Top-Down NOX Emissions of European Cities Based on the Downwind Plume of Modelled and Space-Borne Tropospheric NO2 Columns

Top-down estimates of surface NOX emissions were derived for 23 European cities based on the downwind plume decay of tropospheric nitrogen dioxide (NO2) columns from the LOTOS-EUROS (Long Term Ozone Simulation-European Ozone Simulation) chemistry transport model (CTM) and from Ozone Monitoring Instrument (OMI) satellite retrievals, averaged for the summertime period (April–September) during 2013. Here we show that the top-down NOX emissions derived from LOTOS-EUROS for European urban areas agree well with the bottom-up NOX emissions from the MACC-III inventory data (R2 = 0.88) driving the CTM demonstrating the potential of this method. OMI top-down NOX emissions over the 23 European cities are generally lower compared with the MACC-III emissions and their correlation is slightly lower (R2 = 0.79). The uncertainty on the derived NO2 lifetimes and NOX emissions are on average ~55% for OMI and ~63% for LOTOS-EUROS data. The downwind NO2 plume method applied on both LOTOS-EUROS and OMI tropospheric NO2 columns allows to estimate NOX emissions from urban areas, demonstrating that this is a useful method for real-time updates of urban NOX emissions with reasonable accuracy.


Background
High levels of nitrogen oxides (NO X = NO + NO 2 ) are toxic and adversely impact both human health [1] and ecosystems [2,3]. NO X is mainly generated in polluted regions by anthropogenic combustion of fuels from traffic, industrial processes and household activities that typically occur in densely populated urban areas. In 2013 for the EU-28, 46% of the anthropogenic NO X emissions originated from the transport sector, 21% from the energy and 15% from the industry sector [4], excluding emissions from international shipping within European seas. According to the European Environment Agency, around 10% of the urban population in the EU-28 is exposed to air pollutant concentrations above EU and WHO reference levels (2011)(2012)(2013) for NO 2 [4]. Since 86% of the exceedances are measured at traffic stations, the percentage of the urban population exposed to high NO 2 concentrations may be somewhat underestimated as >20% of the European urban population now lives less than 400 m from busy roads [5]. Hence, millions of people may potentially suffer from health issues and loss of productive labour. NO X controls the photochemical formation rate of O 3 and thus the production of the hydroxyl radical and hence the chemical lifetime of key atmospheric pollutants and reactive greenhouse gases [6,7]. An end product of the NO X reaction chain is nitric acid, which acts as an efficient aerosol pre-cursor and an acidifying substance. Accurate NO X emission inventories are essential in order for regional and global chemistry transport models (CTM) to capture the lifetimes and mixing ratios of tropospheric pollutants. However, current state-of the-art emission databases vary substantially and uncertainties are high [8][9][10] since reported emissions factors may differ by an order of magnitude or more. For example, NO X emissions of diesel cars have been underestimated up to 20-fold in officially announced data [11]. Moreover, the most recent emission estimates proposed for the latest round of the Climate Model Intercomparison Project result in 10-15% more annual NO X emissions than previous estimates [12].
Satellite sensors have proven records in the retrieval of tropospheric NO 2 columns over many large cities worldwide [10,[13][14][15][16]. From these NO 2 observations NO 2 lifetimes and up-to-date top-down NO X emissions can be derived [10,[15][16][17][18][19][20][21][22][23] demonstrating the ability of satellite data to bridge the gap between actual emission fluxes and the reported inventory data, which typically have a delay of 3-5 years before they are available.

Objectives
Modelled tropospheric NO 2 concentrations and lifetimes have large uncertainties associated with them [24] due to the highly non-linear small-scale chemistry that occurs in urban areas, uncertainties in the chemical reaction rate data, missing nitrogen (N) species, too low volatile organic compounds (VOC) emissions, incomplete knowledge of NO X chemistry reaction coefficients, extended chemical reactions [7,25] and recycling of NO X via nitrate photolysis [26]. Overestimation in the chemical lifetime of NO 2 may point out missing NO X chemistry in current CTM's [25]. By simultaneously estimating both the NO 2 lifetime and NO 2 emissions from the downwind plume evolution independent NO X emission flux estimate can be derived [10].
A frequently applied and proven methodology to estimate the lifetime of NO X from satellite observations is based on the downwind plume of tropospheric NO 2 data that evaluates the effect of pre-selected wind speed and wind direction on observed tropospheric NO 2 distributions over and downwind of pollution hotspots. This method is not considering vertical mixing and vertical profiles of NO X /NO 2 ratios but is almost free of a-priori assumptions or model input [10,15,16].
