On the contribution of nocturnal heterogeneous reactive nitrogen chemistry to particulate matter formation during wintertime pollution events in Northern Utah

Mountain basins in Northern Utah, including the Salt Lake Valley (SLV), suffer from wintertime air pollution events associated with stagnant atmospheric conditions. During these events, fine particulate matter concentrations (PM_2.5) can exceed national ambient air quality standards. Previous studies in the SLV have found that PM_2.5 is primarily composed of ammonium nitrate (NH₄NO₃), formed from the condensation of gas-phase ammonia (NH₃) and nitric acid (HNO₃). Additional studies in several western basins, including the SLV, have suggested that production of HNO₃ from nocturnal heterogeneous N₂O₅ uptake is the dominant source of NH₄NO₃ during winter. The rate of this process, however, remains poorly quantified, in part due to limited vertical measurements above the surface, where this chemistry is most active. The 2017 Utah Winter Fine Particulate Study (UWFPS) provided the first aircraft measurements of detailed chemical composition during wintertime pollution events in the SLV. Coupled with ground-based observations, analyses of day- and nighttime research flights confirm that PM_2.5 during wintertime pollution events is principally composed of NH₄NO₃, limited by HNO₃. Here, observations and box model analyses assess the contribution of N₂O₅ uptake to nitrate aerosol during pollution events using the ${\mathrm{NO}}_{\mathrm{3}}^{-}$ production rate, N₂O₅ heterogeneous uptake coefficient (γ(N₂O₅)), and production yield of ClNO₂ (φ(ClNO₂)), which had medians of 1.6 µg m⁻³ h⁻¹, 0.076, and 0.220, respectively. While fit values of γ(N₂O₅) may be biased high by a potential under-measurement in aerosol surface area, other fit quantities are unaffected. Lastly, additional model simulations suggest nocturnal N₂O₅ uptake produces between 2.4 and 3.9 µg m⁻³ of nitrate per day when considering the possible effects of dilution. This nocturnal production is sufficient to account for 52 %–85 % of the daily observed surface-level buildup of aerosol nitrate, though accurate quantification is dependent on modeled dilution, mixing processes, and photochemistry.

1 Introduction

Over 80 % of Utah's population lives in counties that experience periods of elevated fine particulate matter (PM_2.5 < 2.5 µm in diameter) during the winter season (U.S. Census Bureau, 2018; Whiteman et al., 2014). In these counties, the highest levels have been limited to three northern valleys along the Wasatch Mountains, shown in Fig. 1 (north to south: Cache Valley (Logan nonattainment area, NAA), Salt Lake Valley (Salt Lake NAA), and Utah Valley (Provo NAA)). These valleys were designated by the United States Environmental Protection Agency (EPA) as “moderate” nonattainment areas (NAA) in December 2009, with the Salt Lake and Provo areas reclassified from moderate to “serious” in May 2017 (Utah Department of Environmental Quality, 2019). Elevated PM_2.5 concentrations in these regions impact public health and are associated with increases in emergency room visits for asthma (Beard et al., 2012). Short-term exposure to PM_2.5 has also been shown to increase the chance of triggering acute ischemic heart disease events by 4.5 %–6 % per 10 µg m⁻³ in sensitive populations living in the Wasatch region (Pope et al., 2006, 2015).

Figure 1 (a) Elevation map of Utah's Wasatch region (Utah State in insert), with the Great Salt Lake (north) and Utah Lake (south) shown in blue and county borders in gray. The US-EPA-designated nonattainment areas (NAA) for PM_2.5 are shown by red boundaries. From north to south these NAAs include the Logan NAA: moderate status, Salt Lake City NAA: serious status, and Provo NAA: serious status. UWFPS Twin Otter flight tracks are shown in pink. Purple markers indicate the locations of major cities, including Logan in the Cache Valley, Ogden and Salt Lake City in the SLV, and Provo in the Utah Valley. The locations of missed approaches conducted with the aircraft are shown by dark pink circles. The Hawthorne (HW) measurement site in the SLV is labeled. (b) Expanded view of the SLV, with analyzed flight tracks highlighted in green.

