Inferring the anthropogenic NOx emission trend over the United States during 2003–2017 from satellite observations: was there a flattening of the emission trend after the Great Recession?

We illustrate the nonlinear relationships among anthropogenic NOx emissions, NO2 tropospheric vertical column densities (TVCDs), and NO2 surface concentrations using model simulations for July 2011 over the contiguous United States (CONUS). The variations in NO2 surface concentrations and TVCDs are generally consistent and reflect anthropogenic NOx emission variations for high anthropogenic NOx emission regions well. For low anthropogenic NOx emission regions, however, nonlinearity in the anthropogenic-emission–TVCD relationship due to emissions from lightning and soils, chemistry, and physical processes makes it difficult to use satellite observations to infer anthropogenic NOx emission changes. The analysis is extended to 2003–2017. Similar variations in NO2 surface measurements and coincident satellite NO2 TVCDs over urban regions are in sharp contrast to the large variation differences between surface and satellite observations over rural regions. We find a continuous decrease in anthropogenic NOx emissions after 2011 by examining surface and satellite measurements in CONUS urban regions, but the decreasing rate is lower by 9 %–46 % than the pre-2011 period.


Introduction
Anthropogenic emissions of nitrogen oxides (NO x = NO 2 + NO) adversely affect the environment, not only because of their direct detrimental impacts on human health (Greenberg et al., 2016(Greenberg et al., , 2017;;Heinrich et al., 2013;Weinmayr et al., 2009) but also because of their fundamental roles in the formation of ozone, acid rain, and fine particles, all of which have negative environmental impacts (Crouse et al., 2015;Kampa and Castanas, 2008;Myhre et al., 2013;Pandey et al., 2005;Singh and Agrawal, 2007).About 48.8 Tg N yr −1 of NO x are emitted globally from both anthropogenic (77 %) and natural (23 %) sources, such as fossil fuel combustion, biomass and biofuel burning, soil bacteria, and lightning (Seinfeld and Pandis, 2016).In total, 3.85, 0.24, and 0.66 Tg N of anthropogenic, soil, and lightning NO x , respectively, were emitted from the US in 2014 on the basis of the 2014 National Emission Inventory (NEI2014) and the GEOS-Chem model simulations (Silvern et al., 2019); vehicle sources and fuel combustions accounted for 93 % of the total anthropogenic NO x emissions (EPA, 2017).
The US anthropogenic NO x emissions during the 2010s declined dramatically compared to the mid-2000s (EPA, 2018b;Xing et al., 2013) due to stricter air quality regulations and emission control technology improvements, such as the phase-in of Tier II vehicles during 2004-2009 and the switch of power plants from coal to natural gas (De Gouw et al., 2014;McDonald et al., 2018).The overall reduction (about 30 %-50 %) of anthropogenic NO x emissions from the mid-2000s to the 2010s was corroborated by observed decreases in vehicle NO x emission factors, NO 2 surface concentrations, nitrate wet deposition flux (Fig. S1 in the Supplement), and NO 2 tropospheric vertical column densities (TVCDs) (Bishop and Stedman, 2015;Georgoulias et al., 2019;Li et al., 2018;McDonald et al., 2018;Miyazaki et al., 2017;Russell et al., 2012;Tong et al., 2015).How-ever, the detailed NO x emission changes after the Great Recession (from December 2007 to June 2009) are highly uncertain.On the one hand, the U.S. Environmental Protection Agency (EPA) estimated that the Great Recession had a slight impact on the anthropogenic NO x emission trend and the anthropogenic NO x emissions decreased steadily from 2002 to 2017 (Fig. S2), although the emission decrease rate slowed down by about 20 % after 2010 (−5.8 % yr −1 for 2002-2010 and −4.7 % yr −1 for 2010-2017; Table 1) (EPA, 2018b).Fuel-based emission estimates in Los Angeles also showed a steady decrease in anthropogenic NO x emissions after 2000 and a small impact of the Great Recession on the anthropogenic NO x emission decrease trend (Hassler et al., 2016).The continuous decrease in anthropogenic NO x emissions was consistent with the ongoing reduction in vehicle emissions (McDonald et al., 2018).On the other hand, Miyazaki et al. (2017) and Jiang et al. (2018) found that the US NO x emissions derived from satellite NO 2 TVCDs, including OMI (the Ozone Monitoring Instrument), SCIA-MACHY (SCanning Imaging Absorption SpectroMeter for Atmospheric CHartography), and GOME-2A (Global Ozone Monitoring Experiment 2 onboard METOP-A), were almost flat from 2010-2015 and suggested that the decrease in NO x emissions was only significant before 2010, which was completely different from the bottom-up and fuel-based emission estimates.
A complicating factor in inferring anthropogenic NO x emission trends from the observations of NO 2 surface concentrations and satellite NO 2 TVCDs is their nonlinear dependences on anthropogenic NO x emissions (Gu et al., 2013(Gu et al., , 2016;;Lamsal et al., 2011).Although the decrease rates of both NO 2 surface concentrations and coincident OMI NO 2 TVCDs slowed down after the Great Recession over the United States, Tong et al. (2015), Lamsal et al. (2015), and Jiang et al. (2018) found that the slowdown of the decrease rates derived from NO 2 surface concentrations is 12 %-79 % less than those of NO 2 TVCDs (Table 1).Secondly, the slowdown of the decrease rates of NO 2 surface concentrations and OMI TVCDs over cities and power plants (Russell et al., 2012;Tong et al., 2015) is significantly less than those over the whole contiguous United States (CONUS) (Jiang et al., 2018;Lamsal et al., 2015).Moreover, Zhang et al. (2018) found that filtering out lightning-affected measurements could significantly improve the comparison of NO 2 surface concentration and OMI NO 2 TVCD trends over the CONUS.