An important goal of this study is to test the downwind plume method for European cities that so far has only been applied directly on observed tropospheric NO 2 column fields for US and Chinese cities and power plants. We also evaluate to what extend the known a-priori emissions used in a high-resolution model simulation of tropospheric column fields over European cities are represented using the adapted method for polluted backgrounds of Liu et al. (2016) [16]. Instead of assuming point sources, this method uses the mean NO 2 distribution under calm conditions as proxy for the spatial distribution of NO X emissions and derives the NO 2 lifetime from the difference of NO 2 patterns between calm and windy conditions. Many European cities cannot be considered as point sources of NO X given the short distances between cities and other sources close to cities. For example, the distance between Brussels and Antwerp with a major port is less than 50 km. So, pollution of these cities overlaps and is smeared out from multiple sources over a larger area.
The magnitude of the discrepancies between the bottom-up NO X emissions and the top-down estimates derived with the downwind plume approach provide a direct test of the robustness of the method and can be used to quantify the uncertainties in the NO X emissions and lifetime estimates. We show that a small dataset of only one season (April-September 2013) can be used to derive robust values of NO X emissions and NO 2 lifetimes.
Tropospheric NO 2 column model fields simulated with the LOTOS-EUROS (Long Term Ozone Simulation-European Ozone Simulation, [27]) CTM averaged for the period April-September 2013 over 23 selected European urban areas under windy conditions (averaged surface to 500 m wind speeds >5 m s −1 ) were used in the downwind plume approach adapted for polluted backgrounds. As an end-to-end test, we then compare the top-down derived surface NO X emissions with the 2011 MACC-III emission inventory [28], used in the LOTOS-EUROS model as input to simulate the NO 2 columns. We compare the NO 2 lifetimes derived from LOTOS-EUROS with values reported in the literature and we discuss possible cross-correlations between the lifetime and emission estimates.
After demonstrating that the downwind plume method works on model fields and estimating the intrinsic uncertainties of the method, we apply it on OMI (Ozone Monitoring Instrument) tropospheric NO 2 column data, providing us with real-time observation-based estimates of midday NO 2 lifetime and NO X emissions over 23 European cities in 2013. Where available in these cities, the top-down estimated NO X emissions are also compared with reported surface NO 2 concentrations which are converted to NO X emissions using the LOTOS-EUROS CTM. In Section 3 the used datasets are described. Both the OMI tropospheric NO 2 column retrieval and processing (Section 3.1) as well as the LOTOS-EUROS tropospheric NO 2 data (Section 3.2) are discussed. We also make use of surface NO 2 concentrations over some European cities (Section 3.3). In Section 4 we describe the methodology of the downwind plume approach applied on European cities in polluted backgrounds. In Section 5 we present the results and add discussions on the NO 2 lifetime (Section 5.1), NO X the emissions (Section 5.2) and the involved uncertainties (Section 5.3). In Section 6 we wrap-up with a summary and conclusions.

OMI Tropospheric NO 2 Column Retrieval and Processing
The 2013 April to September OMI tropospheric NO 2 columns are retrieved (DOMINO v2 [29]) with a three-step approach: (i) a retrieval of NO 2 slant columns with Differential Optical Absorption Spectroscopy (405-465 nm wavelength range, spectral resolution of 0.5 nm), (ii) assimilation of OMI NO 2 slant columns in the global CTM TM4 for providing stratospheric background columns and a-priori NO 2 profile shapes needed to calculate the tropospheric air mass factors [30], which are then used to (iii) convert the tropospheric slant columns into vertical columns. The OMI pixel size varies from 24 km × 13 km at nadir to 140 km × 26 km at the edges of the swath. Individual OMI pixels were re-gridded to 0.125 • latitude by 0.125 • longitude. Pixels affected by the OMI row anomaly were excluded from the analysis [29]. It has been shown that OMI tropospheric NO 2 vertical column densities exhibit substantial sensitivity to boundary layer NO 2 levels [29][30][31][32] and the DOMINO v2 product has been used and validated extensively [33]. Retrievals with cloud fractions higher than 30% at~13h30 local time are not considered in the analysis.

LOTOS-EUROS Datasets
LOTOS-EUROS is a 3D CTM with focus on simulating the atmospheric composition in the lower troposphere [27]. For this study, the model was driven by ERA-Interim meteorological fields from the ECMWF (European Centre for Medium-Range Weather Forecasts) and the emission inventory developed by TNO (Netherlands Organisation for Applied Scientific Research) for the MACC-III project (Monitoring Atmospheric Composition & Climate) and covers Europe with a resolution of 7 × 7 km 2 [28]. Model simulations were performed for Europe (25 • W-45 • E, 30 • N-70 • N) with a spatial resolution of 0.25 • by 0.125 • with MACC-III emissions data updated until 2011 as input. In the vertical domain, the model uses a bulk boundary layer scheme with four layers. The first layer is the surface layer of 25 m and layer 2 is a single boundary layer with a thickness depending on the time of day. The layer 2 height is obtained by temporal interpolating the boundary layer height field provided by ECMWF, available every three hour. Layers 3 and 4 are reservoir layers and the top of the model is set to 3.5 km height. The NO 2 dataset used in this study was produced using version 1.10 of the model, which was run in forecast mode. The tropospheric NO 2 column datasets derived from the model are columns collocated at the OMI measurement points using LOTOS-EUROS data up to the model top (3.5 km) and then complemented by MOZART-IFS data [34] for the rest of the troposphere (defined at 200 hPa).