Elevated wintertime PM_2.5 concentrations in these valleys typically correspond to multiday events of high atmospheric stability (e.g., Whiteman et al., 2014; Silcox et al., 2012; Gillies et al., 2010; Wang et al., 2012; Green et al., 2015; Silva et al., 2007; Baasandorj et al., 2017), associated with large, synoptic-scale high-pressure systems that transit from west to east, simultaneously impacting multiple basins across the intermountain western US (e.g., Reeves and Stensrud, 2009). Warm temperatures aloft cause boundary layer stratification that reduces mixing and traps cold air and emissions near the surface, illustrated in Fig. 2 and discussed further below. These events, termed persistent cold air pools (PCAPs), typically mix out after 1–5 d but have been observed to persist for as long as 18 d (Whiteman et al., 2014). Similar meteorological patterns have been linked to wintertime PM_2.5 accumulation in basins across the western US (e.g., Chen et al., 2012; Green et al., 2015). During past PCAP and pollution events in Utah, data from ground-based measurements in the Salt Lake Valley (SLV) have reported day-to-day buildup rates of total PM_2.5 mass in the range of ∼6–10 µg m⁻³ d⁻¹ (Baasandorj et al., 2017; Silcox et al., 2012; Whiteman et al., 2014) before plateauing after ∼6 d into an event (Baasandorj et al., 2017). Average 24 h concentrations reported during PCAP events between 2001 and 2016 have been as large as 40–80 µg m⁻³ in Salt Lake (Baasandorj et al., 2017; Silcox et al., 2012) and Utah valleys (Malek et al., 2006) and up to 132.5 µg m⁻³ in Logan, Utah (Cache Valley) (Malek et al., 2006).

Previous ground-based studies have identified ammonium nitrate (NH₄NO₃) as the main component of PM_2.5 (70 %–80 % by mass) during PCAP events in all three Northern Utah valleys (Silva et al., 2007; Hansen et al., 2010; Kuprov et al., 2014; Kelly et al., 2013; Long et al., 2003, 2005a, b; Baasandorj et al., 2017). Ammonium nitrate formation is thermodynamically favorable under cold wintertime conditions from the equilibrium between gas-phase ammonia (NH₃) and nitric acid (HNO₃), shown in Reaction (R1) in Fig. 2 (e.g., Kuprov et al., 2014; Nowak et al., 2012; Mozurkewich, 1993). PM_2.5 mitigation strategies that are based on control of these gas-phase species are expected to be more effective if the limiting reagent and its sources can be identified. Both observationally and model-informed ground-based analyses have suggested that NH₄NO₃ formation in Cache and Salt Lake valleys is limited by the production of HNO₃ (Kuprov et al., 2014; Mangelson et al., 1997; Martin, 2006; Utah Division of Air Quality, 2014a, b, c; Franchin et al., 2018), though uncertainties remain in how this limitation may be impacted by temporal and spatial variations.

While NH₃ is directly emitted from agricultural sources, industrial processes, waste disposal, and automobile emissions (Behera et al., 2013; Livingston et al., 2009), HNO₃ forms chemically in the atmosphere from the oxidation of NO_x ($=\mathrm{NO}+{\mathrm{NO}}_{\mathrm{2}}$), which in turn arises mainly from combustion emissions. There are two mechanisms by which this formation occurs, illustrated by Reactions (R2)–(R6) in Fig. 2. The first is through daytime NO₂ oxidation by the hydroxyl radical (OH) (Fig. 2, Reaction R2) and the second is through the nocturnal heterogeneous uptake of dinitrogen pentoxide (N₂O₅) (Reaction R6), which itself is a product of nocturnal NO_x oxidation (Reactions R3–R5). The former is relatively more important during the summer (Brown et al., 2004), whereas the latter, the focus of this study, may be relatively more important in winter (e.g., Wagner et al., 2013) due to reduced OH concentrations, colder temperatures that favor N₂O₅ in its equilibrium with NO₃ (Reaction R5), and longer nights that allow more time for nocturnal reactions to occur. The nocturnal heterogeneous production of HNO₃ is also expected to be largest in the residual layer (RL), due to the near-surface accumulation of NO, which titrates O₃ (Reaction R3) and reacts with NO₃ (Reaction R7), the precursor to N₂O₅ (e.g., Brown and Stutz, 2012).

