Variability of nitrogen oxide emission fluxes and lifetimes estimated from Sentinel-5P TROPOMI observations

Satellite observations of the high-resolution TROPOspheric Monitoring Instrument (TROPOMI) on Sentinel-5 Precursor can be used to observe nitrogen dioxide (NO2) at city scales, to quantify short time variability of nitrogen oxides (NOx) emissions and lifetimes on a seasonal and daily basis. In this study, two years of TROPOMI tropospheric NO2 columns, having a spatial resolution of up to 3.5 km x 5.5 km, have been analyzed together with wind and ozone data. NOx lifetimes and emission fluxes are calculated for 50 different NOx sources comprising cities, isolated power plants, industrial regions, oil 5 fields and regions with a mix of sources, distributed around the world. The retrieved emissions are in agreement with other TROPOMI based estimates, can reproduce the variability seen in power plant stack measurements, but are in general lower than the analyzed stack measurements and emission inventory results. Separation into seasons shows a clear seasonal dependence of emissions with in general the highest emissions during winter, except for isolated power plants and especially sources in hot desert climates, where the opposite is found. The NOx lifetime shows a systematic latitudinal dependence with an increase 10 in lifetime from two to eight hours with latitude but only a weak seasonal dependence. For most of the 50 sources including the city of Wuhan in China, a clear weekly pattern of emissions is found with weekend-to-week day ratios of up to 0.5, but with a high variability for the different locations. During the Covid-19 lockdown period in 2020 strong reductions in the NOx emissions were observed for New Delhi, Buenos Aires and Madrid.

In the troposphere NO x are a precursor of the health hazard and greenhouse gas O 3 but NO 2 is also an important health hazard 30 in its own right (Jacob, 1999). Consequently, monitoring and understanding its behavior is of particular importance in cities and urban agglomerations, where high emissions from multiple sources are found in combination with high population density.
As a result, a large part of the population is exposed to polluted air (Molina and Molina, 2004). NO x are short-lived in the atmosphere with a lifetime of several hours in the boundary layer during daytime. This explains in part the high spatial and temporal variability observed for NO 2 . Other factors leading to large concentration gradients in NO 2

