Using satellite observations of tropospheric NO 2 columns to infer long-term trends in US NOx emissions : the importance of accounting for the free tropospheric NO 2 background

The National Emission Inventory (NEI) of the US Environmental Protection Agency (EPA) reports a steady decrease of US NOx emissions over the 2005-2017 period at a rate of 0.1 Mt a (53% decrease over the period), reflecting sustained efforts to improve air quality. Tropospheric NO2 columns observed by the satellite-based Ozone Monitoring Instrument (OMI) over the US show a steady decrease 25 until 2009 but a flattening afterward, which has been attributed to a flattening of NOx emissions in contradiction with the NEI. We show here that the steady 2005-2017 decrease of NOx emissions reported by the NEI is in fact consistent with observed network trends of surface NO2 and ozone concentrations. The OMI NO2 trend is instead similar to that observed for nitrate wet deposition fluxes, where post-2009 flattening is due to an increasing relative contribution of non-anthropogenic background (mainly lightning 30 and soils) and not to a flattening of anthropogenic emissions. This is confirmed by contrasting OMI NO2 trends in urban winter, where the background is low and OMI NO2 shows a steady 2005-2017 decrease consistent with the NEI, and rural summer, where the background is high and OMI NO2 shows no significant 2005-2017 trend. A GEOS-Chem model simulation driven by NEI emission trends for the 20052017 period reproduces these different trends except for the post-2009 flattening of OMI NO2, which we 35 attribute to a model underestimate of free tropospheric NO2. Better understanding is needed of the factors controlling free tropospheric NO2 in order to relate satellite observations of tropospheric NO2 columns to the underlying NOx emissions and their trends. Focusing on urban winter conditions in the satellite data minimizes the effect of this free tropospheric background. Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2019-168 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 25 February 2019 c © Author(s) 2019. CC BY 4.0 License.

Abstract. The National Emission Inventory (NEI) of the US Environmental Protection Agency (EPA) reports a steady decrease in US NO x emissions over the 2005-2017 period at a rate of 0.1 Tg N a −1 (53 % decrease over the period), reflecting sustained efforts to improve air quality. Tropospheric NO 2 columns observed by the satellite-based Ozone Monitoring Instrument (OMI) over the US show a steady decrease until 2009 but a flattening afterward, which has been attributed to a flattening of NO x emissions, contradicting the NEI. We show here that the steady 2005-2017 decrease in NO x emissions reported by the NEI is in fact largely consistent with observed network trends of surface NO 2 and ozone concentrations. The OMI NO 2 trend is instead similar to that observed for nitrate wet deposition fluxes, which is weaker than that for anthropogenic NO x emissions, due to a large and increasing relative contribution of non-anthropogenic background sources of NO x (mainly lightning and soils). This is confirmed by contrasting OMI NO 2 trends in urban winter, where the background is low and OMI NO 2 shows a 2005-2017 decrease consistent with the NEI, and rural sum-mer, where the background is high and OMI NO 2 shows no significant 2005-2017 trend. A GEOS-Chem model simulation driven by NEI emission trends for the 2005-2017 period reproduces these different trends, except for the post-2009 flattening of OMI NO 2 , which we attribute to a model underestimate of free tropospheric NO 2 . Better understanding is needed of the factors controlling free tropospheric NO 2 in order to relate satellite observations of tropospheric NO 2 columns to the underlying NO x emissions and their trends. Focusing on urban winter conditions in the satellite data minimizes the effect of this free tropospheric background. 8864 R. F. Silvern et al.: Using satellite observations of tropospheric NO 2 columns to infer long-term trends 2000s, the US Environmental Protection Agency (EPA) implemented increasingly stringent NO x emission controls targeted principally at improving ozone air quality. The EPA National Emission Inventory (NEI) reports a steady decrease in US NO x emissions over the 2005-2017 period at a rate of 0.10 Tg N a −1 or 53 % overall (EPA, 2018). However, Jiang et al. (2018) showed that tropospheric NO 2 columns observed by the OMI satellite instrument over the US stopped decreasing after 2009, and they concluded that NO x emissions have been decreasing much less than reported by the NEI. Here we show that the flattening of the OMI NO 2 trend is in fact not inconsistent with the sustained decrease in NO x emissions reported by the NEI and that the NEI emission trend is consistent with other atmospheric observations of NO x and ozone trends. Our results demonstrate the importance of accounting for the free tropospheric NO 2 background when using satellite observations of NO 2 columns to infer NO x emissions and their trends.