The role of this nocturnal reactive nitrogen chemistry in the formation of PM_2.5 has been considered in previous wintertime studies, though nocturnal, vertically resolved measurements have been relatively limited. Previous studies using ground- and tower-based observations, as well as midmorning aircraft vertical profiles, have identified heterogeneous chemistry and subsequent morning transport from aloft as a major source of surface-level NH₄NO₃ in California's San Joaquin Valley (e.g., Brown et al., 2006; Prabhakar et al., 2017; Pusede et al., 2016; Watson and Chow, 2002). Similarly, a box model analysis of tower- and ground-based observations in Beijing, China, also identified these processes as important contributors to surface-level particulate nitrate the following day (Wang et al., 2018). In Northern Utah specifically, nocturnal heterogeneous chemistry has been considered a source for PM_2.5 (Baasandorj et al., 2017; Kuprov et al., 2014), though vertically resolved measurements have been limited to ground-based observations at different elevations along the Wasatch Mountains (Baasandorj et al., 2017). In an analysis of ground-based HNO₃ and PM_2.5 observations in the SLV, Kuprov et al. (2014) suggested that daytime HNO₃ formation was dominant over the contribution from nocturnal heterogeneous chemistry. Baasandorj et al. (2017), however, noted that ground-based measurements in this region may not capture the extent of heterogeneous chemistry aloft in the RL, which is expected to be distinct from the surface composition (e.g., Brown et al., 2007; Brown and Stutz, 2012; Stutz et al., 2004). Therefore, vertical gradients in NO_x and oxidants could promote efficient HNO₃ and NH₄NO₃ formation aloft, which could contribute to enhanced surface-level PM_2.5 concentrations the following day. Regardless of altitude, the absolute contribution at all altitudes will depend on (1) the rate of NO₃ and N₂O₅ production, (2) the efficiency of N₂O₅ uptake onto aerosol (γ(N₂O₅)), and (3) the heterogeneous production yield of HNO₃ relative to ClNO₂ (φ(ClNO₂)) (Osthoff et al., 2008; Behnke et al., 1997). Net accumulation of NH₄NO₃ at the surface, however, also depends on mixing and dilution associated with growth of the convective boundary layer and mixing of the RL down to the surface the following day. Quantification of these processes is key in designing effective mitigation strategies for Utah's wintertime air pollution and requires vertically resolved observations of chemical composition at night.

Figure 2 Illustration of the day–night dynamics and chemical cycles of reactive nitrogen oxides, O₃, and NH₄NO₃ during PCAP conditions in the SLV. The development of the nocturnal boundary layer and morning growth and mix-out are illustrated by the dashed lines. Figure is not to scale. Reaction (R6) represents the reaction ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\stackrel{\mathit{\gamma }\left({\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right),M}{⟶}\mathrm{2}\cdot \left(\mathrm{1}-\mathit{\phi }\right)\cdot {\mathrm{HNO}}_{\mathrm{3}}+\mathit{\phi }\cdot {\mathrm{ClNO}}_{\mathrm{2}}$.

In this study, we present results from the Utah Winter Fine Particulate Study (UWFPS), which consisted of aircraft and ground-based observations throughout the Cache, Salt Lake, and Utah valleys during January and February 2017. This analysis focuses on data from 16 aircraft flights (5 at night) during two pollution events between 16 January and 1 February 2017. These flights were carried out in the SLV, the most populated of the three Utah nonattainment areas. The first section presents an overview of PM_2.5 during winter 2016–2017. In the second section, ambient mixing ratios of total (gas and particle phase) oxidized and reduced nitrogen are used to identify the limiting reagent to NH₄NO₃ aerosol formation, as well as its spatial and temporal trends. The final section presents upper-limit NH₄NO₃ production rate estimates and results from an observationally fit chemical box model to calculate γ(N₂O₅), φ(ClNO₂), and an estimated contribution of nocturnal heterogeneous chemistry to NH₄NO₃ formation in the SLV. The contribution of nocturnal production relative to photochemically driven NO₂ oxidation will have consequences for the development of effective mitigation strategies as day- and nighttime production processes may have different sensitivities to NO_x emissions and VOC radical sources (Pusede et al., 2016; Womack et al., 2019), such that net sensitivities will be determined by the dominant formation mechanism.

