Nitrogen oxides in the free troposphere: implications for tropospheric oxidants and the interpretation of satellite NO₂ measurements

Satellite-based retrievals of tropospheric NO₂ columns are widely used to infer NO_x (≡ NO + NO₂) emissions. These retrievals rely on model information for the vertical distribution of NO₂. 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 (SEAC⁴RS, DC3, and ATom) and four atmospheric chemistry models (GEOS-Chem, GMI, TM5, and CAMS) to evaluate the model capabilities for simulating NO_x in the free troposphere and attribute it to sources. NO₂ measurements during the Studies of Emissions and Atmospheric Composition, Clouds, and Climate Coupling by Regional Surveys (SEAC⁴RS) and Deep Convective Clouds and Chemistry (DC3) campaigns over the southeastern U.S. in summer show increasing concentrations in the upper troposphere above 10 km, which are not replicated by the 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 (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 SEAC⁴RS and DC3 but overestimates NO₂ concentrations by about a factor of 2. The model underestimates MPN and alkyl nitrate concentrations, suggesting missing organic NO_x chemistry. On the other hand, the standard GEOS-Chem model underestimates NO observations from the Atmospheric Tomography Mission (ATom) campaigns over the Pacific and Atlantic oceans, indicating a missing NO_x 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 × 10¹⁴ molec. cm⁻², and the NO₂ column density simulated by the four models is in the range of 1.4–2.4 × 10¹⁴ molec. cm⁻², implying that the uncertainty from using modeled NO₂ tropospheric columns over clean areas in the retrievals for stratosphere–troposphere separation is about 1 × 10¹⁴ molec. cm⁻². We find from GEOS-Chem that lightning is the main primary NO_x 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 (parts per billion by volume) 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 19 %. The contribution of the free tropospheric background to the tropospheric NO₂ columns observed by satellites over the contiguous U.S. 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 NO_x emissions from satellite NO₂ column measurements.

1 Introduction

Retrievals of NO₂ tropospheric columns from satellite measurements of solar backscatter are used extensively to infer anthropogenic NO_x (≡ NO + 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, which is the part of the atmosphere between the top of the boundary layer (∼ 2 km altitude) and the tropopause. NO_x 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 NO_x emissions have decreased in the U.S. 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 (Travis et al., 2016; Silvern et al., 2018). Here we use the vertical distribution of tropospheric NO_x from aircraft measurements over land and ocean, simulated with the 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 NO_x emissions.

Accurate in situ measurements of NO₂ in the free troposphere are challenging because of low NO₂ concentrations and interferences from labile non-radical NO_x 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 or P-CL; Walega et al., 1991; Ryerson et al., 2000; Bourgeois et al., 2022) 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 – parts per billion by volume) 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 (parts per trillion by volume) and 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., 1990b; 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 the NO–NO₂ photochemical steady state (PSS; Davis et al., 1993; Fan et al., 1994; Crawford et al., 1996). This 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 (Nault et al., 2015; Reed et al., 2016).

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 the 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 NO₂ measurements in the upper troposphere over the southeastern U.S. during the Studies of Emissions and Atmospheric Composition, Clouds, and Climate Coupling by Regional Surveys (SEAC⁴RS) 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.

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-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, 2021).

Atmospheric chemistry models are often used alongside satellite NO₂ measurements to determine surface NO_x emissions and their trends, as they provide a way to relate changes in NO₂ columns to surface NO_x 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 parameterized lightning NO_x 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 NO_x 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 their importance for the production of tropospheric ozone and the hydroxyl radical (OH) and have generally found agreement within a factor of 2 (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 Mission (ATom) campaign's first deployment (July–August 2016) found a 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 NO_x in models over the subtropical oceans from fast photolysis of particulate nitrate (Ye et al., 2016; Reed et al., 2017; Kasibhatla et al., 2018; Andersen et al., 2023) or from oceanic emissions (Fisher et al., 2018).

Here we use data from the SEAC⁴RS and the Deep Convective Clouds and Chemistry (DC3) aircraft campaigns to demonstrate the pervasiveness of interference from non-radical NO_x reservoirs in NO₂ measurements in the upper troposphere. We go on 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 SEAC⁴RS, DC3, and ATom campaigns. We use the model results to examine the sources of NO_x in the free troposphere, effects on tropospheric ozone and OH, and contribution of the free tropospheric background to satellite NO₂ columns over the U.S.

2 Methods

2.1 Aircraft observations

We use observations from the SEAC⁴RS (August–September 2013; Toon et al., 2016) and DC3 (April–May 2012; Barth et al., 2015) campaigns over the southeastern U.S. (25–40^∘ N; 65–100^∘ W) and the ATom campaign (four seasonal deployments in 2016–2018) 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 describe the NO₂ and NO measurements, as they are most relevant. NO₂ measurements during the SEAC⁴RS and DC3 campaigns were made using the UC 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 SEAC⁴RS 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) and the fractional thermal decomposition of MPN in the NO₂ channel, considering the temperature of the channel (15–25 ^∘C) and the instrument residence time (0.23 s for SEAC⁴RS 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 National Oceanic and Atmospheric Administration (NOAA) Nitrogen Oxides and Ozone (NOyO3) instrument, using the P-CL technique (Ryerson et al., 2000; Bourgeois et al., 2022). The NOAA instrument also provided NO₂ measurements in SEAC⁴RS 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, 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 20–30 ^∘C 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 much of the troposphere where HONO concentration is generally less than 10 pptv (Ye et al., 2016; Andersen et al., 2023). 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 10 nm > 10⁴ cm⁻³), fresh NO_x emissions (NO_y $/$ NO < 3 mol mol⁻¹), biomass burning plumes (CO > 200 ppbv and CH₃CN > 200 pptv), and stratospheric intrusions (O₃ > 100 ppbv or CO < 45 ppbv).

Table 1 Measurements from the SEAC⁴RS, DC3, and ATom aircraft campaigns^a.

^a Measurements used in this work to evaluate the NO_x simulations and to select data for analysis. ^b Instrument acronyms: TD-LIF is thermal dissociation laser-induced fluorescence, ATHOS is the Airborne Tropospheric Hydrogen Oxides Sensor, CIMS is the chemical ionization mass spectrometer, NCAR is the National Center for Atmospheric Research, CAFS is the charged-coupled device (CCD) actinic flux spectroradiometer, HR-AMS is the high-resolution aerosol mass spectrometer, SAGA is soluble acidic gases and aerosols, PANTHER is the PAN and Trace Hydro-halocarbon ExpeRiment, CPC is the condensation particle counter, DACOM is the differential absorption carbon monoxide monitor, and PTR-MS is proton transfer reaction mass spectrometry. ^c Estimated accuracy at analyte concentrations well above the detection limit. ^d Total reactive nitrogen oxides, including NO_x and its oxidation products. ^e The AMS measures the composition of non-refractory submicron aerosols. SAGA measures the ionic composition of water-soluble bulk aerosols with a diameter of less than about 4 µm. ^f Commercial instrument operated by the NASA Langley Aerosol Research Group Experiment.