The Ozone Monitoring Instrument (OMI) aboard the US National Aeronautics and Space Administration (NASA) Aura satellite has been making continuous daily global observations of NO 2 since late 2004 (Levelt et al., 2006(Levelt et al., , 2018. The NO 2 retrieval (Boersma et al., 2011;Bucsela et al., 2013) involves spectral fitting of measured nadir solar backscatter at 400-500 nm, yielding "slant" NO 2 columns along the line of sight from which the contribution from the stratosphere is removed (Martin et al., 2002;Richter and Burrows, 2002;Bucsela et al., 2013). The slant tropospheric columns are then converted to actual tropospheric NO 2 columns by accounting for surface and atmospheric scattering, and assuming a vertical distribution of NO 2 within the column ("shape factor"). In polluted regions with high NO x emissions, most of the information in the NO 2 tropospheric column is presumed to originate from the boundary layer. Thus, the column is commonly viewed as a proxy for NO x emissions.
Satellite observations of tropospheric NO 2 columns have been used extensively to infer NO x emissions and their trends (Leue et al., 2001;Martin et al., 2003;Richter et al., 2005;Boersma et al., 2008). OMI NO 2 observations from the early part of the record showed decreasing trends over the US consistent with the decreases in NO x emissions reported by the NEI Duncan et al., 2013Duncan et al., , 2016Krotkov et al., 2016) and also consistent with trends in NO 2 concentrations observed from surface networks (Kharol et al., 2015;Lamsal et al., 2015;Lu et al., 2015;Tong et al., 2015;Zhang et al., 2018). Several studies reported a steepening of the OMI NO 2 decrease during the Great Recession of 2007-2009 and a subsequent flattening attributed to economic recovery Tong et al., 2015;de Foy et al., 2016). However, the analysis of the 2005-2015 record by Jiang et al. (2018) shows that the post-2009 flattening of the NO 2 trend extends well beyond the initial economic recovery period.
The NEI is a "bottom-up" national inventory compiled by the EPA every 3 years using continuous emission monitoring systems (CEMS) for large point sources, and estimates derived from activity data and emission factors (NO x emitted per unit of activity) for smaller and distributed sources. Emissions in 2017 estimated by EPA (2018) included 35 % from on-road mobile sources, 25 % from off-road mobile sources, 12 % from industrial point sources, and 27 % from electricity generating units (EGUs). Mobile emissions are estimated with the Motor Vehicle Emission Simulator (MOVES) model using vehicle population, vehicle miles traveled (VMT), and operating modes as inputs. Long-term trends in NO x emissions are recomputed with each new NEI release using updated emission models so that national trends are selfconsistent for a given NEI version.
Many recent studies using near-source, urban, and regional observations of atmospheric NO x have found that the NEI greatly overestimates US NO x emissions (Castellanos et al., 2011;Brioude et al., 2013;Anderson et al., 2014;Goldberg et al., 2016;Souri et al., 2016;Travis et al., 2016). CEMS measurements of point sources are considered reliable but tunnel and roadside measurements show that the MOVES inventory for mobile sources may be too high (Fujita et al., 2012). Fuel-based approaches for estimating emissions from mobile sources appear to be more reliable than the MOVES VMT approach (Dallmann and Harley, 2010;McDonald et al., 2012;Kim et al., 2016). McDonald et al. (2018) showed that on-road gasoline NO x emission factors used by NEI are a factor of 2 too high compared to roadside observations and their fuel-based inventory. All these studies were conducted under summertime or warm conditions. By contrast, atmospheric observations of NO x and related species during the WINTER campaign over the northeastern US during February-March 2015 showed good agreement with the NEI Salmon et al., 2018).
The uncertainty regarding NEI NO x emissions suggests that the trend in these emissions could be uncertain as well. However, a flattening out of US NO x emissions over the past decade, as inferred by Jiang et al. (2018) from the OMI data, would be difficult to reconcile with observations of steady improvement in ozone air quality (Astitha et al., 2017;Chang et al., 2017), which has been attributed specifically to NO x emission controls (Hidy and Blanchard, 2015;Simon et al., 2015;Strode et al., 2015;Xing et al., 2015;Blanchard and Hidy, 2018;Li et al., 2018). Here we conduct a more comprehensive analysis of 2005-2017 trends in US NO x emissions by using the GEOS-Chem chemical transport model  to concurrently interpret the trends observed in OMI NO 2 columns, nitrogen wet deposition fluxes, and surface observations of NO 2 and ozone.
