and/or socio-economic characteristics. The Live Stock and L -Agriculture Others. The TNO-GHGco inventory also separates fossil fuel and biofuel emissions of CO 2 and CO. Emissions of NO x are converted to units of kg NO 2 m −2 s −1 for both the global (CEDS) and the regional (TNO-GHGco) 120 inventories, and used as such in the GEOS-Chem model simulations. Consequently, we report NO x emissions in the same units. We combine emissions from ten GNFR sectors (public power, industry, other stationary combustion, fugitives, all three types of road transport, shipping, aviation and off road transport) that involve the combustion of fossil fuel and biofuel to form combustion emissions. This step is in recognition that we cannot separate emissions from different sectors or the combustion of two fuel types, in terms of their contribution to observed atmospheric CO 2 and NO 2 columns. 125 Figure 1 shows the European distribution of TNO-GHGco combustion emission estimates (kg m -2 s -1 ) of CO 2 , NO x , and CO for July and December 2018. Combustion emissions are high over major cities (e.g., London, Paris, Madrid), industrial areas, and over major land and ocean transportation networks, as expected. Figure 2 shows monthly sector contributions to national total combustion emissions of CO 2 , NO x , and CO during July and December 2018 from the six highest emitting European countries, including the United Kingdom. In general, differences in the spatial distributions of emissions ( Fig. 1) 130 of these three trace gases and between July and December reflect the relative national importance of individual sectors (Fig. 2) that contribute to our combustion emission. Combustion emissions during December are generally higher than July, due primarily to a contribution from residential heating (C: Other Stationary Combustion) during the colder month ( Fig. 2). We find that the six top CO 2 emitting countries for these three gases are consistently Germany, United Kingdom, France, Italy, Poland, and Spain. Germany is the largest emitter of NO x , CO, and CO 2 , except for CO during December 2018. The largest 135 contributing sectors for these top CO 2 emitting countries for NO x , CO, and CO 2 are usually public power, industry, residential heating and transportation (Fig. A1). In terms of fuel type, the majority of CO 2 emissions comes from fossil fuel combustion in both July and December for the top 14 CO 2 emitting countries in the domain (Fig. A2), while for CO more than 50% of the emissions during December comes from biofuel combustion for France, Italy, Spain, Austria, Sweden and Portugal (Fig. A3).
2.2 Satellite observations of CO 2 , NO 2 , and CO 140 We use dry-air column CO 2 (XCO 2 ) observations retrieved by the NASA Orbiting Carbon Observatory-2 (OCO-2), launched in July 2014 into a sun-synchronous orbit with a local equatorial crossing time of 13:30 in its ascending node (Eldering et al., 2017). The dimensions of the ground footprint of XCO 2 is nominally 1.25 km across track and 2.4 km along track, determined by the instrument field of view, the orbital speed of the satellite, and the measurement integration time. OCO-2 includes three spectrometers that measure two CO 2 bands (1.61 and 2.06 µm) and the O 2 A-Band (0.765 µm) (Crisp et al., 2004). For this 145 study, we use OCO-2 Version 10 "Lite" (v10r) data, which is a bias-corrected and quality filtered Level 2 XCO 2 retrievals. First, the bias correction procedure maps the raw XCO 2 retrievals of the OCO-2 Level 2 algorithm to the best available estimate of XCO 2 , using multi-model mean and TCCON measurements as training data sets (O'dell et al., 2018). Then, additional outlier filtering is applied to screen out low quality data based on parameters such as albedo, aerosol optical depth and cloud fraction (Crisp et al., 2021). On monthly timescales, 7 to 12 % of these measurements are considered clear-sky data (cloud and aerosol 150 free) that pass all quality tests, with single measurement random errors between 0.5 and 1 ppm at solar zenith angles smaller than 70°(Eldering et al., 2017).