Surface NO 2 Measurements
Surface NO 2 measurements of European cities are available from the website http://www. eea.europa.eu (Air Base). Since monthly anthropogenic NO X fluxes do not change significantly throughout the year, an average retrieved value will provide a good estimate [27,35]. Measured surface NO 2 concentrations were converted to NO X surface emission values by assuming that the observed NO X /NO 2 ratio at the surface approximates the modelled NO X /NO 2 ratio obtained from the MACC-III NO X emissions and the corresponding LE simulated NO 2 concentrations for the model surface layer. This scaling approach can be written as: where E NO X ,LE is the MACC-III input NO X emission, NO 2,LE the concentration of NO 2 at the surface layer in LE, NO 2,obs the observed NO 2 surface concentration and finally E NO X ,obs the scaled NO X emission. Next numerical example for Brussels is given as illustration. In Brussels, an annual mean

Methods
In order to test the downwind plume approach on model fields, we sampled LOTOS-EUROS (LE) tropospheric NO 2 columns at locations where OMI cloud fractions (determined from the OMI O 2 -O 2 retrieval [36]) are below 30% at~13h30 local time to ensure that both OMI and LOTOS-EUROS are sampled for comparable clear-sky circumstances. We then re-grid both datasets onto a common 0.125 • × 0.125 • grid, so that both datasets are directly comparable. Next, we compute for each grid cell the prevailing wind direction (sector) from eight possible choices (N, NE, E, SE, S, SW, W and NW) using ECMWF ERA-interim wind direction data [37]. For each wind sector, we select two datasets of tropospheric NO 2 columns. One dataset for calm conditions and one dataset for windy days using the wind speed threshold of <5 m s −1 (averaged from surface up to 500 m altitude) [10,15,16] in order to have sufficient spatial coverage for both wind conditions. Finally, we averaged the data over the period April-September 2013. For every eight wind sectors, we then compute a subset of tropospheric NO 2 for a chosen European city according to the major up and down-wind distance of~300 km (~600 km in total) and an across wind direction distance of~100 km (~200 km in total) for both OMI and LE. This procedure is illustrated in Figure 1 for respectively the LE ( Figure 1a) and OMI tropospheric NO 2 columns (Figure 1b) for the city of Brussels for the case of winds coming from the north. Wind sectors with gaps due to missing data larger than 10% in the across-wind integration interval and larger than 20% in the fit interval in wind direction are not used for the retrievals of lifetimes and NO X emissions [16]. The panels (a) and (d) in Figure 1 show the complex patterns of the NO 2 wind plumes due to the many local NO X sources with high tropospheric NO 2 columns in the middle and south of the Netherlands as well as in Flanders (North-Belgium) and the relatively lower values south of Brussels in Wallonia. From the difference maps of NO 2 columns between windy and calm conditions in panels (b) and (e) of Figure    Next, we have computed for each wind sector the NO 2 line density function over a distance of 300 km downwind and~300 km upwind from the city centre [15,16]. By averaging the NO 2 data over the specified across-wind interval (2 × 100 km), the NO 2 line densities are obtained as illustrated in Figure 1 for Brussels using LE (panel (c)) and OMI tropospheric NO 2 columns (panel (f)) for each wind sector for both calm (indicated by +) as windy conditions (>5 m s −1 ) (indicated by •).
The first tropospheric NO 2 peak of~7 × 10 15 molec. cm −2 in the NO 2 line density for the LE case (panel (c) of Figure 1) is observed at~150 km north of Brussels and originates from the high tropospheric NO 2 values over the mid-Netherlands ranging from west to east. The second tropospheric NO 2 peak (~8 × 10 15 molec. cm −2 ) occurs just north of Brussels and is the result of averaging the accumulated high NO 2 columns from west to east from the Flemish coast over parts of Rotterdam, Antwerp and further to the east. South from Brussels, the line density drops rapidly due to the more rural character of the area. The little tropospheric NO 2 peaks (~4 × 10 15 molec. cm −2 ) at 100 and 200 km south of Brussels are due to the inclusion of NO 2 hotspots over Saint-Quentin and Paris, respectively. South of Paris the tropospheric NO 2 values drop to background values.
