Nitrogen oxides in the free troposphere: Implications for tropospheric oxidants and the interpretation of satellite NO 2 measurements

. Satellite-based retrievals of tropospheric NO 2 columns are widely used to infer NO x ( º NO+NO 2 ) emissions. These retrievals rely on model information for the vertical distribution of NO 2 . The free tropospheric background above 2 km is particularly important because the sensitivity of the retrievals increases with altitude. Free tropospheric NO x also has a strong effect on tropospheric OH and ozone concentrations. Here we use observations from three aircraft campaigns (SEAC 4 RS, DC3, and ATom) and four atmospheric chemistry models (GEOS-Chem, GMI, TM5

DC3 campaigns over the southeastern US in summer show increasing concentrations in the upper troposphere above 10 km, which are not replicated by GEOS-Chem although the model is consistent with the NO measurements. Using concurrent NO, NO2, and ozone observations from a DC3 flight in a thunderstorm outflow, we show that the NO2 measurements in the upper troposphere are biased high, plausibly due to interference from thermally labile NO2 reservoirs such as peroxynitric acid 45 (HNO4) and methyl peroxy nitrate (MPN). We find that NO2 concentrations calculated from the NO measurements and NO-NO2 photochemical steady state (PSS) are more reliable to evaluate the vertical profiles of NO2 in models. GEOS-Chem reproduces the shape of the PSS-inferred NO2 profiles throughout the troposphere for SEAC 4 RS and DC3 but overestimates NO2 concentrations by about a factor of 2. The model underestimates MPN and alkyl nitrate concentrations, suggesting missing organic NOx chemistry. On the other hand, the standard GEOS-Chem model underestimates NO observations from the ATom 50 campaigns over the Pacific and Atlantic Oceans, indicating a missing NOx source over the oceans. We find that we can account for this missing source by including in the model the photolysis of particulate nitrate on sea salt aerosols at rates inferred from laboratory studies and field observations of nitrous acid (HONO) over the Atlantic. The median PSS-inferred tropospheric NO2 column density for the ATom campaign is 1.7 ± 0.44⨯10 14 molec cm -2 and the NO2 column density simulated by the four models is in the range of 1.4-2.4×10 14 molec cm -2 , implying that the uncertainty from using modeled NO2 tropospheric 55 columns over clean areas in the retrievals for stratosphere-troposphere separation is about 1⨯10 14 molec cm -2 . We find from GEOS-Chem that lightning is the main primary NOx source in the free troposphere over the tropics and southern midlatitudes, but aircraft emissions dominate at northern midlatitudes in winter and in summer over the oceans. Particulate nitrate photolysis increases ozone concentrations by up to 5 ppbv in the free troposphere in the northern extratropics in the model, which would largely correct the low model bias relative to ozonesonde observations. Global tropospheric OH concentrations increase by 60 19%. The contribution of the free tropospheric background to the tropospheric NO2 columns observed by satellites over the contiguous US increases from 25 ± 11 % in winter to 65 ± 9% in summer according to the GEOS-Chem vertical profiles. This needs to be accounted for when deriving NOx emissions from satellite NO2 column measurements.

Introduction
Retrievals of NO2 tropospheric columns from satellite measurements of solar backscatter are used extensively to infer 65 anthropogenic NOx (ºNO+NO2) emissions near the surface and their trends (e.g., Martin et al., 2003;Richter et al., 2005;Beirle et al., 2011;Krotkov et al., 2016). This is complicated by the presence of background NO2 in the free troposphere, the part of the atmosphere between the top of the boundary layer (~2 km altitude) and the tropopause. NOx sources in the free troposphere include lightning, aircraft, transport from the boundary layer and the stratosphere, and chemical recycling from HNO3 and organic nitrates (Singh et al., 1996;Jaeglé et al., 1998a;Levy et al., 1999;Hudman et al., 2007). As fossil fuel NOx 70 emissions have decreased in the US and other post-industrial countries, the relative contribution of the free tropospheric background to the tropospheric NO2 columns has increased (Silvern et al., 2019). Satellite instruments are more sensitive to NO2 in the free troposphere than in the boundary layer because of atmospheric scattering, so the NO2 column retrievals must assume a vertical distribution of NO2 (shape factor) specified by an atmospheric chemistry model for the local conditions (Martin et al., 2002;Eskes and Boersma, 2003). However, these models may be subject to large errors in the free troposphere 75 (Travis et al., 2016;Silvern et al., 2018). Here we use the vertical distribution of tropospheric NOx from aircraft measurements over land and ocean, simulated with GEOS-Chem and other atmospheric chemistry models, to diagnose the confidence to be had in these models and in the aircraft observations. We discuss the implications for global tropospheric oxidants and the retrieval and interpretation of satellite NO2 measurements in terms of surface NOx emissions.

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Accurate in situ measurements of NO2 in the free troposphere are challenging because of low NO2 concentrations and interferences from labile non-radical NOx reservoirs (HNO4, N2O5, and organic nitrates) when sampling at cold temperatures (Bradshaw et al., 1999;Browne et al., 2011;Reed et al., 2016;Nussbaumer et al., 2021). Current techniques to measure NO2 in situ involve either (i) the conversion of NO2 to NO by photolysis followed by measurement of NO through chemiluminescence (photolysis-chemiluminescence; P-CL) (Walega et al., 1991;Ryerson et al., 2000;Bourgeois et al., 2022), 85 or (ii) the direct measurement of NO2 through laser induced fluorescence (LIF) (e.g. Thornton et al., 2000;Matsumoto et al., 2001;Javed et al., 2019), cavity ring-down spectroscopy (Osthoff et al., 2006), or cavity enhanced differential optical absorption spectroscopy (Platt et al., 2009). Intercomparisons of NO2 instruments have generally found agreement among the different techniques at high (>1 ppbv) NO2 concentrations (Thornton et al., 2003;Fuchs et al., 2010;Sparks et al., 2019;Bourgeois et al., 2022), but poor agreement in free tropospheric conditions where NO2 concentrations are below 50 pptv and 90 close to the instrument detection limits (Gregory et al., 1990a;Sparks et al., 2019). In contrast, NO measurements in the free troposphere are generally found to be reliable down to about 10 pptv (Gregory et al., 1990a;Rollins et al., 2020). The NO2 photolysis technique has been used for NO2 measurements from aircraft since the 1980s (Ridley et al., 1988;Sandholm et al., 1990). However, the free tropospheric NO2 concentrations from these measurements were often found to be higher than expected from NO-NO2 photochemical steady state (PSS) (Davis et al., 1993;Fan et al., 1994;Crawford et al., 1996). This 95 was later attributed to an artifact in the NO2 measurements from the decomposition of peroxyacetyl nitrate (PAN), HNO4 and methyl peroxy nitrate (MPN) in the sample line and the photolysis cell (Bradshaw et al., 1999;Browne et al., 2011;Reed et al., 2016). These species are present at relatively high concentrations at cold temperatures of the upper troposphere (Murphy et al., 2004;Kim et al., 2007;Singh et al., 1986) and can cause significant interference in the NO2 measurements when the instrument temperature is higher than the ambient temperature Reed et al., 2016). 100 The LIF technique was developed to eliminate interferences associated with the photolytic conversion of NO2 (Thornton et al., 2000) and has been widely used in aircraft campaigns to measure free tropospheric profiles of NO2 over North America and remote regions (Murphy et al., 2004;Bertram et al., 2007;Browne et al., 2011;Nault et al., 2015) and to evaluate satellite NO2 retrievals (Bucsela et al., 2008;Boersma et al., 2008;Laughner et al., 2019). However, Silvern et al. (2018) found that the LIF 105 NO2 measurements in the upper troposphere over the southeastern US during the Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC 4 RS) aircraft campaign were much higher than the NO2 concentrations expected from the NO-NO2 PSS, indicating either an error in the NO-NO2-O3 kinetics at low temperatures or a remaining bias in the measurement.