2 The 2005-2017 trends of OMI tropospheric NO 2 columns Figure 1 shows the 2005-2017 trends of OMI tropospheric NO 2 columns averaged spatially and annually over the con-tiguous US. The observations are from the NASA operational retrieval (level 2, version 3.0; Krotkov et al., 2017) after removing cloudy scenes (cloud radiance fraction > 0.5), bright surfaces (surface reflectivity > 0.3), and observations affected by the so-called row anomaly . OMI is in a sun-synchronous orbit with overpass at 13:30 LT. It measures backscattered solar radiation in the nadir and off-track, with 13 × 24 km 2 nadir pixel resolution and global daily coverage. The retrieval fits the backscattered radiance spectrum to obtain the total slant NO 2 column along the line of sight from the Sun to the satellite. The stratospheric contribution to the total slant column is estimated using OMI observations over clean background and cloudy areas and applying an interpolating-filtering-smoothing algorithm (Bucsela et al., 2013). The remaining tropospheric slant column is then converted to a vertical column with an air mass factor (AMF; Palmer et al., 2001) that convolves the altitudedependent sensitivity from atmospheric scattering (scattering weights) with the local relative vertical distribution of NO 2 from the Global Modeling Initiative (GMI) model (shape factor). Over continental source regions, the AMF dominates the overall retrieval error due to uncertainties in a priori NO 2 profiles, surface albedo, and aerosol and cloud parameters Boersma et al., 2011;Lamsal et al., 2014;Lorente et al., 2017). We recomputed the AMFs using GEOS-Chem rather than GMI shape factors and found little difference in the mean (Fig. 1). The OMI data show an evident flattening of NO 2 columns after 2009, as pointed out by Jiang et al. (2018), who also find the same flattening in alternative OMI NO 2 retrievals produced by KNMI (Boersma et al., 2011) and UC Berkeley . NO 2 tropospheric columns decrease at a mean rate of 6 ± 0.5 % a −1 over the 2005-2009 period but then do not change significantly post-2009. We find that data for the western, central, northeastern, and southeastern US all show similar trends. Hence, we focus our analysis on the mean trends over the contiguous US, following Jiang et al. (2018).
Also shown in Fig. 1 are trends from a 13-year simulation (2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017) with the GEOS-Chem global chemical transport model at 0.5 • × 0.625 • nested horizontal resolution over North America. The model is driven by NEI NO x emissions for fuel combustion, decreased by 60 % for non-EGU sources following Travis et al. (2016). It also includes NO x emissions from background (nonfuel combustion) sources, including open fires (Darmenov and da Silva, 2013), lightning (Murray et al., 2012), and soil and fertilizer . Further details on the model are in the Appendix. The model NO 2 column averages 28 % lower than observed, due to both an underestimate in background NO 2 , discussed below, and because the Travis et al. (2016) correction to the NEI is excessive, which we will address in a separate paper. More to the point here, the model shows a sustained decrease, averaging 3.3 ± 0.1 % a −1 over the 2005-2017 period, at odds with the OMI observations, though lower than the NEI reported decrease of 5.9 % a −1 over the same period. Here and throughout this paper we derive linear trends by ordinary regression and express them in units of percent per annum (% a −1 ) relative to the mean over the data period, following Jiang et al. (2018). We compute uncertainty using the bootstrapping method as the error standard deviation of the linear trend.
The weaker relative trend in the model compared to the NEI is because of the contribution from background NO x sources. Figure 1c shows the annual total US NO x emissions for 2005-2017 in the GEOS-Chem simulation. Anthropogenic emissions from fuel combustion decrease at a rate of 5.9 % a −1 , following the NEI trend. But these emissions account for only 61 % of total US emissions in 2005 and 42 % in 2017. Natural emissions from lightning and soils play a relatively increasing role as anthropogenic emissions decrease. They have interannual variability but no significant 2005-2017 trend. The trend of total US NO x emissions for 2005-2017 in GEOS-Chem is −3.5 % a −1 , closely matching the simulated NO 2 column trend.
Trends in the NO x chemical lifetime over the 2005-2017 period would affect the relationship between trends in NO x emissions and atmospheric NO 2 . Many factors could contribute to a trend in NO x lifetime (Laughner, 2018;. We find in GEOS-Chem that the daily tropospheric NO 2 column lifetime over the contiguous US is 8.1 h in 2005 (annual mean) and 7.7 h in 2017. In the model at least, the trend in NO x lifetime is much weaker than the trend in emissions, so that the trend in concentrations mainly follows that of emissions.