In order to derive the NO 2 lifetime and NO X emissions from the line densities of tropospheric NO 2 columns, we follow the approach of Reference [16] for polluted backgrounds. The NO 2 spatial pattern under calm wind conditions (polluted background field) are used as proxy for the distribution of NO X sources, that is, multiple sources of NO X are accounted for (as observed on the maps in f panels (a) and (d) of Figure 1). The effective atmospheric NO 2 lifetime is determined from the change of spatial patterns measured at windy conditions. Emissions are subsequently derived from the NO 2 mass above the background, integrated around the source of interest. Next convolution function of tropospheric NO 2 under calm conditions with the exponential decay function under windy conditions is fit on the data: C(x) is the NO 2 pattern under calm wind conditions; x 0 is the length scale of the NO 2 decay; µ is the location of the apparent source relative to the city centre; α and β are scaling parameters to account for possible differences between windy and calm wind conditions (e.g., cloud conditions, vertical profiles, lifetimes [16]). The accompanying fits of the convolved function using NO 2 observations for calm wind condition and the exponential decay function on the windy condition data of Equation (2) for each wind direction are shown in Figure 1. This procedure was then applied on 23 selected European urban areas as presented in Table 1. The effective lifetime is then derived by the ratio of the fitted e-folding distance (x 0 ) (decay time) and the mean ECMWF derived wind speed (ω) like in Reference [10] (Equation (3)) but we have subtracted the residual mean wind speed under calm wind conditions from the windy conditions as suggested by [16] indicated as ω*: The assumption is that the removal of NO 2 can be described by a first order loss. Stated otherwise, the chemical decay of NO 2 follows an exponential decay function with an e-folding distance x 0 , which results in an overall and effective NO 2 lifetime. For Brussels, the effective lifetime based on OMI observations is 6.7 h for the N wind direction with a fit R 2 value of 0.84 (see also Figure 1, panels (c) and (f)). Similar to Reference [16], the fit results are averaged for wind sectors with a good fit of the convolution function (R 2 > 0.80 and lower bound >0 h and <10 h) (in this case 4.5, 5.1, 6.7, 3.2 h for SW, W, N, NE respectively) and weighted by the R 2 values (0.92, 0.81, 0.84, 0.92, respectively) which yields 4.8 ± 2.3 h. The effective lifetime based on LE data weighted for the different wind sectors is 3.8 ± 2.5 h (see also Figure 1), which is slightly lower than the derived lifetime for the OMI case.  Based on the mass balance, the total mass of NO X is the product of the emission rate with lifetime. We follow the methodology described by Reference [16] to estimate the emissions using a three-step approach by computing the total mass of NO 2 (i), then scale NO 2 to NO X (ii) and (iii) finally dividing the total NO X mass by the lifetime. More detailed, at first (i) we integrate the observed NO 2 columns over the area source of interest to compute the total mass of NO 2 while avoiding interferences with neighbouring sources and by accounting for the polluted background using line density functions under calm wind conditions computed for a smaller interval across (40 km) and along (200 km) wind directions. A nonlinear least-squares fit of a modified Gaussian function g(x) (see Equation (4)) to the NO 2 line densities under calm wind condition for the different wind sector pairs (N-S, E-W, NE-SW and NW-SE) is performed. Figure 2 shows this procedure for Brussels.
For each wind sector pair, the total amount of NO 2 molecules is given by A, the relative source centre is µ, the standard deviation of the Gaussian function is σ, β is the slope of the linear part of the function and ε is the offset (background). By fitting the functions g(x) simultaneously for all available wind sector pairs, the total amount of NO 2 molecules (parameter A) around the source is determined. Only the best fits of the g(x) functions are used. The fit of total NO 2 mass is performed over an interval in the wind direction which is set to 200 km (see Figure 2) accordingly to Reference [16] in order to have a meaningful fit of g(x). This interval potentially includes interfering NO X sources but is indirectly accounted for by the linear variation of the background fit. The small across-wind interval (40 km) (see Figure 2) excludes neighbouring sources but does not capture the full plume in across wind direction due to dilution which is corrected by scaling A afterwards by a factor based on the ratio of the Gaussian function integrated over −20 and +20 km and the Gaussian function integrated between −∞ and +∞. Next, (ii) in order to derive total NO X mass, NO 2 to NO X is scaled by computing local scaling factors from LOTOS-EUROS, which typically range from 1.31 to 1.56 at 13h30 local time. This scaling is compared with the factor of 1.32 as applied in Reference [10]. indirectly accounted for by the linear variation of the background fit. The small across-wind interval (40 km) (see Figure 2) excludes neighbouring sources but does not capture the full plume in across wind direction due to dilution which is corrected by scaling A afterwards by a factor based on the ratio of the Gaussian function integrated over −20 and +20 km and the Gaussian function integrated between −∞ and +∞.