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Free tropospheric NO2 concentrations have also been derived using remote sensing techniques. The Airborne Multi-AXis Differential Optical Absorption Spectroscopy (AMAX-DOAS) instrument has been used to measure vertical profiles of NO2 in the free troposphere (Baidar et al., 2013;Volkamer et al., 2015). Ground-based MAX-DOAS instruments can measure NO2 vertical profiles in the boundary layer but have low sensitivity to the free troposphere (Vlemmix et al., 2011). NO2 concentrations in the upper troposphere (8-12 km) have been retrieved from satellite NO2 column measurements using cloud-115 slicing techniques based on measuring differences in partial NO2 columns above clouds of different heights (Belmonte Rivas et al., 2015;Choi et al., 2014;Marais et al., 2021). These provide extensive spatial coverage but there are inconsistencies among different products and large differences compared to aircraft LIF measurements (Marais et al., 2018(Marais et al., , 2021. Atmospheric chemistry models are often used alongside satellite NO2 measurements to determine surface NOx emissions and 120 their trends, as they provide a way to relate changes in NO2 columns to surface NOx emissions (Martin et al., 2003;Lamsal et al., 2011). But the sensitivity of modeled NO2 columns to surface emissions depends on the relative contribution of the free troposphere to NO2 columns. Modeled NO2 vertical profiles over the continents generally agree with aircraft observations below about 6 km (Lamsal et al., 2014;Choi et al., 2020), but underestimate NO2 measurements in the upper troposphere (Martin et al., 2006;Travis et al., 2016;Williams et al., 2017;Miyazaki et al., 2020). This could reflect model errors in the 125 parametrized lightning NOx emissions (Martin et al., 2006;Allen et al., 2010;Hudman et al., 2007;Zhu et al., 2019), convective transport of surface pollutants (Travis et al., 2016), or NOx chemistry (Nault et al., 2016;Silvern et al., 2018), but also measurement errors.
A number of global modeling studies have evaluated NO simulations over remote regions because of its importance for the 130 production of tropospheric ozone and the hydroxyl radical (OH), and have generally found agreement within a factor of two (e.g., Emmons et al., 1997;Wang et al., 1998;Levy et al., 1999;Bey et al., 2001;Horowitz et al., 2003). However, a recent comparison of six global models with aircraft observations over the Pacific and Atlantic oceans made during the NASA Atmospheric Tomography (ATom) campaign's first deployment (July-August 2016) found significant underestimate of NO in all models below 4 km in the tropics and subtropics (Guo et al., 2021a). Other studies also suggest a missing source of NOx 135 in models over the subtropical oceans from fast photolysis of particulate nitrate (Ye et al., 2016b;Reed et al., 2017;Kasibhatla et al., 2018;Andersen et al., 2022) or from oceanic emissions (Fisher et al., 2018).
Here we use data from the SEAC 4 RS and the Deep Convective Clouds and Chemistry (DC3) aircraft campaigns to demonstrate the pervasiveness of interference from non-radical NOx reservoirs in NO2 measurements in the upper troposphere. We go on 140 to use the more reliable NO measurements and the NO2 concentrations derived by applying PSS to the NO measurements to evaluate the NO and NO2 vertical profiles from different models for the SEAC 4 RS, DC3, and ATom campaigns. We use the model results to examine the sources of NOx in the free troposphere, effects on tropospheric ozone and OH, and contribution of the free tropospheric background to satellite NO2 columns over the US.

Aircraft observations
We use observations from the SEAC 4 RS (August-September 2013; Toon et al., 2016) and DC3 (April-May 2012; Barth et al., 2015) campaigns over the southeastern US (25º-40ºN; 65º-100ºW), and the ATom campaign (4 seasonal deployments in 2016-18) over the Pacific and Atlantic oceans (Thompson et al., 2022). For all three campaigns, we use measurements from the NASA DC-8 aircraft, which has a ~12 km ceiling. Table 1 lists the measurements used in this work. Here, we briefly 150 describe the NO2 and NO measurements as they are most relevant. NO2 measurements during the SEAC 4 RS and DC3 campaigns were made using the Berkeley LIF instrument (Thornton et al., 2000;Cleary et al., 2002;Nault et al., 2015). The LIF measurements have little (<5%) interference from HNO4, but there is interference from the thermal decomposition of MPN, for which a correction was applied (0-21% for SEAC 4 RS and 0-40% for DC3). The correction was calculated using concurrent measurements of MPN concentrations (from the same instrument using thermal decomposition in a heated channel) 155 and the fractional thermal decomposition of MPN in the NO2 channel considering the temperature of the channel (15-25ºC) and the instrument residence time (0.23 s for SEAC 4 RS and 0.5 s in DC3), as described by Nault et al. (2015). The LIF measurements have an accuracy of 5% and a detection limit of ~30 pptv for 1 Hz measurements (Thornton et al., 2000;Day et al., 2002;Wooldridge et al., 2010). NO2 measurements in ATom were made with the NOAA NOyO3 instrument using the P-CL technique (Ryerson et al., 2000;Bourgeois et al., 2022). The NOAA instrument also provided NO2 measurements in 160 SEAC 4 RS and DC3. The instrument has an accuracy of ~7% and a detection limit of 20-30 pptv for 1 Hz measurements (Pollack et al., 2010(Pollack et al., , 2012. Interference in the NO2 measurement from HNO4 and MPN is estimated to be 30-40% for HNO4 and 100% for MPN based on an estimated photolysis cell temperature of 20-30ºC and the residence time of air in the cell of 0.75 s during ATom (Bourgeois et al., 2022). The P-CL NO2 measurements are not corrected for this interference. The P-CL NO2 measurements also have photolytic interference from HONO (5% of the HONO mixing ratio), but this is negligible in 165 much of the troposphere where HONO concentration is generally less than 10 pptv (Ye et al., 2016b;Andersen et al., 2022).
NO measurements in all three campaigns were made by the NOAA NOyO3 instrument, with an accuracy of 4% and a detection limit of 6-10 pptv for 1 Hz measurements (Ryerson et al., 2000). For comparison with the model, we exclude measurements influenced by fresh convection (condensation nuclei larger than 10nm > 10 4 cm -3 ), fresh NOx emissions (NOy/NO < 3 mol mol -1 ), biomass burning plumes (CO > 200 ppbv and CH3CN > 200 pptv), and stratospheric intrusions (O3 > 100 ppbv or CO < 45 170 ppbv).   (Travis et al., 2016), but these are not needed here as the free tropospheric NO2 concentrations do not vary much at regional scales and finer resolution tests showed similarity in results (Yu et al., 2016). The horizontal grid resolution can lead to localized differences in the upper troposphere from stratospheric 195 intrusions, convective transport, and lightning NOx emissions (Schwantes et al., 2022), and we minimize these effects by filtering out data influenced by the stratosphere, fresh convection, and fresh NOx emissions, as described above. The spin-up period for our simulations is six months. Comparison to aircraft measurements is done by sampling the model along the flight path as an online diagnostic during the model simulation. and China (Zheng et al., 2018). The US EPA 2011 NEI is scaled annually using EPA-estimated emissions trends (US EPA Air Pollutant Emissions Trends Data, 2015). Travis et al. (2016) had to scale down the NEI NOx emissions in GEOS-Chem by 40% to reproduce the SEAC 4 RS NOx observations, but we do not do this in our simulations as it leads to an underestimate of NOx in other seasons Silvern et al., 2019). Open fire NOx emissions are from the GFEDv4 inventory (Giglio et al., 2013). Ship NOx emissions are from CEDS and are processed using the PARAmetrization of emitted NOX 215 (PARANOX) model to account for fast in-plume NOx oxidation (Vinken et al., 2011;Holmes et al., 2014). Aircraft NOx emissions are from the Aviation Emissions Inventory Code (AEIC) inventory (Stettler et al., 2011;Simone et al., 2013), and are updated here with flight traffic data for 2015. Lightning NOx emissions follow Murray et al. (2012), with lightning flash rates calculated as a function of the cloud top height and scaled to match the observed climatology from satellite data.