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are the heterogeneous distribution of sources and variations of meteorological parameters, such as wind speed, temperature and illumination, which impact on the atmospheric lifetime and dilution of NO 2 (Beirle et al., 2003;Stavrakou et al., 2008).
Measurements of NO 2 with adequate spatial and temporal resolution are required to assess and compare the variability of NO x emissions and lifetimes around the world. Provided that tropospheric NO 2 columns retrieved from satellite sensors have sufficient spatial resolution, the typically short daytime lifetime of NO x in urban agglomerations provides an opportunity 40 to disentangle and quantify local sources of NO x and their variations over time. The TROPOspheric Monitoring Instrument (TROPOMI) on Sentinel-5 Precursor (S5P), which was launched in October 2017, provides higher spatial resolution than its predecessors as for example the Ozone Monitoring Instrument (OMI). Tropospheric columns of NO 2 retrieved from TROPOMI thus offer the best opportunity so far to deconvolve urban daytime sources of NO x (Veefkind et al., 2012;Griffin et al., 2019).
Making use of the NO 2 tropospheric columns from TROPOMI, but also from its predecessors, a number of studies on the 45 variability of NO x have been carried out.
The high spatial resolution of TROPOMI makes it possible to identify NO x point sources and quantify their emissions which has high potential for checking and improving emission inventories (Beirle et al., , 2021. Investigation of seasonal emission estimates enables the disentanglement of the NO x sources in a region and the identification of their individual contributions (van der A et al., 2008). The analysis of TROPOMI data for Paris showed that residential 50 heating, rather than transport emissions, is the main source of NO x in winter. This is not well accounted for in current emission inventories, in which residential heating is underestimated during winter and overestimated during summer (Lorente et al., 2019). NO x emissions also change from day to day, as a result of the human behavior, especially between work and rest days. Such patterns are readily identified (Beirle et al., 2003). A recent study by Stavrakou et al. (2020) investigated the weekly NO 2 55 cycle and its trends using the long-term satellite observations of OMI and one year of TROPOMI NO 2 column measurements.
Significant weekly cycles were found. A weakening trend over Europe and the US could be observed. The opposite behavior was found for regions with increasing emissions. The decreases or respectively increases in the contribution of anthropogenic emissions to the observed NO 2 levels are thus revealed. With TROPOMI data it is possible to use relatively short periods of data to analyze day to day variability. For Chicago a clear weekend effect with reduced NO x emissions of 30 % during week-60 ends was found analyzing one season of TROPOMI measurements (Goldberg et al., 2019). Lorente et al. (2019) investigated the day-to-day variability of NO x emissions in Paris for individual days, with the highest emissions on cold weekdays and the lowest on warm weekend days.
Beginning in early 2020, first China and subsequently the majority of countries around the world took containment measures to limit the spread of Covid-19. These measures resulted in significant changes of human behavior with reductions in traffic 65 density and industrial activity and consequently anthropogenic emissions. Temporally fine resolved emission estimates help to identify the different potential origins of such changes. This provides an approach and an opportunity to better quantify source contributions and to distinguish between different anthropogenic and natural sources of NO x . Several recent studies have analyzed satellite measurements of NO 2 columns, and report substantial decreases in the NO 2 tropospheric column in early 2020 over China (Liu et al., 2020;Bauwens et al., 2020), northern Italy, South Korea and the United States (Bauwens 70 et al., 2020). However, because of the high variability of NO 2 columns these reductions cannot be simply directly attributed to a decrease in NO x emissions resulting from the Covid-19 containment measures. The tropospheric column of NO 2 is influenced by behavioral patterns of anthropogenic activity, seasonality, and meteorology. To account for meteorology, which led to lower NO 2 values in spring 2020, as compared to spring 2019 in North America, Goldberg et al. (2020) combined TROPOMI NO 2 column data with meteorological data and a chemical transport model and calculated normalized NO 2 changes that provide a 75 better representation of Covid-19-related NO x emission changes.
In addition to NO x emissions, NO x lifetimes can be investigated with satellite data (Leue et al., 2001;Beirle et al., 2003;Kunhikrishnan et al., 2004). The NO x lifetime in daylight depends on the rate of loss of NO x which is attributed primarily to the reaction of the hydroxyl radical (OH) with NO 2 to form HNO 3 . Consequently, there is a nonlinear relationship between the tropospheric concentrations of OH and NO x , which again depends in a complex fashion on the NO x concentration (Valin 80 et al., 2013;Stavrakou et al., 2008). Laughner and Cohen (2019) showed that NO x lifetime has changed significantly between 2005 and 2014 in North American cities, changes being of the same order of magnitude as those in NO x emissions. Another important factor influencing NO x lifetime is the actinic radiation photolyzing NO 2 , which varies diurnally and is modulated by the presence of clouds. Shorter lifetimes at smaller solar zenith angles in summer or at lower latitudes due to higher photolysis frequencies are expected . Typical lifetimes of NO x range from two to eight hours in polluted air 85 masses and extend to about a day for cleaner more rural background concentrations for which nighttime chemistry also has to be considered (Beirle et al., 2011;Valin et al., 2014;de Foy et al., 2014;Seinfeld and Pandis, 2006). Studies for winter months and especially for winter months at higher latitudes are limited, analyses with the chemical transport model GEOS-Chem show a tendency towards longer lifetimes of about one day (Martin et al., 2003;Shah et al., 2020).
In this study, we use the method first developed by Beirle et al. (2011) and refined by later studies (Pommier et al., 2013;Valin 90 et al., 2013) to estimate the NO x emissions and lifetimes from TROPOMI NO 2 column amounts. Studies on NO x emissions and lifetimes have been reported using this method for OMI data, which has coarser spatial resolution, for a limited number of sources and using long time periods of data (Ialongo et al., 2014;de Foy et al., 2015;Lu et al., 2015;Liu et al., 2016). Other studies, which applied this method to TROPOMI data are reported by Goldberg et al. (2019) or Lorente et al. (2019). In this work, we provide the first study of NO x emissions and lifetimes for a large data set, comprising 50 NO x source regions, well 95 distributed over the world, consisting of cities, isolated power plants, industrial regions, oil fields and regions with a mix of sources. We show that the spatial resolution and good signal-to-noise ratio of TROPOMI NO 2 columns allow to investigate two years of data and additionally divide it into the following time periods: Seasons, weekend and working days, and times before and during Covid-19 restrictions to examine short-term variability. Focus of our investigation is to assess the variability of NO x emissions and lifetimes in space and time during the period of observation.   (Veefkind et al., 2012). The two-dimensional CCD detectors measure spectra in 450 separate viewing directions across the 2600 km swath with an integration time of approximately one second. This results in a high spatial resolution of 3.5 km x 7 km in nadir with little variation across the swath. In August 2019, the pixel size was reduced further to 3.5 km x 5.5 km by reducing along track averaging. One orbit around the Earth takes about 100 minutes, which, in combi-110 nation with the wide swath, results in a daily global coverage. At higher latitudes, on some days up to three overpasses, with approximately 100 minutes in between the measurements, are available. In the rare case of three overpasses, two of them are only on the outer edge of the swath. The equator overpass time of S5P is 13:30 mean local solar time in the ascending node.
In this study, the operational NO 2 product of TROPOMI is used (van Geffen et al., 2018). The NO 2 product from TROPOMI extends NO 2 measurements from earlier instruments such as GOME (1995( -2011( , (Burrows et al., 1999), SCIAMACHY 115 (2002( -2012( , (Bovensmann et al., 1999), GOME-2 (since 2007, (Munro et al., 2006)), OMI (since 2004, (Levelt et al., 2006)) and OMPS (since 2011, (Dittman et al., 2002)). These instruments had increasing spatial coverage and resolution, OMI being the first instrument with daily global coverage. However, with a resolution of 13 km x 24 km at nadir, its spatial resolution is one order of magnitude poorer than that of TROPOMI in the center of the swath and much lower at the edges. Differences in resolution are larger at the edges, which is due to the fact that for TROPOMI always averages of two pixels in the center of the 120 scan, but not at the edges, are used to compensate for the geometric effect caused by the slanted view to the ground.
The level-1b spectra measured by TROPOMI are analyzed with the Differential Optical Absorption Spectroscopy (DOAS) technique in the fitting window 405 nm -465 nm. The retrieved NO 2 slant column densities are separated into a stratospheric and a tropospheric part based on data assimilation by the TM5-MP global chemistry transport model. The resulting tropospheric slant columns are then converted to tropospheric vertical columns by tropospheric air mass factors (AMFs) based on 125 a look-up table of altitude-dependent AMFs, NO 2 vertical profiles from the TM5-MP model, the OMI climatological surface albedo and cloud characteristics derived using the FRESCO algorithm (van Geffen et al., 2018). The final product is the tropospheric vertical column, defined as the vertically integrated number of molecules per unit area between the surface and the tropopause.
In this study, we use the operational level-2 TROPOMI tropospheric vertical column NO 2 product from March 2018 to Novem-130 ber 2020, the first two years of data for the general study, and additional months from 2020 for the Covid-19 impact study.
This includes the reprocessed (RPRO) and offline mode (OFFL) data of version V01.00.01 to version V01.03.02. Changes between the versions before V01.04. are minor and data can be mixed. V01.04. was activated on 02 December 2020 and implemented major changes, which led to a substantial increase in the tropospheric NO 2 column over polluted areas for scenes with small cloud fractions. We only use the data up to end of November 2020 for our analysis to ensure better comparability, 135 since mixing data from before version V1.04. and after is not recommended. Further major updates in the TROPOMI NO 2 retrieval algorithm are done in V02.02. released on 1 July 2021 (van Geffen et al., 2021). A complete mission reprocessing will be performed to get a harmonized data set (Eskes and Eichmann, 2021). Data from 30 April 2018 onwards is freely available on https://s5phub.copernicus.eu/. Data before the 30 April is only available on the S5P Copernicus Expert Hub and therefore not publicly accessible. The data with a spatial resolution of up to 3.5 km x 5.5 km is oversampled to a finer resolution of 0.01°140 x 0.01°. Each TROPOMI ground pixel is accompanied by a quality assurance value (qa_value). The qa_value ranges from zero (error, no output) to one (no errors or warnings) and indicates the quality of the processing and retrieval result. Based on the recommendation by van Geffen et al. (2018), measurements with a qa_value lower than 0.75 are filtered and not used.
A qa_value of 0.75 removes problematic retrievals, errors, partially snow/ice covered scenes and measurements with cloud radiance fractions of more than 50 %.