We also use satellite column observations of CO, NO 2 , and HCHO from the TROPOMI, aboard the European Space Agency's Sentinel-5 Precursor satellite. TROPOMI satellite was launched in 2017 into a sun-synchronous orbit with a local equatorial overpass time of 13:30 in its ascending node. TROPOMI is a nadir viewing instrument that contains four spectrom-155 eters that cover UV-Vis-NIR-SWIR wavelengths. With a cross-track swath of 2600 km and a high spatial ground footprint resolution of 7×7 km 2 , TROPOMI has near-daily global coverage, subject to cloud-free scenes (Veefkind et al., 2012). Its operational level 2 trace gas data products include NO 2 , CO, CH 4 , O 3 , HCHO, and SO 2 ). For the purposes of brevity, we refer the reader to dedicated studies that describe the retrieval of CO (Vidot et al., 2012;Landgraf et al., 2016), NO 2 (Boersma et al., 2010Van Geffen et al., 2015;Lorente et al., 2017;Zara et al., 2018;Van Geffen et al., 2020), and HCHO (Platt and 160 Stutz, 2008;Smedt et al., 2018). Tropospheric column retrieval biases of CO, NO 2 , and HCHO are <10%, 25-50%, and 80%, respectively. We use TROPOMI satellite retrievals that have a quality assurance flag with a value >0.5 for CO, >0.75 for NO 2 and >0.5 for HCHO, which removes cloud-covered scenes, partially snow/ice covered scenes, errors and problematic retrievals, as recommended by respective technical descriptions (https://sentinels.copernicus.eu/web/sentinel/technical-guides/ sentinel-5p/products-algorithms, last accessed 14th July 2021) 165

Results
Here we report our analysis of TNO-GHGco emissions estimates of CO, NO x , and CO 2 and their ratios, and the corresponding model atmospheric column concentrations and their ratios, which we compare with observed values calculated from OCO-2 and TROPOMI. We do not consider emission ratios that include HCHO because the direct emission is small compared to the contribution from methane and non-methane VOCs. 3.1 Inventory emission ratios of combustion NO x :CO 2 and CO:CO 2 Figure 3 shows the inventory combustion emission ratios, described as mole fractions, of NO x :CO 2 and CO:CO 2 during July and December 2018, corresponding to values shown in Fig. 1. These gridded ratios represent the net combustion efficiency of total emissions weighted by the influence of individual sectors. Generally, higher values of CO:CO 2 and NO x :CO 2 denote a lower combustion efficiency, with higher NO x :CO 2 values also associated with higher combustion temperatures. We find that 175 the NO x :CO 2 ratio is higher in July than December, but CO:CO 2 ratio is generally higher in December than July, which is reflected in the national mean values (Fig. 4). This is due to a larger contribution from residential heating (C: Other Stationary Combustion) to net emissions during December (Fig. 2) for which NO x :CO 2 values (0.49-1.95) are lower and CO:CO 2 values (0.60-4.25) are generally higher than for other sectors (Fig. 4). (in descending order). We find NO x :CO 2 values are higher in shipping, off-road transport and diesel road transport. CO:CO 2 values are generally higher in off-road transport, residential heating and gasoline road transport. These ratios are assumed to be the same in different months of the year (Super et al., 2020), hence total combustion ratios in July and December only differ 185 in the relative contribution from each sector ( Fig. 2 and A1). In terms of NO x :CO 2 , Portugal, Norway and Spain are higher than neighbouring European countries, with Germany having the lowest value. In terms of CO:CO 2 , Germany has a lower values than its neighbouring countries. The differences between countries for the two months reflect the relative importance of individual sectors (Fig. 2, 4 and A1), in particular, the relative importance of transport, domestic heating and shipping emission.
Closer inspection of Fig. 1 reveals hotspots of CO 2 that correspond to cities, large point sources, and transport network. These 190 CO 2 hotspots manifest themsleves as low values of the emission ratios (Fig. 3). Emissions in the marine troposphere are mainly due to ship exhaust, which emits more NO x and less CO than land-based sectors, resulting in the rapid gradient of the ratios between land and ocean. Figure 4 also shows the corresponding nationwide mean combustion emission ratios of NO x :CO 2 and CO:CO 2 during July and December 2018. Generally, CO:CO 2 ratios are higher than NO x :CO 2 (note the different scaling factor), reflecting higher 195 fossil fuel emission factors for CO than for NO x . We find that national values of NO x :CO 2 show a smaller dynamic range than corresponding values of CO:CO 2 , particularly during July. This will have implications for using these ratios to determine combustion CO 2 emissions from individual countries, particularly those that are geographical neighbours. Portugal has the highest NO x :CO 2 value in the domain, mostly determined by large industrial sources, shipping and off-road transportation.
Norway has the highest value for CO:CO 2 , mostly contributed by emissions from large industries, residential heating and 200 off-road transportation.
3.2 Comparison of observed and model column variations of CO 2 , CO, NO 2 and HCHO Figure A4 shows typical column averaging kernels for OCO-2 CO 2 , and TROPOMI CO, NO 2 , and HCHO, which describe the sensitivity of the retrieved columns to changes in these gases as a function of altitude through the atmosphere. Model output, sampled at the time and location of each observation, is convolved with scene-dependent averaging kernels so it can 205 be directly compared with observed columns. These averaging kernels generally show that the retrieved columns of all four gases are sensitive to varying degrees to changes in the lower troposphere where surface emissions have the largest impact on. Differences between the vertical sensitivities may result in the misinterpretation of the ratios that we attempt to avoid by applying the kernels to the model output.