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Emissions are computed at the native MERRA-2 resolution (0.5º⨯0.625º). NO yields of 500 moles per flash are used for the 220 northern midlatitudes (>35ºN) and 260 moles per flash elsewhere. Emissions are distributed in the vertical following Ott et al. (2010). Soil and fertilizer NOx emissions are from Hudman et al. (2012) and are computed at 0.5º⨯0.625º resolution (Weng et al., 2020).
GEOS-Chem includes a detailed representation of NOx-HOx-VOC-aerosol-halogen chemistry (Mao et al., 2013;Travis et al., 225 2016;Holmes et al., 2019;Wang et al., 2021;McDuffie et al., 2021;Pai et al., 2020). Recent improvements to the model's NOx chemistry include addition of detailed tropospheric halogen chemistry (Wang et al., 2021), addition of methyl, ethyl, and propyl nitrate emissions and chemistry (Fisher et al., 2018), and updates to the heterogeneous NOx reactions in aerosols and cloud droplets (Holmes et al., 2019;McDuffie et al., 2021). Here we follow Schmidt et al. (2016) and exclude bromine release from sea salt aerosol debromination because it leads to excessive model BrO in the marine boundary layer (MBL). Equilibrium 230 partitioning of HNO3 to pNO3on fine mode aerosols is calculated using ISORROPIA II (Fountoukis and Nenes, 2007;Wang et al., 2019). The fine mode aerosols are treated as internal mixtures of sulfate, nitrate, ammonium, and sea salt components, representing well-aged particles that have undergone coagulation and cloud processing (Fridlind and Jacobson, 2000). The model also includes the formation and uptake of sulfate and nitrate in alkaline sea salt aerosols (Wang et al., 2019). Uptake of HNO3 as pNO3on coarse sea salt aerosols is treated as a kinetic process, following Wang et al. (2019). Sea salt aerosol 235 emissions follow Jaeglé et al. (2011) and are calculated at 0.5º⨯0.625º resolution (Weng et al., 2020). Our simulation does not include HNO3 uptake on alkaline dust particles, which could be important in dust plumes over the ocean (Fairlie et al., 2010;Karydis et al., 2016). Photolysis frequencies in the model are calculated using Fast-JX (Wild and Prather, 2000;Eastham et al., 2014).

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Previous studies examining the GEOS-Chem NO simulation for the ATom campaign showed underestimates in the lower troposphere (Fisher et al., 2018;Travis et al., 2020;Guo et al., 2021a). Measurements in the marine atmosphere indicate elevated levels of HONO that originate likely from pNO3photolysis (Ye et al., 2016b;Andersen et al., 2022) and would provide a fast source of NOx missing from the model. We address this by including pNO3photolysis in our simulation, following the implementation of this reaction in GEOS-Chem by Kasibhatla et al. (2018). The photolysis frequency of pNO3 -245 is calculated by scaling the photolysis frequency of HNO3 by an enhancement factor (EF). There is high uncertainty in the EF, with laboratory studies in the range of 1-1000 (Ye et al., 2016a;Bao et al., 2018;Gen et al., 2019;Shi et al., 2021). Field and modeling studies find that EFs of 10-500 are needed to explain the NOx and HONO observations over the oceans (Ye et al., 2016b(Ye et al., , 2017aReed et al., 2017;Kasibhatla et al., 2018;Zhu et al., 2022;Andersen et al., 2022), with higher values for pNO3in sea salt aerosols (Andersen et al., 2022). In consistency with these studies, we find that we can match the ATom NO 250 observations by using an EF of 100 for pNO3in sea salt aerosol. In our model, coarse mode pNO3is only present in sea salt aerosols and has an EF of 100, but fine mode pNO3is internally mixed with sulfate, ammonium, and sea salt aerosol and so we decrease the EF of fine mode pNO3depending on the relative amounts of pNO3and sea salt aerosol: , 10)  (Millero et al., 2008), and where Na + is the chemically inert sea salt aerosol species simulated by GEOS-Chem. We choose a lower limit of 10 for the EF based on the results of Romer et al. (2018), who estimated EF values for non-sea-salt pNO3aerosols in the range 1-30 from observations over South Korea. The relative yields of HONO:NO2 from pNO3photolysis are taken as 2:1 (Ye et al., 2017b;Kasibhatla et 260 al., 2018). We will discuss the effect of pNO3photolysis on remote NOx concentrations in more detail in Section 3.2.