The 2005-2017 trends of surface observations
Long-term records of surface NO 2 concentrations over the US are available at a large number of monitoring sites from the US EPA Air Quality System (AQS) (https://www.epa.gov/aqs, last access: 4 September 2018; Demerjian, 2000) and at additional sites in the southeast from the Southeastern Aerosol Research and Characterization Study (SEARCH) network (https://www.dropbox.com/sh/o9hxoa4wlo97zpe/ AACbm6LetQowrpUgX4vUxnoDa?dl=0, last access: 27 July 2018; Hansen et al., 2003;Edgerton et al., 2006). AQS sites are mainly urban and measure NO 2 with a chemiluminescence analyzer equipped with a molybdenum converter, known to have positive interferences from NO x oxidation products including peroxyacetyl nitrate (PAN) and nitric acid (HNO 3 ; Dunlea et al., 2007;Steinbacher et al., 2007;Reed et al., 2016). SEARCH sites are both urban and rural and use a more specific photolytic converter instrument in which broadband photolysis of NO 2 is followed by chemiluminescence detection of the NO product with accuracy better than 10 % (Ryerson et al., 2000;Pollack et al., 2010).  . Also shown for the AQS sites are the values corrected for interferences based on local GEOS-Chem monthly mean NO 2 , alkyl nitrate, PAN, and HNO 3 concentrations and following the correction factor in Lamsal et al. (2008). The AQS data show decreasing trends throughout the 2005-2017 period, generally consistent with the NEI. The rural SEARCH sites also show a steady decrease but are more noisy (only two sites). One would expect the trend in the urban AQS data to be most indicative of the trend in anthropogenic NO x emissions from fuel combustion. GEOS-Chem underestimates the AQS observations because of the urban nature of the sites, but the model relative decreases agree closely with observations for both the AQS and the SEARCH data. This is in sharp contrast to the OMI NO 2 data. Jiang et al. (2018) reported AQS surface NO 2 trends of −6.6 ± 1.4 % a −1 for 2005-2009 and −2.6 ± 1.5 % a −1 for 2011-2015, indicating a significant weakening of the trend with time. But they used all AQS sites in that analysis including those with incomplete records. We find that when using only sites with continuous records, the slope is steeper for the latter time period. Specifically, we find the AQS trend to be −6.6 ± 1.2 % a −1 for 2005-2009 and −4.5 ± 1.7 % a −1 for 2011-2015. In comparison, the NEI emission trend is −6.4 % a −1 for 2005-2009 and −5.3 % a −1 for 2011-2015. Thus, the surface data suggest a slight weakening of the NO x emission trend relative to the NEI but not the flattening implied by the OMI data. Jiang et al. (2018) presented an alternative fuel-based NO x emission inventory to the NEI, featuring a slowdown in the trend of US NO x emissions after 2009 due to a slower rate of reduction for industrial, off-road mobile, and on-road diesel sources as well as a smaller relative contribution of on-road gasoline. That inventory shows a −2.9 % a −1 trend for 2011-2015. The AQS trend is in somewhat better agreement with the NEI inventory but could accommodate either inventory within its error standard deviation.
Figure 2e-f show observed and simulated trends in nitrate (NO − 3 ) wet deposition fluxes for the 138 National Acid Deposition Program (NADP; https://nadp.slh.wisc.edu/data/ NTN/, last access: 14 August 2018) sites with continuous yearlong records for 2005-2017. Nitric acid gas and nitrate aerosol are both efficiently scavenged by precipitation and the lifetime of NO x is sufficiently short that nitrate wet deposition fluxes should relate to total NO x emissions. The relationship is not one-to-one because of competition from dry deposition but one would not expect a long-term trend in the wet/dry deposition ratio. GEOS-Chem model values for individual years are corrected for precipitation bias using the high-resolution PRISM precipitation data (http://prism.oregonstate.edu, last access: 14 August 2018; Di Luzio et al., 2008), as described by  and Travis et al. (2016). Model values average 17 % lower than observed values, again because the model may underestimate emissions, but the trends are consistent. The fluxes show a decrease over the 2005-2017 time period (averaging 2.7 ± 0.3 % a −1 observed, 2.9 ± 0.3 % a −1 modeled), weaker than for surface NO 2 concentrations. After 2012, there is still a significant decrease in nitrate wet deposition, though it is less than during the earlier time period (averaging 1.3 ± 0.9 % a −1 observed and 1.7 ± 0.7 % a −1 modeled).