In this study, we carefully investigate the relationships among anthropogenic NO x emissions, NO 2 surface concentrations, and NO 2 TVCDs over the CONUS and evaluate the impact of the relationships on inferring anthropogenic NO x emission changes and trends from surface and satellite observations.Section 2 describes the model and datasets used in this study, including the Regional chEmistry and trAnsport Model (REAM), the EPA Air Quality System (AQS) NO 2 surface observations, and NO 2 TVCD products from OMI, GOME-2A, GOME-2B (GOME2 onboard METOP-B), and SCIAMACHY.In Sect.3, we examine the nonlinear relationships among anthropogenic NO x emissions, NO 2 surface concentrations, and NO 2 TVCDs using model simulations.Accounting for the effects of background sources, physical processes, and chemical nonlinearity, we then investigate the anthropogenic NO x emission trends and changes from 2003 to 2017 over the CONUS.Finally, Sect. 4 gives a summary of the study.
2 Model and data description 2.1 REAM REAM has been applied and evaluated in many research applications including ozone simulation and forecast, emission inversion and evaluations, and mechanistic studies of chemical and physical processes (Alkuwari et al., 2013;Cheng et al., 2017Cheng et al., , 2018;;Choi et al., 2008a, b;Gu et al., 2013Gu et al., , 2014;;Koo et al., 2012;Liu et al., 2012Liu et al., , 2014;;Wang et al., 2007;Yang et al., 2011;Zhang et al., 2017Zhang et al., , 2018;;Zhang and Wang, 2016;Zhao and Wang, 2009;Zhao et al., 2009aZhao et al., , 2010)).REAM as used in this work, the model domain of which is shown in Fig. 3, has 30 vertical layers in the troposphere, and the horizontal resolution is 36 × 36 km 2 .The model is driven by meteorology fields from a Weather and Research Forecasting (WRF, version 3.6) model simulation initialized and constrained by the NCEP coupled forecast system model version 2 (CFSv2) products (Saha et al., 2011).The chemistry mechanism is based on GEOS-Chem v11.01 with updated reaction rates and aerosol uptake of isoprene nitrates (Fisher et al., 2016).Chemistry boundary conditions and initializations are from a GEOS-Chem (2 • × 2.5 • ) simulation.Hourly anthropogenic emissions on weekdays are based on the 2011 National Emission Inventory (NEI2011), while weekend anthropogenic emissions are set to be twothirds of the weekday emissions (Beirle et al., 2003;Choi et al., 2012).Biogenic volatile organic compound (VOC) emissions are estimated using the Model of Emissions of Gases and Aerosols from Nature (MEGAN) v2.10 (Guenther et al., 2012).NO x emissions from soils are based on the Yienger and Levy (YL) scheme (Li et al., 2019;Yienger and Levy, 1995).The cloud-to-ground (CG) lightning flashes are calculated following Choi et al. (2005) and Zhao et al. (2009a) with the parameterization of the CG flash rate as a function of convective mass fluxes and convective available potential energy (CAPE).The ratios of intra-cloud (IC) lightning flashes to CG flashes are parameterized as a function of the height between the freezing layer and the cloud top (Luo et al., 2017;Price and Rind, 1992).In this study, 250 mol of NO are emitted per CG or IC flash (Zhao et al., 2009a).As a result, on weekdays in July 2011, REAM has mean anthropogenic NO x emissions of 7.4 × 10 10 molecules cm −2 s −1 , mean soil NO x emissions of 1.2 × 10 10 molecules cm −2 s −1 , and mean Since different studies used different time division methods, we list the period of each study in the table.2 Trends are based on an exponential model: , where "y" denotes year and "y 0 " denotes the initial year, "E(y)" denotes the value at year "y" and "E 0 " denotes the value at the initial year, and r − 1 is the relative trend.3 Slowdown ratios = trend in "period 3"/trend in "period 1"−1.4 Trends in our study are calculated based on the national seasonal trends shown in Table 3. 5 The information on satellite products used in this study is summarized in Table S2.6 We updated EPA anthropogenic NOx emissions with the newest Continuous Emission Monitoring Systems (CEMS) datasets.Figure S2 shows the comparison between our updated and original EPA anthropogenic NOx emissions (EPA, 2018b).7 Denotes the averaged trends of 13:00 and 10:00 local time (LT) based on the values in Table 3. 8 The study used NO 2 TVCD from urban and power plant grid cells across the US. 9 Since previous studies used linear models to calculate trends and the results are sensitive to their calculation methods and the selection of initial years, we recalculate the trends based on the above exponential model, which makes all the results consistent.Our results are the bold numbers in parentheses, while the numbers in normal font are from the original publications.10 The study uses NO 2 TVCD and surface concentrations from Los Angeles, Dallas, Houston, Atlanta, Philadelphia, Washington,D.C.,New York,and Boston. 11 The two studies used the EPA Air Quality System (AQS) NO 2 surface measurements and coincident satellite NO 2 TVCD data over the US.