Other models
In addition to GEOS-Chem simulations, we analyze results from three other global atmospheric chemistry models: the Global Modeling Initiative (GMI) model, the Tracer Model version 5's "massively parallel" version (TM5-MP), and the Copernicus 265 Atmosphere Monitoring Service (CAMS) reanalysis product. The GMI model simulates tropospheric and stratospheric chemistry (Duncan et al., 2007;Strahan et al., 2007;Strode et al., 2015) using meteorological fields from NASA GMAO's MERRA-2 reanalysis. GMI NO2 vertical profiles are used to specify shape factors in the OMI NO2 retrievals (Krotkov et al., 2017;Lamsal et al., 2021). The version used here has a horizontal resolution of 1º⨯1.25º. Strode et al. (2021)   temperatures (Jaeglé et al., 1998a;Bertram et al., 2007;Hudman et al., 2007;Nault et al., 2017). The GEOS-Chem NO2 profiles are similar to the LIF NO2 profiles below 10 km but differ in the upper troposphere (Fig. 1b, e), as previously noted by Travis et al. (2016). LIF NO2 concentrations in SEAC 4 RS increase from 20 pptv at 9 km to 120 pptv at 12 km, but GEOS-Chem NO2 concentrations remain below 30 pptv. The difference between GEOS-Chem and the P-CL NO2 observations in the upper troposphere during DC3 is even larger. 290 Travis et al. (2016) and Silvern et al. (2018) showed that the difference between the measured and GEOS-Chem NO2 in the upper troposphere in SEAC 4 RS can be explained by the departure of the measured NO/NO2 ratio from that expected from calculated PSS between NO and NO2. In daytime, NO and NO2 interconvert rapidly through the following main reactions: Here RO2 represents the ensemble of organic peroxy radicals. At PSS, the NO/NO2 ratio is given by: 300 (2) where NO 2 is the NO2 photolysis frequency and ki is the rate constant of reaction i. We calculate the PSS NO/NO2 ratio for the SEAC 4 RS and DC3 data using concurrent aircraft measurements and GEOS-Chem simulated values along the flight path for quantities that were not measured. [O3] and NO 2 were measured in both campaigns.
[HO2] was measured only in DC3, but H2O2 concentrations measured in SEAC 4 RS are consistent with GEOS-Chem (Silvern et al., 2018), which provides support 305 for the model [HO2]. Rate constants are as recommended by the JPL evaluation (Burkholder et al., 2020) and adjusted for temperature and pressure. We take the NO + CH 3 O 2 reaction rate constant as k3.
[RO2] and [BrO] are taken from GEOS-Chem but make only small contributions. In the free troposphere, NO-NO2 PSS is largely governed by the NO + O 3 reaction (Bradshaw et al., 1999;Silvern et al., 2018). Thus, the PSS NO/NO2 ratio depends mainly on observed quantities and on relatively well-established kinetics (Silvern et al., 2018  325 Figure 1 (c, f) show the vertical profiles of the measured and the PSS NO/NO2 ratios. The PSS NO/NO2 ratio increases with altitude because of the slower rate of the NO + O3 reaction at colder temperatures (Burkholder et al., 2020). There is relatively little change in NO 2 with altitude (Silvern et al., 2018). The measured and PSS ratios match below 5 km, but at higher altitudes the measured ratios are smaller than the PSS ratios. Between 10 and 12 km, the NO/NO2 ratios using the LIF measurements are in the range of 1 to 2, while the PSS NO/NO2 ratios are in the range of 3 to 6. The NO/NO2 ratios using the P-CL 330 measurements at this altitude are close to 1. The GEOS-Chem NO/NO2 ratios are similar to the PSS ratios throughout the troposphere.
The P-CL NO2 instrument has significant interference from the dissociation of HNO4 and MPN (Reed et al., 2016;Nussbaumer et al., 2021;Bourgeois et al., 2022), and we find that the ratio of NO/NO2* (NO2*ºNO2+HNO4+MPN) in GEOS-Chem 335 matches the NO/NO2 ratio for the P-CL NO2 measurements (Fig. 1c, f). The LIF NO2 measurements correct for the thermal dissociation of MPN (there is little thermal dissociation of HNO4), but the correction is affected by the high uncertainty in the concentrations and the thermal stability of MPN . The LIF instrument was modified between DC3 and SEAC 4 RS to shorten the sample residence time and reduce the fraction of MPN dissociating in the instrument , but we do not find that this improved agreement between the measured and PSS NO/NO2 (Fig. 1c, f). It is also possible 340 that HNO4 and MPN (and potentially other labile NO2 reservoir species) dissociate on the inlet walls, which the correction would not account for. Bradshaw et al. (1999) could achieve agreement of their NO2 measurements with the PSS concentrations at all altitudes by using an unusually large inlet (10 cm diameter) and a very high flow rate in the instrument to minimize wall collisions.
345 Silvern et al. (2018) pointed out that the difference between the measured and PSS NO/NO2 ratios could arise from either an error in the NO-NO2-O3 kinetics or a systematic bias in the NO2 measurements in the upper troposphere. Here we arbitrate between these two hypotheses by using quasi-Lagrangian observations in the outflow from a dissipating thunderstorm in the upper troposphere deliberately sampled during DC3 (flight RF17). Nault et al. (2016) previously analyzed the evolution of NOx and NOy (NOy ≡ NOx + non-radical reservoirs) on this flight to determine NOx oxidation rates, and showed a steady 350 decrease with time in the NO and NO2 concentrations and an increase in the NOy oxidation products during the two-hour sampling period. Figure 2a shows the flight path with daytime plume crossings colored by the measured NOy/NO molar ratio.
The NOy/NO ratio increases on each successive plume crossing as NOx, undergoes oxidation in the outflow, and we use the ratio as a measure of chemical aging in the plume Hayes et al., 2013). Figure 2b shows the measured NO, NO2, and the sum of HNO4 and MPN concentrations as a function of the NOy/NO ratio. NO concentrations decreased 355 from 900 pptv to 400 pptv between the start and the end of the measurement period. But there was relatively little change in the NO2 concentrations. The mean LIF NO2 concentrations decreased by 25%, while the mean P-CL NO2 concentrations increased, likely due to increasing interference from HNO4 and MPN produced in the plume. Figure 2b also shows the NO2 concentrations inferred by applying PSS to NO observations: where PSS is calculated from observations using Eq. (2) and measured [O3], [HO2] and NO 2 . In this case, we take [RO2] to be equal to the measured [HO2] as an upper limit, instead of using the value from GEOS-Chem, since we do not expect the model to simulate the thunderstorm plume. The PSS NO2 concentrations decreased by a factor of 2 between the start and end of the measurement period, in line with the NO concentrations.
365 Figure 2c shows the observed ozone concentrations as a function of the NOy/NO ratio. Ozone concentrations increase with the age of the plume, reflecting the NOx-limited conditions for ozone production prevalent in the upper troposphere over the central US in summer (Pickering et al., 1990;Jaeglé et al., 1998b;Apel et al., 2015). We compare the observed ozone increase to that computed from the observed NO 2 and the observed NO, NO2, HO2, and OH concentrations. Ozone is produced through the photolysis of NO2 (reaction R5), and is lost mainly by reaction with NO (reaction R1), photolysis in the presence of water 370 vapor (reaction R6), and oxidation by HO2 and OH (reactions R7 and R8): The instantaneous net ozone production rate is then given as follows: 375 where with N2 and O2 (Seinfeld and Pandis, 2016). We use Eq. (4) to calculate three estimates for the instantaneous net ozone production rate in the plume using NO2 from LIF, P-CL, and PSS. The total ozone increase in the plume is calculated by  The observed ozone concentrations increased by 7 ppbv between the start and the end of the measurement period in the plume.
In comparison, the ozone increase calculated using the NO2 measurements from both the LIF and P-CL instruments is 25 ppbv, 395 while that calculated using the PSS NO2 concentrations is close to the observations. We also examine the effect of potential uncertainties in the NO-NO2-O3 kinetic data by decreasing NO 2 by 20% and increasing k NO"O 3 by 40% in Eq. (4), following Silvern et al. (2018). We find that the ozone increase calculated using the NO2 measurements is lowered to 17 ppbv, still much higher than the observed increase, and implying that the difference between the NO2 measurements and the PSS NO2 concentrations cannot be attributed to errors in the NO-NO2-O3 kinetic data. The most likely explanation is that the LIF NO2 400 measurements are biased high, as are the P-CL measurements. The median LIF and P-CL NO2 concentrations in the outflow plume were both 235 pptv, compared to a median PSS NO2 concentration of 116 pptv. The median measured HNO4 and MPN concentrations were 44 and 90 pptv, respectively, and can explain the difference between the P-CL and PSS NO2 concentrations. The LIF NO2 measurements are thought to have little interference from HNO4, and were corrected for the partial dissociation of MPN, but it appears that this correction may have been underestimated. For this flight, the median 405 correction to the NO2 measurements was just 7%. The correction is affected by high uncertainty in the thermal dissociation rate constant of MPN (±30%) and in the MPN measurements (±40%+20 pptv for 1 Hz; Nault et al., 2015). The MPN measurements themselves would be affected by a bias in the NO2 measurements as they are based on the difference in the NO2 measured between the heated MPN channel and the NO2 channel at cabin temperature. Interference from other known nonacyl peroxy nitrates would not be significant (Khan et al., 2020), but there could be other unknown organic NO2 reservoir 410 species forming in convective outflows (Silvern et al., 2018).
Considering this bias in the LIF and P-CL NO2 measurements in the upper troposphere, we instead use the NO observations and the related PSS NO2 concentrations inferred from the NO and other observations (Eq. 3) to evaluate the modeled NOx in the free troposphere (Fig. 1). GEOS-Chem reproduces the shape of the NO and the PSS NO2 profiles throughout the 415 troposphere for SEAC 4 RS and DC3 (Fig. 1b, d). There is no increase in the modeled or the PSS NO2 concentrations in the upper troposphere, as higher NO concentrations are compensated by higher NO/NO2 ratios. GEOS-Chem NO concentrations are about 2 times higher than the observations in the free troposphere, consistent with previous work for SEAC 4 RS (Travis et al., 2016;Silvern et al., 2018). We calculate the NO2 column density corresponding to the PSS and GEOS-Chem NO2 profiles by converting the median NO2 concentrations at each altitude to a partial column density (product of the NO2 number density 420 and the height of the altitude bin) and summing them from the surface to 12 km. We find that the PSS NO2 column densities in the free troposphere for the SEAC 4 RS and DC3 profiles in Fig. 1 are 3.6⨯10 14 and 3.8⨯10 14 molec cm -2 , respectively, compared to 6.5⨯10 14 and 10.4⨯10 14 molec cm -2 in GEOS-Chem. However, the model does not overestimate NOy concentrations, suggesting that the model may be missing NOx oxidation chemistry, which is likely organic. We find that the median MPN concentration in the free troposphere in GEOS-Chem is about 5 pptv compared to about 40 pptv in the 425 observations, consistent with the findings of Silvern et al. (2018) for SEAC 4 RS. Similarly, median alkyl nitrate concentration in the model is about 12 pptv but 60 pptv in the observations. NOx emissions are likely overestimated in the US EPA NEI inventory used in our simulations (Travis et al., 2016), which explains the NO2 overestimate in the boundary layer, but this would have little effect in the free troposphere, where lightning emissions supply the majority of NOx. Finally, we find little difference in the SEAC 4 RS and DC3 NOx profiles in the free troposphere between our baseline simulation and the simulation 430 without pNO3photolysis, indicating that chemical recycling through pNO3photolysis is a minor source of NOx over the US compared to emissions.
Retrieval of NO2 columns from satellite-based instruments generally involves the following steps: (i) using the observed solar backscatter radiance to calculate a total slant NO2 column density along the light path, (ii) removal of the stratospheric 435 contribution to calculate the tropospheric slant column density Ω ! , and (iii) conversion of the tropospheric slant column density to a tropospheric vertical column density Ω " , using an air mass factor (AMF) that depends on the vertical profile of NO2 (Palmer et al., 2001;Martin et al., 2002): where AMFG is the geometric AMF that describes the satellite viewing geometry, w(z) are the scattering weights that describe 440 the sensitivity of the backscattered radiance to the NO2 abundance as a function of altitude (z), S(z) is the NO2 shape factor describing the vertical profile of the NO2 number density normalized to the NO2 vertical column density, and zt is the tropopause height. w(z) is computed with radiative transfer modeling, and in clear skies is 3-4 times higher in the upper troposphere than in the boundary layer because of atmospheric scattering (Martin et al., 2002). Here we use scattering weights from the NASA OMI NO2 retrieval (v4.0; Lamsal et al., 2021), and exclude scenes with cloud fraction greater than 0.1 and 445 surface albedo greater than 0.3.
We use Eq. 6 to calculate AMFs corresponding to PSS and GEOS-Chem NO2 profiles for SEAC 4 RS and DC3. AMFG over the southeastern US in summer for OMI is about 2.6. The shape factors are calculated by converting the NO2 concentration profiles (Fig. 1) to number density profiles and normalizing them to the respective NO2 columns. For SEAC 4 RS, both the PSS 450 and GEOS-Chem NO2 profiles yield an AMF of 1.0, reflecting the similar shapes of the NO2 profiles despite the GEOS-Chem overestimate of the NO2 concentrations. For DC3, the AMFs corresponding to the PSS and GEOS-Chem profiles are 0.91 and 1.03, respectively. These results suggest that using the GEOS-Chem NO2 profiles as a priori in the NO2 column retrievals over the southeast US would result in an error of 0-10%, compared to the previous error estimate of 30% based on the LIF NO2 measurements in SEAC 4 RS (Silvern et al., 2018). The sensitivity of satellite retrievals to NO2 vertical profiles is discussed 455 further in Section 3.5.

