A new method for inferring city emissions and lifetimes of nitrogen oxides from high-resolution nitrogen dioxide observations: A model study

15 We present a new method to infer nitrogen oxides (NO x ) emissions and lifetimes based on tropospheric nitrogen dioxide (NO 2 ) observations together with reanalysis wind fields for cities located in polluted backgrounds. Since the accuracy of the method is difficult to assess due to lack of “true values” that can be used as a benchmark, we apply the method to synthetic NO 2 observations derived from the NASA-Unified Weather Research and Forecasting (NU-WRF) model at a high horizontal spatial resolution of 4 km × 4 km for cities over the continental US. We compare the inferred emissions and lifetimes with the values given by the NU- 20 WRF model to evaluate the method. The method is applicable to 26 US cities. The derived results are generally in good agreement with the values given by the model, with the relative differences of 2 % ± 17 % (mean ± standard deviation) and 15 % ± 25 % for lifetimes and emissions, respectively. Our investigation suggests that the use of wind data prior to satellite overpass time improves the performance of the method. The correlation coefficients between inferred and NU-WRF lifetimes increase from 0.56 to 0.79 and for emissions increase from 0.88 to 0.96 when comparing results based on wind fields sampled simultaneously with satellite 25 observations and averaged over 9 hours data prior to satellite observations, respectively. We estimate

3 al., 2020), and therefore improve knowledge about uncertainties in satellite-derived emissions. Existing studies usually quantify the uncertainties based on results from sensitivity analyses (e.g., Beirle et al., 2011), since we usually lack "true values" that can be used as a benchmark for validation. de Foy et al. (2014) tested CTM-independent approaches using simulated NO2 column 75 densities from a single point source with a specified emission and chemical lifetime. The good consistency between the derived values and the specified values given to drive the simulation suggests that the uncertainty of the Beirle et al. (2011) approach is small for an ideal, isolated source. However, the performance of the approach in the real world with complex source distributions has not yet been evaluated.
Here, on the basis of previous approaches (Beirle et al., 2011;Liu et al., 2016b), we develop a new CTM-independent approach 80 for inferring NOx lifetimes and emissions for cities with polluted backgrounds and complex spatial distribution of interfering emissions. We use synthetic NO2 observations derived from a model simulation to evaluate the performance of the new approach and to estimate its uncertainties. An overview of the synthetic observations, the methodology and features of the new CTMindependent approach is provided in Sect. 2. We evaluate results by comparing the inferred emissions and lifetimes with values from the model simulation in Sect. 3.1. Section 3.2 compares the performance of the method developed in this work with previous 85 approaches (Beirle et al., 2011;Liu et al., 2016b). Section 3.3 discusses the uncertainties of NOx lifetimes and emissions derived from the new approach. Section 4 presents a summary of the performance of the new method and the future work plans for applying the method to satellite observations.

Data and method
In this section, we develop an evaluation system to assess the performance of our newly-developed CTM-Independent SATellite-90 derived Emission estimation Algorithm for Mixed-sources (MISATEAM). Figure 1 displays the schematic of the evaluation system. MISATEAM uses satellite retrievals of tropospheric NO2 vertical column densities (VCDs), together with wind information from a meteorological reanalysis, to infer NOx lifetimes and emissions for cities. Cities are usually non-isolated sources with polluted backgrounds (Fig. S1). Additionally, emissions from cities may spread out and make cities not (quasi) point sources even at the footprint of satellite observations (a few km; Fig. 3). We refer to these cities as mixed-sources. 95 To evaluate MISATEAM, we replace satellite observations with synthetic NO2 VCDs derived from the NASA-Unified Weather Research and Forecasting (NU-WRF) model (Tao et al., 2013;Peters-Lidard et al., 2015) (Sect. 2.1). We then apply MISATEAM to the synthetic NO 2 VCDs and NU-WRF meteorological fields to infer urban NO x lifetimes and emissions (Sect. 2.2). We investigate the impact of temporal variations in wind fields on derived NOx lifetimes and emissions (Sect. 2.3). In Section 2.4, we describe the benchmark NOx emissions directly given by NU-WRF and NOx lifetimes deduced from known NOx emissions and 100 concentrations (hereafter referred to as "given emissions and NU-WRF lifetimes") that we will compare with the MISATEAMderived lifetimes and emissions. Analysis of the uncertainties in these datasets, including satellite observations and wind fields, is outside the scope of the study. We briefly discuss the potential impact of ignoring systematic errors in Sect. 3.3.2.