Nitrate wet deposition is more sensitive to background (nonfuel combustion) influences than NO 2 concentrations because (1) the wet deposition sites are prevailingly rural and (2) precipitation scavenges a deeper column. Indeed, in GEOS-Chem, the mean nitrate wet deposition trend is more consistent with the −3.5 % a −1 trend of total NO x emissions (including lightning and soils) than that of emissions from fuel combustion (−5.9% a −1 ). The relative contribution from background sources to nitrate wet deposition would be expected to increase over time as fuel combustion emissions decrease. In order to quantify this, we performed GEOS-Chem sensitivity simulations for 2005 and 2017 with only background NO x emissions (shutting off NO x emissions from US fuel combustion). We find that background contributed 50 % of nitrate wet deposition at NADP sites in 2005 but 69 % in 2017. In contrast, background only contributed 5 % to surface NO 2 at AQS sites in 2005 and 10 % in 2017. Figure 3 shows summertime ozone trends for 2005-2017 as further evidence of a sustained decrease in anthropogenic NO x emissions. Data are from the AQS and Clean Air Status and Trends Network (CASTNET; https://www.epa. gov/castnet, last access: 27 July 2018) networks. We show records for the 47 CASTNET and 427 AQS sites with continuous summertime records for 2005-2017. The trends are for the 95th percentiles in the maximum daily 8 h average (MDA8) values determined at individual sites and then averaged across all sites for each summer. We excluded highelevation (> 1.5 km) CASTNET sites in the western US because they have different trends driven in part by the larger influence from background ozone (Cooper et al., 2011;Lin et al., 2017;Jaffe et al., 2018). Much of the interannual variability in ozone concentrations in Fig. 3 can be explained by surface temperatures, including the 2012 peak in ozone in the observations and captured by GEOS-Chem, which is due to anomalously high temperatures (Fiore et al., 2015;Jia et al., 2016;Lin et al., 2017)   decline of emissions over the 2005-2017 time period. This behavior is well captured by GEOS-Chem, which confirms the 1 : 1 relationship expected between surface NO 2 concentrations and NO x emissions. Nitrate wet deposition observations show a much weaker trend, which we attributed in Sect. 3 to a larger contribution of the background. The GEOS-Chem trend for nitrate wet deposition and tropospheric NO 2 columns is similarly weaker than for surface NO 2 , reflecting the influence of the background, but shows a steeper decrease than observed after 2009. This suggests that GEOS-Chem may underestimate the background contribution.
Satellite-based tropospheric NO 2 columns show trends remarkably similar to those of nitrate wet deposition fluxes, both in the OMI observations and in GEOS-Chem, suggesting that the post-2009 flattening of the OMI trend is due to a large and increasing relative influence of the background rather than to a leveling of US NO x emissions.

Background contribution to OMI NO 2 trends
We showed in Sect. 4 that the 2005-2017 trend of OMI NO 2 columns over the US is similar to that of nitrate wet deposition and much weaker than that of surface NO 2 concentrations, pointing to the importance of background in affecting the NO 2 column. To further examine this effect, we segregated the OMI observations into winter and summer as well as urban and rural. Urban conditions are defined as the top 10 % NO x -emitting 0.5 • × 0.625 • grid squares in the US according to the NEI. We expect background influences to be relatively higher at rural than urban sites, and higher in summer (lightning, soil, intercontinental transport;Fischer et al., 2014) than in winter. Thus, background influences should be at a minimum in winter urban conditions and a maximum under summer rural conditions. Figure 5 shows the results. OMI NO 2 observations in urban winter show a steady decline at a mean rate of 3.3 ± 0.5 % a −1 , with no post-2009 flattening, though there is some suggestion of a slightly weaker trend after 2009 when compared to GEOS-Chem driven by NEI. By contrast, the OMI NO 2 observations in rural summer show no significant trend over the 2005-2017 period. GEOS-Chem for rural summer shows a significant decreasing trend for 2005-2017 but weaker than for urban winter and become insignificant for the 2009-2017 period. The winter rural and summer urban conditions in Fig. 5 show trends that are intermediate between these two limiting cases. The ability of GEOS-Chem to capture the observed post-2009 weakening of the trend in the summer urban case argues against a seasonal flattening of emissions that would affect summer but not winter.