Wind data
In addition to the TROPOMI NO 2 data, wind speed and direction are required for the emissions and lifetime calculations.
The wind data used is provided by the European Centre for Medium-Range Weather Forecast (ECMWF), ERA5 reanalysis hourly data with a horizontal resolution of 0.25°x 0.25°on model levels. To merge the wind data in space and time with the 150 TROPOMI observations, they are interpolated to the overpass time and oversampled to the same 0.01°x 0.01°resolution as the TROPOMI data. The chosen height of wind data can be critical for wind speed and direction, because of increasing wind speeds and turning with height, and therefore also for emissions and lifetime estimates. Beirle et al. (2011) investigated the dependence of calculated emissions and lifetimes on the wind data level height by comparing the results calculated with wind fields averaged from ground up to 200 m, 500 m and 1000 m and showed low dependence of the results on the wind level 155 height. The resulting emissions and lifetimes change less than 2 % (5 %) on average when using 200 m (1000 m) instead of 500 m and less than 15 % for individual sources. We use wind data averaged over the boundary layer, with the boundary layer height also provided by ERA5. At the early afternoon overpass of TROPOMI, it can be assumed that the boundary layer is well mixed and wind information averaged over this layer are representative for the emissions and lifetimes investigated in this study. Using wind data averaged over the boundary layer instead of using a fix height has the advantage that seasonality in 160 wind data due to the seasonal variability of the boundary layer height is considered.

Ozone volume mixing ratios
Ozone volume mixing ratios, for scaling the NO 2 column measurements to NO x columns to estimate emissions in terms of NO x , were taken from the ECMWF ERA5 reanalysis. The ozone data has the same resolution as the used wind data, hourly data with a horizontal resolution of 0.25°x 0.25°on model levels. It is averaged over the boundary layer, interpolated to 165 TROPOMI overpass time and oversampled to the same 0.01°resolution as the TROPOMI data just as the wind data. available in EDGAR v5.0, which does not reflect the recent negative and positive trends, which were found in trend analysis of NO 2 column satellite data (Georgoulias et al., 2019). Since a large part of the regions analyzed in this study is located in industrialized and highly populated regions, where NO 2 has generally decreased according to (Georgoulias et al., 2019), we 180 anticipate that the TROPOMI estimates for the majority of the analyzed regions are lower than the EDGAR estimates for 2015.

Method
The method to estimate emissions and lifetimes from satellite column data builds on the heritage of the method introduced by Beirle et al. (2011) and refined by later studies (Pommier et al., 2013;Valin et al., 2013). We use two years of TROPOMI NO 2 tropospheric vertical column data from 01 March 2018 to 29 February 2020 for the general analysis, excluding data for which 185 Covid-19 regulations influenced emissions. For the two Chinese cities included in this study, the analyzed period is limited to 22 January 2020 due to early Covid-19 regulations. The Covid-19 impact study in section 4.5 is based on the months January through November of 2019 and 2020. The three steps of the analysis are shown in Fig. 1 for the Medupi and Matimba power plants in South Africa as an example. First, the source region is selected. The choice of sources is described in more detail in section 3.1. The next step is a rotation of the satellite measurements around the selected source with the corresponding ERA5 190 reanalysis wind data to a common wind direction resulting in an upwind-downwind pattern, which is described in more detail in section 3.2. The NO 2 column of each pixel is converted into NO x column and the mean NO x distribution is calculated. In the last step, we apply a line density fit with an exponentially modified Gaussian (EMG) function to the averaged NO x columns to calculate the NO x emissions and lifetime (see section 3.3). terns, facilitates the detection of the outflow patterns, which is further enhanced by filtering out data with wind speeds of less than 2 m s −1 (Beirle et al., 2011). Some, initially promising sources like Santiago de Chile, were omitted. This was a result of their location in coastal and mountainous regions with inhomogeneous terrain, resulting in inhomogeneous wind patterns, which are more difficult to interpret and lead to larger uncertainties in NO x emission rates and lifetimes. For this study, many of the sources with high NO 2 signal in China were not used, because the influence of large NO x emitting sources nearby resulted 210 in low contrast of the NO 2 column amount between the target and the local background. For such conditions, other methods to determine NO x emission rates and lifetimes are more appropriate (Liu et al., 2016). Despite efforts to select a broad range of regions in many respects, some selection bias could have been introduced, for example, by not analyzing regions with low wind speeds, mostly cloudy conditions or areas in regions with many emission sources and higher background levels.
If the conditions are favorable (e.g clear-sky, homogeneous and strong wind condition) even a single overpass can deliver good

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results for some regions (Lorente et al., 2019;Goldberg et al., 2019). For analyzing the variability due to seasonal or weekday effects in a more general way, it is useful to have some statistics to not for example introducing a bias into the seasonal analysis by weekday variability. Due to the high spatial resolution and the good signal to noise ratio of the TROPOMI data, it is possible to use a data set of only two-years length to analyze successfully regions, which are covered more frequently by clouds or have low NO 2 signals. Nevertheless, not every source region is used for every analysis in this study because of data availability after 220 separating data into seasons or week and weekend days. From the 50 targeted regions shown in Fig. 2, eight are in the southern hemisphere. In order to integrate them into the analysis, they are mirrored in latitude and shifted by six months in season. All source regions are listed in the appendix table A1. Surgut (Russia) is the NO x source with the highest latitude at 61.25°N, and Singapore (Singapore) is the one closest to the equator at 1.3°N.
One example of the selected source regions is shown in Fig. 1. Figure 1 (a) shows the average of NO 2 tropospheric vertical 225 columns for two years of data from 1 March 2018 to 29 February 2020 for days with wind speeds > 2 m s −1 in the region of the power plants Medupi and Matimba in South Africa. The NO 2 distribution shows an isolated source and its plume which has a high contrast to a low background concentration. In the south eastern part of the map high tropospheric NO 2 columns are visible. These originate from the South African Highveld conurbation near Johannesburg.