Synthetic NO2 VCDs: NU-WRF simulations
We use a regional modelling system, NU-WRF (Tao et al., 2013;Peters-Lidard et al., 2015), to simulate tropospheric NO2 VCDs 105 over the continental US. NU-WRF was developed from the advanced research versions of WRF (Michalakes et al., 2001) and WRF-Chem (Grell et al., 2005) with the addition of several NASA-developed components (e.g., Chou and Suarez, 1999;Chin et al., 2002Chin et al., , 2007Kumar et al., 2006;Peters-Lidard et al., 2007;Shi et al., 2010). The gas-phase chemical mechanism in NU-WRF is the second-generation regional acid deposition model (RADM2, Gross and Stockwell, 2003). The aerosol module is the Goddard 4 Chemistry Aerosol Radiation and Transport (GOCART) model (Chin et al., 2002). We use the anthropogenic emissions based on 110 the 2011 National Emissions Inventory (NEI) compiled by the US Environmental Protection Agency (US EPA, NEI 2011) but with a few modifications, in which the measurements from OMI, the ground-based Air Quality System (AQS), the in-situ continuous emissions monitoring in power plants, and the Air Pollutant Emissions Trends Data compiled by the US EPA (https://www.epa.gov/air-emissions-inventories/air-pollutant-emissions-trends-data), have been employed to adjust the baseline emissions to the simulation year of 2016 Tao et al., 2020). As such, the total anthropogenic NO x emissions in 115 2016 were approximately 72% of those in 2011, the baseline NEI year. The simulation also includes the fire emissions from the Global Fire Data version 4 with small fires (GFED v4s, van der Werf et al., 2017;Randerson et al., 2015); biogenic emissions from the online calculation using the Model of Emissions of Gases and Aerosols from Nature version 2 (MEGAN2, Guenther et al., 2006); dust emissions from the on-line estimation based on the surface wind speed, soil moisture, and soil erodibility (Ginoux et al., 2001;Kim et et al., 2017); and sea salt emissions from the on-line computation based on the method by Gong (2003). 120 We run NU-WRF for 2016 at a high horizontal spatial resolution of 4 km × 4 km and 40 vertical layers extending from surface to 50 hPa in this study. Figure 2 illustrates the domain of the simulation, which covers the continental US. We integrate NO2 concentrations from the surface to the tropopause to calculate tropospheric NO2 VCDs. We assume a consistent tropopause height of 10 km over the model domain to accelerate the data process, because NU-WRF outputs do not include tropopause height and NO2 VCDs integrated above 10 km increase slightly. We have performed a sensitivity analysis by integrating NO2 concentrations 125 from the surface to altitudes ranging from 8 to 16 km, where the seasonal mean tropopause heights may occur over the US (Pan et al., 2011;Rieckh et al, 2014). The derived NO2 VCDs over the fit domain of individual cities vary slightly above 10 km, with the relative difference of 3 % ± 2 % when increasing the integration altitude from 10 to 12 km, since most NO2 stays near the surface over the polluted urban areas. The meteorological initial and lateral boundary conditions are derived from the Modern Era Retrospective-Analysis for Research and Applications version 2 (MERRA-2, Rienecker et al., 2011;Gelaro et al., 2017). The 130 chemical initial and lateral boundary conditions are derived from the results of the Community Atmosphere Model with chemistry (CAM-chem, Lamarque et al., 2012). A 7-day model spin up following the recommendation by Berge et al. (2001) is used. Figure 2A illustrates the six-month average of the simulated hourly mean tropospheric NO2 VCDs sampled at 14:00 local time, which approximately corresponds to the early afternoon overpass time of OMI and TROPOMI. The NOx emissions used to drive NU-WRF over the model domain for the same time period are presented in Fig. 2B. We focus on cities with populations > 200,000, 135 which have been defined as medium-size urban areas in Organisation for Economic Co-operation and Development (OECD) countries. Nearby cities (located within 50 km of the largest city in a given urban area) are considered as one city cluster when applying MISATEAM to infer lifetimes and emissions. Cities on the boundary of the model domain, e.g., Seattle and San Francisco, are excluded from the following analysis, because the data for their inflow/outflow plumes are partially missing from the model output and thus do not meet the requirements of MISATEAM (see details of the fit interval in Sect. 2.2). This filtering results in a 140 total of 60 cities and urban conglomerations (see Table S1) as the candidates for applying MISATEAM, of which 26 have valid results. The locations of the 26 cities are shown in Figure 2. Cities without valid results either lack observations under calm wind conditions or are associated with large fitting errors (see details in Section 3.1).