NOx in the remote troposphere: interpreting the ATom data
We now examine the distribution of NOx over the Pacific and Atlantic oceans during the ATom campaign in order to contrast the NO2 profiles in the remote troposphere to the SEAC 4 RS and DC3 NO2 profiles over land. Modeled NO2 over remote regions is often used in the stratospheric-tropospheric separation of satellite NO2 columns (Bucsela et al., 2013). NOx in the 460 remote troposphere is also important for global tropospheric ozone and OH production. Figures 3 and 4 show the median vertical profiles of NO and the PSS NO2 concentrations over the Pacific and Atlantic Oceans separated by seasons and latitude bands. The PSS NO2 concentrations in Fig. 4 are inferred from the ATom observations of NO, ozone, HO2 and NO 2 using Eqs.
(2) and (3). The observed NO concentrations increase from 10 pptv near the surface to 20-100 pptv in the upper troposphere above 8 km because of the longer NOx lifetime and the increase in NO/NO2 ratios with altitude. The PSS NO2 profiles show a 465 decrease in NO2 concentrations with altitude because of an increase in the NO/NO2 ratio. PSS NO2 concentrations in the upper troposphere are generally lower than 10 pptv, except in the northern midlatitudes upper troposphere in August and October, where NO2 concentrations increase in the upper troposphere. The upper tropospheric NOx concentrations over the Atlantic in August are similar to those observed over the southeastern US during SEAC 4 RS and DC3 and reflect the transport of lightninggenerated NOx from the US to the Atlantic Ocean (Crawford et al., 2000;Cooper et al., 2006;. There is little 470 seasonal variation in NOx below 8 km. The column density for PSS NO2 has a campaign median of 1.7⨯10 14 molec cm -2 and a range of 1.2-3.0⨯10 14 molec cm -2 for the different seasons and latitude bands, which is similar in magnitude to NO2 columns retrieved from OMI observations over remote regions (Hains et al., 2010;Lamsal et al., 2021). The free tropospheric PSS NO2 column density over the northern Atlantic (30-60ºN) in August is 2.1⨯10 14 molec cm -2 , about 45% lower than that observed in SEAC 4 RS and DC3. 475   without the NOx source from pNO3photolysis. The GEOS-Chem simulation without pNO3photolysis underestimates NO observations below 6 km by a factor of 2-5 in most cases. The underestimate does not extend to the upper troposphere so it cannot be attributed to errors in lightning or aircraft NOx emissions. The underestimate is not related to NOx recycling from HNO3, PAN, or alkyl nitrates either. GEOS-Chem generally overestimates ATom HNO3 observations ( Fig. S1; Travis et al., 2020;Luo et al., 2020). The model is consistent with the ATom observations of PAN in the tropics and southern midlatitudes 500 and underestimates it a little in the northern midlatitudes (Fig. S1). GEOS-Chem simulation of methyl, ethyl, and propyl nitrates is generally consistent with the ATom observations (Fisher et al., 2018). Fisher et al. (2018) also considered whether missing oceanic NO emissions in the model could explain the underestimate in NO in the MBL. This source is largely limited to the equatorial region and is estimated to be about 10 8 molecules cm -2 s -1 (Torres and Thompson, 1993;Tian et al., 2020), which is 100 times smaller than that would be required to correct the NO underestimate in the model. The NOx sink from 505 reaction with OH is not overestimated in the model either, considering that GEOS-Chem's OH concentrations are consistent with ATom observations (Travis et al., 2020). There is some uncertainty in the NO2+OH+M→ HNO3+M rate constant used in models, as reported in laboratory (Mollner et al., 2010;Burkholder et al., 2020) and field studies (Henderson et al., 2011;Seltzer et al., 2015;Nault et al., 2016), but not large enough to explain the NO underestimate. The representation of heterogenous NOx chemistry in the model reflects current knowledge and includes an empirical parameterization for the N2O5 510 reaction probability derived from aircraft observations McDuffie et al., 2018;Holmes et al., 2019). These processes are not well-constrained, but they are important mainly in the extratropical latitudes in winter and spring (Alexander et al., 2020).
Recent studies suggest that photolysis of pNO3could be much faster than photolysis of gas-phase HNO3 and contribute an 515 important source of NOx over the oceans (Ye et al., 2016a, b;Reed et al., 2017;Kasibhatla et al., 2018). pNO3photolysis produces NO2 and HONO (Scharko et al., 2014;Ye et al., 2017b), and HONO photolyzes further to produce NO: HONO + ℎ 0⎯⎯⎯⎯2 NO + OH (R10) 520 In bulk solution, the absorption cross-section of NO3is about 100 times larger than that of HNO3 (Burley and Johnston, 1992) but the effective quantum yields for Reactions (R9a) and (R9b) are low (~1%) (Warneck and Wurzinger, 1988;Benedict et al., 2017), because the products are surrounded by water molecules and recombine before they can escape to the gas phase (Nissenson et al., 2010;Richards-Henderson et al., 2015). However, the photolysis of NO3on aerosols is thought to be much 525 more efficient than that in the gas and bulk aqueous phases. Field studies trying to explain the observed HONO and NOx concentrations over the oceans postulate enhancement factors (EF) for pNO3photolysis rate relative to that of HNO3 of 10-500 (Ye et al., 2016b(Ye et al., , 2017aReed et al., 2017;Kasibhatla et al., 2018;Zhu et al., 2022;Andersen et al., 2022). Similar EFs have also been observed in laboratory studies of photolysis of pNO3in ambient aerosols from urban and remote areas (Ye et al., 2017b;Bao et al., 2018;Gen et al., 2019). The high EFs could reflect the higher absorption cross-sections and quantum 530 yields for NO3molecules at the surface of the particles (Zhu et al., 2008(Zhu et al., , 2010Du and Zhu, 2011;Nissenson et al., 2010).
The fraction of NO3at the surface is larger in the presence of halides as found in sea salt aerosols (Wingen et al., 2008;Richards-Henderson et al., 2013;Zhang et al., 2020). Other factors that could contribute to higher EFs include high aerosol [H + ] (Scharko et al., 2014;Mora Garcia et al., 2021) and the presence of organic species that can act as photosensitizers, Hdonors, electron donors, or promote secondary reactions (Ye et al., 2019;Mora Garcia et al., 2021). Laboratory studies on 535 NaNO3 and NH4NO3 particles find EFs of less than 10 (Shi et al., 2021), suggesting that aerosol composition is an important factor in the photolysis rate of pNO3 -. The relative yields of HONO:NO2 in Reactions (R9a) and (R9b) also vary substantially in laboratory results. Ye et al. (2016) found relative yields for HONO:NO2 ranging from 1:1 to 30:1, with lower values for marine aerosol samples and higher values for urban samples. Bao et al. (2018) found median relative yields for HONO:NO2 of 3.5:1 for aerosol samples from Beijing. 540 Our baseline simulation assumes EFs of 10-100 depending on the relative amount of pNO3and sea salt aerosols (Eq. 1), and a HONO:NO2 yield of 2:1 following Kasibhatla et al. (2018). Figure 5 shows the spatial distribution of EFs at the surface and as a function of altitude. The simulated EF decrease from 100 in the MBL to less than 30 over the continents, where much of the pNO3is present as NH4NO3. The values over the oceans are consistent with EFs required to explain high daytime HONO 545 concentrations (more than 10 pptv) observed over the oceans (Ye et al., 2016b;Andersen et al., 2022). Kasibhatla et al. (2018) found that an EF of 100 and a HONO:NO2 yield of 15:1 were needed in GEOS-Chem to reproduce the observed diurnal cycle of HONO at Cape Verde, although EFs of 25-50 and HONO:NO2 yield of 2:1 were sufficient to explain the NOx observations. Romer et al. (2018) suggested an upper limit for the EF of 30, arguing that higher values would lead to inconsistency between the calculated steady state NOx/HNO3 ratios and observations from seven aircraft campaigns. Most of these campaigns were 550 over or near continents in the northern midlatitudes, where EFs in our simulation are also generally low. In the northern midlatitudes, EFs decrease with altitude reflecting the increase in the fraction of pNO3present as NH4NO3 relative to that present on sea salt aerosols. There is little change in the EFs with altitude elsewhere.
pNO3concentrations were measured by the AMS and SAGA instruments during ATom and were found to be very low (Fig.  555   S1). The AMS measures total (inorganic and organic) nitrate in non-refractory particles smaller than 1 µm diameter, while SAGA measures water-soluble NO3ions in particles smaller than about 4 µm diameter. Almost all of the nitrate measured by the AMS was organic (Nault et al., 2021;Hodzic et al., 2020;Guo et al., 2021b), and (inorganic) pNO3concentrations were less than 1 ng sm -3 . The median SAGA measured pNO3concentration was 44 ng sm -3 . In comparison, the median pNO3concentrations in GEOS-Chem were 2.1 ng sm -3 in the fine mode and 1.8 ng sm -3 in the coarse mode. GEOS-Chem 560 overestimated the observed pNO3concentrations in the northern midlatitudes (Fig. S1), likely reflecting the overestimate in HNO3 concentrations and aerosol pH compared to the ATom measurements (Travis et al., 2020;Luo et al., 2020;Nault et al., 2021), but the effect on the NOx source from pNO3photolysis is dampened because the EF for fine mode pNO3photolysis decreases at higher pNO3concentrations (Eq. 1). GEOS-Chem pNO3concentrations are lower compared to the SAGA observations in 30ºN-30ºS, but much of the pNO3measured there is associated with dust, and probably has a lower EF than 565 that of pNO3on sea salt aerosols (Andersen et al., 2022).