Satellite NO 2 TVCDs
In this study, we use NO 2 TVCD products from four satellite sensors in the past decade, including SCIAMACHY, GOME-2A, GOME-2B, and OMI -the spectrometers onboard sunsynchronous satellites to monitor atmospheric trace gases.The SCIAMACHY instrument onboard the Environmental Satellite (ENVISAT) has an Equator overpass time of 10:00 local time (LT) and a nadir pixel resolution of 60 × 30 km 2 .The GOME-2 instruments on Metop-A (named GOME-2A) and Metop-B (GOME-2B) satellites cross the Equator at 09:30 LT and have a nadir resolution of 80 × 40 km 2 .After 15 July 2013, the nadir resolution of GOME-2A became 40 × 40 km 2 with a smaller scanning swath.The OMI onboard the EOS-Aura satellite has a nadir resolution of 24 × 13 km 2 and overpasses the Equator around 13:45 LT.More detailed information about these instruments is summarized in Table S1.These instruments measure backscattered solar radiation from the atmosphere in the ultraviolet and visible wavelength.The radiation measurements in the wavelength of 402-465 nm are then used to retrieve NO 2 vertical column densities (VCDs).The retrieval process consists of three steps: (1) converting radiation observations to NO 2 slant column densities (SCDs) by using the differential optical absorption spectroscopy (DOAS) spectral fitting method; (2) separating tropospheric SCDs and stratospheric SCDs from the total NO 2 SCDs; (3) dividing the NO 2 tropospheric SCDs by the tropospheric air mass factors (AMFs) to compute TVCDs.
The product archives we use in this study include GOME-2B (TM4NO2A v2.3), SCIAMACHY (QA4ECV v1.1), GOME-2A (QA4ECV v1.1), OMI (QA4ECV v1.1, hereafter referred to as OMI-QA4ECV), OMNO2 (SPv3, hereafter referred to as OMI-NASA), and the Berkeley High-Resolution NO 2 products (v3.0B, hereafter referred to as OMI-BEHR).OMI-BEHR uses the tropospheric SCDs from OMI-NASA products but updates some inputs for the tropospheric AMF calculation (Laughner et al., 2018b).These product archives have been previously validated (Boersma et al., 2018;Drosoglou et al., 2017Drosoglou et al., , 2018;;Krotkov et al., 2017;Laughner et al., 2018b;Wang et al., 2017;Zara et al., 2018).Generally, the pixel-size uncertainties of these products are > 30 % over polluted regions under clear-sky conditions.We summarize the basic information about these products in Table S2.To keep the high quality and sampling consistency of NO 2 TVCD datasets, we chose pixel-size NO 2 TVCD data using the criteria listed in Table S3.After the selection, we re-gridded the pixel-size data into the REAM 36 × 36 km 2 grid cells and calculated the seasonal means of each grid cell with corresponding daily values on weekdays (winter: January, February, and December; spring: March, April, and May; summer: June, July, and August; autumn: September, October, and November).We excluded weekend data in this study to minimize the impacts of weekend NO x emission reduction, leading to different NO 2 TVCDs between weekdays and weekends (Fig. S3).
Satellite TVCD measurements can show large variations and apparent discontinuities due in part to the effects of cloud, lightning NO x , the shift in satellite pixel coverage, and retrieval uncertainties (Fig. S3; e.g., Boersma et al., 2018;Zhang et al., 2018).However, continuous and consistent measurements are required for reliable trend analyses.In addition to the criteria of data selection in Table S3, we compute the seasonal relative 90th percentile confidence interval, defined as RCI = (X(95th percentile) -X(5th percentile)) / mean(X), where X is the daily NO 2 TVCD for a given season.To compute the seasonal trend, we require that RCI is < 50 % for the selected season every year in the analysis period (Table S3).About 45 % of data are removed as a result.