Emission estimation algorithm
We develop MISATEAM based on the methods of Beirle et al. (2011) and Liu et al. (2016b). We develop a new model function 145 aiming for determining emissions for mixed-sources, instead of isolated sources within a clean background considered by Beirle et al. (2011). It is also different from that of Liu et al. (2016b), which was developed for complex sources, but adapted an additional model function to fit emissions in a separate step. More comparisons with those two previous methods will be discussed in Sect.

5
We adapt the basic approach of Liu et al. (2016b) that estimates NO2 emission rates, E(x), using NO2 observations, LDcalm(x), 150 where E(x) is a function of distance from the city center (denoted by x) in a particular direction and integrated over a given distance in a direction y (perpendicular to that of x). The mean emission maps (two-dimensional, 2D) are reduced to 1D along the respective direction x by integration across the direction y. LDcalm(x) are the so-called NO2 line densities, defined as the observed NO2 VCDs 155 (units molec cm -2 ) under calm wind conditions (wind speed < 2 m s -1 ) integrated in the same way as E(x) to give units of molec cm -1 as in Beirle et al. (2011).
: 2 is the ratio of NOx to NO2. We use : 2 of 1.32 to represent "typical urban conditions and noontime sun" (Seinfeld and Pandis, 2006). We investigate the effect of using a constant value of : 2 on derived emissions in Sect. 3.1; it is found to be insignificant. 160 b represents the NO2 background for each city, which is derived by analyzing the distribution of NO2 VCDs. We first calculate the mean NO2 VCD under calm wind conditions for grid cells within the lowest 5th percentile of NO2 VCDs for each city. This produces a good approximation of the mean NO2 VCD for grid cells with low NOx emissions (i.e., the lowest 5th percentile of NOx emissions). We then multiply this mean VCD value by the spatial width of the across-wind integration interval to derive b. τ is the NOx lifetime. Note that τ is assumed to be an effective mean dispersion lifetime (i.e., the result of the effect of deposition, 165 chemical conversion, and wind advection) because we do not consider downwind changes in the fitting functions, such as due to variations in wind speeds or : 2 or lifetime itself.
We then use the following model function, f(x), to describe NO2 line densities under windy conditions (wind speed > 2 m s -1 ) LDwindy(x): where w is the mean wind speed at the emission level in a given direction x, and * denotes convolution. Figure 3 illustrates the calculation of LDwindy(x). Additional technical details of the model function f(x) and its differences compared to those proposed by Liu et al. (2016b) are given in Appendix A.
Finally, we use estimates of b and : 2 in Eq.
(2), along with values of w, LDcalm(x), and LDwindy(x) from the model simulation 175 to infer τ and E(x). As displayed in Fig. 1, we use the NU-WRF high-resolution tropospheric NO2 VCDs sampled at 14:00 local time as the synthetic NO2 VCD observations, together with the NU-WRF meteorological wind information, to estimate urban NOx emissions. In other words, here we assume perfect knowledge of the winds and do not further consider the impact of errors in w.
As in previous studies, we only analyze data from April to September, in order to exclude winter data that have larger uncertainties and longer NOx lifetimes. We also investigate the impact of the inclusion of winter data in Sect. 3.3.1; it is found to be associated 180 with a larger uncertainty. We further compute total emissions for each city, , by summing E(x).
We perform a nonlinear least-squares fit of f(x) to the observed line densities under windy conditions, LD windy (x), with τ as the single fitting parameter. We use the package of scipy.optimize.curve_fit from the Python software library to perform the fitting.
We set the fit interval to 150 km in downwind direction, which corresponds to the e-folding distance for τ = 6 h and w = 7 m s -1 . 6 The fit interval in the upwind direction and the y direction are set to half the e-folding distance (75 km); the resulting area is large 185 enough to cover a highly populated and spread-out metropolitan region such as New York City. The definition of the fit interval in upwind and downwind direction, and the across-wind integration interval are illustrated in Fig. 3. Note that we use LDcalm(x) over a larger horizontal interval of 450 km to calculate the convolution in Eq. (2), in order to eliminate the edge effect of convolution. Fitting results of insufficient quality (i.e., the correlation coefficient R between the fitted and observed NO2 LD < 0.9, and one standard deviation error of τ > 10%) are discarded. We infer emissions simultaneously by summing E(x) in Eq. (1). We 190 perform the fit for all wind direction sectors and then average the fitted τ and corresponding total emission with good quality, using the fit residuals as inverse weights, to yield a best estimate of <τ> and < > for a given city. The standard deviation of the fit results for different wind directions has been used to quantify uncertainties in Sect. 3.3.2.
We use the city of New York as a case study to demonstrate our approach. This city is well suited for illustrating the strength of MISATEAM to estimate emissions for mixed sources, because it is a large city with multiple point and areal sources and is 195 surrounded by many other large sources. Figure 3 displays the complex spatial distribution of sources around New York. Under southwesterly wind, the city of Philadelphia is located in the upwind direction and Long Island is located in the downwind direction, both of which are significant NOx sources. Note that we do not exclude cloudy days from our analysis to make the most of the NU-WRF NO2 simulations and to avoid additional uncertainties arising from the inconsistent definitions of cloud fractions in the NU-WRF and satellite NO2 products. The uncertainty of the presence of clouds is discussed in Sect.