575
Including pNO3photolysis in the model significantly increases modeled NOx concentrations below 6 km and improves agreement with the NO observations (Fig. 3) and with the PSS NO2 concentrations inferred from NO observations (Fig. 4).
The largest increase is in the tropics (30ºS-30ºN), where pNO3photolysis is faster because of high actinic flux and high EFs, 580 and because the NOx source from PAN decomposition is small there (Moxim et al., 1996;Fischer et al., 2014). The effect of pNO3photolysis is generally smaller above 6 km because of lower pNO3concentrations, except in the midlatitudes in spring when pNO3concentrations are high and there is sufficient actinic flux. GEOS-Chem NO2 concentrations are slightly higher than the PSS NO2 concentrations in the upper troposphere, because of higher NO concentrations and higher ozone concentrations driving down the NO/NO2 ratios in the model. The ozone concentrations in the upper troposphere in the model 585 are on average 20 ppbv higher than the ATom observations. Travis et al. (2020) had also reported a similar overestimate in ozone concentrations in GEOS-Chem in the upper troposphere for ATom.   6 for 30ºS-30ºN and 3.7 for 30ºS-60ºS and 30ºN-60ºN. Error bars show the standard deviations of the medians and are calculated using jackknife resampling. Figure 4 also shows the NO2 profiles simulated by the GMI, TM5, and CAMS models, and Figure 6 compares the NO2 column density and AMFs for the PSS and the modeled NO2 profiles. The TM5 and CAMS results are available only for August, so 600 the NO2 column density and AMFs for August are shown separately. The NO2 column densities and AMFs are calculated from the median PSS and modeled NO2 profiles for the campaign, with the AMF calculation further assuming AMFG values of 2.6 for tropics (0º-30º) and 3.7 for midlatitudes (30º-60º), and a scattering weight profile from the NASA OMI NO2 retrieval (v4.0) for scenes with cloud fraction < 0.1 and surface albedo < 0.3. The campaign median (all seasons) NO2 column density is 2.4⨯10 14 molec cm -2 in our baseline GEOS-Chem simulation compared to 1.7 ± 0.44⨯10 14 molec cm -2 for PSS NO2, and 605 the corresponding AMFs are about equal (1.8). The NO2 column density in the simulation without pNO3photolysis is 1.5⨯10 14 molec cm -2 . GMI NO2 concentrations are much lower than the PSS NO2 concentrations below 4 km, similar to the GEOS-Chem simulation without the pNO3photolysis source, and generally higher than the PSS NO2 concentrations in the upper troposphere. The campaign average NO2 column density in GMI is 1.4⨯10 14 molec cm -2 and the AMF is 2.2. GMI NO2 concentrations are consistent with PSS NO2 in the northern midlatitudes in February and in the southern midlatitudes in August, 610 even though GMI does not include NOx formation from pNO3photolysis. This is likely because GMI does not include NOx loss through the hydrolysis of NO3 and N2O5 in clouds (Holmes et al., 2019) or the formation of halogen nitrates (Wang et al., 2021). The TM5 and CAMS models slightly overestimate the PSS NO2 columns. Overall, the difference in NO2 column densities among the four models is ~1⨯10 14 molec cm -2 . In comparison, the uncertainty in the NO2 retrievals from using modeled NO2 tropospheric columns over clean areas for stratosphere-troposphere separation is estimated to be 2⨯10 14 molec 615 cm -2 (Bucsela et al., 2013;Boersma et al., 2018). The difference among the models in the AMFs is ~20%, which is higher than the assumed uncertainty of 10% in the QA4ECV NO2 column retrievals associated with the a priori profiles (Boersma et al., 2018). The uncertainty associated with NO2 spectral fitting and stratosphere-troposphere separation in remote regions is large for single-pixel retrievals (~100%), but this reduces when averaging spatially and temporally (Boersma et al., 2018). Figure 7 shows the change in the annual mean NOx, OH, and ozone concentrations at the surface and zonally between our baseline simulation and the sensitivity simulation without pNO3photolysis. pNO3photolysis increases NOx, OH and ozone tropospheric masses in the model by 9%, 19%, and 10%, respectively, but there are much larger changes in certain areas (Fig.   7). In comparison, Kasibhatla et al. (2018) found increases in the NOx, OH, and ozone tropospheric masses of 1-3% in simulations that included photolysis of only coarse mode pNO3at an EF of 100 and increases of 3-6% when fine mode pNO3 -625 photolysis was also included at an EF of 25. We find that NOx concentrations increase by a factor of 2 on average in the MB though there is little increase in the northern extratropical MBL, as PAN concentrations are high (Fig. S1) and provide the main source of NOx in the region. There is little change in surface NOx concentrations over continents as local emissions dominate the NOx source. NOx concentrations decrease slightly over some regions because the increase in OH concentrations resulting from HONO photolysis shortens the NOx lifetime. The increase in NOx concentrations in the tropics and subtropics 630 is limited mostly to the MBL, since pNO3concentrations are low at higher altitudes. In the free troposphere of the northern midlatitudes, pNO3photolysis increases NOx concentrations by just 20%, because pNO3concentrations and EFs for pNO3photolysis are generally low (Fig. 5). The effect of pNO3photolysis is larger in spring, when there is a seasonal peak in pNO3concentrations in the model. There is a large increase in NOx concentrations over Antarctica, as there are few other NOx sources in the region in the model. Our simulations do not include snow NO3photolysis, which is an important source of NOx in the 635 region (Zatko et al., 2016).

Effect of pNO3photolysis on global NOx, OH, and ozone concentrations 620
pNO3photolysis increases the production of OH and ozone because of the increase in NOx concentrations in low-NOx regions, where OH and ozone production are most sensitive to NOx concentrations. OH is also produced by the photolysis of HONO released to the gas phase during pNO3photolysis (Reaction R10), which would be an important source of OH in winter when 640 OH production from Reaction (R6) is slow (Elshorbany et al., 2012). The increase in OH concentrations is particularly large (~30%) in the MBL. Travis et al. (2020) showed that the GEOS-Chem OH concentrations from a simulation without pNO3photolysis are consistent with the ATom observations, but they also found an underestimate in the modeled OH reactivity in the lower troposphere due to missing VOCs in the model. The source of these VOCs is likely oceanic and would depress model OH (Thames et al., 2020). The OH source from pNO3photolysis could then compensate for the increase in OH reactivity. The 645 OH increase implied by pNO3recycling decreases the global atmospheric methane lifetime from 8.0 years to 7.0 years, reducing the agreement with the value of 9.1 ± 0.9 years inferred from the methylchloroform proxy (Prather et al., 2012), but again this could be compensated by an increase in the model OH reactivity (Travis et al., 2020;Kim et al., 2022).
pNO3photolysis increases surface ozone concentrations by 3.6 ± 0.94 ppbv on average at the surface, and up to 8 ppbv in the 650 tropics and subtropics. In the northern extratropics, the ozone increase is small at the surface, but about 5 ppbv in the free troposphere, reflecting the spatial pattern of increase in NOx concentrations. Wang et al. (2021) recently evaluated the GEOS-Chem ozone simulation with ozonesonde observations and found an underestimate in simulated free tropospheric ozone of 5-15 ppbv in the northern hemisphere and up to 5 ppbv in the southern hemisphere, depending on whether halogen chemistry was included or not. Including the NOx source from pNO3photolysis improves GEOS-Chem's ozone simulation. We will 655 examine this further in a future publication.