2.2 GEOS-Chem model

We use the GEOS-Chem atmospheric chemistry model (12.9.3; https://doi.org/10.5281/zenodo.3959279, The International GEOS-Chem User Community, 2020​​​​​​​) with a modification to include inorganic particulate nitrate (pNO${}_{\mathrm{3}}^{-}$) photolysis as described below. Our simulations are driven by assimilated meteorology from NASA Global Modeling and Assimilation Office (GMAO)'s Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2; Gelaro et al., 2017). We conduct global simulations at 4^∘ × 5^∘ horizontal resolution (47 levels in the vertical) for the time periods corresponding to the following aircraft campaigns: SEAC⁴RS (July–August 2013), DC3 (May–June 2012), and ATom (July–August 2016, January–February 2017, September–October 2017, and April–May 2018), as well as an annual simulation for 2015. Previous work on the SEAC⁴RS campaign used finer-resolution simulations (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 similar results (Yu et al., 2016). The horizontal grid resolution can lead to localized differences in the upper troposphere from stratospheric intrusions, convective transport, and lightning NO_x emissions (Schwantes et al., 2022), and we minimize these effects by filtering out data influenced by the stratosphere, fresh convection, and fresh NO_x emissions, as described above. The spin-up period for our simulations is 6 months. Comparison to aircraft measurements is done by sampling the model along the flight path as an online diagnostic during the model simulation.

Table 2 lists the global NO_x emissions in our 2015 simulation. Anthropogenic NO_x emissions are from the Community Emissions Data System (CEDS) global inventory (Hoesly et al., 2018), superseded with regional emission inventories for the U.S. (U.S. EPA 2011 NEI, 2021), Canada (Air Pollutant Emissions Inventory, 2021), Africa (Marais and Wiedinmyer, 2016), and China (Zheng et al., 2018). The U.S. EPA 2011 National Emissions Inventory (NEI) is scaled annually using EPA-estimated emissions trends (U.S. EPA Air Pollutant Emissions Trends Data, 2021). Travis et al. (2016) had to scale down the NEI NO_x emissions in GEOS-Chem by 40 % to reproduce the SEAC⁴RS NO_x observations, but we do not do this in our simulations as it leads to an underestimate of NO_x in other seasons (Jaeglé et al., 2018; Silvern et al., 2019). Open fire NO_x emissions are from the GFEDv4 inventory (Giglio et al., 2013). Ship NO_x emissions are from CEDS and are processed using the PARAmetrization of emitted NO_x (PARANOX) model to account for fast in-plume NO_x oxidation (Vinken et al., 2011; Holmes et al., 2014). Aircraft NO_x 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 NO_x 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. Emissions are computed at the native MERRA-2 resolution (0.5^∘ × 0.625^∘). NO yields of 500 mol per flash are used for the northern midlatitudes (> 35^∘ N) and 260 mol per flash elsewhere. Emissions are distributed in the vertical following Ott et al. (2010). Soil and fertilizer NO_x emissions are from Hudman et al. (2012) and are computed at 0.5^∘ × 0.625^∘ resolution (Weng et al., 2020).

Table 2 Global NO_x emissions in 2015^a.

^a As used in our GEOS-Chem simulation. ^b References for the different sources are given in the text. ^c Not including the NO_x source of ∼ 0.5 Tg N a⁻¹ from downwelling of stratospheric NO_y produced from N₂O.

GEOS-Chem includes a detailed representation of NO_x–HO_x–VOC–aerosol–halogen chemistry (where VOC is a volatile organic compound; Mao et al., 2013; Travis et al., 2016; Holmes et al., 2019; Wang et al., 2021; McDuffie et al., 2021; Pai et al., 2020). Recent improvements to the model's NO_x chemistry include the 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 NO_x 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 partitioning of HNO₃ to pNO${}_{\mathrm{3}}^{-}$ on 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 pNO${}_{\mathrm{3}}^{-}$ on coarse sea salt aerosols is treated as a kinetic process, following Wang et al. (2019). Sea salt aerosol emissions follow Jaeglé et al. (2011) and are calculated at 0.5^∘ × 0.625^∘ 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).

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 likely originate from pNO${}_{\mathrm{3}}^{-}$ photolysis (Ye et al., 2016; Andersen et al., 2023) and would provide a fast source of NO_x missing from the model. We address this by including pNO${}_{\mathrm{3}}^{-}$ photolysis in our simulation, following the implementation of this reaction in GEOS-Chem by Kasibhatla et al. (2018). The photolysis frequency of pNO${}_{\mathrm{3}}^{-}$ 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., 2017b; 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 NO_x and HONO observations over the oceans (Ye et al., 2016, 2017a; Reed et al., 2017; Kasibhatla et al., 2018; Zhu et al., 2022; Andersen et al., 2023), with higher values for pNO${}_{\mathrm{3}}^{-}$ in sea salt aerosols (Andersen et al., 2023). Consistent with these studies, we find that we can match the ATom NO observations by using an EF of 100 for pNO${}_{\mathrm{3}}^{-}$ in sea salt aerosol. In our model, coarse-mode pNO${}_{\mathrm{3}}^{-}$ is only present in sea salt aerosols and has an EF of 100, but fine-mode pNO${}_{\mathrm{3}}^{-}$ is internally mixed with sulfate, ammonium, and sea salt aerosol. So we decrease the EF of fine-mode pNO${}_{\mathrm{3}}^{-}$, depending on the relative amounts of pNO${}_{\mathrm{3}}^{-}$ and sea salt aerosol, as follows:

$$\begin{array}{}\text{(1)}& \mathrm{EF}=max\left(\mathrm{100}\times {\displaystyle \frac{\mathrm{1}}{\mathrm{1}+\frac{\left[p{\mathrm{NO}}_{\mathrm{3}}^{-}\right]}{\left[\mathrm{SSA}\right]}}},\mathrm{10}\right).\end{array}$$

Here $\left[p{\mathrm{NO}}_{\mathrm{3}}^{-}\right]$ and [SSA] are the molar concentrations in air of fine-mode pNO${}_{\mathrm{3}}^{-}$ and sea salt aerosol. The molar concentration of sea salt is taken as $\left[\mathrm{SSA}\right]=\mathrm{2.39}\left[{\mathrm{Na}}^{+}\right]$, based on the fraction of Na⁺ in seawater (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 pNO${}_{\mathrm{3}}^{-}$ aerosols in the range 1–30 from observations over South Korea. The relative yields of HONO : NO₂ from pNO${}_{\mathrm{3}}^{-}$ photolysis are taken as 2 : 1 (Ye et al., 2017b; Kasibhatla et al., 2018). We will discuss the effect of pNO${}_{\mathrm{3}}^{-}$ photolysis on remote NO_x concentrations in more detail in Sect. 3.2.