2 Methods

2.1 UWFPS campaign overview and instrumentation

The UWFPS campaign included both aircraft and ground-based measurements throughout the Salt Lake, Cache, and Utah valleys during January and February 2017 (Fig. 1). A total of 23 research flights were conducted during both day and night with the NOAA Twin Otter (TO) aircraft. The TO was equipped with aerosol- and gas-phase instrumentation (summarized in Table 1) to probe the regional sources and formation mechanisms of PM_2.5. While flights were conducted over three valleys, the focus of this analysis will be on the more densely populated SLV, with relevant flight tracks highlighted in the right panel of Fig. 1.

Table 1 Aircraft measurements used in this analysis.

^a NOAA, cavity ring-down spectrometer (CRDS, NOxCaRD). ^b Hawthorne. ^c University of Washington, iodide time-of-flight chemical ionization mass spectrometer. ^d University of Toronto, quantum cascade tunable infrared laser differential absorption spectrometer (see Moravek et al., 2019, for details on instrument accuracy). ^e NOAA, aerosol mass spectrometer. ^f Droplet Measurement Techniques, ultra-high-sensitivity aerosol spectrometer. ^g Estimated according to the performance of a different UHSAS in the WINTER campaign.

Briefly, the TO payload included gas-phase measurements of NO_x, NO₂, NO_y, and O₃ (1 Hz sample frequency) from a NOAA cavity ring-down spectrometer (NOxCaRD) (Wild et al., 2014); NH₃ (1 Hz sample frequency) measurements from an Aerodyne midinfrared absorption instrument (QC-TILDAS) from the University of Toronto (Ellis et al., 2010); and N₂O₅, HNO₃, and ClNO₂ (1 Hz sample frequency) measurements from an iodide time-of-flight chemical ionization mass spectrometer (I⁻ToF-CIMS) from the University of Washington (Lee et al., 2014, 2018). Accuracies for NO_x, NO₂, and O₃ were 5 % and 12 % for NO_y, with stated detection limits of 60 pptv (2σ) (Wagner et al., 2011; Wild et al., 2014) in the boundary layer. Gas-phase NH₃ was measured with a detection limit of 450 pptv (1 s 3σ), as described in further detail by Moravek et al. (2019). Accuracy and detection limits for N₂O₅, ClNO₂, and HNO₃ were similar to those reported from the same instrument deployed during the Wintertime Investigation of Transport, Emissions, and Reactivity (WINTER) campaign (≤0.6 pptv (1 s 1σ), 30 %) (Lee et al., 2018). Non-refractory submicron aerosol composition (sampled every ∼10 s) was measured with the NOAA aerosol mass spectrometer (AMS) (Bahreini et al., 2009; Middlebrook et al., 2012) and aerosol size (sample every ∼3 s) with a commercial ultra-high-sensitivity aerosol spectrometer (UHSAS) (Brock et al., 2011). Average detection limits for AMS aerosol composition were 0.04, 0.09, 0.33, 0.03, and 0.07 µg sm⁻³ (sm⁻³ refers to m³ under standard conditions: 1 atm and 273.15 K) for particulate nitrate, ammonium, organics, sulfate, and chloride, respectively. Uncertainties were ∼20 % for all species (Franchin et al., 2018). Ambient temperature and pressure (1 Hz sample frequency) were measured with a commercial (Avantech) meteorological probe. The accuracy of the commercial UHSAS instrument was also expected to be similar to that used during WINTER (dry surface area density: ∼34 %).