200
We use wind fields averaged from the surface to 1000 m altitude for w in this study. The synthetic NO2 VCDs around New York are sorted by wind directions ( Figure S1). Figure

Impact of temporal variations in wind fields
CTM-independent emission estimation algorithms usually assume a steady wind field over the duration of NOx lifetime. In the demonstration in Sect. 2.2, we use the wind fields sampled at the satellite overpass time to drive MISATEAM, consistent with 210 previous studies (e.g., Beirle et al., 2011;Valin et al., 2013;Lu et al., 2015;Liu et al., 2017Liu et al., , 2020Goldberg et al., 2019). This is expected to be reasonable for species with a short lifetime of a few hours such as NOx near noon of non-winter seasons. In reality, wind fields are variable over the NOx lifetime. Consequently, NOx emitted at a time prior to the satellite overpass may be transported under different wind conditions than those at the overpass time. Figure 5 illustrates the temporal variations in wind fields around New York. We use the northeasterly wind direction (with a good 215 fitting result) for demonstration. We select northeasterly winds observed at 14:00 local time as the baseline and find their backward trajectories for up to 8 hours. The backward trajectories are given at a time step of one hour. Not surprisingly, winds are n ot constant during the 9 hours from 8 hours before the baseline to the exact hour of the baseline. However, the temporal variations in wind directions are rather small for the northeasterly wind; wind directions are almost constant over time. For wind directions without good fit results, we observe larger variations. For instance, for the westerly wind with a poor correlation coefficient R of 220 0.76, the wind directions deviate from the west direction gradually for the time prior to the baseline (Fig. S3). These results shed light on the robustness of MISATEAM's steady-wind assumption. It is most likely that the fit fails when the assumption of steady 7 wind is not satisfied. In other words, the inherent fitting assumption is robust when the fit results have sufficient quality as defined in Sect. 2.2.
We perform sensitivity analyses to investigate the potential impact of temporal variations in winds on the fit results. We extend 225 the time windows used for calculating averaged wind fields from 1 h (i.e., at the overpass time of 14:00 local time) to 3 h (i.e., starting from the overpass time and extending into the past 2 h), 6, 9, and 12 h. We weight the winds based on their temporal proximity, i.e., the wind closer to the overpass time is given larger weight, following Eq. (3).
Where h represents the number of hours prior to the overpass time. i and d denote an individual grid cell and day, respectively. This is significantly smaller than the difference between the fit results based on weighted average winds and the winds at the overpass time (shown in Sect. 3.1).

Performance evaluation
In order to evaluate the fitting results, we infer given emissions and NU-WRF lifetimes from the NU-WRF inputs/outputs. The where E'(x) is the given NOx emission line densities under calm wind conditions, as function of distance x from the city center.
For evaluation, we compute the correlation coefficient (R), the Normalized Mean Bias (NMB), and the Root Mean Squared Error (RMSE) of the fitted emissions and the given emissions for all investigated cities. The model performance metrics of NMB and 245 RMSE for the emission ( ) evaluation are defined as

