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., 2017, 2018; Choi et al., 2008a, b; Gu et al., 2013, 2014; Koo et al., 2012; Liu et al., 2012, 2014; Wang et al., 2007; Yang et al., 2011; Zhang et al., 2017, 2018; Zhang and Wang, 2016; Zhao and Wang, 2009; Zhao et al., 2009a, 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 km2. 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 two-thirds 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). NOx 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 NOx emissions of 7.4×1010 molecules cm-2 s-1, mean soil NOx emissions of 1.2×1010 molecules cm-2 s-1, and mean lightning NOx emissions of 3.4×1010 molecules cm-2 s-1 over the CONUS.

In this study, we use NO2 TVCD products from four satellite sensors in the past decade, including SCIAMACHY, GOME-2A, GOME-2B, and OMI – the spectrometers onboard sun-synchronous 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 km2. 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 km2. After 15 July 2013, the nadir resolution of GOME-2A became 40×40 km2 with a smaller scanning swath. The OMI onboard the EOS-Aura satellite has a nadir resolution of 24×13 km2 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 NO2 vertical column densities (VCDs). The retrieval process consists of three steps: (1) converting radiation observations to NO2 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 NO2 SCDs; (3) dividing the NO2 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 NO2 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., 2017, 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 NO2 TVCD datasets, we chose pixel-size NO2 TVCD data using the criteria listed in Table S3. After the selection, we re-gridded the pixel-size data into the REAM 36×36 km2 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 NOx emission reduction, leading to different NO2 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 NOx, 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 NO2 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.

Hourly surface NO2 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 NO2. 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 NO2 is first converted to NO and then NO is measured through chemiluminescence measurement of NO2* produced by NO + O3. The difference is that FRM uses heated catalysts for the conversion of NO2 to NO and FEM uses photolysis of NO2 to NO. The conversion to NO in the FRM instruments is not specific to NO2, and non-NOx active nitrogen compounds (NOz) can also be reduced by the catalysts, which would cause high biases of NO2 measurements, while the FEM is sensitive to the photolysis conversion efficiency of NO2 to NO (Beaver et al., 2012, 2013; Lamsal et al., 2015). The CAPS method directly determines NO2 concentrations based on an NO2-induced phase shift measured by a photodetector. The CAPS instrument operates at a wavelength of about 450 nm and may overestimate NO2 concentrations due to the absorption of other molecules at the same wavelength (Beaver et al., 2012, 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 NO2 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 NO2 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).

NO2 surface concentrations and NO2 TVCDs are not linearly correlated with NOx emissions due to chemical nonlinearity, NO2 hydrolysis on aerosols (NO2 ⟶aerosol,H2O0.5HNO3+0.5HNO2), 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 NOx emissions, NO2 surface concentrations, and TVCDs over the CONUS before we compare the trends between NO2 surface concentrations and TVCDs. The nonlinearity between NOx emission and NO2 TVCD is analyzed by examining the local sensitivity of NO2 TVCD to NOx emissions (Gu et al., 2013; Lamsal et al., 2011; Tong et al., 2015), which is defined as β in Eq. (). We further define γ as the sensitivity of NO2 surface concentration to NOx emission: 1ΔEE=βΔΩΩ, 2ΔEE=γΔcc, where E denotes NOx emission and E denotes the change in NOx emission; Ω denotes NO2 TVCD, c denotes surface NO2 concentration, and ΔΩ and Δc 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 NOx 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 NOx 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 NOx emissions.

Figure 2 shows the distributions of our β and γ ratios as a function of anthropogenic NOx 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 NOx emissions. Figure S6 shows the distributions of NO2 TVCD fraction in the boundary layer at 13:00–14:00 LT and 10:00–11:00 LT and the fraction of soil NOx 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, NO2 hydrolysis on aerosols, and dry deposition) to the nonlinear relationships (β and γ) among anthropogenic NOx emissions, NO2 surface concentrations, and NO2 TVCDs. While the model simulation is for 1 summer month, several key points on the surface and column concentration sensitivities to anthropogenic NOx emissions have implications for comparing the trends of AQS and satellite TVCD data.

Both β and γ values are negatively correlated with anthropogenic NOx emissions due to chemical nonlinearity, transport, and background NOx 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 NOx 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 NOx and VOCs and regional circulation patterns (Zhao et al., 2009b).