Rotation technique 230
To investigate the spatial pattern of NO 2 column measurements we combine the approach from Beirle et al. (2011) of a directional classification to determine the distribution, as a function of downwind distance, with a rotation of each TROPOMI measurement with its merged wind direction around the source to a common wind direction (Pommier et al., 2013;Valin et al., 2013).
Each TROPOMI observation is merged with the ERA5 wind data and rotated with its wind direction about a reference point

Line density calculation 245
The average outflow pattern of the NO 2 tropospheric vertical column with a decay of the signal with distance from the reference source point reflects transport and nonlinear effects of atmospheric chemistry. Beirle et al. (2011) proposed a model to estimate the NO x emissions and lifetimes by integrating the mean NO 2 columns in the across-wind direction and thereby reducing the two-dimensional maps to one-dimensional so-called line densities with units molecules cm −1 . In this study, we first converted the NO 2 columns for each pixel into NO x columns to obtain NO x line densities from which NO x emissions are calculated 250 directly (comparable to Beirle et al. (2021)) instead of applying the commonly used fixed [NO x ]/[NO 2 ] ratio of 1.32. Assuming that the Leighton photostationary state applies for the polluted air masses investigated, the NO 2 is considered a surrogate for NO x and concentrations of NO and NO 2 are coupled by: with J NO2 the photolysis frequency of NO 2 and k NO+O3 the rate constant for the reaction of NO with O 3 (Seinfeld and Pandis, Ozone data is taken from ERA5 and interpolated to the S5P overpass as described in section 2.3. For clear-sky conditions the photolysis frequency in the boundary layer is parameterized as a function of solar zenith angle (SZA) as proposed by Dickerson et al. (1982): The rate constant k NO+O3 can in general be well represented by the Arrhenius expression, following the recommendation by Atkinson et al. (2004): with temperature T (in kelvin) taken from the ERA5 reanalysis; hourly data with a horizontal resolution of 0.25°x 0.25°, averaged about the boundary layer, interpolated to TROPOMI overpass time and oversampled to the same spatial resolution.
with a convolution of the exponential e and the Gaussian G function scaled by a multiplicative emission factor E and shifted by a background concentration offset B. The exponential function describes transport and chemical decay: with x > X (downwind) and else zero, where X is the location of the apparent source relative to the source reference point and x 0 the distance over which the line density decreases by a factor of e (e-folding distance). The Gaussian function represents 280 the broadening of the source by spatial smoothing with the Gaussian function width σ, which accounts for spatial smoothing caused by the extent of the spatial source, the TROPOMI pixel size and wind variations: This results in: The fitted e-folding distance x 0 and the mean wind speed w from the line density sector is then used to calculate the mean lifetime: The calculated lifetime includes effects of deposition, chemical conversion and wind advection but must be considered as an effective mean dispersion lifetime. This is because, downwind changes for example due to a changing [NO 2 ]/[NO x ] ratio or 290 the effects of non-linearities in the NO x lifetime in the plume are not considered in the method used.
The multiplicative emission factor E characterizes the total amount of NO x near the source and is used together with the mean wind speed w from the line density sector to derive the NO x flux in mol s −1 : with the Avogadro constant N A = 6.02214076 · 10 23 mol −1 .

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The described method to calculate emissions and lifetimes will be named exponentially modified Gaussian (EMG) method.
Uncertainties and error bars for emissions and lifetime estimates presented in the following results are based on 1-sigma uncertainties (standard deviation) derived by the EMG fitting procedure and are calculated with error propagation. The total uncertainty of NO x emissions and lifetimes is influenced additionally by many different error sources, especially the TROPOMI NO 2 tropospheric vertical column itself, which are mainly systematic and lead to an overall low bias of the derived emissions 300 which is discussed in more detail in section 4.6.

Results and Discussion
The EMG method was applied to the mean TROPOMI NO 2 column data of the selected regions and NO x emissions and lifetimes were calculated. For all available TROPOMI measurements of the two years period from 01 March 2018 to 29 February 2020, and also separated into seasons, working days and weekends and pre Covid-19 times and the Covid-19 pandemic. Not 305 all source regions are used for all analysis due to sometimes poor statistics when separating the two years of data into specific periods.

Comparison to similar studies and emission inventories
The NO x emission estimates from this study are first compared to results from other recent studies Goldberg et al., 2019;Lorente et al., 2019), which estimated NO x emissions with TROPOMI data. The studies used for comparison focused only on specific regions, used different periods, and the methods differ slightly but have in common that all used TROPOMI data for their emission calculations. columns, as compared to ground based or aircraft measurements of the tropospheric NO 2 column. This underestimation is more pronounced for regions with larger NO 2 columns , which is in agreement with our finding that differences to EDGAR are largest for the source regions with high emissions such as Tokyo, Wuhan, Moscow and New York.
This underestimation of TROPOMI will probably be reduced using the reprocessed data set with V02.02 and is discussed in more detail in section 4.6. The calculated emissions for the Medupi and Matimba power plants are an exception as they show The EMG method is a widely used method but mostly used for data around summer. In this study we will also extensively use winter data which bring greater uncertainties to the analysis, for example due to longer lifetimes in winter and additionally 365 data availability is often worse during winter than summer. Therefore, we wanted to verify if the EMG method can reproduce