2.3 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 massively parallel version of the tracer model version 5 (TM5-MP), and the Copernicus 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 Ozone Monitoring Instrument (OMI) NO₂ retrievals (Krotkov et al., 2017; Lamsal et al., 2021). The version used here has a horizontal resolution of 1^∘ × 1.25^∘. Strode et al. (2021) describe the GMI model simulations for the ATom campaign. The TM5-MP model is a high-resolution (1^∘ × 1^∘) version of the TM5 global atmospheric chemistry model developed specifically for application to satellite retrievals (Williams et al., 2017; Huijnen et al., 2010). It is driven by assimilated meteorology from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis. The TM5 NO₂ profiles are used in the Quality Assurance for Essential Climate Variables (QA4ECV) OMI and TROPOspheric Monitoring Instrument (TROPOMI) NO₂ retrievals (Boersma et al., 2018; van Geffen et al., 2022). CAMS provides a global reanalysis of atmospheric composition at a horizontal resolution of 80 km (T255) for the period from 2003 onwards (Inness et al., 2019). It is based on ECMWF's Integrated Forecast System (IFS) and uses 4D-Var data assimilation of satellite retrievals of NO₂, O₃, CO, and aerosol optical depth. The CAMS NO₂ profiles are planned for use in NO₂ retrievals from the European Sentinel-4 geostationary satellite (ESA Sentinel-4 Data Products, 2022). The TM5 and CAMS output along the ATom flight tracks was available only for the first ATom deployment (July–August 2016).

3 Results and discussion

3.1 Vertical distribution of NO_x over the U.S.

Figure 1 compares the median vertical profiles of the observed and GEOS-Chem NO and NO₂ concentrations for the SEAC⁴RS and DC3 aircraft campaigns. For both campaigns, the observed and GEOS-Chem NO concentrations (Fig. 1a, d) peak in the boundary layer and again in the upper troposphere because of lightning and aircraft emissions, convective lifting of surface emissions, long NO_x lifetime (except near fresh convection), and a shift in the daytime NO $/$ NO₂ ratio toward NO at low 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 SEAC⁴RS 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.

Figure 1 Median vertical profiles of observed and GEOS-Chem simulated NO concentrations (a, d), NO₂ concentrations (b, e), and NO $/$ NO₂ molar ratios (c, f) during the SEAC⁴RS (August–September 2013) and DC3 (April–May 2012) aircraft campaigns over the southeastern U.S. The NO measurements are from the NOAA P-CL instrument. NO₂ was measured by the Berkeley LIF and the NOAA P-CL instruments. The NO $/$ NO₂ ratios at the photochemical steady state (PSS; Eq. 2) and the corresponding NO₂ concentrations (Eq. 3) are also shown in panels (c) and (f). The PSS calculation is based mostly on observed quantities but uses modeled values for quantities that were not measured, as described in the text. Also shown in panels (c) and (f) are the NO $/$ NO${}_{\mathrm{2}}^{\ast }$ (NO${}_{\mathrm{2}}^{\ast }$ ≡ NO₂ + HNO₄ + MPN) ratios from GEOS-Chem. MPN is methyl peroxy nitrate. We exclude measurements in early mornings and late evenings (solar zenith angle > 70^∘) and those influenced by fresh NO_x emissions recent convection, biomass burning, and the stratosphere, as described in Sect. 2.1. The horizontal bars show the interquartile ranges of the measurements in each 1 km altitude bin.

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 SEAC⁴RS can be explained by the departure of the measured NO $/$ NO₂ ratio from that expected from the calculated PSS between NO and NO₂. In the daytime, NO and NO₂ interconvert rapidly through the following main reactions:

$$\begin{array}{}\text{(R1)}& {\displaystyle }\mathrm{NO}+{\mathrm{O}}_{\mathrm{3}}⟶{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{2}}\text{(R2)}& {\displaystyle }\mathrm{NO}+{\mathrm{HO}}_{\mathrm{2}}⟶{\mathrm{NO}}_{\mathrm{2}}+\mathrm{OH}\text{(R3)}& {\displaystyle }\mathrm{NO}+{\mathrm{RO}}_{\mathrm{2}}⟶{\mathrm{NO}}_{\mathrm{2}}+\mathrm{RO}\text{(R4)}& {\displaystyle }\mathrm{NO}+\mathrm{BrO}⟶{\mathrm{NO}}_{\mathrm{2}}+\mathrm{Br}\text{(R5)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+h\mathit{\nu }\stackrel{+{\mathrm{O}}_{\mathrm{2}}}{⟶}\mathrm{NO}+{\mathrm{O}}_{\mathrm{3}}.\end{array}$$

Here RO₂ represents the ensemble of organic peroxy radicals. At PSS, the NO $/$ NO₂ ratio is given by the following:

$$\begin{array}{}\text{(2)}& \begin{array}{rl}\mathrm{PSS}& ={\displaystyle \frac{\left[\mathrm{NO}\right]}{\left[{\mathrm{NO}}_{\mathrm{2}}\right]}}\\ & ={\displaystyle \frac{j_{{\mathrm{NO}}_{\mathrm{2}}}}{k_{\mathrm{1}}\left[{\mathrm{O}}_{\mathrm{3}}\right]+k_{\mathrm{2}}\left[{\mathrm{HO}}_{\mathrm{2}}\right]+k_{\mathrm{3}}\left[{\mathrm{RO}}_{\mathrm{2}}\right]+k_{\mathrm{4}}[\mathrm{BrO}]}},\end{array}\end{array}$$

where $j_{{\mathrm{NO}}_{\mathrm{2}}}$ is the NO₂ photolysis frequency, and k_i is the rate constant of reaction i. We calculate the PSS NO $/$ NO₂ ratio for the SEAC⁴RS and DC3 data using concurrent aircraft measurements and GEOS-Chem-simulated values along the flight path for quantities that were not measured. [O₃] and $j_{{\mathrm{NO}}_{\mathrm{2}}}$ were measured in both campaigns. [HO₂] was measured only in DC3, but H₂O₂ concentrations measured in SEAC⁴RS are consistent with GEOS-Chem (Silvern et al., 2018), which provides support for the model [HO₂]. Rate constants are as recommended by the Jet Propulsion Laboratory (JPL) evaluation (Burkholder et al., 2020) and adjusted for temperature and pressure. We take the NO+CH₃O₂ 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+O₃ 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). We estimate the uncertainty in the PSS NO $/$ NO₂ ratio at 1 Hz of about ± 20 %, based on uncertainties in the [O₃], [HO₂], and $j_{{\mathrm{NO}}_{\mathrm{2}}}$ measurements (Table 1), rate constants (10 %; Burkholder et al., 2020), and model [RO₂] and [BrO] (assumed to be 50 %).

Figure 1c, 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 $j_{{\mathrm{NO}}_{\mathrm{2}}}$ 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 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 $/$ NO${}_{\mathrm{2}}^{\ast }$​​​​​​​ (NO${}_{\mathrm{2}}^{\ast }$ ≡ NO₂ + HNO₄ + MPN) in GEOS-Chem 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 (Nault et al., 2015). The LIF instrument was modified between DC3 and SEAC⁴RS to shorten the sample residence time and reduce the fraction of MPN dissociating in the instrument (Nault et al., 2015), but we do not find that this improved agreement between the measured and PSS NO $/$ NO₂ (Fig. 1c, f). It is also possible 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.