Surface NO 2 measurements
Hourly surface NO 2 measurements from 2003 to 2017 are from the EPA AQS monitoring network (archived on https: //www.epa.gov/outdoor-air-quality-data, last access: 27 June 2018).Most AQS monitoring sites use the Federal Reference Method (FRM) gas-phase chemiluminescence to measure NO 2 .Few sites use the Federal Equivalent Method (FEM) photolytic chemiluminescence or the cavity attenuated phase shift spectroscopy (CAPS) method.FRM and FEM are indirect methods, in which NO 2 is first converted to NO and then NO is measured through chemiluminescence measurement of NO 2 * produced by NO + O 3 .The difference is that FRM uses heated catalysts for the conversion of NO 2 to NO and FEM uses photolysis of NO 2 to NO.The conversion to NO in the FRM instruments is not specific to NO 2 , and non-NO x active nitrogen compounds (NO z ) can also be reduced by the catalysts, which would cause high biases of NO 2 measurements, while the FEM is sensitive to the photolysis conversion efficiency of NO 2 to NO (Beaver et al., 2012(Beaver et al., , 2013;;Lamsal et al., 2015).The CAPS method directly determines NO 2 concentrations based on an NO 2 -induced phase shift measured by a photodetector.The CAPS instrument operates at a wavelength of about 450 nm and may overestimate NO 2 concentrations due to the absorption of other molecules at the same wavelength (Beaver et al., 2012(Beaver et al., , 2013;;Kebabian et al., 2005).
Due to the different characteristics of the above three methods and demonstrated biases between the FRM and the FEM by Lamsal et al. (2015), we firstly investigate the measurement discrepancies among the above three methods.There are three sites having FRM and FEM measurements simultaneously during some periods from 2013 to 2014, two sites having both FRM and CAPS data during some periods from 2015 to 2016, and one site using all three measurement methods during some periods in 2015.Figure S4 shows the hourly averaged ratios of FEM and CAPS to FRM data for four seasons during 2013-2016.The CAPS/FRM ratios are in the range of 0.94-1.06,and the FEM/FRM ratios are 0.86-1.11.Furthermore, Zhang et al. (2018) discussed that the relative trends are not affected by scaling the observation data.As in the work by Zhang et al. (2018), we analyze the relative trends in the surface NO 2 data.We, therefore, did not scale the FRM data.At sites with FEM or CAPS measurements, we use these measurements in place of FRM data.If both FEM and CAPS data are available, we use the averages of the two datasets.
Since NO 2 surface concentrations have significant diurnal variations (Fig. S5), we choose the data at 09:00-10:00 LT for comparison with GOME-2A/2B data, those at 10:00-11:00 LT for comparison with SCIAMACHY data, and those at 13:00-14:00 LT for OMI data.The seasonal RCI < 50 % requirement is also used here to be consistent with the analysis of satellite TVCD data, and thus about 1.5 % of the data is removed.We also require that the measurement site must have valid measurements in the aforementioned 3 h for at least one season from 2003 to 2017.The locations of the 179 selected sites using the site selection criteria are shown in Fig. 1.The region definitions follow the U.S. Census Bureau (https://www2.census.gov/geo/pdfs/maps-data/maps/reference/us_regdiv.pdf, last access: 6 February 2019).−→ 0.5HNO 3 + 0.5HNO 2 ), dry deposition, transport effects, and background sources (Gu et al., 2013;Lamsal et al., 2011).Therefore, it is necessary to first investigate the nonlinearities among NO x emissions, NO 2 surface concentrations, and TVCDs over the CONUS before we compare the trends between NO 2 surface concentrations and TVCDs.The nonlinearity between NO x emission and NO 2 TVCD is analyzed by examining the local sensitivity of NO 2 TVCD to NO x emissions (Gu et al., 2013;Lamsal et al., 2011;Tong et al., 2015), which is defined as β in Eq. ( 1).We further define γ as the sensitivity of NO 2 surface concentration to NO x emission: where E denotes NO x emission and E denotes the change in NO x emission; denotes NO 2 TVCD, c denotes surface NO 2 concentration, and and c denote the corresponding changes.
We computed β and γ values for July 2011 over the CONUS using REAM.To compute local β and γ values, we added another independent group of chemistry species ("group 2") in REAM in order to compute the standard and sensitivity simulations concurrently.The original chemical species in the model ("group 1") were used in the standard simulation.For group 2 chemical species, anthropogenic NO x emissions were reduced by 15 %.In the model simulation, we first computed the advection of group 1 tracers.The horizontal tracer fluxes were therefore available.All influxes into a grid cell for the group 2 tracer simulation were from the group 1 tracer simulation; only outfluxes were computed using group 2 tracers.The outflux was one way in that nitrogen species were transported out but the transport did not affect adjacent grid cells because the influxes were from the group 1 tracer simulation.Using this procedure, the effects of anthropogenic NO x emission reduction were localized.The β and γ values were computed by the ratio of TVCD and surface concentration changes to a 15 % change in anthropogenic NO x emissions.
Figure 2 shows the distributions of our β and γ ratios as a function of anthropogenic NO x emissions for July 2011 over the CONUS.Results essentially the same as Fig. 2 were obtained when a perturbation of 10 % was used for anthropogenic NO x emissions.Figure S6 shows the distributions of NO 2 TVCD fraction in the boundary layer at 13:00-14:00 LT and 10:00-11:00 LT and the fraction of soil NO x emissions in all surface sources (soil + anthropogenic) on weekdays for July 2011.In Fig. S7, we analyzed the contributions of background sources, chemical nonlinearity, and other factors (transport, NO 2 hydrolysis on aerosols, and dry deposition) to the nonlinear relationships (β and γ ) among anthropogenic NO x emissions, NO 2 surface concentrations, and NO 2 TVCDs.While the model simulation is for 1 summer month, several key points on the surface and column concentration sensitivities to anthropogenic NO x emissions have implications for comparing the trends of AQS and satellite TVCD data.
1.Both β and γ values are negatively correlated with anthropogenic NO x emissions due to chemical nonlinearity, transport, and background NO x contributions (Figs. 2, S6, and S7) (Gu et al., 2016;Lamsal et al., 2011).It is consistent with the distribution of β as a function of NO x emissions in China (Gu et al., 2013), although the β ratios for the US are generally larger than for China due primarily to different emission distributions of NO x and VOCs and regional circulation patterns (Zhao et al., 2009b).
2. The uncertainties of β and γ values increase significantly as anthropogenic NO x emissions decrease, which means regions with low anthropogenic NO x emissions are more sensitive to environmental conditions, such as NO x transport from nearby regions which may even produce negative β and γ values (Figs. 2 and S7).
3. The value of γ is generally less than β, especially for low anthropogenic NO x emission regions, which reflects the significant contribution of free tropospheric NO 2 to NO 2 TVCD but not to NO 2 surface concentrations (Figs. 2, S6, and S7).
4. Generally, the standard deviations of β and γ tend to be larger at 10:00-11:00 LT than at 13:00-14:00 LT, reflecting a stronger transport effect due to weaker chemical losses in the morning (Figs. 2 and S7).