(b) (c) Next, (ii) in order to derive total NOX mass, NO2 to NOX is scaled by computing local scaling factors from LOTOS-EUROS, which typically range from 1.31 to 1.56 at 13h30 local time. This scaling is compared with the factor of 1.32 as applied in Reference [10].
Finally, (iii) the NOX emission rates (mg m −2 day −1 ) are derived by dividing of the total NOX mass by the lifetime. We use milligrams of NOX per square meter per day in order not to make any assumptions on the exact area of each individual city. For Brussels, based on OMI observations, the total NOX mass per unit area is 741.6 mg m −2 , with the NO2:NOX scaling of 1.43 instead of 1.32. Using the derived effective lifetime of 4.8 h (per day 4.8 × 24), the total NOX emissions derived for Brussels is 6.42 mg m −2 day −1 . Based on the LE tropospheric NO2 data, the total NOX emission is 4.90 mg m −2 (a) Finally, (iii) the NO X emission rates (mg m −2 day −1 ) are derived by dividing of the total NO X mass by the lifetime. We use milligrams of NO X per square meter per day in order not to make any assumptions on the exact area of each individual city. For Brussels, based on OMI observations, the total NO X mass per unit area is 741.6 mg m −2 , with the NO 2 :NO X scaling of 1.43 instead of 1.32. Using the derived effective lifetime of 4.8 h (per day 4.8 × 24), the total NO X emissions derived for Brussels is 6.42 mg m −2 day −1 . Based on the LE tropospheric NO 2 data, the total NO X emission is 4.90 mg m −2 day −1 . The top-down derived NO X emissions are also compared with airbase surface NO 2 concentrations converted to emissions based on the LE data as described in Section 3.3. Table 1 summarizes the results of the downwind plume method applied to the LOTOS-EUROS and OMI averaged April-September 2013 tropospheric NO 2 column distributions over 23 European cities. On average, for the cities the effective NO 2 lifetime is 4.1 ± 2.2 h derived from OMI tropospheric NO 2 columns and 3.7 ± 2.0 derived from LE simulated tropospheric NO 2 columns. The slight overall difference in NO 2 lifetimes is small and not significant (t-test, p-value > 0.34). For some cities (Amsterdam, Warsaw, Paris, Milan, Marseille, Rome, Naples, Istanbul), the OMI derived lifetimes are smaller than the LE derived values but in general the differences are small. Only for Rome and Istanbul the discrepancies are larger (1.8 vs. 3.5 h and 4.5 vs. 6.4 h respectively) ( Table 1).

Lifetimes
For Rome, the lifetime for LE is derived for a wind speed threshold of 3 m s −1 , for western winds since no reasonable fit was found at the threshold of 5 m s −1 . The OMI derived lifetime is for southwestern winds at speeds of >5 m s −1 . Reference [19] reports that for higher wind speeds generally shorter lifetimes are observed. For Istanbul, the OMI peak NO 2 column (>4 × 10 15 molec. cm −2 ) is much larger and contrasts more with the background (~2 × 10 15 molec. cm −2 ) than for the LE data (peak at 2 × 10 15 molec. cm −2 and background of~1 × 10 15 molec. cm −2 ). Thus, the LE NO 2 plume decays much faster suggesting a shorter NO 2 lifetime. For London, Antwerp, Brussels, Kiev and Vienna, the LE derived lifetimes tend to be lower than the OMI ones. This might be due to the fact that OMI NO 2 is more smeared and smoothed with higher background NO 2 concentrations (see Figure 1) while LE NO 2 values show large differences between hotspots and background NO 2 concentrations (see also in Figure 1), which is in agreement with literature reports [38]. Again, these substantial differences between OMI and LE background NO 2 concentrations (see also in Figure 1) may slow-down the decrease in NO 2 columns away from the city centre, leading to a higher NO 2 lifetime.
The average lifetimes (4.1 h for OMI and 3.7 h for LE, see Table 1) are similar to the reported ones in the literature as shown in Table 2. Our LE NO 2 effective lifetimes of Madrid and Moscow (4.6 and 4.1 h respectively, Table 1) are in the same order of magnitude than the estimates from [10] with slightly different parameters settings (the across-wind direction was set to 100 km for eight wind sectors and wind speeds >2 m s −1 ). The OMI derived lifetimes for these cities are slightly higher than the LE based estimates (5.7 and 5.4 h, respectively), given the higher contrast between peak and background NO 2 in LE. For Helsinki and St-Petersburg the LE-based NO 2 lifetime estimates (3.1 and 3.8 h, respectively) are similar to the reported values by [14] but the OMI derived lifetimes are slightly higher (4.7 and 3.9 h, respectively). This could be due to different parameter settings, especially for the across-wind intervals used wind sectors. Summer season NO 2 [10,16] tends to lower lifetimes compared to spring and autumn due to higher OH concentrations promoting conversion to HNO 3 . As in Reference [16], no overall correlation exists between NO 2 lifetimes and tropospheric NO 2 columns, NO X emissions, wind speed or latitude (all R 2 < 0.03). This is probably due to the complex NO X chemistry which is also affected by meteorological and chemical variability, like variations in UV flux, water vapour and VOC levels [16].