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 NO_x and NO_y (NO_y ≡ NO_x + non-radical reservoirs) on this flight to determine NO_x oxidation rates and showed a steady decrease with time in the NO and NO₂ concentrations and an increase in the NO_y oxidation products during the 2 h sampling period. Figure 2a shows the flight path with daytime plume crossings colored by the measured NO_y $/$ NO molar ratio. The NO_y $/$ NO ratio increases on each successive plume crossing as NO_x undergoes oxidation in the outflow, and we use the ratio as a measure of chemical aging in the plume (Kleinman et al., 2008; Hayes et al., 2013). Figure 2b shows the measured NO, NO₂, and the sum of HNO₄ and MPN concentrations as a function of the NO_y $/$ NO ratio. NO concentrations decreased from 900 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 as follows:

$$\begin{array}{}\text{(3)}& [{\mathrm{NO}}_{\mathrm{2}}{]}_{\mathrm{PSS}}={\displaystyle \frac{\left[\mathrm{NO}\right]}{\mathrm{PSS}}},\end{array}$$

where PSS is calculated from observations using Eq. (2) and measured [O₃], [HO₂], and $j_{{\mathrm{NO}}_{\mathrm{2}}}$. 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.

Figure 2 Evolution of NO_x and O₃ concentrations in a thunderstorm outflow targeted for quasi-Lagrangian sampling by DC3 flight 17 over the central U.S. at 12 km altitude. Panel (a) shows the flight track with data points within the outflow colored by the observed NO_y $/$ NO ratio as a measure of chemical aging. The arrow shows the mean wind direction. Panel (b) shows the measured concentrations of NO, NO₂, and the sum of HNO₄ and MPN as a function of the NO_y $/$ NO molar ratio. Also shown are the PSS NO₂ concentrations (Eq. 3). Panel (c) shows the measured ozone concentrations as a function of the NO_y $/$ NO molar ratio along with the ozone concentrations calculated from Eq. (4), with NO₂ concentrations from LIF, P-CL, or PSS NO₂. The circles and the error bars in panels (b) and (c) show the means and standard deviations for each NO_y $/$ NO bin.

Figure 2c shows the observed ozone concentrations as a function of the NO_y $/$ NO ratio. Ozone concentrations increase with the age of the plume, reflecting the NO_x-limited conditions for ozone production prevalent in the upper troposphere over the central U.S. 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 $j_{{\mathrm{NO}}_{\mathrm{2}}}$ 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 vapor (Reaction R6), and oxidation by HO₂ and OH (Reactions R7 and R8).

$$\begin{array}{}\text{(R6)}& {\mathrm{O}}_{\mathrm{3}}+h\mathit{\nu }\stackrel{+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}{⟶}\mathrm{2}\mathrm{OH}+{\mathrm{O}}_{\mathrm{2}}\end{array}$$

$$\begin{array}{}\text{(R7)}& {\displaystyle }{\mathrm{O}}_{\mathrm{3}}+{\mathrm{HO}}_{\mathrm{2}}⟶\mathrm{2}{\mathrm{O}}_{\mathrm{2}}+\mathrm{OH}\text{(R8)}& {\displaystyle }{\mathrm{O}}_{\mathrm{3}}+\mathrm{OH}⟶{\mathrm{HO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{2}}.\end{array}$$

The instantaneous net ozone production rate is then given as follows:

$$\begin{array}{}\text{(4)}& \begin{array}{rl}{\displaystyle \frac{\mathrm{d}\left[{\mathrm{O}}_{\mathrm{3}}\right]}{\mathrm{d}t}}& =j_{{\mathrm{NO}}_{\mathrm{2}}}\left[{\mathrm{NO}}_{\mathrm{2}}\right]-k_{\mathrm{NO}+{\mathrm{O}}_{\mathrm{3}}}\left[\mathrm{NO}\right]\left[{\mathrm{O}}_{\mathrm{3}}\right]\\ & -k_{{\mathrm{O}}_{\mathrm{3}}\to \mathrm{OH}}\left[{\mathrm{O}}_{\mathrm{3}}\right]-k_{{\mathrm{HO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}}\left[{\mathrm{HO}}_{\mathrm{2}}\right]\left[{\mathrm{O}}_{\mathrm{3}}\right]\\ & -k_{\mathrm{OH}+{\mathrm{O}}_{\mathrm{3}}}\left[\mathrm{OH}\right]\left[{\mathrm{O}}_{\mathrm{3}}\right],\end{array}\end{array}$$

where

$$\begin{array}{}\text{(5)}& k_{{\mathrm{O}}_{\mathrm{3}}\to \mathrm{OH}}={\displaystyle \frac{j_{{\mathrm{O}}_{\mathrm{3}}\to \mathrm{O}{(}^{\mathrm{1}}\mathrm{D})}{k}_{\mathrm{O}{(}^{\mathrm{1}}\mathrm{D})+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}{k_{\mathrm{O}{(}^{\mathrm{1}}\mathrm{D})+\mathrm{M}}}}{\displaystyle \frac{\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]}{\left[\mathrm{M}\right]}},\end{array}$$

and $j_{{\mathrm{O}}_{\mathrm{3}}\to \mathrm{O}{(}^{\mathrm{1}}\mathrm{D})}$ is the frequency of the O₃ photolysis channel producing O(¹D) and was measured on the flight. [H₂O] and [M] are calculated from meteorological observations on the flight. $k_{\mathrm{O}{(}^{\mathrm{1}}\mathrm{D})+\mathrm{M}}$ is the weighted-average reaction rate constant of O(¹D) 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 integrating $\frac{\mathrm{d}\left[{\mathrm{O}}_{\mathrm{3}}\right]}{\mathrm{d}t}$ over the measurement period.

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, 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 $j_{{\mathrm{NO}}_{\mathrm{2}}}$ by 20 % and increasing ${\mathrm{k}}_{\mathrm{NO}+{\mathrm{O}}_{\mathrm{3}}}$ 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, which is still much higher than the observed increase, 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 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 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 non-acyl peroxy nitrates would not be significant (Khan et al., 2020), but there could be other unknown organic NO₂ reservoir 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 NO_x in the free troposphere (Fig. 1). GEOS-Chem reproduces the shape of the NO and the PSS NO₂ profiles throughout the troposphere for SEAC⁴RS 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 SEAC⁴RS (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 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 SEAC⁴RS and DC3 profiles in Fig. 1 are 3.6 × 10¹⁴ and 3.8 × 10¹⁴ molec. cm⁻², respectively, compared to 6.5 × 10¹⁴ and 10.4 × 10¹⁴ molec. cm⁻² in GEOS-Chem. However, the model does not overestimate NO_y concentrations, suggesting that the model may be missing NO_x 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 observations, consistent with the findings of Silvern et al. (2018) for SEAC⁴RS. Similarly, median alkyl nitrate concentration in the model is about 12 pptv but 60 pptv in the observations. NO_x emissions are likely overestimated in the U.S. 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 NO_x. Finally, we find little difference in the SEAC⁴RS and DC3 NO_x profiles in the free troposphere between our baseline simulation and the simulation without pNO${}_{\mathrm{3}}^{-}$ photolysis, indicating that chemical recycling through pNO${}_{\mathrm{3}}^{-}$ photolysis is a minor source of NO_x over the U.S. 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 contribution to calculate the tropospheric slant column density Ω_s, and (iii) conversion of the tropospheric slant column density to a tropospheric vertical column density Ω_v, using an air mass factor (AMF) that depends on the vertical profile of NO₂ (Palmer et al., 2001; Martin et al., 2002).

$$\begin{array}{}\text{(6)}& {\displaystyle \frac{{\mathrm{\Omega }}_{\mathrm{s}}}{{\mathrm{\Omega }}_{\mathrm{v}}}}=\mathrm{AMF}={\mathrm{AMF}}_{\mathrm{G}}\underset{\mathrm{0}}{\overset{z_t}{\int }}w\left(z\right)S\left(z\right)\mathrm{d}z,\end{array}$$

where AMF_G is the geometric AMF that describes the satellite viewing geometry, w(z) are the scattering weights that describe 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 z_t 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 surface albedo greater than 0.3.