Evaluation
We apply MISATEAM to 60 large cities over the US (see the selection criteria of cities in Sect. 2.1). For 5 cities, we are not able 255 to initiate the fitting procedure, due to lack of observations under calm wind conditions to calculate LDcalm(x). We derive valid fitting results for 26 cities. The locations of the 26 cities are shown in Fig. 2. The other 29 cities without valid results either had small correlation coefficients (< 0.9) or large fitting errors (standard deviation error of τ > 10 %); those cities tend to have larger temporal variations in winds (similar to Fig. S3), which do not satisfy MISATEAM's requirement for steady winds prior to satellite overpass. 260 : 2 ). The errors arising from the differences between : 2 for 265 individual cities and a constant value of 1.32 will be propagated into the resulting emissions. The impact of the prescribed : 2 on inferring emissions will be discussed in more detail in this section (Fig. 7).
The use of wind data over 9 hours prior to the overpass time improves the performance of MISATEAM. Figure 6 compares the inferred lifetimes and emissions based on the 9 h weighted average of wind data (hereafter referred to as "9 h wind"; blue dots).
The results derived from the weighted average wind data show larger correlations with R increasing from 0.56 to 0.79 for lifetimes 270 and from 0.88 to 0.96 for emissions; and smaller bias with NMB decreasing from -0.04 to 0.02 for lifetimes and from 0.23 to 0.13 for emissions, when comparing with those derived from the 1 h wind. We have performed the comparison using results based on the weighted averages of 3 h, 6 h, and 12 h wind data as well. The use of wind information prior to the satellite overpass time succeeds in improving the performance of MISATEAM in all these cases (Fig. S4). Note that the correlation between the inferred and the NU-WRF lifetimes based on 12 h wind (R=0.64) is not as good as that based on 3 h (R=0.74), 6 h (R=0.78), and 9 h 275 (R=0.79) wind, which is most likely caused by the inclusion of overnight wind information.
The importance of applying wind information prior to the satellite overpass time should not be overinterpreted. The fitting function Eq. (2) by definition is not capable of describing the NO2 plumes under significantly varying wind directions because such temporal variations are not considered in the fitting function. In this way, wind directions and the results inferring from different wind scenarios are not expected to vary significantly, as far as fits with sufficient quality are yielded. Only 6 out of 26 cities show 280 relative differences larger than 20 % when comparing results derived from 1 h wind to those derived from 9 h wind.
We examine a scenario, namely "NU-WRF NO x /NO 2 ", to investigate possible errors from the assumption of a constant : 2 .
We replace : 2 with the ratio of NOx and NO2 calculated directly from NO2 and NO VCDs per grid cell by NU-WRF outputs, and then use MISATEAM for inferring NOx emissions. Any difference in the inferred emissions compared to the emissions based on the prescribed ratio of 1.32 ("this study") can then be assumed to originate from errors in the assumption of : 2 . Figure 7  285 compares the results using a prescribed ratio (blue dots) with those using NU-WRF NOx/NO2 (grey dots). The comparison shows nearly the same correlations to the given emissions, but a smaller bias for results based on NU-WRF NOx/NO2 with NMB dropping from 0.13 to almost zero (0.03). The comparison suggests that the influence of changing ratio on derived emissions is limited, because its spatial variation is significantly smaller than that of NOx lifetime and NO2 columns (τ and LDcalm(x) in Eq. (1)).
Considering the investigated cities are located all over the country and have a wide range of geographic features, we conclude that 290 a constant ratio is a reasonable assumption without resulting in significant bias to the derived emissions for typical US cities. The errors associated with the assumption is estimated to be 10 %, consistent with our previous estimates based on literature reviews (Beirle et al., 2011;Liu et al., 2016b). However, for applications based on geostationary satellites with changing local observation time, the approach using a constant value for : 2 is subject to larger uncertainties arising from the diurnal cycle of : 2 (Han et al., 2011). 295 We examine an additional scenario, namely "constant lifetime", to show the necessity of deriving lifetimes for individual cities.
Instead of individually fitted lifetimes for each city, we use the mean NU-WWRF lifetime of all cities (2.5 h) for the calculation of emissions in the "constant lifetime" scenario. The emissions correlation drops to -0.03 (Fig. 7), showing that individually fitted lifetimes are critical for this method. The bias is also larger with RMSE increasing by a factor of 3 compared to results based on the individually fitted lifetimes. This further improves our confidence that the derived variation of the fitted lifetimes carries 300 important information on local variability of the oxidizing capacity of urban plumes. The individual lifetimes are well suited for the determination of emissions, suggested by the significantly improved consistency with given emissions.