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From this comparison we can conclude that power plant emissions can vary strongly over time and that the TROPOMI based NO x emissions can be lower by about a factor of two for power plants as already discussed in previous publications . But most importantly for this study we can conclude that the EMG method applied to TROPOMI data at least for this power plant can reproduce the temporal variability seen in the CEMS data reasonably well, and does not show a clear seasonal bias. Therefore, it can be assumed that the method also gives reasonable results analyzing winter data.   Overall, the investigation of seasonality shows higher NO x emissions in winter than in summer for the majority of source regions, which is expected due to the location of the majority of the selected regions in mid-latitudes and temperate climate. Not all ratios are significantly different from unity, and some results are unexpected, but the trend from the source regions at high latitudes with higher emissions in winter to the regions in desert climate with higher emissions in summer is plausible. In some part our results differ from previous literature (Crippa et al., 2020;Zheng et al., 2018) where generally weaker seasonality is 415 found, which however is based on emission inventories and analyzes average values for countries that probably does not reflect the specific situation in cities, where the composition of sources is expected to be different. Further detailed investigations and comparisons would be helpful to understand the discrepancies. Nevertheless, it should be considered that the uncertainties for emission estimates from the EMG method can be large and especially the analysis of winter data has not been performed often and is influenced even more by uncertainties (see section 4.1 and 4.6).

Latitudinal and seasonal dependence of lifetimes
Another parameter retrieved by the EMG method is the mean effective lifetime of NO x . Thus, in addition to the seasonality of emissions, the seasonality of lifetimes is investigated as well as their latitudinal dependence. When data averaged over the two years is considered, lifetimes can be calculated for all 50 source regions. Separating the data set into seasons reduces the number of available data and lifetimes can be estimated for 34 of the in total 50 source regions.  In Figure 6 (b) estimated NO x lifetimes for ten source regions are shown as function of season. Only a selection of the sources is shown here, which are a mix of regions from southern and northern latitude, distributed over many latitudes and with different source types. In general these source regions show similar behavior with the longest lifetimes in winter, shortest in summer 435 and quite similar lifetimes in spring and autumn that fall between the summer and winter estimates. Also deviations are visible as could already be seen for the case of Madrid, where the autumn lifetime is much shorter than in spring. Seasonal differences are the strongest for higher latitudes and the lowest for sources the closest to equator. In general, the results are in agreement with values shown in Beirle et al. (2011), where eight different source regions were analyzed yielding lifetimes within a range of two to six hours and a maximum of 8.5 hours during wintertime for Moscow.

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The averaged lifetimes over the full two-years period for these 50 source regions as a function of latitude are shown in Fig.   6 (c). As a result of the lower sun and thus reduced photolysis and likely lower OH at higher latitudes, one would expect an increase of NO x lifetime with latitude (Martin et al., 2003;Stavrakou et al., 2013). This is broadly confirmed by the results, averaged lifetimes increasing from approximately two hours for source regions at low latitudes near the equator to about six to eight hours for source regions at high latitudes of around 60 degrees.

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The retrieved lifetimes can be used to estimate atmospheric OH concentrations. Assuming that the decay of NO x is determined by the termolecular reaction of OH with NO 2 with the rate constant k OH+NO2+M for 298 K and 1 atm based on Burkholder et al. (2020), the mean OH concentration ranges from 0.3 · 10 7 -1 · 10 7 molec cm −3 for a range of NO x lifetimes of two to eight hours. This is in a reasonable range for OH concentrations at midday (Holland et al., 2003;Smith et al., 2006;Lu et al., 2013). be not yet sufficient statistics, a clear-sky bias and also the midday observation time of TROPOMI, which all lead to more balanced lifetimes in summer and winter. Furthermore, it should be considered that the total uncertainty for lifetime estimates is larger than just the 1-sigma uncertainties derived by the EMG fit, especially in winter due to longer lifetimes and often 460 reduced data availability (section 4.6). The large data set used in this study reveals a clear but complex latitudinal dependence of NO x lifetimes. This can be used for studies similar to those of Beirle et al. (2019Beirle et al. ( , 2021 where an assumption about the lifetime is necessary to calculate emissions and can also provide relevant observational constraints for model simulations of NO x lifetimes.

Weekend effect 465
The presence of a weekend effect in NO 2 on a global scale was first shown by Beirle et al. (2003) with GOME measurements.
Anthropogenic activities have their maximum during the week and are reduced during the weekend. Thus, we expect less NO x emissions in cities at weekends. This behavior should be reflected in a comparison of NO x emissions on weekdays and weekends. How large the difference between weekends and weekdays is depends on the types of NO x sources and the different patterns of anthropogenic activity in the source region. To investigate the weekly cycle, the TROPOMI data is separated into week and weekend days and emissions and lifetimes were calculated separately. Weekend days can be one or two days and those days can also differ according to religious tradition. For source regions for example in Europe and the United States, weekend days were set to be Saturday and Sunday, for Saudi Arabia weekend days are Friday and Saturday (see also Table   A1). Still, often one weekend day can be different than the other, for example, emissions on Saturdays are often not as low as those on Sundays, even if they are already lower than those from Monday to Friday (Crippa et al., 2020;Goldberg et al., 2021).

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If the weekend would be limited to one day in the analysis, this would lead to a strengthening of the weekend-to-week ratio for some cities. Figure 7 shows the weekend-to-weekday ratio, with higher emissions during weekdays than on the weekend for most of the source regions albeit with rather high variability. For Paris (France), the emissions are reduced by 40 % on the weekend, which agrees with Lorente et al. (2019). Chicago shows only a reduction of 16 % on the weekend versus weekdays which is less than the weekend reductions of 30 % found in Goldberg et al. (2019Goldberg et al. ( , 2021. This could be attributed to the fact that in Goldberg et al. (2019Goldberg et al. ( , 2021 Sunday only was assumed to be a weekend day which gives a more pronounced weekend reduction than with Saturday and Sunday as weekend days as done in this study. Despite showing large NO 2 columns, Chinese cities did not show a weekend effect in previous studies (Beirle et al., 2003;490 Stavrakou et al., 2020). Stavrakou et al. (2020) showed an average weekend-to-weekday ratio in NO 2 column over all large -April 2019). Ratios of NO 2 columns are related but not identical to ratios in NO x emissions as discussed here, as effects from meteorology and lifetime are not accounted for as well as tropospheric background is contained which is removed in the EMG method by fitting the background. Using the EMG method to investigate the weekly cycle we calculated a weekend- no such effect. This can be analyzed in more detail as more TROPOMI data become available.