We use Eq. (6) to calculate AMFs corresponding to PSS and GEOS-Chem NO₂ profiles for SEAC⁴RS and DC3. AMF_G over the southeastern U.S. 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 SEAC⁴RS, both the PSS 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 southeastern U.S. would result in an error of 0 %–10 %, compared to the previous error estimate of 30 % based on the LIF NO₂ measurements in SEAC⁴RS (Silvern et al., 2018). The sensitivity of satellite retrievals to NO₂ vertical profiles is discussed further in Sect. 3.5.

3.2 NO_x in the remote troposphere: interpreting the ATom data

We now examine the distribution of NO_x over the Pacific and Atlantic oceans during the ATom campaign in order to contrast the NO₂ profiles in the remote troposphere to the SEAC⁴RS 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). NO_x in the 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 $j_{{\mathrm{NO}}_{\mathrm{2}}}$ 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 NO_x lifetime and the increase in NO $/$ NO₂ ratios with altitude. The PSS NO₂ profiles show a decrease in NO₂ concentrations with altitude because of the increase in NO $/$ NO₂ ratios. PSS NO₂ concentrations in the upper troposphere are generally lower than 10 pptv, except in the northern midlatitudes in August and October, where NO₂ concentrations increase in the upper troposphere. The upper tropospheric NO_x concentrations over the Atlantic in August are similar to those observed over the southeastern U.S. during SEAC⁴RS and DC3 and reflect the transport of lightning-generated NO_x from the U.S. to the Atlantic Ocean (Crawford et al., 2000; Cooper et al., 2006; Singh et al., 2007). There is little seasonal variation in NO_x below 8 km. The column density for PSS NO₂ has a campaign median of 1.7 × 10¹⁴ molec. cm⁻² and a range of 1.2–3.0 × 10¹⁴ 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 (30–60^∘ N) in August is 2.1 × 10¹⁴ molec. cm⁻², which is about 45 % lower than that observed in SEAC⁴RS and DC3.

Figure 3 Median vertical profiles of NO concentrations over the Pacific and Atlantic oceans during the ATom flight campaigns (2016–2018), separated by seasons and latitude bands. Observations (black) are from the NOAA P-CL instrument. The data selection criteria are as described in the caption of Fig. 1. Horizontal bars show the interquartile ranges in 1 km altitude bins. Model results are from our baseline GEOS-Chem simulation and a sensitivity simulation without pNO${}_{\mathrm{3}}^{-}$ photolysis. The model is sampled along the flight tracks. NO concentrations are plotted on a log scale to show the values in the lower troposphere clearly.

Figure 4 Median vertical profiles of NO₂ concentrations over the Pacific and Atlantic oceans during the ATom flight campaigns (2016–2018), separated by seasons and latitude regions. Observations are based on the photochemical steady state (PSS) with local measurements of NO concentrations and other quantities, following Eqs. (2) and (3). Horizontal bars show the interquartile ranges in 1 km altitude bins. The data selection criteria are as described in the caption of Fig. 1. NO₂ measurements from the P-CL instrument are also shown for reference. Model results are from our baseline GEOS-Chem simulation (including pNO${}_{\mathrm{3}}^{-}$ photolysis), GMI, TM5, and CAMS, which are sampled along the flight tracks. The TM5 and CAMS NO₂ profiles are available only for August. NO₂ concentrations are plotted on a log scale. For clarity, the interquartile ranges for the GMI, TM5, and CAMS profiles are shown separately in Fig. S2.

Figure 3 compares the NO observations to results from our baseline GEOS-Chem simulation and from a sensitivity simulation without the NO_x source from pNO${}_{\mathrm{3}}^{-}$ photolysis. The GEOS-Chem simulation without pNO${}_{\mathrm{3}}^{-}$ photolysis 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 NO_x emissions. The underestimate is not related to NO_x recycling from HNO₃, PAN, or alkyl nitrates either. GEOS-Chem generally overestimates ATom HNO₃ observations (Fig. S1 in the Supplement; Travis et al., 2020; Luo et al., 2020). The model is consistent with the ATom observations of PAN in the tropics and southern midlatitudes 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 10⁸ molec. 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 NO_x sink from 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 it is not large enough to explain the NO underestimate. The representation of heterogenous NO_x chemistry in the model reflects current knowledge and includes an empirical parameterization for the N₂O₅ reaction probability derived from aircraft observations (Jaeglé et al., 2018; 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 pNO${}_{\mathrm{3}}^{-}$ could be much faster than photolysis of gas-phase HNO₃ and contribute an important source of NO_x over the oceans (Ye et al., 2016; Reed et al., 2017; Kasibhatla et al., 2018). pNO${}_{\mathrm{3}}^{-}$ photolysis produces NO₂ and HONO (Scharko et al., 2014; Ye et al., 2017b), and HONO photolyzes further to produce NO, as follows:

$$\begin{array}{}\text{(7a)}& {\displaystyle }p{\mathrm{NO}}_{\mathrm{3}}^{-}+h\mathit{\nu }& {\displaystyle }\stackrel{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\left(l\right)}{⟶}\mathrm{HONO}\left(\mathrm{g}\right)+{\mathrm{OH}}^{-}+\mathrm{O}{(}^{\mathrm{3}}\mathrm{P})\text{(7b)}& {\displaystyle }& {\displaystyle }\stackrel{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\left(l\right)}{⟶}{\mathrm{NO}}_{\mathrm{2}}\left(\mathrm{g}\right)+{\mathrm{OH}}^{-}+\mathrm{OH}\end{array}$$

$$\begin{array}{}\text{(8)}& \mathrm{HONO}+h\mathit{\nu }⟶\mathrm{NO}+\mathrm{OH}.\end{array}$$

In a bulk solution, the absorption cross section of NO${}_{\mathrm{3}}^{-}$ is 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 NO${}_{\mathrm{3}}^{-}$ on aerosols is thought to be much more efficient than that in the gas and bulk aqueous phases. Field studies trying to explain the observed HONO and NO_x concentrations over the oceans postulate enhancement factors (EFs) for the pNO${}_{\mathrm{3}}^{-}$ photolysis rate relative to that of HNO₃ of 10–500 (Ye et al., 2016, 2017a; Reed et al., 2017; Kasibhatla et al., 2018; Zhu et al., 2022; Andersen et al., 2023). Similar EFs have also been observed in laboratory studies of photolysis of pNO${}_{\mathrm{3}}^{-}$ in 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 yields for NO${}_{\mathrm{3}}^{-}$ molecules at the surface of the particles (Zhu et al., 2008, 2010; Du and Zhu, 2011; Nissenson et al., 2010). The fraction of NO${}_{\mathrm{3}}^{-}$ at 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, H donors, electron donors, or promote secondary reactions (Ye et al., 2019; Mora Garcia et al., 2021). Laboratory studies on 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 pNO${}_{\mathrm{3}}^{-}$. The relative yields of HONO : NO₂ in Reactions (R9a) and (R9b) also vary substantially in laboratory results. Ye et al. (2017b) 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.