Both background sources and non-emission factors con-
tribute much more to β and γ values in low anthropogenic NO x emission regions than in high anthropogenic NO x emission regions (Fig. S7).
7. Chemical nonlinearity contributes much less to β and γ values than background sources and transport effects in low anthropogenic NO x emission regions (Fig. S7).
8. Generally, non-emission factors (mainly transport) contribute more to β and γ values than background sources in low anthropogenic NO x emission regions (Fig. S7c  and d) except for the first bin where background sources contribute more to β and γ values than non-emission factors at 10:00-11:00 LT, which is partly caused by some grid cells with extremely low anthropogenic NO x emissions, increasing the mean contributions of background sources in the first bin.
trends derived from satellite TVCD data do not directly represent anthropogenic NO x emissions and that the variations in TVCD data may not be comparable to the corresponding surface NO 2 concentrations.We define a region a "urban" if anthropogenic NO x emissions from NEI2011 are > 10 11 molecules cm −2 s −1 .All the other regions are defined as "rural".Figure 3 shows the distributions of anthropogenic NO x emissions and urban and rural regions defined in this study.Such defined urban regions account for 69.8 % of the total anthropogenic NO x emissions over the CONUS, the trend of which is, therefore, representative of anthropogenic emission changes.A caveat is that some urban regions would become rural if anthropogenic NO x emissions decreased after 2011 as the EPA anthropogenic NO x emission trend suggested (Fig. S2).In a sensitivity study, we define an urban region using a stricter criterion of anthropogenic NO x emissions > 2×10 11 molecules cm −2 s −1 , and the analysis results are similar to those shown in the next section.