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A side effect of the reduced emissions on weekends could be lower OH levels due to the NO + HO 2 reaction and therefore longer NO x lifetimes (Stavrakou et al., 2008). However, in our data set the retrieved lifetimes for week and weekend days do not show a clear enhancement of lifetimes on weekends (see Fig. A1). This may possibly be due to insufficient number of data points, required for a statistically significant result and this question should be revisited once a larger TROPOMI data set becomes available.

Covid-19 effect
In early 2020, several countries took containment measures against the spread of the coronavirus outbreak (Covid-19), which caused reductions in industrial activities and traffic volume. Due to the link of NO x emissions to human activities, it is possible to investigate the impact of the Covid-19 induced activity reductions with the TROPOMI NO 2 column data Liu et al., 2020;Goldberg et al., 2020). Part of the observed decreases in the NO 2 columns may result from effects 510 other than the measures designed to limit transmission of Covid-19, e.g. meteorological variability, seasonal variability or environmental policy regulations. Consequently, it is problematic to identify a clear Covid-19 effect using only NO 2 column amounts. Besides the possibility of using models to separate the Covid-19 effect from other factors (Goldberg et al., 2020), it is also possible to use the EMG method. This approach accounts for wind conditions and NO x lifetime, which influence the NO 2 columns observed for similar NO x emissions. Since the EMG method can only be used to investigate point sources, the 515 range of possible study areas is limited. In addition, the analysis of the Covid-19 effect is also much more limited compared to the rest of the study, because we decided to compare only monthly means from two different years with each other to minimize influence by meteorology. We focused on the cities Buenos Aires (Argentina), New Delhi (India) and Madrid (Spain), which are considered to be point sources and have an appropriate number of days with satellite data available during the comparative periods. The EMG method was used, and monthly means of emissions from 2019 and 2020 were calculated and compared. If 520 only a few days per month are available, fit results can be of low quality if conditions on these days are not ideal and statistics are missing so that, for example, weekday effects can also have significant influence. Therefore, even for the selected cities not all months can be considered. Covid-19 periods with periods of containment measures. In case emissions from different months are compared, seasonality of NO x emissions must be considered. The NO x emissions retrieved for Buenos Aires are low during summer from January to March (months 1-3), are increasing towards the winter months with a maximum in July and decreasing again towards summer.
The emissions for New Delhi do not show such a strong seasonality as those for Buenos Aires but in general are also higher during the winter months January and February (months 1-2). The seasonality is also clearly visible for Madrid, which must In India, a nationwide strict lockdown started on 24 March 2020. In January calculated NO x emissions are almost equal for 545 both years. The significantly higher emissions in February 2020 compared to 2019 probably cannot be explained by a Covid-19 effect and are more likely to be due to reduced number of TROPOMI observations, of on average only five days in February 2019, which will reveal more natural variability. In April 2020, the first complete month in lockdown, the emissions are 87 % lower than in April 2019, and also in May and June the emissions are with 54 % and 31 % much lower than in 2019. For July to September, comparisons are not possible as less than three days of measurements per month are available due to cloud 550 coverage and statistic and fit results are not good. In October and November 2020, emissions are almost equal to 2019 levels, suggesting that life is back to the way it was before the Covid-19 containment measures.
In Europe Madrid was one of the strongly effected cities. A strict lockdown was enacted mid of March 2020, some restrictions were lifted from mid of April and in May the government followed a plan for easing lockdown restrictions slowly. Due to again rising cases, new restrictions started in early October 2020. Emission comparisons are not possible for January, April and 555 November due to lack of data caused by cloud coverage. The significantly higher emissions in February 2019 compared to 2020 are probably mainly caused by two factors, first a strong synoptic meteorological variability in Europe and second February is also a month with typically persistent cloud cover, resulting in a reduced number of TROPOMI observations which will reveal more natural variability. Similar findings are also described in Bauwens et al. (2020) and Levelt et al. (2021). For the months May and October 2020, when Covid restrictions were in place, the calculated NO x emissions in Madrid are 43 % respectively 560 63 % lower than in 2019. This is comparable to results from NO 2 column comparisons which showed reduction of around 30 % from mid of March to early April 2020 relative to 2019 . The larger reductions in October may be due to stricter restrictions resulting in larger emission reductions. However, even with monthly averages, the high variability of NO x emissions is still not negligible and could also have an influence here.
Despite the shortness of the periods available for analysis, it is possible to investigate short-term variability of NO x emissions 565 induced by Covid-19 with TROPOMI NO 2 data and the EMG method. Strong decreases due to lockdown measures of 57 % in Buenos Aires and 87 % in New Delhi are shown for April 2020 compared to April 2019, as well as a general tendency towards lower emissions in 2020 after the start of the Covid-19 pandemic than 2019. Nevertheless, even with monthly averages, the high variability of NO x must still be considered for particular months. These emission estimates account for wind conditions and NO x lifetime and can therefore give a better estimate of the Covid-19 measures on NO x emissions than just comparing 570 NO 2 column measurements. For some cities and months, the number of days in monthly means is limited due to cloud cover. This is also a problem when comparing monthly NO 2 column levels.