It thus appears that the post-2009 flattening of the OMI NO 2 trend over the US is due to increasing relative importance of the NO 2 background, rather than to flattening of US NO x emissions. Satellite observations of tropospheric NO 2 columns are more sensitive to the free troposphere than to the boundary layer because of atmospheric scattering; the sensitivity increases by a factor of 3 from the surface to the upper troposphere for clear sky and by much more for a cloudy atmosphere (Martin et al., 2002). For the OMI NO 2 data set used here, the sensitivity increases by over a factor of 4 from the surface to the upper troposphere on average, as given by the scattering weights . The AMF is intended to correct for this effect but relies on an assumed model vertical distribution of NO 2 that may not correctly account for free tropospheric levels or for the changing ratio between the free troposphere and the boundary layer as anthropogenic NO x emissions decrease. There is indeed evidence that free tropospheric NO 2 makes a large contribution to OMI NO 2 columns and that models underestimate this contribution. Measurements of NO 2 vertical profiles during the SEAC 4 RS aircraft campaign over the southeastern US in August-September 2013 showed a median concentration of 300 ppt near the surface, dropping to a 50 ppt background in the free troposphere at 2-10 km, and rising back to 130 ppt at the 12 km aircraft ceiling (Silvern et al., 2018). By applying OMI scattering weights to this median vertical profile, most representative of a rural profile, Travis et al. (2016) found that the boundary layer below 1.5 km contributed only 19 %-28 % of the OMI NO 2 tropospheric column. A GEOS-Chem simulation of the SEAC 4 RS conditions matched the observed 50 ppt background (mostly from lightning) but could not reproduce the enhancement above 10 km Silvern et al., 2018). The GMI model used to compute AMFs in the NASA OMI NO 2 retrievals also has little NO 2 in the upper troposphere (Lamsal et al., 2014). Measurements of NO 2 in the upper troposphere are prone to positive interferences because of inlet decomposition of labile reservoirs (Reed et al., 2016), but the measurements in SEAC 4 RS were designed to minimize and correct for these interferences (Thornton et al., 2000;Day et al., 2002;Wooldridge et al., 2010;Nault et al., 2015). Silvern et al. (2018) suggested that errors in the kinetics of NO-NO 2 -O 3 cycling reactions could explain model underestimates of NO 2 concentrations in the upper troposphere. Choi et al. (2014) and Belmonte Rivas et al. (2015) used the so-called cloud-slicing method to isolate the upper tropospheric contribution to the OMI NO 2 observations by comparing neighboring cloudy scenes with cloud tops at different altitudes. They report in this manner partial NO 2 columns at 6-10 km altitude. Marais et al. (2018) evaluated these data in comparison with aircraft observations and found large uncertainties but concluded that GEOS-Chem underestimates NO 2 at 6-10 km over North America by 20-30 ppt in winter with no significant bias in summer. The good agreement in summer is consistent with the comparison to SEAC 4 RS observations, which shows, however, a low model bias above 10 km.
We conducted a sensitivity test, adding 50 ppt of background NO 2 to the GEOS-Chem vertical profiles above 5 km altitude in winter and above 10 km in summer, up to the local tropopause. The resulting normalized vertical profiles (shape factors) were convolved with the vertical distribution of sensitivities (scattering weights) provided by the NASA retrieval to recompute the AMFs. The implications for the model trends are shown in Fig. 5 as the blue lines. The effect is large for winter rural conditions, where the added free tropospheric background is particularly important and largely reconciles the model trend with the OMI observations. It is much less in summer, where the addition is only above 10 km and there is already substantial background NO 2 present. The discrepancy between the model and the observations in summer is largely driven by the uptick in the summer rural observations for 2016-2017.