Comparison with previous methods
We further evaluate MISATEAM by comparing the results with those derived from two previous approaches including Beirle et al. (2011) and Liu et al. (2016b). The comparison of the technical details between MISATEAM and those two previous approaches 305 is given by Fig. S5. We apply all three approaches to fit lifetimes and emissions for all 26 cities investigated by this study. Note that we use the 9 h wind for all approaches for best performance and consistency. convolved with a Gaussian function, and was not intended to be applied to mixed-sources with interfering emissions from nearby cities or industrial areas. For instance, it is capable of giving an accurate estimate for an isolated city of St. Louis in Missouri, with a relative difference of less than 10 % compared to the NU-WRF lifetime. However, for most cities with a polluted background, the fitted lifetimes are biased significantly due to the interference from surroundings. This is consistent with the previous findings 315 for this approach: an additional source at 100 km with only 10% of the emissions of the source under investigation causes a lifetime bias of 20 %; for an interfering source of the same order as the source of interest, the method fails completely (Liu et al., 2016b).
Several studies adopted a plume rotation technique (Pommier et al., 2013;Valin et al., 2013) to advance the approach of Beirle et al. (2011), which is not applicable to mixed-sources as well. These techniques rotate NO2 measurements centered over the city center so that NO2 columns under different wind directions are aligned in a common upwind-to-downwind direction. This increases 320 the number of observations used for analysis without introducing additional errors for (quasi) point sources, compared with individually analyzing observations by wind directions as done in this study. However, for mixed-sources investigated in this study, use of such rotation techniques may result in significant bias by allocating the NO2 from interfering sources into a ring of elevated NO2 values around the source of the interest and thus amplifying the NO2 signal of the source. An illustration of this amplification can be found in Fig. S2 of Fioletov et al. (2015). 325 We note that the performance of MISATEAM is also better than that of the approach reported in Liu et al. (2016b), although they share the same concept of using the NO2 patterns observed under calm wind conditions as proxy of emission patterns instead of assuming a single point source as in Beirle et al. (2011). It is most likely that Liu et al. (2016b) overfits the model by introducing too many degrees of freedom. As suggested by Fig. 8A, the model function of Liu et al. (2016b) occasionally tries to "explain" changes of scaling factors by a shorter lifetime, resulting in a small R of 0.21. In MISATEAM, we decrease the number of fitting 330 parameters from three in Liu et al. (2016b) to only one (see details in Eq. (A4) of Appendix A), which improves the robustness of the fit results.
Emission comparisons in Fig. 8B show better agreement than lifetime comparisons in Fig. 8A for all approaches. MISATEAMderived emissions show the best consistency with the given emissions. According to mass balance, the magnitude of emissions equals the total mass of NOx divided by lifetime. In the evaluation for MISATEAM, the given emissions range from 57 mol h -1 to 335 717 mol h -1 for all investigated cities, the variation in which is significantly larger than that in lifetimes ranging from 1.5 h to 3.7 h. This finding also holds for the other two approaches. The other two approaches can achieve a good correlation with the given emissions by providing reasonable estimates for the magnitude of the total NOx mass, even though they fail to predict variations in lifetimes between cities. For instance, the results derived from the approach of Liu et al. (2016b)  , and thus RMSE are smaller than that for MISATEAM.

Uncertainty analysis
The good consistency in Sect. 3.1 increases our confidence that the fitted lifetimes and emissions represent the real-word characteristics well. We investigate their uncertainties in this session.