Our baseline simulation assumes EFs of 10–100, depending on the relative amount of pNO${}_{\mathrm{3}}^{-}$ and 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 decreases from 100 in the MBL to less than 30 over the continents, where much of the pNO${}_{\mathrm{3}}^{-}$ is present as NH₄NO₃. The values over the oceans are consistent with EFs required to explain high daytime HONO concentrations (more than 10 pptv) observed over the oceans (Ye et al., 2016; Andersen et al., 2023). 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 Cabo Verde, although EFs of 25–50 and the HONO : NO₂ yield of 2 : 1 were sufficient to explain the NO_x 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 NO_x $/$ HNO₃ ratios and observations from seven aircraft campaigns. Most of these campaigns were 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 pNO${}_{\mathrm{3}}^{-}$ present as NH₄NO₃ relative to that present on sea salt aerosols. There is little change in the EFs with altitude elsewhere.

Figure 5 Annual mean (2015) enhancement factors (EFs) for the photolysis frequency of pNO${}_{\mathrm{3}}^{-}$ with respect to the photolysis frequency of HNO₃ in our baseline simulation. Panel (a) shows EFs at the surface, and panel (b) shows the zonal mean EFs. The EF for fine pNO${}_{\mathrm{3}}^{-}$ varies from 10 to 100, according to Eq. (1), and that for coarse pNO${}_{\mathrm{3}}^{-}$ is set at 100. The values shown here are the concentration-weighted average EFs for total (fine plus coarse) pNO${}_{\mathrm{3}}^{-}$. The zonal mean EFs are calculated as pNO${}_{\mathrm{3}}^{-}$ concentration-weighted averages for the band of grid cells in each altitude and latitude bin. The white shading in the zonal mean plots denotes the stratosphere.

pNO${}_{\mathrm{3}}^{-}$ concentrations were measured by the AMS and SAGA instruments during ATom and were found to be very low (Fig. S1). The AMS measures total (inorganic and organic) nitrate in non-refractory particles smaller than 1 µm diameter, while SAGA measures water-soluble NO${}_{\mathrm{3}}^{-}$ ions 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) pNO${}_{\mathrm{3}}^{-}$ concentrations were less than 1 ng sm⁻³. The median SAGA-measured pNO${}_{\mathrm{3}}^{-}$ concentration was 44 ng sm⁻³. In comparison, the median pNO${}_{\mathrm{3}}^{-}$ concentrations 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 overestimated the observed pNO${}_{\mathrm{3}}^{-}$ concentrations 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 NO_x source from pNO${}_{\mathrm{3}}^{-}$ photolysis is dampened because the EF for fine-mode pNO${}_{\mathrm{3}}^{-}$ photolysis decreases at higher pNO${}_{\mathrm{3}}^{-}$ concentrations (Eq. 1). GEOS-Chem pNO${}_{\mathrm{3}}^{-}$ concentrations are lower compared to the SAGA observations in 30^∘ N–30^∘ S, but much of the pNO${}_{\mathrm{3}}^{-}$ measured there is associated with dust and probably has a lower EF than that of pNO${}_{\mathrm{3}}^{-}$ on sea salt aerosols (Andersen et al., 2023).

Including pNO${}_{\mathrm{3}}^{-}$ photolysis in the model significantly increases modeled NO_x 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 (30^∘ S–30^∘ N), where pNO${}_{\mathrm{3}}^{-}$ photolysis is faster because of high actinic flux and high EFs and because the NO_x source from PAN decomposition is small there (Moxim et al., 1996; Fischer et al., 2014). The effect of pNO${}_{\mathrm{3}}^{-}$ photolysis is generally smaller above 6 km because of lower pNO${}_{\mathrm{3}}^{-}$ concentrations, except in the midlatitudes in spring when pNO${}_{\mathrm{3}}^{-}$ concentrations 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 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.

Figure 6 Tropospheric NO₂ column densities and NO₂ air mass factors (AMFs) over the Pacific and Atlantic oceans during ATom. The observed values are based on the median NO₂ vertical profiles calculated using the photochemical steady state (PSS) with local measurements of NO concentrations and other quantities following Eqs. (2) and (3). Model results are from our baseline GEOS-Chem simulation, GEOS-Chem simulation without pNO${}_{\mathrm{3}}^{-}$ photolysis, and GMI, TM5, and CAMS sampled along the flight tracks. Values shown are medians for all four ATom deployments and for the August deployment, as the TM5 and CAMS NO₂ profiles are available only for August. AMFs are calculated using the NASA OMI NO₂ v4.0 scattering weights, following Eq. (6), with geometric AMF (AMF_G) values of 2.6 for 30^∘ S–30^∘ N and 3.7 for 30–60^∘ S and 30–60^∘ N. 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 Fig. 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 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 AMF_G values of 2.6 for tropics (0–30^∘) and 3.7 for midlatitudes (30–60^∘), 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 × 10¹⁴ molec. cm⁻² in our baseline GEOS-Chem simulation compared to 1.7 ± 0.44 × 10¹⁴ molec. cm⁻² for PSS NO₂, and the corresponding AMFs are about equal (1.8). The NO₂ column density in the simulation without pNO${}_{\mathrm{3}}^{-}$ photolysis is 1.5 × 10¹⁴ 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 pNO${}_{\mathrm{3}}^{-}$ photolysis source, and generally higher than the PSS NO₂ concentrations in the upper troposphere. The campaign average NO₂ column density in GMI is 1.4 × 10¹⁴ 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, even though GMI does not include NO_x formation from pNO${}_{\mathrm{3}}^{-}$ photolysis. This is likely because GMI does not include NO_x 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 × 10¹⁴ 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 × 10¹⁴ molec. 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).

3.3 Effect of pNO${}_{\mathrm{3}}^{-}$ photolysis on global NO_x, OH, and ozone concentrations

Figure 7 shows the change in the annual mean NO_x, OH, and ozone concentrations at the surface and zonally between our baseline simulation and the sensitivity simulation without pNO${}_{\mathrm{3}}^{-}$ photolysis. pNO${}_{\mathrm{3}}^{-}$ photolysis increases NO_x, 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 NO_x, OH, and ozone tropospheric masses of 1 %–3 % in simulations that included photolysis of only coarse-mode pNO${}_{\mathrm{3}}^{-}$ at an EF of 100 and increases of 3 %–6 % when fine-mode pNO${}_{\mathrm{3}}^{-}$ photolysis was also included at an EF of 25. We find that NO_x concentrations increase by a factor of 2 on average in the MBL, though there is little increase in the northern extratropical MBL as the PAN concentrations are high (Fig. S1) and provide the main source of NO_x in the region. There is little change in surface NO_x concentrations over continents, as local emissions dominate the NO_x source. NO_x concentrations decrease slightly over some regions because the increase in OH concentrations resulting from HONO photolysis shortens the NO_x lifetime. The increase in NO_x concentrations in the tropics and subtropics is limited mostly to the MBL, since pNO${}_{\mathrm{3}}^{-}$ concentrations are low at higher altitudes. In the free troposphere of the northern midlatitudes, pNO${}_{\mathrm{3}}^{-}$ photolysis increases NO_x concentrations by just 20 % because pNO${}_{\mathrm{3}}^{-}$ concentrations and EFs for pNO${}_{\mathrm{3}}^{-}$ photolysis are generally low (Fig. 5). The effect of pNO${}_{\mathrm{3}}^{-}$ photolysis is larger in spring when there is a seasonal peak in pNO${}_{\mathrm{3}}^{-}$ concentrations in the model. There is a large increase in NO_x concentrations over Antarctica, as there are few other NO_x sources in the region in the model. Our simulations do not include snow NO${}_{\mathrm{3}}^{-}$ photolysis, which is an important source of NO_x in the region (Zatko et al., 2016).