Satellite column observations
210 Figure 5a, b and c shows monthly OCO-2 CO 2 , TROPOMI NO 2 and CO columns during July 2018, gridded on the GEOS-Chem nested model 0.25 • ×0.3125 • grid. We find that NO 2 has the largest spatial variability across Europe, mainly reflecting its much shorter atmospheric lifetimes compared with CO and CO 2 . Tropospheric NO 2 columns are generally elevated over major cities (e.g., London, Paris, Madrid), conurbations (e.g., Manchester, Liverpool) and industrial areas (e.g., Po Valley, northern Italy) across Europe (Pope et al., 2018;Griffin et al., 2019;Finch et al., 2021). We do not consider December 2018 215 because the distribution of CO 2 used below to examine atmospheric trace gases ratios is too sparse due to cloudy scenes (Fig.   A5).  (Palmer et al., 2006;Surl et al., 2018). There are also small direct emissions and contributions 220 from industrial activity via the oxidation of anthropogenic VOCs (e.g., Po Valley). The rate at which HCHO is produced from the oxidation of anthropogenic VOCs tends to be much larger than biogenic VOCs so that the resulting HCHO column is smeared over neighbouring grid boxes (Palmer et al., 2003;Abbot et al., 2003;Fu et al., 2007b). Given the limited use of HCHO as a tracer of combustion we do not pursue this tracer any further.
In contrast to TROPOMI that has a wide cross-track swath, OCO-2 data are sparse that also reflects much stricter filtering For OCO-2 column CO 2 , the equivalent model XCO m 2 is calculated using: where F (x) denotes the GEOS-Chem model that relates a priori flux estimates x to a scene-dependent CO 2 profile and the log-linear interpolation of those values on the model pressure levels to i pressure levels used by the XCO 2 retrieval algorithm, which uses its own a priori values denoted by y a (corresponding to the the column XCO a 2 ). The pressure weighting function η i includes the pressure intervals assigned to the satellite retrieval levels, and a i denotes the scene-dependent averaging kernel 240 that describes the sensitivity of the instrument to CO 2 as a function of altitude (e.g., Fig. A4). For TROPOMI columns of CO and NO 2 , we use a similar method to translate the model into observation space. For NO 2 , we consider only the tropospheric column. A detailed description of the method is given by Van Geffen et al. (2020). (R = 0.18) across Europe, but has a relative bias of -0.33%, -14.6% and +50.8%, respectively. In addition to capturing the major NO 2 column hotspots, e.g., southern England, Belgium, Netherlands and northern Italy, Fig. 5 shows that elevated NO 2 columns are more widespread in GEOS-Chem than TROPOMI. Higher model values over land likely reflect over-reporting of NO x emissions from rural areas of France, Germany, Poland and other eastern European countries, i.e., errors in emission inventory, temporal profile and errors in vertical mixing and lifetime of NO x against chemical oxidation. This positive model 250 bias could also be due to the mismatch between emission timing and satellite overpass. Overestimation of NO 2 columns over the Bay of Biscay and the northern Mediterranean Sea reflect errors in the modelling of lightning (influencing the upper troposphere), vertical mixing over water, NO x lifetime, over-reporting of NO 2 shipping emission, and challenges in detecting surface concentrations of NO 2 from shipping (Laughner et al., 2016) (Fig. 1). The lifetime of NO x is of the order of hours and changes with the chemical environment, including the NO x concentration itself, e.g. Laughner and Cohen (2019). GEOS-Chem fails to capture the highest values in TROPOMI NO 2 columns, especially over London, Paris, Madrid, Belgium, Netherlands and western Germany, which is due to some combination of underestimating emissions from these large urban sources, errors in the model description of NO x photochemistry, and the low sensitivity of averaging kernels to lower levels of the atmosphere (Fig. A4).