NO X Emissions
For all the selected European cities, the averaged top-down NO X emissions derived from LE (7.11 ± 4.03) are similar to the MACC emissions input into the LE model (7.59 ± 3.97 g m −2 d −1 ) and certainly within reported errors [10,15,16]. This demonstrates the ability of the applied methodology on the selected cities to reproduce NO X emissions based on tropospheric NO 2 columns derived from a short time period. Figure 3 shows the top-down derived NO X emissions estimated from the tropospheric NO 2 line densities for different European cities against the MACC emissions as used in LOTOS-EUROS (see Table 1) and the corresponding slopes, intercepts and R 2 values. A strong correlation exists for both the OMI (without St.-Petersburg as explained below) as LE derived emissions against the model input (R 2 = 0.79 and 0.88 respectively). Panel (b) of Figure 3 shows the distribution of the difference between the top-down and MACC-3 input emissions for both LE (negatively skewed) as well as the OMI data (slightly positively skewed). Simple t-tests between the OMI-MACC and LE-MACC data pairs show that the differences are not significantly different from zero (OMI: p-value > 0.32; LE: p-value > 0.79). These R 2 values are similar to the reported values (R 2 = 0.87 for the US, [15]; R 2 = 0.74-0.87 for China and the US, [16]). Since the estimated emissions are directly influenced by the [NO]:[NO 2 ] ratio, we substituted the general factor 1.32 [10] with the one directly computed from the modelled [NO]/[NO 2 ] concentration ratio for each city. The LE based ratios range between 1.31 and 1.56. Using the generic 1.32 factor (which is in general only 5% lower than the variable scale factors), the correlation between the MACC input and the top-down emissions remains high (R 2 = 0.77 and 0.88 for OMI and LE respectively) but the NO X emission values are 6.5 and 8.3% lower. by meteorological and chemical variability, like variations in UV flux, water vapour and VOC levels [16].

NOX Emissions
For all the selected European cities, the averaged top-down NOX emissions derived from LE (7.11 ± 4.03) are similar to the MACC emissions input into the LE model (7.59 ± 3.97 g m −2 d −1 ) and certainly within reported errors [10,15,16]. This demonstrates the ability of the applied methodology on the selected cities to reproduce NOX emissions based on tropospheric NO2 columns derived from a short time period. Figure 3 shows the top-down derived NOX emissions estimated from the tropospheric NO2 line densities for different European cities against the MACC emissions as used in LOTOS-EUROS (see Table 1) and the corresponding slopes, intercepts and R 2 values. A strong correlation exists for both the OMI (without St.-Petersburg as explained below) as LE derived emissions against the model input (R 2 = 0.79 and 0.88 respectively). Panel (b) of Figure 3 shows the distribution of the difference between the top-down and MACC-3 input emissions for both LE (negatively skewed) as well as the OMI data (slightly positively skewed). Simple t-tests between the OMI-MACC and LE-MACC data pairs show that the differences are not significantly different from zero (OMI: p-value > 0.32; LE: p-value > 0.79). These R 2 values are similar to the reported values (R 2 = 0.87 for the US, [15]; R 2 = 0.74-0.87 for China and the US, [16]). Since the estimated emissions are directly influenced by the [NO]:[NO2] ratio, we substituted the general factor 1.32 [10] with the one directly computed from the modelled [NO]/[NO2] concentration ratio for each city. The LE based ratios range between 1.31 and 1.56. Using the generic 1.32 factor (which is in general only 5% lower than the variable scale factors), the correlation between the MACC input and the top-down emissions remains high (R 2 = 0.77 and 0.88 for OMI and LE respectively) but the NOX emission values are 6.5 and 8.3% lower. For St-Petersburg the OMI derived top-down emission estimates is 4.28 ± 1.68 mg m −2 day −1 which is notably lower than the corresponding MACC value (27.02 ± 26.55 mg m −2 day −1 ) while the LE derived emissions are comparable (21.95 ± 12.79). This might be due to rapid changes in anthropogenic activities [39] that are not captured by the MACC inventory. A decline in the NOX emission trend for the period 2011-2014 over large parts of Europe was reported [23], which might explain the lower OMI top-down estimates for 2013 compared with MACC-III (2011 update) in our study for most of the selected cities. The average peak tropospheric NO2 column (maximum value in the line density functions) for St-Petersburg from LE is ~12 × 10 15 molec. cm −2 , while OMI only observes ~8 × 10 15 molec. cm −2 in 2013 (and ~6 × 10 15 molec. cm −2 in 2012). The