Figure 7 Annual mean (2015) changes in NO_x, OH, and ozone concentrations from including pNO${}_{\mathrm{3}}^{-}$ photolysis in GEOS-Chem. Panel (a) shows changes at the surface, and panel (b) shows the zonal means. Changes in NO_x and OH are shown as percent change in concentrations in our baseline simulation relative to that in the sensitivity simulation without pNO${}_{\mathrm{3}}^{-}$ photolysis, and changes in ozone are shown as differences in concentrations (in ppbv) between the two simulations. The white shading in the zonal mean plots denotes the stratosphere.

pNO${}_{\mathrm{3}}^{-}$ photolysis increases the production of OH and ozone because of the increase in NO_x concentrations in low NO_x regions, where OH and ozone production are most sensitive to NO_x concentrations. OH is also produced by the photolysis of HONO released to the gas phase during pNO${}_{\mathrm{3}}^{-}$ photolysis (Reaction R10), which would be an important source of OH in winter when 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 pNO${}_{\mathrm{3}}^{-}$ photolysis 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 pNO${}_{\mathrm{3}}^{-}$ photolysis could then compensate for the increase in OH reactivity. The OH increase implied by pNO${}_{\mathrm{3}}^{-}$ recycling decreases the global atmospheric methane lifetime from 8.0 to 7.0 years, reducing the agreement with the value of 9.1 ± 0.9 years inferred from the methyl chloroform 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).

pNO${}_{\mathrm{3}}^{-}$ photolysis increases surface ozone concentrations by 3.6 ± 0.94 ppbv on average at the surface and up to 8 ppbv in the 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 NO_x 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 NO_x source from pNO${}_{\mathrm{3}}^{-}$ photolysis improves GEOS-Chem's ozone simulation. We will examine this further in a future publication.

3.4 Primary sources of NO_x in the free troposphere

NO_x in the free troposphere originates from diverse primary sources with differing spatial and seasonal characteristics. The sources include in situ emissions from lightning and aircraft, uplifting of NO_x emitted from surface sources, and downwelling of stratospheric NO_y produced from the photolysis of N₂O. Lightning is the main in situ source of NO_x in the free troposphere globally (Table 2), but it is concentrated over continents and has a strong seasonality in the midlatitudes. 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 NO_x in the free troposphere.

Figure 8 shows the vertical profiles of NO_x over the Pacific and Atlantic oceans and the contiguous U.S. 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 NO_y 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 and are calculated as $\left([{\mathrm{NO}}_x{]}_{\mathrm{0}}-[{\mathrm{NO}}_x{]}_i\right)/\sum _{i=\mathrm{1}}^{\mathrm{3}}\left([{\mathrm{NO}}_x{]}_{\mathrm{0}}-[{\mathrm{NO}}_x{]}_i\right)$, where [NO_x]₀ is the NO_x concentrations in the baseline simulation and [NO_x]_i is the NO_x concentration in the sensitivity simulation i. The source contributions for the northern midlatitudes are shown separately for February and August, but for the tropics and southern midlatitudes, the February and August average is shown.

Figure 8 Vertical profiles of NO_x concentrations from three primary source categories over the Pacific and Atlantic oceans and over the contiguous U.S. in GEOS-Chem. The source categories include surface emissions (fuel combustion, soil, fertilizer use, and fires), aircraft emissions, and lightning emissions. The profiles for the Pacific and Atlantic oceans are means for the regions sampled in ATom (160^∘ E–160^∘ W and 25–50^∘ W in the Northern Hemisphere and 160^∘ E–160^∘ W and 0–30^∘ W in the Southern Hemisphere) and are separated into three latitude bands. The northern midlatitude (30–60^∘ N) profiles are further separated by month (February and August), while the other profiles are averages for the 2 months. The profiles for the contiguous U.S. (defined as 25–50^∘ N and 65–130^∘ W) are shown separately for February and August.

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

Comparing the NO_x source contributions over the northern midlatitude oceans to those over the contiguous U.S., we find that the NO_x sources over the two regions are similar in winter. Surface and aircraft sources each supply about 40 % of NO_x in the free troposphere in February over the U.S., with surface sources dominating below 4 km and aircraft sources in the upper troposphere. In August, lightning emissions supply 73 % of the NO_x in the free troposphere over the U.S., much more than in winter and over the oceans. Previous modeling studies have also found lightning to be the main source of NO_x in the tropics 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 NO_x in our simulation is higher than in these previous studies, reflecting a nearly 2-fold increase in global aircraft NO_x emissions in the past 3 decades (Hoesly et al., 2018).

3.5 Implications for the retrieval and interpretation of satellite NO₂ data

We showed that the previously reported model underestimate of NO₂ concentrations in the upper troposphere over the U.S. 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 SEAC⁴RS, 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 U.S. Figure 9 shows the GEOS-Chem vertical profiles of the NO₂ number density in the early afternoon (OMI and TROPOMI overpass time) over the contiguous U.S. for the 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 pNO${}_{\mathrm{3}}^{-}$ photolysis over the U.S. (Fig. 1), except in spring when the NO₂ concentrations in the free troposphere are about 10 % higher due to the pNO${}_{\mathrm{3}}^{-}$ photolysis source.

Figure 9 Seasonal mean vertical profiles of sensitivity (scattering weights) of the OMI satellite instrument, NO₂ number density, and cumulative percent contributions to tropospheric NO₂ columns as would be observed by OMI over the contiguous U.S. Panel (a) shows the mean profile of the scattering weights from the NASA OMI NO₂ (v4.0) retrievals averaged over summer and winter for scenes with cloud fraction < 0.1 and surface albedo < 0.3. There is little difference in the scattering weight profile between winter and summer. Panel (b) shows the afternoon NO₂ profiles simulated by GEOS-Chem and GMI for summer (June, July, and August) and winter (December, January, and February) for the year 2015. The x axis is shown on a log scale. Panel (c) shows the cumulative percent contribution from NO₂ at different altitudes to the tropospheric NO₂ columns, as measured by OMI for summer and winter. It is calculated using Eq. (7). The shaded areas in panels (b) and (c) depict the standard deviations.