Figure 5 also shows there is better relative agreement between GEOS-Chem and TROPOMI for CO than for NO 2 , with 260 a mean percentage bias of -14.6% compared with 50.8% for NO 2 , and a better spatial correlation. This reflects the longer atmospheric lifetime for CO (weeks during summertime) against oxidation by the hydroxyl radical so that atmospheric distributions are less influenced than NO 2 columns by immediate and local surface emissions. Observed variations of CO columns represent the sum of direct emissions from incomplete combustion and a secondary source from the oxidation of methane and non-methane VOCs (Duncan et al., 2007). The secondary source is usually assumed to be a diffuse source of CO because of 265 the time it typically takes to produce CO. Using GEOS-Chem, we find that the secondary source is typically 10-20% of the total CO source in winter months but in July can be as much as 75% of the total CO source over Europe. This secondary source will therefore need to be considered if CO is to be used to isolate combustion CO 2 .
Large model bias for CO (negative) and NO 2 (positive), as reported above, limits our ability to infer directly combustion CO 2 from these data. However, the reasonably high spatial correlation between GEOS-Chem and TROPOMI (R=0.60 for NO 2 270 and R=0.82 for CO) provide us with some confidence in our ability to use enhancement ratios of column CO and NO 2 (∆NO 2 and ∆CO). To calculate these enhancements, we first determine latitude-dependent background values of the satellite data and then subtract those from the data. We calculate these background values (i.e., not directly influenced by urban enhancements) using monthly mean values over the remote Pacific Ocean (175°W to 165°W) in 10°latitude bins. Mean monthly observed background levels of XCO 2 , column NO 2 and column CO over the remote Pacific Ocean are 390 ppm, 2.46 µ mol m -2 and 275 20578 µ mol m -2 , respectively. We compute the corresponding background levels for GEOS-Chem model by adjusting the satellite observed background levels with the model bias (domain mean) in Fig. 5, assuming that model bias is mostly caused by the background level (boundary condition simulated by the global full chemistry simulation). We subtract these values from the observations and the GEOS-Chem model to determine ∆XCO 2 , ∆XCO and ∆XNO 2 . In the next section, we explore the relationship between ∆NO 2 and ∆CO and the corresponding value of ∆CO 2 .   Fig. 3. We find that model fails to capture ∆XNO 2 :∆XCO 2 hotspots such as Madrid and Paris due to failure to capture hotspots in column NO 2 concentration in Figure   5. To understand the relationship between the emissions and corresponding atmospheric values, we correlate the two sets of ratios at grid cell level and at national level for July 2018. NO 2 with CO, with the model having a smaller enhancement of NO 2 per unit of column CO enhancement. This suggests that the inventory is in error and that the NO x :CO should be smaller, and/or there is a larger NO 2 chemical loss than we describe in 310 GEOS-Chem (or a smaller chemical loss of CO). Figure 9 shows the model and observed relationship between the emission-based ratios of NO x :CO 2 and CO:CO 2 and the corresponding atmospheric ratios of ∆XNO 2 :∆XCO 2 and ∆XCO:∆XCO 2 . Figures A7 and A8. show the grid-cell resolution analysis for the nine countries with the most amount of data. Figure 9 shows good agreement between model and measurements in terms of the variation of the atmospheric ratio. The situation for the NO 2 -based ratio (Fig. 9a) is more encouraging. Model 315 and observed ∆XNO 2 :∆XCO 2 ratio are both negatively related to the inventory based NO x :CO 2 ratio, with correlations of -0.69 for GEOS-Chem and -0.50 for the satellite observations. At the grid-scale resolution, the United Kingdom, Italy and Norway demonstrate the similar negative correlation. These countries do not differ significantly from other countries in terms of relative contribution from different sectors ( Fig. 2 and Fig. A1), or national mean combustion ratios (Fig. 4). Hence, the negative relationships between the inventory-based and atmospheric-based ratios reflect a strong non-linearity between NO x emissions 320 and NO 2 concentration. This is most likely due to NO x photochemistry, since other factors are generally similar between our CO and NO 2 based ratios, e.g., meteorology. This strong negative correlation in NO 2 based ratios requires further investigation to understand how to best use this information to interpret combustion CO 2 . Nevertheless, good (negative) correlations between emission-based ratios and the observed and model atmospheric column ratios could indicate the feasibility to infer combustion CO 2 from satellite measurements and GEOS-Chem model using co-emitted CO and NO x .

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For CO (Fig. 9b), there is only a weak correlation between combustion CO:CO 2 and ∆XCO:∆XCO 2 for both GEOS-Chem and the satellite observations, at national (Fig. 9) and at grid-cell resolutions (Fig. A8). Generally, we find there is more national variation between the inventory-based CO:CO 2 ratio than the corresponding atmospheric ratio, which is due to atmospheric mixing of CO that has an e-folding lifetime much longer than the transport time over Europe. Similar to the NO 2 based ratios, GEOS-Chem overestimates the column enhancement ratio (Fig. 7b and d).