Uncertainties
The uncertainties and error bars for emission and lifetime estimates given in this work are based on 1-sigma uncertainties (standard deviation), derived by the fitting procedure and are calculated with error propagation. For emissions this results in: and for lifetimes in: with the emission factor E , the e-folding distance x 0 , the mean wind speed w, the Avogadro's constant N A (see section 1) and the standard deviations σ E' of E and σ x0 of x 0 derived from the fit and σ w derived from the wind field in the line density 580 sector. These estimates are based on the fitting uncertainties.
However, the NO x emissions and lifetimes derived from TROPOMI NO 2 data are influenced by additional error sources. The most important contribution directly influencing our estimates is the accuracy of the TROPOMI NO 2 tropospheric vertical column itself. This uncertainty is dominated by the accuracy of the tropospheric air mass factor (AMF) and is estimated to be in the order of 30 % (Boersma et al., , Bucsela et al., 2013. Recent studies comparing TROPOMI NO 2 column with co-585 located ground based or aircraft measurements reported a low bias for TROPOMI NO 2 columns, which is most likely caused by a-priori information such as the surface albedo, cloud-top-height, cloud fraction and the NO 2 vertical profile, used for tropospheric AMF calculations. This bias differs for different regions and is more pronounced for regions with larger NO 2 columns Ialongo et al., 2020;Judd et al., 2020;Dimitropoulou et al., 2020;Verhoelst et al., 2021). Some studies scaled up the measured NO 2 columns with a factor of 1.33 for Paris (Lorente et al., 2019) up to a factor of 1.98 for Germany 590 . As this suspected underestimation is not yet fully characterized, and as it is not clear without independent measurements how much the various regions used in our study are affected, we decided not to correct the operational product. Therefore, NO x emissions derived in this study are systematically biased low. A new operational NO 2 product version V01.04., activated after the analysis time period of this study on 02 December 2020, implemented first major changes, which led to a substantial increase in the tropospheric NO 2 column over polluted areas for scenes with small cloud fractions. Further 595 major updates in the TROPOMI NO2 retrieval algorithm are done in V02.02. released on 1 July 2021. Tropospheric vertical columns are between 10 and 40 % larger than the v1.x data depending on the level of pollution and season; the largest impact is found in wintertime at mid-and high-latitudes (van Geffen et al., 2021). A complete mission reprocessing will be performed to get a harmonized data set (Eskes and Eichmann, 2021). The use of the reprocessed data set for this study will increase NO x emissions and probably affect the seasonality analysis, but not so much the weekend-to-week comparison results.

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To calculate NO x emissions, we applied a conversion of each TROPOMI pixel from NO 2 column to NO x column by assuming that the Leighton photostationary state applies for the polluted air masses. This is more accurate than using a fixed conversion factor as in many earlier studies, especially for our analysis over a large latitudinal range and for different seasons. Nevertheless, the photolysis frequencies have to be parameterized and the temperatures for the rate constant and the ozone concentrations taken from the monthly ERA5 data set interpolated to the S5P overpass time. Thus, the conversion from NO 2 to NO x adds 605 systematic errors in the emission estimates.
In addition, using satellite data introduces a systematic clear-sky bias, because only measurements from nearly cloudless days are used, which favor specific emission patterns. These may differ from those of cloudier and thereby often cooler days. The limitation to nearly cloudless measurements also influence lifetime estimates, which are systematically lower due to higher photolysis rates on cloudless days. Furthermore, the retrieved NO x emissions and lifetimes are based on measurements in the early afternoon and are therefore systematically biased due to the measurement time. The variability in time can be further analyzed using follow-up sensors on geostationary satellites as for example GEMS, Tempo or Sentinel-4.
The NO 2 tropospheric columns are strongly affected by the wind fields. This affects the calculation of NO x emissions and lifetimes. We filtered the NO 2 measurements depending on the corresponding wind speed and only data with wind speeds > 2 m s −1 are included in the analysis. As a result of the short lifetime of NO 2 , the observed NO 2 distribution should, in general, 615 be dominated by the wind conditions around the satellite overpass. On days with rapidly changing wind directions around the time of measurement, the spatial patterns and thus the estimates of emissions and lifetimes may be affected. An effect observed for some locations on some days are curved plumes, which for the case of strong curvature leads to a part of the plume being outside of the line density calculation sector and an underestimation of both NO x emissions and lifetime. This has a large effect when analyzing estimates for single days and is generally larger for longer lifetimes, so especially on winter days. It 620 has a smaller influence on the overall result analyzing a larger average, if not too many days are affected by rapidly changing wind directions. Nevertheless, the wind field is the largest uncertainty (random and systematic) influencing our estimates after the NO 2 column itself. Lorente et al. (2019) have modified wind speeds by 20 % and found that emissions changed by 20 %, which demonstrates the strong influence of wind speed on NO x emissions. However, reliable global wind information is hard to obtain. Beirle et al. (2011) estimated an uncertainty of 30 % for the wind data. The uncertainties due to the chosen wind 625 fields will vary for different source regions. Overall, we assume an uncertainty of 30 %.
To avoid interference from sources of NO x surrounding the target region, only rather isolated source regions are chosen for the analysis. Since almost no site is perfectly isolated, sectors were defined in which the line density was calculated by integration and fitted with the EMG method to minimize interference between different sources. Due to the rotation of measurements with their corresponding wind direction around the source, the NO 2 signal from sources in the surroundings is smeared around the 630 source region in their distance to the source location. To exclude these contaminants, the sector size used for the EMG method has to be chosen carefully. In order to have an adequate amount of data for a robust EMG fit, the sector must first be large enough in both downwind and across-wind directions, but the size is also influenced by other factors. The sector length in wind direction is mainly determined by the influence of other sources but also the spatial extent of the source region itself and wind speeds. A typical size is 300 km, 100 km upwind and 200 km downwind of the source location and is adjusted visually, if 635 necessary, by inspecting the NO 2 distribution and line density. If the influence of surrounding sources is negligible or becomes negligible by adjusting the sector size, the EMG method is robust in variation of the sector size in wind direction. The sector width in across-wind direction is mainly influenced by the geographical extent of the source region. If the sector width is chosen too small, part of the NO x emissions are outside of the sector due to dilution by wind or due to curved plumes, as described above. This obviously leads to an underestimation of the calculated emissions which acts as an additional apparent loss, leading 640 to the e-folding distance x 0 being systematically biased low and also lifetimes, defined as τ = x 0 · w −1 , with mean wind speed w, are underestimated. Typical sector widths vary between 30 km and 140 km and are determined by visually inspecting the NO 2 distribution after rotation. Beirle et al. (2019) estimated the uncertainty of NO x emissions and lifetimes due to sector size to 10 %.
The EMG method is well suited to investigate point sources. In reality, most of the analyzed sources deviate from the assump- 13 km apart, were investigated as one source using the EMG method (Beirle et al., 2011;Goldberg et al., 2019). With the higher resolution of TROPOMI compared to OMI, it becomes clear that the situation with the two plumes is more complex. This is evidenced by strong irregularities in the line density and fit, indicating that it should not be treated as one point source. In this 650 particular case, re-gridding the TROPOMI data to a coarser resolution would potentially allow an analysis. Other sources such as Tokyo, Moscow or Chicago, all cities with emissions originating from a larger area, are treated as extended point sources but additional uncertainties must be considered. For example, it is not possible to consider a change of the instantaneous NO x lifetime downwind of the source with the EMG method and estimated lifetimes should be interpreted as an effective mean lifetime (Beirle et al., 2011). This effect is particularly pronounced in spatially extended source areas and can lead to low 655 biased lifetimes.
In summary, the total uncertainty of NO x emissions and lifetimes derived from TROPOMI NO 2 data is influenced in addition to the 1-sigma uncertainties, derived by the fitting procedure, by many different error sources, which are mainly systematic and lead to an overall low bias of the derived emissions. Dominated by the systematic errors in the TROPOMI NO 2 tropospheric column itself (30 % -50 %) and in the wind field (30 %). The sector size can lead to low biased emissions and lifetimes and