It is possible that additional background NO 2 missing from the model in summer could be present in the tropopause region and lower stratosphere. The deepest convection in summertime over the US can reach 17 km in the lowermost stratosphere (Randel et al., 2012;Huntrieser et al., 2016b;Anderson et al., 2017;Herman et al., 2017;. Such a deep convective injection could conceivably deliver substantial lightning NO 2 above the tropopause. Although delivered above the tropopause, this NO 2 would be counted as tropospheric in retrievals because it would represent an enhancement above background NO 2 columns in the stratospheric separation. It could have a particularly important effect on the AMF by being delivered above clouds. High NO x mixing ratios in the lowermost stratosphere were observed over the central and southeastern US during the DC3 aircraft campaign in May-June 2012 and were attributed to lightning (Huntrieser et al., 2016a, b), and higher lightning flash rates have been observed in tropopause-penetrating above-anvil cirrus plumes (Bedka et al., 2018). There is suggestive evidence that convective injection into the lowermost stratosphere over the US may have increased during the 2004-2013 period (Cooney et al., 2018), which could further affect the OMI NO 2 column trend, although the Lightning Imaging Sensor (LIS) satellite data do not show a 2003-2012 trend in total lightning over the US (Koshak et al., 2015). While tropopause heights in the GEOS MERRA-2 meteorological data driving GEOS-Chem agree well with SEAC 4 RS observations of water vapor and ozone (Kuang et al., 2017;, models in general do not properly capture the observed convective injections into the lowermost stratosphere Anderson et al., 2019). The 0.5 • × 0.625 • resolution of the MERRA-2 meteorological data would be too coarse to resolve convective overshoots.

Conclusions
US emissions of nitrogen oxides (NO x ≡ NO + NO 2 ) from fuel combustion steadily declined over 2005-2017 at a mean rate of 5.9 % a −1 according to the National Emission Inventory (NEI) of the US EPA. Tropospheric NO 2 columns over the US observed by OMI aboard the Aura satellite instead show a leveling off after 2009, leading to the suggestion that the NEI emission trend is in error and that related air quality gains have halted. Here we re-examined this issue by using trends in surface observations together with a 2005-2017 GEOS-Chem chemical transport model simulation to better understand the relationship between satellite NO 2 observations, NO x emissions, and their trends.
We started by comparing the 2005-2017 GEOS-Chem simulation driven by NEI emission trends to the OMI ob-servations. The model shows a sustained decrease in the tropospheric NO 2 column at a mean rate of 3.3±0.1 % a −1 over the period. The rate is less than the NEI trend because of natural NO x emissions (mainly from lightning and soils) that account in GEOS-Chem for 58 % of total NO x emissions over the US by 2017. Nevertheless, the GEOS-Chem simulation cannot capture the post-2009 flattening in the OMI observations.
We then examined 2005-2017 US trends in surface observations of NO 2 concentrations and nitrate wet deposition fluxes from surface networks (AQS, SEARCH, NADP). Surface NO 2 concentrations measured by the AQS (urban) and SEARCH (rural) surface networks show a decline over the 2005-2017 time period that closely follows the NEI emissions trend, and the same is found in GEOS-Chem. Some deviation between AQS NO 2 and the NEI towards the later part of the time period suggests that the rate of decrease in emissions may have slowed slightly. Nitrate wet deposition shows a much weaker 2005-2017 trend than surface NO 2 and NEI emissions, both in the observations and the model, reflecting a large and increasing relative contribution from background sources (69 % in the model in 2017) as anthropogenic emissions decrease. Surface ozone concentrations from the CASTNET and AQS networks show sustained 2005-2017 decreases, consistent with the model; such sustained decreases would be hard to reconcile with a flattening of NO x emissions.
Bringing together these observed trends, we see two different patterns: (1) a 2005-2017 decrease in surface NO 2 that supports the steady decrease in NO x emissions reported by the EPA NEI and (2) a weaker trend and post-2009 flattening of OMI NO 2 and nitrate wet deposition that reflects a growing influence from the background, rather than large error in NEI NO x emissions.
We confirmed the importance of background NO 2 in driving the post-2009 flattening of OMI NO 2 trends over the US by segregating the OMI observations into urban and rural as well as winter and summer. There is a steady 2005-2017 decrease in the urban winter data where background influence is lowest. By contrast, there is no significant 2005-2017 trend in rural summer (where background influence is highest). The failure of GEOS-Chem to reproduce the observed post-2009 flattening then points to a model underestimate of the NO 2 background. Cloud-sliced OMI NO 2 data indicate a GEOS-Chem underestimate of the upper tropospheric background in winter. Deep convective injections of lightning NO x above the tropopause might add to the NO 2 background in summer. Observations from the NASA SEAC 4 RS aircraft campaign show lower NO / NO 2 ratios than simulated by GEOS-Chem, which could reflect errors in the kinetics of NO-NO 2 -O 3 chemical cycling (Silvern et al., 2018). While such errors would be most important in summertime, chemistry important for wintertime NO x not being comprehensively included in models may help to explain the winter background NO 2 underestimate. Observa-tions of short-chained alkyl nitrates show higher concentrations in the northern extratropical free troposphere in winter than captured by GEOS-Chem and may represent an increasing reservoir of background NO x (Fisher et al., 2018). Measurements from the WINTER campaign suggest models may also overestimate NO x loss via N 2 O 5 hydrolysis Kenagy et al., 2018;McDuffie et al., 2018), and recent laboratory data suggest that models using the recommended NASA-JPL kinetics for the NO 2 + OH reaction may overestimate NO x loss at cold temperatures (Amedro et al., 2019).