Concluding remarks
We assessed how three reactive trace gases, nitrogen dioxide (NO 2 ), carbon monoxide (CO) and formaldehyde (HCHO), can be used as proxies to determine the combustion contribution to atmospheric CO 2 in July and December, two contrasting months in terms of sector emissions and photochemical environment, in 2018. Our choice to focus on combustion emissions reflects varying contributions of biofuel combustion to national CO 2 emission budgets across Europe. We use satellite column 335 measurements of CO 2 from the NASA Orbiting Carbon Observatory (OCO-2) and satellite tropospheric column data products of CO, NO 2 , and HCHO from the European TROPospheric Ozone-Monitoring Instrument (TROPOMI) aboard Sentinel-5P.
We focus our analysis on 2018 when there is a full year of data from OCO-2 and TROPOMI. We use a nested atmospheric chemistry transport model (GEOS-Chem) driven by self-consistent combustion emissions of CO 2 , nitrogen oxides (NO x ), CO, and volatile organic compounds (VOCs) that are precursors to HCHO. 340 We found that HCHO as a tracer of incomplete combustion is compromised during the summer by biogenic VOC emissions, particularly over the Mediterranean, and during the winter when the lifetimes of parent anthropogenic VOCs are too long to relate elevated HCHO columns to anthropogenic activity. Based on our assessment, we conclude that HCHO is unlikely to play a substantive role in quantifying the combustion contribution to CO 2 .
Combustion emission estimates for CO 2 , CO and NO x in July and December 2018 show different spatial distribution due to 345 different dominating emission sectors for these trace gases and also in contrasting months, which resulted in spatial variation in CO:CO 2 and NO x :CO 2 . Hence, we find that NO 2 and CO are the better proxies for combustion, but both have their own challenges. When using satellite measured ∆XNO 2 and ∆XCO as a way to identify characteristic ∆X:∆XCO 2 ratios (where X = NO 2 or CO and ∆ denotes elevated values above a regional background value) that correspond to combustion, we find that photochemistry must be taken into account. In the case of NO 2 , rapid cycling with NO (the sum of which is known as 350 NO x ) must be considered, which varies with latitude and season. Similarly, any additional production or loss of NOx reservoir species, e.g., peroxyacyl nitrate (PAN), could significantly alter the ratio. CO is made up of direct anthropogenic and biomass burning emissions, in addition to a secondary production source from the oxidation of VOCs and methane that can contribute up to 75% of the total source in summer months. Neglecting atmospheric chemistry will compromise the ability to use these tracers to determine combustion CO 2 .

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When investigating corresponding ratios in reported emission data, we find a weak positive relationship between CO:CO 2 and NO x :CO 2 ratios on national levels (R<0.4), which suggests that combustion efficiency in terms of co-emitting CO and NO x are weakly correlated within a country. We also find a weak positive correlation between emission-based ratio CO:CO 2 and satellite observed column enhancement ∆XCO:∆XCO 2 (R<0.2), which suggests the consistency and linearity in CO chemistry and transport. Conversely for NO 2 , we find a stronger negative correlation between NO x :CO 2 and enhancement 360 ∆XNO 2 :∆XCO 2 (R<0.50), which suggests nonlinearity in NO x photochemistry. Both of these relationships are described reasonably well (similar R values) by the atmospheric chemistry transport model, providing confidence that the model is a useful tool for interpreting these tracer-tracer ratios.
Some of the challenges we faced in our study, in particular the coincidence of TROPOMI and OCO-2 data, will be partly addressed with upcoming missions that measure both NO 2 and CO 2 . These missions currently include the Copernicus CO 2 365 Monitoring (CO2M) mission (Kuhlmann et al., 2021) and the Japanese Greenhouse Gases Observing Satellite Greenhouse gases and Water cycle (GOSAT-GW). The proposed CO2M mission is temporally staggered three-satellite constellation, resulting in better spatial coverage of the globe per day than currently provided by OCO-2. Developing virtual constellations, i.e. integrating measurements from independent missions, is an ongoing key objective but relies on rigorous calibration of data collected by different sensors. Another current challenge is understanding how to use together CO 2 and reactive trace gases 370 to infer robust combustion emission estimates of CO 2 . Our work has shown that even over Europe, where our knowledge of emissions should be relatively good compared to many parts of the world, we find there are sometimes large differences between model photochemical calculations and satellite observations. Addressing this issue will need an integrated approach that draws together the atmospheric chemistry and carbon cycle communities.