Trend comparisons between NO 2 AQS surface
concentrations and coincident satellite NO 2 tropospheric VCD over urban and rural regions By using anthropogenic NO x emissions of 10 11 molecules cm −2 s −1 as the threshold value, 157 AQS sites are urban, and the remaining 22 sites are rural.Their properties are summarized in Table 2. Figure 4 shows the relative annual variations in AQS NO 2 surface measurements at 13:00-14:00 LT and coincident OMI-QA4ECV NO 2 TVCD data from 2005 to 2017 in each season for urban and rural regions.The contrast between the two regions is apparent in all seasons.For comparison purposes, we scale the time series of TVCD and AQS surface NO 2 to = 0.98), reflecting the comparable and stable β and γ values (Fig. 2).However, over rural regions, the scaled TVCD data significantly deviate from AQS NO 2 data (TVCD = 1.15 × AQS + 0.09, R 2 = 0.87).It is noteworthy that the discrepancies between urban and rural data are smaller in winter than in spring, summer, and autumn due to a more dominant role of transport than chemistry and lower natural NO x emissions in winter.
We further investigate OMI-QA4ECV NO 2 TVCD relative annual variations from 2005 to 2017 over the regions with different anthropogenic NO x emissions in Fig. 5.We find clear flattening of NO 2 TVCD variations as anthropogenic NO x emissions decrease, which is consistent with the above analysis.Similar to Fig. 4, the spread of TVCD variation is much less in winter than the other seasons.The differences between Figs. 5 and 4 are due to a much larger dataset used in the former than the latter.Only coincident AQS and OMI-QA4ECV data are used in Fig. 4, but all OMI-QA4ECV data are used in Fig. 5. (Table 1).In Fig. 6, we show the comparisons among the relative variations in the updated EPA anthropogenic NO x emissions, AQS NO 2 surface measurements at 10:00-11:00 LT and 13:00-14:00 LT, and coincident satellite NO 2 TVCDs for urban regions in four seasons from 2003 to 2017.Also shown are the comparisons among the updated EPA anthropogenic NO x emissions and satellite NO 2 TVCDs.There are many more data points for the latter comparison because the data selection is no longer limited to those coincident with the AQS surface data, and therefore, the uncertainty spread is much lower.The comparisons, in general, show that the updated EPA anthropogenic NO x emissions, AQS surface measurements, and satellite TVCD data are in agreement.The agreement of decreasing trends among the datasets is just as good for the post-2011 period as the pre-2011 period.This result differs from Miyazaki et al. (2017) and Jiang et al. (2018), who suggested no significant decreasing trend for OMI TVCD data and inversed NO x emissions after 2010.The disagreement can be explained by the results of Fig. 5. Including the low anthropogenic NO x emission regions leads to underestimates of NO x decreases.Since the area of low anthropogenic NO x emission regions is larger than high anthropogenic NO x emission regions (Table 2), the arithmetic averaging will lead to a large weighting of rural observations, which do not reflect anthropogenic NO x emission changes.Miyazaki et al. (2017) and Jiang et al. (2018) included all regions in their analyses, but we exclude rural regions.Figure S9 shows the seasonal variations if the TVCDs over rural regions are included; the result shows a much lower decreasing rate of TVCDs over the CONUS.The much slower satellite TVCD trends for regions with low NO x emissions was previously discussed by Zhang et al. (2018).In addition, Miyazaki et al. (2017) and Jiang et al. (2018) conducted NO x emission inversions by using the Model for Interdisciplinary Research on Climate (MIROC)-Chem with a coarse resolution of 2.8 • × 2.8 • , which was insufficient to separate urban and rural regions and might distort predicted NO 2 TVCDs and inversed NO x emissions due to nonlinear effects (Valin et al., 2011;Yu et al., 2016), which is another possible reason for their finding of flattening NO x emission trends after 2010.