lower derived emissions For St-Petersburg the OMI derived top-down emission estimates is 4.28 ± 1.68 mg m −2 day −1 which is notably lower than the corresponding MACC value (27.02 ± 26.55 mg m −2 day −1 ) while the LE derived emissions are comparable (21.95 ± 12.79). This might be due to rapid changes in anthropogenic activities [39] that are not captured by the MACC inventory. A decline in the NO X emission trend for the period 2011-2014 over large parts of Europe was reported [23], which might explain the lower OMI top-down estimates for 2013 compared with MACC-III (2011 update) in our study for most of the selected cities. The average peak tropospheric NO 2 column (maximum value in the line density functions) for St-Petersburg from LE is~12 × 10 15 molec. cm −2 , while OMI only observes~8 × 10 15 molec. cm −2 in 2013 (and~6 × 10 15 molec. cm −2 in 2012). The lower derived emissions from OMI may reflect the slow-down in the Russian economic growth (1.3% in 2013 versus 3.4% in 2012 and only 1 4 of the growth during the last decade, [40]) and by the slightly decrease in anthropogenic emissions (0.8% decrease in CO 2 from cement production, less CO 2 emissions per energy production unit and per capita, 1.5% reduction in NO X emissions) [40] and is consistent with reported reductions of tropospheric NO 2 by [38]. Interesting and not completely clear is that for the city of Moscow both OMI as well as the LE top-down NO X estimates correspond well with the MACC emissions. The OMI NO 2 peak is~6 × 10 15 molec. cm −2 while the LE peak is 8 × 10 15 molec. cm −2 . Although this is 33% higher, this might be offset by the 30% higher lifetime for OMI (5.4 h vs. 4.1 h). Scaled Airbase measurements of surface NO 2 concentrations to surface emissions using the LE model are 13% higher than the top-down derived NO X emissions estimated from OMI tropospheric NO 2 line densities and 11% lower than the LE derived values. However, the correlation (R 2 ) between these scaled values and OMI derived emissions is 0.53 and much higher than for the LE derived emissions (R 2 = 0.16) (Figure 4). This might be attributable to the fact that both OMI as the Airbase data are real-time observations, rather than modelled data without the timely updated emissions input. For cities such as London, Prague, Budapest and Madrid the surface data derived emissions are substantially larger than the OMI derived ones (1.2 to 5.8 times). This might be due to surface measurements being conducted in hotspot emission areas which correspond to high observations that cannot be captured by the coarser spatial resolution data used in the top-down methodology (values are more smoothed and area averaged). In general, background surface measurements agree better with the MACC emissions compared with the surface measurements including urban traffic data. The difference between the top-down and converted emissions based on surface NO 2 observations are centred around zero (panel (b) in Figure 4). Scaled Airbase measurements of surface NO2 concentrations to surface emissions using the LE model are 13% higher than the top-down derived NOX emissions estimated from OMI tropospheric NO2 line densities and 11% lower than the LE derived values. However, the correlation (R 2 ) between these scaled values and OMI derived emissions is 0.53 and much higher than for the LE derived emissions (R 2 = 0.16) (Figure 4). This might be attributable to the fact that both OMI as the Airbase data are real-time observations, rather than modelled data without the timely updated emissions input. For cities such as London, Prague, Budapest and Madrid the surface data derived emissions are substantially larger than the OMI derived ones (1.2 to 5.8 times). This might be due to surface measurements being conducted in hotspot emission areas which correspond to high observations that cannot be captured by the coarser spatial resolution data used in the top-down methodology (values are more smoothed and area averaged). In general, background surface measurements agree better with the MACC emissions compared with the surface measurements including urban traffic data. The difference between the top-down and converted emissions based on surface NO2 observations are centred around zero (panel (b) in Figure 4).

Uncertainties
The downwind plume methodology is prone to different sources of error. Some errors only affect the lifetimes or the emissions, some of them affect both. A detailed uncertainty analysis of the approach can be found in Reference [16] and their supplementary information. Summarized, the along and across line density intervals, fit results and wind fields contribute to the uncertainty of both the lifetimes as well as the emissions.