The largely varying β and γ values for anthropogenic NOx emissions <1011 molecules cm-2 s-1 imply that the trends derived from satellite TVCD data do not directly represent anthropogenic NOx emissions and that the variations in TVCD data may not be comparable to the corresponding surface NO2 concentrations. We define a region a “urban” if anthropogenic NOx emissions from NEI2011 are >1011 molecules cm-2 s-1. All the other regions are defined as “rural”. Figure 3 shows the distributions of anthropogenic NOx emissions and urban and rural regions defined in this study. Such defined urban regions account for 69.8 % of the total anthropogenic NOx 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 NOx emissions decreased after 2011 as the EPA anthropogenic NOx emission trend suggested (Fig. S2). In a sensitivity study, we define an urban region using a stricter criterion of anthropogenic NOx emissions >2×1011 molecules cm-2 s-1, and the analysis results are similar to those shown in the next section.

By using anthropogenic NOx emissions of 1011 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 NO2 surface measurements at 13:00–14:00 LT and coincident OMI-QA4ECV NO2 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 NO2 to their corresponding 2005 values, and the resulting data are therefore unitless. Over urban regions, NO2 surface concentrations are highly correlated with NO2 TVCDs (TVCD = 1.03 × AQS + 0.11, R2=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 NO2 data (TVCD = 1.15 × AQS + 0.09, R2=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 NOx emissions in winter.

We also examine the correlations of AQS NO2 surface concentrations with coincident OMI-NASA, OMI-BEHR, SCIAMACHY, GOME-2A, and GOME-2B TVCD measurements. The results of OMI-NASA and OMI-BEHR are similar to those of OMI-QA4ECV (Fig. 4). SCIAMACHY and GOME-2B TVCD observations at 09:00–11:00 LT also show a large contrast between urban (SCIAMACHY: TVCD = 0.92 × AQS - 0.005, R2=0.94; GOME-2B: TVCD = 0.54 × AQS + 0.56, R2=0.96) and rural regions (SCIAMACHY: TVCD = 0.77 × AQS + 0.83, R2=0.63; GOME-2B: TVCD = 0.46 × AQS + 0.73, R2=0.59). The correlation of coincident GOME-2A NO2 TVCD data with AQS surface concentrations is poor for rural (TVCD = 0.65 × AQS + 0.56, R2=0.44) and urban (TVCD = 0.31 × AQS + 0.56, R2=0.21) regions (Fig. S8), which likely reflects the degradation of the GOME-2A instrument causing a significant increase in NO2 SCD uncertainties (Boersma et al., 2018). Therefore, we excluded GOME-2A in the analysis hereafter.

We further investigate OMI-QA4ECV NO2 TVCD relative annual variations from 2005 to 2017 over the regions with different anthropogenic NOx emissions in Fig. 5. We find clear flattening of NO2 TVCD variations as anthropogenic NOx 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.

We first updated the Continuous Emission Monitoring Systems (CEMS) measurement data used in the EPA NOx 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 NOx emissions during the Great Recession (2008–2009) 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 NO2 and SCIAMACHY TVCD products (Figs. 4, 6, and S9) and AQS NO2 surface measurements (Figs. 4, 6, and S5) and are also noted by Russell et al. (2012) and Tong et al. (2015) (Table 1).

In Fig. 6, we show the comparisons among the relative variations in the updated EPA anthropogenic NOx emissions, AQS NO2 surface measurements at 10:00–11:00 LT and 13:00–14:00 LT, and coincident satellite NO2 TVCDs for urban regions in four seasons from 2003 to 2017. Also shown are the comparisons among the updated EPA anthropogenic NOx emissions and satellite NO2 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 NOx 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 NOx emissions after 2010. The disagreement can be explained by the results of Fig. 5. Including the low anthropogenic NOx emission regions leads to underestimates of NOx decreases. Since the area of low anthropogenic NOx emission regions is larger than high anthropogenic NOx emission regions (Table 2), the arithmetic averaging will lead to a large weighting of rural observations, which do not reflect anthropogenic NOx 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 NOx emissions was previously discussed by Zhang et al. (2018). In addition, Miyazaki et al. (2017) and Jiang et al. (2018) conducted NOx 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 NO2 TVCDs and inversed NOx emissions due to nonlinear effects (Valin et al., 2011; Yu et al., 2016), which is another possible reason for their finding of flattening NOx emission trends after 2010.

We summarize the decreasing rates of NO2 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 NO2 TVCD, and updated EPA anthropogenic NOx 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 NO2 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 including AQS sites with incomplete measurement records (Silvern et al., 2019).

Over the CONUS urban regions, updated EPA anthropogenic NOx emissions show a slowdown of 22 % compared to 29 %–46 % for three OMI NO2 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 NO2 TVCD measurement uncertainties also contribute to the difference. From 2013 to 2017, GOME-2B NO2 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 NO2 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 study directly, Silvern et al. (2019) relied more on multiyear model simulations. As a result, Silvern et al. (2019) can clearly identify the contributions of the NO2 columns by natural emissions and make use of additional observations such as nitrate deposition fluxes. They also identified model biases in simulating the trends of NO2 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.