In summer, simulated NO₂ partial columns in the boundary layer and the free troposphere are 6.9 × 10¹⁴ and 5.8 × 10¹⁴ molec. cm⁻², respectively. In comparison, the simulated wintertime NO₂ partial columns are 15.4 × 10¹⁴ and 1.9 × 10¹⁴ molec. cm⁻² in the boundary layer and the free troposphere. The boundary layer NO₂ column is higher in winter because of longer NO_x chemical lifetimes (Kenagy et al., 2018; 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 summertime NO₂ column density in the free troposphere over the U.S. is about 3 times higher than the PSS-inferred NO₂ column over the oceans during ATom. Whereas, in winter, the free tropospheric NO₂ column over the U.S. is similar to that over the oceans, indicating little contrast in free tropospheric NO₂ between the U.S. and surrounding oceans, as was previously discussed in the context of Fig. 8. The similarity in free tropospheric NO₂ between the U.S. and the oceans in winter reflects the longer lifetime of NO_x and higher pNO${}_{\mathrm{3}}^{-}$ concentrations over the ocean. It also implies that ATom observations over the northern midlatitudes in February could be used to estimate the free tropospheric NO₂ concentrations over the U.S. 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 2005–2007 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 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.

Figure 9b also shows the afternoon NO₂ number density from the GMI model. The GEOS-Chem and GMI profiles have consistent shapes, but there are differences in the free tropospheric NO₂ concentrations because of differences in NO_x oxidation chemistry and lightning and aircraft NO_x emissions. The NO_x lifetime is longer in GMI compared to GEOS-Chem because of lower summertime OH concentrations in GMI and because GMI does not include NO_x loss through the hydrolysis of NO₃ and N₂O₅ in clouds and the formation of halogen nitrates. Both models use similar parameterizations for lightning emissions (Allen et al., 2010; Murray et al., 2012), but GMI assumes a higher NO yield over the U.S. (500 mol per flash north of 26^∘ N and 250 mol per flash south of it) than GEOS-Chem (500 mol per flash north of 35^∘ N and 260 mol per flash south of it). Aircraft emissions in GMI are from an older inventory (Duncan et al., 2007) with global NO_x emissions of 0.56 Tg N a⁻¹ compared to 1.2 Tg N a⁻¹ in our simulation.

We calculate the seasonal AMFs corresponding to the GEOS-Chem and GMI NO₂ profiles (Eq. 6) to determine the effect of 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 U.S. 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 AMF_G 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 SEAC⁴RS and DC3 (Fig. 1). If we decrease 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 U.S. 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 errors in the a priori NO₂ profiles in summer is larger than 10 %.

Figure 9c shows the cumulative contribution from different altitudes to the tropospheric NO₂ columns, as would be measured by OMI. It is calculated as follows:

$$\begin{array}{}\text{(4)}& \mathrm{\Gamma }\left(z\right)=\mathrm{100}\times {\displaystyle \frac{{\int }_z^{z_t}w\left(z\right)n\left(z\right)\mathrm{d}z}{{\int }_{\mathrm{0}}^{z_t}w\left(z\right)n\left(z\right)\mathrm{d}z}},\end{array}$$

where Γ(z) is the percent contribution to the tropospheric NO₂ column from NO₂ at and above altitude z, z_t 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 U.S. 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 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 SEAC⁴RS.

The large contribution of the free troposphere to NO₂ columns affects the interpretation of satellite data in terms of NO_x emissions. It greatly diminishes the sensitivity of the summertime NO₂ columns to changes in surface NO_x emissions over the U.S. The free tropospheric contribution would be relatively smaller over major cities, where summertime NO₂ columns exceed 3 × 10¹⁵ molec. cm⁻² (Lamsal et al., 2021), but it still needs to be accounted for. Urban NO_x 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 include lightning and aircraft NO_x emissions are used to relate NO₂ columns to NO_x emissions, but there is substantial uncertainty in the magnitude and distribution of lightning NO_x emissions (Schumann and Huntrieser, 2007; Murray, 2016), which is the main source of NO₂ in the free troposphere in summer. Missing organic NO_x chemistry in summer would also contribute to model errors in the free tropospheric NO₂, as suggested by our SEAC⁴RS and DC3 analysis. Wintertime NO₂ columns will respond more strongly to changes in NO_x emissions, but the uncertainty in the NO₂ retrievals associated with surface albedo and clouds is larger in winter (Boersma et al., 2018). Better observational constraints on free tropospheric NO₂ concentrations are needed.

4 Conclusions

We used aircraft measurements from the SEAC⁴RS, DC3, and ATom campaigns to evaluate the vertical distribution of NO_x in the free troposphere in the GEOS-Chem, GMI, TM5, and CAMS atmospheric chemistry models in the context of their use 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 ozone production. This indicates a positive interference in the NO₂ measurements, presumably from dissociation of non-radical NO_y 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 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 SEAC⁴RS and DC3 over the southeastern U.S. in summer. The NO₂ air mass factors (AMFs) calculated using the 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 SEAC⁴RS and DC3 by about a factor of 2 and underestimates concentrations of MPN and alkyl nitrates, suggesting missing organic NO_x chemistry in the model that needs further examination.

The NO concentrations measured over the Pacific and Atlantic oceans were reproduced by GEOS-Chem when pNO${}_{\mathrm{3}}^{-}$ photolysis was included in the model with photolysis frequencies 10–100 times higher than that of gas-phase HNO₃, as suggested by laboratory studies of pNO${}_{\mathrm{3}}^{-}$ photolysis and field studies of HONO sources in the marine atmosphere (Ye et al., 2016, 2017b; Andersen et al., 2023). The median NO₂ column density for the ATom campaign was 1.7 ± 0.44 × 10¹⁴ molec. cm⁻² for the observed PSS NO₂ concentrations and 2.4 × 10¹⁴ molec. cm⁻² for GEOS-Chem with pNO${}_{\mathrm{3}}^{-}$ photolysis and 1.5 × 10¹⁴ molec. cm⁻² without. The NO₂ column density for the GMI, TM5, and CAMS models was between 1.4 and 2.5 × 10¹⁴ 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 NO_x columns over the Pacific and Atlantic oceans and over the U.S. in GEOS-Chem and found that lightning is the main NO_x source over the tropics and southern midlatitudes and over the U.S. in the summer, contributing 62 %–73 % of the NO_x columns in the free troposphere. However, aircraft emissions are the main source of free tropospheric NO_x in the northern midlatitudes in winter and in summer over the oceans.

pNO${}_{\mathrm{3}}^{-}$ photolysis increases the global tropospheric mass of NO_x, OH, and ozone in GEOS-Chem by 9 %, 19 %, and 10 %, respectively. NO_x concentrations increase most in the tropical MBL where NO_x sources from PAN are small. There is a small increase in NO_x concentrations in the free troposphere over the continents, particularly in spring when the pNO${}_{\mathrm{3}}^{-}$ concentration 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. pNO${}_{\mathrm{3}}^{-}$ photolysis increases ozone concentrations by up to 8 ppbv at the surface in the tropics and subtropics and by 5 ppbv in the free troposphere over the northern extratropics, which would largely correct the model bias relative to ozonesonde observations (Wang et al., 2021).

The seasonal GEOS-Chem and GMI afternoon NO₂ profiles over the contiguous U.S. are largely consistent with each other and show higher boundary layer NO₂ columns in winter than in summer because of longer NO_x chemical lifetimes and slower 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 U.S., but in summer this increases to 65 %–75 % and weakens the sensitivity of the summertime NO₂ columns to changes in surface NO_x emissions. This is less of a problem for urban areas where boundary layer NO₂ columns are generally much larger than the free tropospheric columns.