Changing the along and across intervals with 100 km affects the resulting lifetimes by only about 10%. Fit errors are typically in the order of 30% for the lifetimes and 20% for the emission parameter (A in Equation (3)). The uncertainties associated with the wind data are estimated as 30% and uncertainties due to the fit of the total NO2 mass as 20% [16]. The uncertainty in tropospheric NO2 column observations from OMI is about 30% [29]. The uncertainty of the NOX/NO2 scaling factor is

Uncertainties
The downwind plume methodology is prone to different sources of error. Some errors only affect the lifetimes or the emissions, some of them affect both. A detailed uncertainty analysis of the approach can be found in Reference [16] and their supplementary information. Summarized, the along and across line density intervals, fit results and wind fields contribute to the uncertainty of both the lifetimes as well as the emissions.
Changing the along and across intervals with 100 km affects the resulting lifetimes by only about 10%. Fit errors are typically in the order of 30% for the lifetimes and 20% for the emission parameter (A in Equation (3)). The uncertainties associated with the wind data are estimated as 30% and uncertainties due to the fit of the total NO 2 mass as 20% [16]. The uncertainty in tropospheric NO 2 column observations from OMI is about 30% [29]. The uncertainty of the NO X /NO 2 scaling factor is estimated to be 10% [10] which is in agreement with the individual scaling factors derived in this study which differ in general only 5% from the 1.32 factor. Last both uncertainties affect the emission estimates only, since lifetimes are derived from the relative decay pattern only. According to Reference [16], the interference between the NO X sources cannot be distinguished within 20 km distance and from 40 km on, the interfering sources will not be included in the emission estimates.
Following the theory on general error propagation and assuming that all errors are independent, the average error on OMI derived lifetimes is 55% (range 41-81%) based on wind field errors of 30% using sum of squares of the relative errors. The average fitting error is 47% (15-113%), which is much larger than 30% as reported in Reference [16]. The corresponding LE derived lifetime errors are 63% (40-116%) and 53% (16-124%). Adding 30% error to the derivation of the total amount of NO 2 molecules (parameter A in Equation (3)), plus 10% on the 1.32 scaling factor and 30% on the OMI NO 2 retrieval or LE NO 2 simulation as done in Reference [10], we can estimate the error on the computed NO X emissions. Based on the OMI data, we have on average 55% error on the NO X emissions (41-81%). Using the LE data, an average error of 62% is obtained (40-101%). Reference [10] reports a total error on lifetimes estimates of 36 to 58% and 46-63% for emissions with the highest value of 78%. Reference [16] has estimated that total uncertainties of NO X lifetime and emissions are within 39-80% and 55-91% range, respectively. Compared to [10] and [16] our estimated uncertainty is larger but in the same order of magnitude. The larger uncertainty might be due to the much shorter dataset that we used to estimate lifetimes and emissions only covering one season (April-September 2013) only, while Reference [15]  , we show that it is possible to derive the NO 2 lifetime and NO X emissions using the downwind plume method on a short time period of one season with reasonable accuracy.

Summary and Conclusions
In order to test the appropriateness of the downwind plume approach to derive surface NO X emissions from tropospheric NO 2 columns, we applied this methodology on 2013 LOTOS-EUROS (LE) tropospheric NO 2 model fields for 23 selected European cities and compared the top-down derived NO X estimates with the MACC input NO X model emissions. In addition, the top-down LE derived surface NO X emissions were evaluated with up-to-date NO X estimates obtained by applying the same approach on OMI data and where available we compared it with surface data of NO 2 concentrations.
Overall, no substantial differences are observed in NO 2 lifetimes for 23 selected European cities derived from LE and OMI tropospheric NO 2 columns. In general, the top-down derived NO X emissions from LE and OMI tropospheric NO 2 column data are comparable with the MACC inventory. Furthermore, in agreement with literature reports, the top-down NO X estimates are biased low with respect to reported surface NO 2 observations. The total errors on the derived NO 2 lifetimes and NO X emissions are larger but in the same order of magnitude with reported literature values.
In summary, the downwind plume approach applied to LE tropospheric NO 2 columns reproduce the MACC NO X emission LOTOS-EUROS model input well, given the applied chemistry schemes and reactions in LOTOS-EUROS. This demonstrates the ability of this technique to estimate up-to-date NO X emissions from other datasets including satellite observations of tropospheric NO 2 over a short period which can bridge the gap between fixed date inventory emissions and today's emitted NO X at the surface of many European cities.
Author Contributions: W.W.V., K.F.B., F.L., S.B. conceived and designed the method set-up; W.W.V. analysed the data and wrote the paper; K.F.B. contributed with data delivery, data interpretation and assisted in writing the manuscript; J.E.W. assisted in data interpretation and text revisions; J.D. and H.E. contributed with model data, data interpretation and manuscript revisions; S.B. contributed with data interpretation and text revisions; A.W.D. contributed with ECMWF data analysis and text revisions.