We conclude that the sustained 2005-2017 decrease in US NO x emissions reported by the EPA is supported by observations and that better understanding of the free tropospheric background is needed to interpret satellite observations of NO 2 tropospheric columns in terms of their implications for NO x emissions and their trends. The concern is minor in highly polluted areas where NO x emissions are sufficiently high to dominate over the background influence. In the US, however, NO x emissions have now decreased to the point that NO 2 columns over nonurban areas are mostly contributed by the free tropospheric background. Accounting for this poorly understood background will become increasingly important as NO x emissions continue to decrease in the developed world and in tropical regions that are undergoing rapid development but have a deep troposphere and intense lightning. We conducted a 13-year simulation (2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017) with the GEOS-Chem global 3-D chemical transport model version 11-02c (http://www.geos-chem.org, last access: 14 August 2018) using NASA MERRA-2 assimilated meteorological data (Gelaro et al., 2017). We use the nested North American version of GEOS-Chem at the native MERRA-2 0.5 • × 0.625 • horizontal resolution over North America and adjacent oceans (10-70 • N, 140-40 • W) with dynamic boundary conditions from a global simulation with 4 • × 5 • horizontal resolution. The simulation includes detailed NO xhydrocarbon-aerosol chemistry as described in  and Marais et al. (2016). US anthropogenic emissions are distributed spatially following the NEI2011 inventory (EPA, 2018). NEI2011 is scaled for individual years using national annual totals (EPA, 2018), and we decrease non-EGU NO x emissions by 60 %, as in Travis et al. (2016), for all years. Open fire emissions are from the daily Quick Fire Emissions Database (QFED; Darmenov and da Silva, 2013) with diurnal variability from the Western Regional Air Partnership (Air Sciences, 2005). Soil NO x emissions, including emissions from fertilizer application, are computed according to Hudman et al. (2012), with a 50 % reduction in the midwestern US for summertime based on a previous comparison with OMI NO 2 observations (Vinken et al., 2014). Lightning NO x emissions are described by Murray et al. (2012) with a horizontal distribution matching climatological observations of lightning flashes, interannual variability driven by MERRA-2 convection, and most of the release at the top of convective updrafts (Ott et al., 2010). The NO x yield per flash is 260 mol to the south of 35 • N and 500 mol to the north (Hudman et al., 2007;Huntrieser et al., 2008Huntrieser et al., , 2009Ott et al., 2010;Travis et al., 2016).
The GEOS-Chem simulation of NO x and related species over the US has been evaluated in a number of recent papers including Zhang et al. (2012), Ellis et al. (2013), and Lee et al. (2016) for nitrogen deposition; Travis et al. (2016) for NO x concentrations over the southeastern US during the SEAC 4 RS campaign; Fisher et al. (2016) for organic nitrates during that same campaign; Jaeglé et al. (2018) for the WIN-TER campaign;and Fischer et al. (2014) for the ensemble of PAN observations. These evaluations find that the model is overall successful with no indication of systematic bias.
Author contributions. DJJ, LJM, and RFS designed the study. RFS and MPS conducted model simulations. RFS analyzed satellite, surface, and model data. KRT contributed NEI emissions in GEOS-Chem and supported data analysis. LJM, EAM, RCC, and JLL helped with scientific interpretation and discussion. SC, JJ, and LNL provided OMI data and supporting guidance. RFS and DJJ wrote the manuscript and all authors provided input on the paper for revision before submission.
Competing interests. The authors declare that they have no conflict of interest.
Disclaimer. This study's contents are solely the responsibility of the grantee and do not necessarily represent the official views of the US EPA. Further, US EPA does not endorse the purchase of any commercial products or services mentioned in the publication.
Financial support. This research has been supported by the US Environmental Protection Agency (grant no. 83587201). Daniel J. Jacob was supported by the NASA Earth Science Division.
Review statement. This paper was edited by Qiang Zhang and reviewed by two anonymous referees.