Sensitivity analysis 350
Analogous to Beirle et al. (2011) andLiu et al. (2016b), we investigate the impact of the a-priori choice of fit and integration intervals, and wind layer height. The dependency of the fit results for τ and on these three choices is tabulated in Table 1.
The fitted lifetimes are generally robust with respect to changes of the fit and integration intervals, because the NO2 distribution under calm wind conditions, LDcalm(x), is a good representation of the emission pattern in any case. An increase of the fit interval in downwind direction by 50 km affects the resulting lifetimes by about -2 ± 11 %. The changes of derived lifetimes are also small 355 when increasing the fit interval in upwind direction (4 ± 12 %) or integration interval (interval i + 25 km in Fig. 3； 4 ± 18 %) by 50 km. MISATEAM succeeds in avoiding choosing intervals city by city manually, which has been done in previous studies in order to minimize the influence of other nearby sources.
We use the change of the ratio of fitted emissions to given emissions km with 33 % for the given emissions and 42 % for the fitted emissions. However, for the scenario of a larger downwind-direction, upwind-direction and integration interval, the change of the ratio of to ′ is rather small, which is 3, 9, and 9 % on 365 average, respectively; the fitted emissions show good consistency with the given emissions, reporting the correlation coefficient of 0.95, 0.92, and 0.86, respectively. It is interesting to note that the fitted emissions are rather insensitive to the extension of the fit interval in downwind direction. Neither the given nor the fitted emissions are significantly changed by increasing the downwinddirection interval from 150 km to 200 km. It suggests that we succeed in capturing the complete downwind plume and reaching the background areas by the default setting of 150 km for the investigated cities in this study. 370 Uncertainties associated with the choice of top wind layer height (e.g., 500 m, 1000 m, or 2000 m) are relatively small. The resulting lifetimes and emissions change about 16 % and -9 % on average when averaging the wind fields from surface to up to 500 m. The average changes are -11 % and 13 % for inferring lifetimes and emissions, respectively, when adopting the wind layer height of 2000 m. This is consistent with the findings in the previous studies (e.g., Beirle et al., 2011 andLiu et al., 2016b).
We also apply MISATEAM to year-round NO2 data to investigate the impact of including winter data on the performance of the 375 method. We keep default settings of MISATEAM as described in Sect. 2.2 for the fit. As expected, the fitted results differ more significantly from given values compared with results based on using only non-winter data. The bias is larger with NMB changing from 0.02 to -0.14 for lifetimes and from 0.13 to 0.27 for emissions. This indicates that MISATEAM, most likely its inherent steady-wind assumption, is less accurate during the winter season with longer NOx lifetimes.

Uncertainty quantification 380
We calculate the uncertainties of inferred results based on the fitting metrics ( Fig. 6 and 7) and the dependencies on the a priori settings as investigated in the above sensitivity studies. We attribute uncertainties of 15 % and 20 % to the derived lifetimes and emissions, respectively, based on the mean of relative differences for all 26 cities (14 % for lifetimes and 21 % for emissions). The derived emissions have higher uncertainties arising from uncertainty in the NOx to NO2 scaling factor. The derived emissions in terms of NO2 are upscaled to NOx based on a constant NOx/NO2 ratio of 1.32, representing typical urban conditions at noon 385 (Seinfeld and Pandis, 2006). Since MISATEAM aims to provide estimates for cloud-free satellite observations at the overpass time close to noon of non-winter seasons and it focuses on polluted regions with generally high tropospheric ozone, this value is reasonably accurate. However, the NOx/NO2 ratio might vary locally. NU-WRF reports 1.4 ± 0.1 with a range of 1.2 -1.6. The overall impact of variations in this ratio is shown to be relatively small (see Sect. 3.1).
We can identify additional uncertainties that would be present when applying MISATEAM to "real" data instead of synthetic data. 390 The uncertainty of satellite NO2 observations propagates into the uncertainty of emissions. The uncertainty of satellite NO2 observations has less impact on the lifetime estimation and only results in errors for lifetimes when satellite observations have systematic errors depending on the distance from the source. The total uncertainty of NO2 VCDs results from uncertainties in the spectral fit in the retrieval, the stratospheric and tropospheric separation, and the tropospheric air mass factor (AMF). In the model function of MISATEAM, a possible bias associated with the stratospheric and tropospheric separation is eliminated by use of the 395 background term b. The uncertainty in the spectral fit in the retrieval is rather small compared to that associated with AMF (Boersma et al., 2007). We estimated the overall uncertainty primarily arising from the uncertainty in the tropospheric AMF is about 25 % based on validation of TROPOMI NO2 products with ground-based measurements (e.g., Griffin et al., 2019;Ialongo et al., 2020;Zhao et al., 2020). Since the random uncertainty of the tropospheric NO2 observations could be suppressed due to the consideration of long-term means, this estimate may be conservative.