Trend analysis of AQS NO
We summarize the decreasing rates of NO 2 after the Great Recession in Table 3.To minimize the effect of the sharp decrease and the subsequent recovery, we chose to analyze the post-2011 period.Table 3 summarizes the results for each season, while Table 1 gives the averaged annual decreasing trends.Generally, Tables 1 and 3 confirm the continuous decreases in AQS surface observations, satellite NO 2 TVCD, and updated EPA anthropogenic NO x emissions after 2011 as in Fig. 6, but the decreasing rates are lower than the pre-2011 period.Over the AQS urban sites, the slowdown magnitudes are 9 % for AQS surface observations and 20 %-40 % for satellite NO 2 TVCD measurements, which may reflect in part smaller γ than β values (Table 2).Our estimated slowdown magnitudes are significantly lower than Lamsal et al. (2015) and Jiang et al. (2018) (Table 1), which might be caused by their different data processing methods, such as "E >= 64" denotes grid cells with anthropogenic NO x emissions over 64 × 10 10 molecules cm −2 s −1 ."E >= 32" denotes grid cells with anthropogenic NO x emissions equal to or larger than 32 × 10 10 molecules cm −2 s −1 but less than 64 × 10 10 molecules cm −2 s −1 ."E >= 16" and "E >= 8" have similar meanings as "E >= 32"."E < 8" denotes grid cells with anthropogenic NO x emissions less than 8 × 10 10 molecules cm −2 s −1 .Shading in a lighter color is added to show the standard deviation of the results; when uncertainty is small due in part to a large number of data points, shading may not show up.
Over the CONUS urban regions, updated EPA anthropogenic NO x emissions show a slowdown of 22 % compared to 29 %-46 % for three OMI NO 2 TVCD products.The difference is partially due to the β ratio of 2.5 ± 1.0 at 13:00-14:00 LT over the CONUS urban regions (Table 2).Satellite NO 2 TVCD measurement uncertainties also contribute to the difference.From 2013 to 2017, GOME-2B NO 2 TVCDs decrease more than OMI products, especially in spring, autumn, and winter (Tables 1 and 3).Finally, trend analyses in different regions (Fig. 7 and Table S4) indicate that generally, the Midwest has the least slowdown of the decreasing rate for urban OMI NO 2 TVCD (−14 % on average) after 2011 compared to the Northeast (−30 %), South (−34 %), and West (−28 %).
The results presented in this study are qualitatively in agreement with the work by Silvern et al. (2019).The two studies were independent.Therefore, the foci of the studies are different despite reaching similar conclusions.While we focused on understanding the detailed data analysis of Jiang et al. (2018) and limited the use of model simulation results so that our results can be compared to the previous   in simulating the trends of NO 2 TVCDs by missing natural emissions in the free troposphere.Our study, on the other hand, explored the data analysis procedure through which the trend of anthropogenic emissions can be derived from satellite observations and its limitations.

Conclusions
Using model simulations for July 2011, we demonstrate the nonlinear relationship of NO 2 surface concentration and TVCD with anthropogenic NO x emissions.Over low anthropogenic NO x emission regions, the ratios of anthropogenic NO x emission changes to the changes in surface concentrations (γ ) and TVCDs (β) have very large variations and β > γ 1.Therefore, for the same emission changes, surface concentration and TVCD changes are much smaller and more variable than urban regions, making it difficult to use the observations to directly infer anthropogenic NO x emission trends.We find that defining urban regions where anthropogenic NO x emissions are > 10 11 molecules cm −2 s −1 and using surface and TVCD observations over these regions can infer the trends that can be compared with the EPA emission trend estimates.
We evaluate the anthropogenic NO x emission variations from 2003 to 2017 over the CONUS by using satellite NO 2 TVCD products from GOME-2B, SCIAMACHY, OMI-QA4ECV, OMI-NASA, and OMI-BEHR, over the urban regions of CONUS.We find broad agreement among the decreases in AQS NO 2 surface observations, satellite NO 2 TVCD products, and the EPA anthropogenic NO x emissions with the CEMS dataset updated.After 2011, they all show a slowdown of the decreasing rates.Over the AQS urban sites, NO 2 surface concentrations have a slowdown of 9 % and OMI products show a slowdown of 20 %-40 %.Over the CONUS urban regions, OMI TVCD products indicate a slowdown of 29 %-46 %, and the updated EPA anthropogenic NO x emissions have a slowdown of 22 %.The different slowdown magnitudes between OMI TVCD products and the other two datasets may be caused by the nonlinear response of TVCD to anthropogenic emissions and the uncertainties of satellite measurements (e.g., GOME-2B TVCD data show a larger decreasing trend than OMI products from 2013 to 2017).
We did not find observation evidence supporting the notion that anthropogenic NO x emissions have not been decreasing after the Great Recession.In future studies, we recommend that the nonlinear relationships of NO x emissions with NO 2 TVCD and surface concentration be carefully evaluated when applying satellite and surface measurements to infer the changes in anthropogenic NO x emissions.
Author contributions.JL and YW designed the study.JL conducted model simulations and data analyses with discussions with YW.JL and YW wrote the paper.
Competing interests.The authors declare that they have no conflict of interest.