Primary sources of NOx in the free troposphere
NOx in the free troposphere originates from a variety of primary sources with differing spatial and seasonal characteristics.
The sources include in situ emissions from lightning and aircraft, uplifting of NOx emitted from surface sources, and downwelling of stratospheric NOy produced from the photolysis of N2O. Lightning is the main in situ source of NOx in the free troposphere globally (Table 2), but it is concentrated over continents and has a strong seasonality in the midlatitudes. 670 Aircraft emissions are largest in the northern midlatitudes, and while most of the aircraft emissions are over land, there are significant emissions over the northern Atlantic and Pacific oceans (Simone et al., 2013). Surface emissions are widely distributed over the tropics and the northern midlatitudes, but their transport to the free troposphere would vary seasonally.
Here we use GEOS-Chem to determine the relative importance of these primary sources for NOx in the free troposphere. 675 Figure 8 shows the vertical profiles of NOx over the Pacific and Atlantic Oceans and the contiguous US for February and August separately for surface emissions (fuel combustion, fires, and soils and fertilizer use), aircraft emissions, and lightning emissions. We focus on the tropospheric sources and exclude the stratospheric NOy source from N2O because it is small in the global troposphere, although it could be important in the upper troposphere in the high latitudes in summer (Levy et al., 1999).
The source contributions are derived from three sensitivity simulations with small (20%) perturbation to each source in turn 680 and are calculated as

685
Over the northern midlatitude oceans, in February, most of the NOx in the free troposphere is supplied by surface and aircraft sources. Both sources contribute equally (42%) to the free tropospheric NOx column, but surface emissions are dominant below 6 km and aircraft emissions above 6 km. In August, lightning is the dominant source of NOx, supplying 55% of the NOx column in the free troposphere. Aircraft emissions contribute 33% but are the major source of NOx between 10 and 12 km. Aircraft emissions account for the higher NOx concentrations in the upper troposphere over the northern midlatitudes than over the 690 tropics and southern midlatitudes. Lightning is the dominant source of NOx in the tropics and the southern midlatitudes, supplying 62-68% of the free tropospheric NOx column, with surface sources supplying 18-30% of NOx. However, Bourgeois et al. (2021) found that models tend to underestimate the contribution of biomass burning emissions to NOx over the remote oceans.

705
Comparing the NOx source contributions over the northern midlatitude oceans to those over the contiguous US, we find that the NOx sources over the oceans and the US are similar in winter. Surface and aircraft sources each supply about 40% of NOx in the free troposphere in February over the US, with surface sources dominating below 4 km and aircraft sources in the upper troposphere. In August, lightning emissions supply 73% of the NOx in the free troposphere over the US, much more than in winter and over the oceans. Previous modeling studies have also found lightning to be the main source of NOx in the tropics 710 and southern midlatitudes, and a seasonal change in the main source in the northern midlatitudes from lightning in summer to surface and aircraft emissions in winter (Lamarque et al., 1996;Levy et al., 1999). But the contribution of aircraft emissions to free tropospheric NOx in our simulation is higher than in these previous studies, reflecting a nearly two-fold increase in global aircraft NOx emissions in the past three decades (Hoesly et al., 2018).

Implications for the retrieval and interpretation of satellite NO2 data 715
We showed that the previously reported model underestimate of NO2 concentrations in the upper troposphere over the US can be attributed to interference in the NO2 measurements, and that when compared with the measured NO and PSS NO2 profiles, the modeled NO2 profiles in the free troposphere are consistent with the SEAC 4 RS, DC3, and ATom observations. This increases our confidence in the modeled NO2 profiles and here we use them to examine the importance of the free troposphere in the retrieval and interpretation of satellite NO2 data over the US. Figure 9 shows the GEOS-Chem vertical profiles of the 720 NO2 number density in the early afternoon (OMI and TROPOMI overpass time) over the contiguous US for summer and winter of 2015. The results are from our baseline simulation, but there is little difference in the NO2 profiles between our baseline simulation and the simulation without pNO3photolysis over the US (Fig. 1), except in spring when the NO2 concentrations in the free troposphere are about 10% higher due to the pNO3photolysis source.

725
In summer, simulated NO2 partial columns in the boundary layer and the free troposphere are 6.9⨯10 14 molec cm -2 and 5.8⨯10 14 molec cm -2 , respectively. In comparison, the simulated wintertime NO2 partial columns are 15.4⨯10 14 molec cm -2 and 1.9⨯10 14 molec cm -2 in the boundary layer and the free troposphere. The boundary layer NO2 column is higher in winter because of longer NOx chemical lifetimes Shah et al., 2020) and slower ventilation to the free troposphere, while the free troposphere NO2 column is higher in summer because of lightning emissions (Fig. 7). The GEOS-Chem 730 summertime NO2 column density in the free troposphere over the US is about three times higher than the PSS-inferred NO2 column over the oceans during ATom. In winter, by contrast, the free tropospheric NO2 column over the US is similar to that over the oceans, indicating little contrast in free tropospheric NO2 between the US and surrounding oceans as was previously discussed in the context of Fig. 8. The similarity in free tropospheric NO2 between the US and the oceans in winter reflects the longer lifetime of NOx and higher pNO3concentrations over the ocean. It also implies that ATom observations over the 735 northern midlatitudes in February could be used to estimate the free tropospheric NO2 concentrations over the US in winter, in the absence of aircraft observations over land that probe the full height of the winter troposphere. Marais et al. (2018) had compared the GEOS-Chem NO2 concentrations at 6-10 km with those derived from the OMI cloud-sliced product (Choi et al., 2014) for 2005-07 and found that GEOS-Chem underestimates NO2 concentrations over North America in winter by about a factor of 3. The successful simulation of the measured NO and the PSS NO2 concentrations over the northern midlatitudes 740 in winter during ATom suggests that there is little bias in the free tropospheric NO2 concentrations in the model, and that the underestimate with respect to the OMI observations likely reflects uncertainties in the cloud-slicing technique.  We calculate the seasonal AMFs corresponding to the GEOS-Chem and GMI NO2 profiles (Eq. 6) to determine the effect of 765 different a priori profiles on the retrieved NO2 columns. As before, we use scattering weights from the NASA OMI NO2 retrieval (v4.0) and exclude scenes with cloud fraction greater than 0.1 and surface albedo greater than 0.3. The scattering weight profile over the US is shown in Fig. 9a and shows values decreasing by a factor of 5 between the upper troposphere and the surface. The gradient is steeper than that for strictly clear-sky conditions (Martin et al., 2002). There is little seasonal difference in the scattering weight profile because scenes with high cloud fraction and bright surfaces were excluded, but 770 AMFG is higher in winter (3.7) than in summer (2.6) because of higher solar zenith angles. In summer, the AMF calculated using the GEOS-Chem profile is 1.14 ± 0.11, compared to 1.33 ± 0.20 calculated with the GMI profile. In winter, the AMFs from the two models are nearly identical (about 1.0). The AMFs are lower in winter than in summer because of higher NO2 concentrations in winter in the boundary layer where satellite measurements are less sensitive. GEOS-Chem NO concentrations in the free troposphere were about 2 times higher than the measurements during SEAC 4 RS and DC3 (Fig. 1). If we decrease 775 the GEOS-Chem NO2 number density in the free troposphere by half in summer, then the AMF decreases to 0.98. Decreasing the NO2 number density by half in the free troposphere and the boundary layer would have no effect on the AMF, since the shape factor (Eq. 6) would remain the same. Boersma et al. (2018) estimated a single-pixel uncertainty in the QA4ECV retrieval AMFs over the US of 20% in summer and 25% in winter, attributing about half (10%) of it to NO2 profile uncertainty and the remaining to uncertainties in surface albedo and cloud properties. However, we find that the uncertainty in AMFs from 780 errors in the a priori NO2 profiles in summer is larger than 10%. where ( ) is the percent contribution to the tropospheric NO2 column from NO2 at and above altitude z, zt is the tropopause altitude, and w(z) and n(z) are the vertical profiles of scattering weight and NO2 number density. The contribution of the free troposphere to NO2 columns is significantly higher in summer than in winter. In summer, the free troposphere contributes 65 ± 9% of the tropospheric NO2 column over the US in GEOS-Chem (75 ± 10% in GMI), whereas in winter, 75 ± 11 % of the NO2 column resides below 2 km. The free tropospheric contribution decreases to 55% if we halve the GEOS-Chem NO2 790 column in the free troposphere in summer. Travis et al. (2016) had also calculated a free troposphere contribution of 70-75% from the GEOS-Chem NO2 profiles in SEAC 4 RS.
The large contribution of the free troposphere to NO2 columns affects the interpretation of satellite data in terms of NOx emissions. It greatly diminishes the sensitivity of the summertime NO2 columns to changes in surface NOx emissions over the 795 US. The free tropospheric contribution would be relatively smaller over major cities, where summertime NO2 columns exceed 3⨯10 15 molec cm -2 (Lamsal et al., 2021), but it still needs to be accounted for. Urban NOx emissions and their trends are commonly derived by fitting an exponential decay function to satellite NO2 columns downwind of the source (e.g., Beirle et al., 2011;Lorente et al., 2019;Goldberg et al., 2021). The fitting function includes a background offset term and thus implicitly accounts for the free tropospheric contribution. The free tropospheric contribution is also accounted for when models that 800 include lightning and aircraft NOx emissions are used to relate NO2 columns to NOx emissions, but there is substantial uncertainty in the magnitude and distribution of lightning NOx emissions (Schumann and Huntrieser, 2007;Murray, 2016), which is the main source of NO2 in the free troposphere in summer. Missing organic NOx chemistry in summer would also contribute to model errors in the free tropospheric NO2, as suggested by our SEAC 4 RS and DC3 analysis. Wintertime NO2 columns will respond more strongly to changes in NOx emissions, but the uncertainty in the NO2 retrievals associated with 805 surface albedo and clouds is larger in winter (Boersma et al., 2018). Better observational constraints on free tropospheric NO2 concentrations are needed.