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In this study, we present investigations of the variability of NO x emissions and lifetimes estimated from Sentinel-5P TROPOMI observations for selected NO x source areas around the world. Similar to earlier studies, we combine TROPOMI NO 2 tropospheric vertical column data with wind information from ECMWF ERA5 reanalysis for the exponentially modified Gaussian, EMG, method. TROPOMI measurements with their high spatial resolution and high signal to noise ratio allow detailed analysis of NO x emissions and lifetimes using only two years of data. Investigating small emission sources not analyzed before and 670 also monitoring the variability on a short-term temporal basis has been possible. Here, a total of 50 NO x sources from different regions, located between the equator and 61°latitude are investigated. Despite efforts to select a broad range of regions, well distributed around the globe and a mix of different sources, predominantly cities, isolated power plants, industrial regions, oil fields and regions with a mix of sources, some selection bias could have been introduced, for example, by not analyzing regions with low wind speeds, mostly cloudy conditions or areas in regions with many emission sources and higher background levels.

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Comparisons to other studies using TROPOMI data and similar methods for emission estimates show small differences and in general good agreement taking into account the differences of the analyses. The emission estimates are compared to the EDGAR (v.5.0 2015) emission inventory, showing higher emissions for most of the source regions in the EDGAR database than estimated with the EMG method. These differences are particularly strong for the source regions with the highest emissions. As the operational TROPOMI tropospheric NO 2 product has been reported to be low in comparison to independent 680 measurements, part of the apparent overestimation by EDGAR could be related to a TROPOMI low bias. On the other hand, NO x emission trends over the last five years are likely to also have an impact. EPA CEMS data for the Colstrip power plant shows that power plant emissions can vary strongly over time. The EMG method applied to TROPOMI data, at least for this power plant, can reproduce the temporal variability seen in the CEMS data reasonably well, and does not show a clear seasonal bias. Therefore, it can be assumed that the method also give reasonable results analyzing winter data. However, the TROPOMI 685 based NO x emissions are lower by about a factor of two for this power plant, in agreement to earlier findings for other power plant sources.
The seasonal separation of the emission estimates in general shows the highest emissions during winter and a trend from source regions at higher latitudes with higher emissions in winter, to regions in hot desert climate with higher emissions in summer. This is best explained by the different contributions to NO x emissions depending on source region, which are typically dom-690 inated by domestic heating in winter or, air conditioning in hot summer months, depending on the climatic conditions of the source region. In some respects our results differ from previous study results which based on emission inventories, analyzing average values for countries, where generally weaker seasonality is found. However, this probably does not reflect the specific situation in cities, where the composition of sources is expected to be different. Further detailed investigations and comparisons would be helpful to understand the discrepancies. Generally, it should be considered that the uncertainties for emission 695 estimates from the EMG method can be large and especially the analysis of winter data has not been performed often and is influenced even more by uncertainties.
The investigation of the seasonal and latitudinal dependence of the NO x lifetime shows an increase in lifetime from two to six hours for increasing latitudes, but only a weak seasonal dependence with longer lifetimes in winter than in summer. Larger differences are expected based on modelling studies. The weak seasonal dependence found in this study could be explained 700 by not yet sufficient statistics, a clear-sky bias and also the midday observation time of TROPOMI, which all lead to more balanced lifetimes in summer and winter. Uncertainties which tend to have a low bias in lifetime estimates, especially in winter due to longer lifetimes and the aforementioned points, should be considered.
Separating NO x emission estimates into working and weekend days indicates that for most NO x source regions, emissions are higher during weekdays than on the weekend, albeit with rather high variability in the weekend-to-weekday ratios. and a general tendency to lower emissions in 2020 than in 2019 are shown for Buenos Aires, New Delhi and Madrid.
tigate the high variability of NO x emissions and lifetimes on a global scale and on short time frames. Depending on the goal of the analysis, already a few days of measurements can be sufficient; for seasonal studies, depending on the local meteorological conditions, one to two seasons are sufficient, and it is not anymore necessary to average over several years. The ability to 720 estimate emissions over short time periods will also allow policy makers to evaluate NO x emission regulations better and more quickly. The presented high variability should be further investigated using follow-up sensors on geostationary satellites as for example GEMS, Tempo or Sentinel-4, which have the potential to investigate in addition the diurnal variability.