Figure 1 .
Figure 1.Region definitions and locations of NO 2 surface observation sites used in this study.

Figure 3 .
Figure 3. Spatial distributions of (a) anthropogenic NO x emissions (unit: 10 10 molecules cm −2 s −1 ) and (b) urban regions satisfying our selection criteria.In (b), light green and blue denote the resulting urban and rural regions, respectively.

Figure 4 .
Figure 4. Relative annual variations in AQS NO 2 surface concentrations and coincident OMI-QA4ECV NO 2 TVCD in each season from 2005 to 2017 for urban (left column) and rural (right column) regions.The observation data are scaled by the corresponding 2005 values.Black and red lines denote AQS surface observations and OMI-QA4ECV NO 2 TVCDs, respectively.Shading in a lighter color is added to show the standard deviation of the results; when uncertainty is small due in part to a large number of data points, shading may not show up.
2 surface concentrations, satellite TVCDs, and updated EPA NO x emissionsWe first updated the Continuous Emission Monitoring Systems (CEMS) measurement data used in the EPA NO x emission trend datasets with the newest datasets obtained from https://ampd.epa.gov/ampd/(last access: 17 June 2018).As shown in Fig.S2, the updated CEMS data lead to a reduction in anthropogenic NO x emissions during the GreatRecession (2008Recession ( -2009) )  and a recovery period in 2010-2011.The sharp drop during the Great Recession and the flattening trend right after the Great Recession are captured by OMI NO 2 and SCIAMACHY TVCD products(Figs.4, 6, and S9)   and AQS NO 2 surface measurements(Figs.4, 6, and S5)  and are also noted byRussell et al. (2012) andTong et al. (2015)

Figure 5 .
Figure 5. Relative annual variations in OMI-QA4ECV NO 2 TVCD for different anthropogenic NO x emission groups based on NEI2011 in each season from 2005 to 2017."E >= 64" denotes grid cells with anthropogenic NO x emissions over 64 × 10 10 molecules cm −2 s −1 ."E >= 32" denotes grid cells with anthropogenic NO x emissions equal to or larger than 32 × 10 10 molecules cm −2 s −1 but less than 64 × 10 10 molecules cm −2 s −1 ."E >= 16" and "E >= 8" have similar meanings as "E >= 32"."E < 8" denotes grid cells with anthropogenic NO x emissions less than 8 × 10 10 molecules cm −2 s −1 .Shading in a lighter color is added to show the standard deviation of the results; when uncertainty is small due in part to a large number of data points, shading may not show up.

Figure 6 .
Figure6.Relative variations in AQS NO 2 surface measurements at 13:00-14:00 LT and 10:00-11:00 LT, updated EPA anthropogenic NO x emissions, and satellite NO 2 TVCD data over the AQS urban sites (left column) and the CONUS urban regions (right column) for four seasons.AQS NO 2 surface measurements are not included in the right column.All datasets are scaled by their corresponding values in 2011 except for GOME-2B.For GOME-2B, we firstly normalized the values in each season to the corresponding 2013 values and plotted the relative changes from the 2013 EPA point of each season to make the GOME-2B relative variations comparable to the other datasets.Shading in a lighter color is added to show the standard deviation of the results; when uncertainty is small due in part to a large number of data points, shading may not show up.

Figure 7 .
Figure 7. Pre-and post-2011 OMI NO 2 TVCD trends for four seasons in the urban regions of Northeast, Midwest, South, and West.Black bars denote OMI-QA4ECV NO 2 TVCD trends from 2005 to 2011; gray bars denote the corresponding trends during 2011-2017.Blue bars denote OMI-NASA trends from 2005 to 2011; cyan bars denote OMI-NASA trends from 2011 to 2016.Red bars denote OMI-BEHR trends from 2005 to 2011; pink bars denote OMI-BEHR trends from 2011 to 2016.

Table 2 .
Properties of urban and rural regions in July 2011.

Table 3 .
Summary of national trends of updated EPA anthropogenic NO *