Conclusions
We used aircraft measurements from the SEAC 4 RS, DC3, and ATom campaigns to evaluate the vertical distribution of NOx in the free troposphere in the GEOS-Chem, GMI, TM5, and CAMS atmospheric chemistry models in the context of their use 810 for retrieval and interpretation of satellite NO2 column measurements. We first examined the accuracy of the in situ NO2 measurements in the upper troposphere using observations made in a thunderstorm outflow during the DC3 campaign. We found that the laser induced fluorescence (LIF) and the photolysis-chemiluminescence (P-CL) NO2 measurements were significantly higher than the NO2 concentrations calculated using the NO measurements and the NO-NO2 photochemical steady state (PSS), and that the ozone production expected based on these NO2 measurements was much higher than the observed 815 ozone production. This indicates a positive interference in the NO2 measurements, presumably from dissociation of non-radical NOy species such as HNO4 and methyl peroxy nitrate (MPN), even though the LIF measurements include a correction for the thermal dissociation of MPN. The underestimate in modeled NO2 concentrations relative to the LIF measurements in the upper troposphere reported previously (Travis et al., 2016;Silvern et al., 2018) is likely due to the interference in the NO2 measurements. There is a need to improve NO2 measurements in the free troposphere. At present, NO2 concentrations inferred 820 by applying PSS to NO and other measurements provide a better estimate of free tropospheric NO2 than the direct measurements, and we use them as basis for evaluating the models.
GEOS-Chem reproduces the shapes of the vertical profiles of the NO observations and the PSS-inferred NO2 concentrations during SEAC 4 RS and DC3 over the southeastern US in summer. The NO2 air mass factors (AMFs) calculated using the 825 measured (PSS) and the GEOS-Chem NO2 vertical profiles combined with scattering weights from the NASA OMI NO2 v4.0 retrievals differ by less than 10%. However, GEOS-Chem overestimates NO2 concentrations in the free troposphere for SEAC 4 RS and DC-3 by about a factor of 2, and underestimates concentrations of MPN and alkyl nitrates, suggesting missing organic NOx chemistry in the model that needs further examination.

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The NO concentrations measured over the Pacific and Atlantic Oceans were reproduced by GEOS-Chem when pNO3photolysis was included in the model with photolysis frequencies 10-100 times higher than that of gas-phase HNO3, as suggested by laboratory studies of pNO3photolysis and field studies of HONO sources in the marine atmosphere (Ye et al., 2016a(Ye et al., , 2017bAndersen et al., 2022). The median NO2 column density for the ATom campaign was 1.7 ± 0.44 ⨯10 14 molec cm -2 for the observed PSS NO2 concentrations, and 2.4⨯10 14 molec cm -2 for GEOS-Chem with pNO3photolysis and 1.5⨯10 14 835 molec cm -2 without. The NO2 column density for the GMI, TM5, and CAMS models was between 1.4 and 2.5⨯10 14 molec cm -2 and the NO2 AMFs calculated using the PSS NO2 profiles and the simulated NO2 profiles differed by less than 20%. We conclude that model errors in the tropospheric NO2 profiles over the remote oceans are not a major source of uncertainty in the satellite NO2 retrievals. We calculated the contribution of surface, aircraft, and lightning emissions to NOx columns over the Pacific and Atlantic Oceans and over the US in GEOS-Chem, and found that lightning is the main NOx source over the 840 tropics and southern midlatitudes, and over the US in the summer, contributing 62-73% of the NOx columns in the free troposphere. However, aircraft emissions are the main source of free tropospheric NOx in the northern mid-latitudes in winter and in summer over the oceans.
pNO3photolysis increases the global tropospheric mass of NOx, OH and ozone in GEOS-Chem by 9%, 19%, and 10%, 845 respectively. NOx concentrations increase most in the tropical MBL where NOx sources from PAN are small. There is a small increase in NOx concentrations in the free troposphere over the continents, particularly in spring when the pNO3concentration is highest. The increase in OH concentrations would degrade the model performance relative to OH measurements in ATom, but the ATom observations also indicate an underestimate in the modeled OH reactivity in the lower troposphere (Travis et al., 2020) implying missing OH sinks in the model. pNO3photolysis increases ozone concentrations by up to 8 ppbv at the 850 surface in the tropics and subtropics, and by 5 ppbv in the free troposphere over the northern extratropics, which would largely correct the low model bias relative to ozonesonde observations (Wang et al., 2021).
The seasonal GEOS-Chem and GMI afternoon NO2 profiles over the contiguous US are largely consistent with each other and show higher boundary layer NO2 columns in winter than in summer because of longer NOx chemical lifetimes and slower 855 ventilation to the free troposphere, but higher free tropospheric NO2 columns in summer because of lightning emissions. In winter, the free troposphere contributes 25 ± 11 % of the NO2 columns that would be observed by satellite instruments over the contiguous US, but in summer this increases to 65-75%, and weakens the sensitivity of the summertime NO2 columns to changes in surface NOx emissions. This is less of a problem for urban areas where boundary layer NO2 columns are generally much larger than the free tropospheric columns. 860 Author contributions: VS and DJJ designed the study and led the analysis. RD helped with interpreting the GEOS-Chem results. LNL, SAS, and SDS provided the GMI simulation results and KFB provided the TM5 and CAMS results. SDE and 870 TMF provided the updated AEIC inventory. CT, JP, IB, IP, BAN, RCC, PCJ, and JLJ made the NO, NO2, NOy, ozone, and pNO3measurements during the SEAC 4 RS, DC3, and ATom campaigns. STA, LJC, TS, and MJE helped with the pNO3photolysis simulation. VS and DJJ wrote the paper with input from all authors.
Competing interests: The authors declare that they have no conflict of interest. 875 Acknowledgements: We are grateful to the instrument teams of the SEAC 4 RS, DC3 and ATom campaigns for making their data freely available. We thank Tom Ryerson (NOAA) for contributing to the NO, NO2, NOy, and O3 measurements in the three campaigns, and Eloïse Marais (U. College London) and Sunny Choi (NASA GSFC) for helpful discussions. This product/document has been created with or contains elements of Base of Aircraft Data (BADA) Family Release which has been made available by EUROCONTROL to MIT. EUROCONTROL has all relevant rights to BADA. ©2019 The European 880 Organisation for the Safety of Air Navigation (EUROCONTROL). All rights reserved. EUROCONTROL shall not be liable for any direct, indirect, incidental, or consequential damages arising out of or in connection with this product or document, including with respect to the use of BADA. GMI is supported by the NASA Modeling, Analysis, and Prediction (MAP) program. GMI simulations used computational resources from the NASA High-End Computing (HEC) Program through the NASA Center for Climate Simulation (NCCS). JLJ and PCJ were supported by NASA Grant 80NSSC21K1451. 885 Financial support: This work was supported by the NASA Aura Science Team and by the US EPA Science To Achieve Results (STAR) program.