12
The presence of clouds is an additional source of uncertainties. We are required to exclude satellite observations with significant cloud fractions in the instrument's field of view. For TROPOMI NO2 products, we usually remove data with cloud radiance fraction ≥ 0.5. A bias is observed in NO2 VCD averages as a result of removing the data during cloudy conditions (Geddes et al., 2012).
The bias is associated with changing photochemistry, meteorology, and pollutant transport, which may also have impacts on NOx/NO2 ratio and NOx lifetime. NOx lifetime on a sunny day with valid satellite observations will likely be shorter than that on a 405 cloudy day since faster photolysis rates are expected for NOx reactions on sunny days. The magnitude of a bias is expected to vary from city to city. We calculate the fraction of cloudy scenes to total scenes over the fit domain of individual cities based on TROPOMI NO2 products from April through September, 2020. The fractions range from 16 -56 % for the considered cities. For cities with heavy cloud cover, like New York, Philadelphia, and Washington D.C. with a fraction > 50%, the impact associated with cloud selection criteria is expected to be larger than cities with more clear sky. We estimated an uncertainty of 10% arising 410 from cloud selection criteria based on the evaluation performed at urban sites (Geddes et al., 2012).
Additionally, the accuracy of wind fields contributes to the uncertainties of both lifetimes and emissions. It can affect the sorting of the NO2 VCDs according to wind directions as well as the conversion of the downwind decay from a function of distance into a function of time in Eq. (2). We estimate the uncertainties associated with the wind data to be approximately 30 % based on the comparison of wind information between reanalysis product and sounding measurements (see Table S3 in Liu et al., 2016b). 415 We define total uncertainties of the resulting lifetimes and emissions as the root of the quadratic sum of the above-mentioned error contributions that are assumed to be independent. We estimated that total uncertainties of NOx lifetime and emissions for a US city are 43 % and 45 %, respectively.

Conclusions and future work
In this work we developed a CTM-independent approach, MISATEAM, to infer NOx lifetimes and emissions from satellite NO2 420 observations. As in Liu et al. (2016b), MISATEAM is developed for sources with polluted backgrounds. It adopts the approach of using NO2 spatial patterns under calm wind conditions as a proxy of the spatial patterns of emission sources to account for interferences from neighboring strong sources. MISATEAM improves upon Liu et al. (2016b) by advancing the fitting function to reduce the number of parameters and to provide estimations of NOx lifetimes and emissions simultaneously.
We applied MISATEAM to synthetic tropospheric NO2 VCDs over the continental US provided by a NU-WRF high resolution 425 model simulation. We found that our new method for determining NOx lifetimes and emissions was applicable to 26 cities. The derived results were generally in good agreement with the NU-WRF given values. In existing studies, wind fields sampled simultaneously with satellite observations were used to drive the CTM-independent approach. We investigated the impact of temporal variations in winds on fitted results and found the use of wind data prior to satellite overpass time improves performance of our approach. R between inferred and NU-WRF lifetimes increased from 0.56 to 0.79 and for emissions increased from 0.88 to 430 0.96 when comparing results based on 1 h and 9 h winds, respectively. The comparison between MISATEAM and the approaches of Beirle et al. (2011) and Liu et al. (2016b) suggests that MISATEAM is more suitable for non-isolated sources, particularly for lifetime estimation. Lifetimes inferred from the previous approaches showed rather weak correlations with respect to NU-WRF lifetimes (0.01 for Beirle et al. (2011) and 0.21 for Liu et al. (2016b)) as compared with that from MISATEAM (0.79).
We plan to apply MISATEAM to observations from TROPOMI and geostationary satellite instruments including the Korean 435 Geostationary Environmental Monitoring Spectrometer (GEMS; Kim et al., 2012), NASA Tropospheric Emissions: Monitoring of Pollution (TEMPO; Chance et al., 2012), and ESA Sentinel-4 . These instruments have spatial resolutions 13 similar to the NU-WRF simulation (4 km) used in this study. For applications based on geostationary satellites with local observation time outside of the early afternoon time frame, additional investigation about the impact of the diurnal cycle of NO2 lifetime is required, since MISATEAM is expected to have a larger uncertainty when the lifetime is longer. We estimate that 440 uncertainties in NOx lifetime and emissions arising from MISATEAM are approximately 15% and 20%, respectively, for typical (US) cities. Additional uncertainties are associated with wind errors in the reanalysis dataset as well as errors in the satellite NO2 retrievals, increasing the total uncertainties of NOx lifetime and emissions to 43 % and 45 %, respectively. The general low bias of NO2 Tropospheric VCDs from TROPOMI for polluted sites (Verhoelst et al. 2021) is directly transferred into the inferred NOx emissions if no correction is performed. We will attempt to reconcile bottom-up and satellite-derived urban emissions to generate 445 a merged inventory (e.g., Liu et al., 2018) to provide timely NOx emissions estimation for air quality and climate modeling communities.
Data availability. The NU-WRF model outputs are available upon request from Zhining Tao (zhining.tao@nasa.gov). Additional data related to this paper may be requested from the corresponding author. Competing interests. The authors declare that they have no competing interests.