Additional ground-based measurements used in this analysis include hourly PM_2.5, NO₂, O₃, and temperature from the Utah Department of Air Quality (UDAQ) instrumentation at the Hawthorne (HW) monitoring site (Fig. 1). Total PM_2.5 mass was measured with a Thermo Scientific 1405-DF dichotomous ambient air monitor, NO₂ with a Teledyne API T200U chemiluminescence detector, and O₃ with a Teledyne API T400 UV absorption spectrometer, all in accordance with EPA guidelines (Environmental Protection Agency, 2018). Select volatile organic compounds (VOCs) were also measured at the University of Utah (UU) ground site by a proton-transfer-reaction mass spectrometer. Further information about the UWFPS campaign and aircraft and ground-based instrumentation can be found in additional publications (Franchin et al., 2018; UWFPS Science Team, 2018; Womack et al., 2019; Moravek et al., 2019).

2.2 Box model

2.2.1 Description

A zero-dimension chemical box model has been developed to simulate the nocturnal chemical evolution of an air parcel from sunset until the time of aircraft measurement (assuming constant temperature and relative humidity). Extensive model details have been previously discussed in McDuffie et al. (2018b). Briefly, the model forward integrates the chemical mechanism (13 reactions, Table S1 in the Supplement) starting 1.3 h prior to sunset (see below), iteratively adjusting the initial concentrations of O₃ and NO₂ until the model-predicted concentrations are both within 0.5 % of the aircraft observations. Holding these initial concentrations constant, the model next adjusts the total heterogeneous loss rate constant of N₂O₅ ($k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$) until the model output reproduces ambient nighttime observations of N₂O₅ to within 1 %. As described in McDuffie et al. (2018b), the model iterates these steps, readjusting initial concentrations of O₃ and NO₂ and values of $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ until aircraft observations of NO₂, O₃, and N₂O₅ are simultaneously reproduced by the model. The final step holds these values constant while iteratively adjusting the production rate of ClNO₂ ($k_{{\mathrm{ClNO}}_{\mathrm{2}}}$) until the modeled mixing ratios of ClNO₂ are within 1 % of the nighttime ClNO₂ observations. The N₂O₅ uptake coefficients (γ(N₂O₅)) and ClNO₂ production yields (φ(ClNO₂)) are then calculated following Eqs. (1) and (2), where c is the mean molecular speed and SA is the ambient wet PM₁ surface area density (described below). The model repeats this entire process every 10 s for all flights conducted at night, as determined by time and aircraft GPS altitude.

$$\begin{array}{}\text{(1)}& {\displaystyle }\mathit{\gamma }\left({\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right)={\displaystyle \frac{\mathrm{4}\cdot k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}}{c\cdot \mathrm{SA}}}\text{(2)}& {\displaystyle }\mathit{\phi }\left({\mathrm{ClNO}}_{\mathrm{2}}\right)={\displaystyle \frac{k_{{\mathrm{ClNO}}_{\mathrm{2}}}}{k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}}}\end{array}$$

Holding the derived $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and $k_{{\mathrm{ClNO}}_{\mathrm{2}}}$ values constant, the model can further simulate the total nitrate produced overnight by forward integrating the model until the time of sunrise, as shown for a representative SLV point in Fig. 3. Here, total nitrate (gas + particulate phase) is represented as HNO₃ only, as this model does not include aerosol thermodynamics that partition nitrate between the gas and particle phases. Modeled gas-phase HNO₃ is assumed to partition to the particle phase with 100 % efficiency, following observations presented in Franchin et al. (2018) that show >90 % of total nitrate is in the particle phase during wintertime pollution events in the SLV. As modeled nitrate is initialized with a concentration of 0 µg m⁻³, concentrations predicted at sunrise represent the total amount of nitrate produced from nocturnal chemistry over the course of a single night (i.e., nocturnal nitrate production rate). These base case values assume no overnight loss from dilution and constant values of γ(N₂O₅) and φ(ClNO₂), as discussed further in Sect. 3.3.3.

Figure 3 Example simulation of total nitrate production from sunset to sunrise for an air parcel sampled over the SLV on 28 January 2017. Model-derived γ(N₂O₅) and φ(ClNO₂) values were 0.05 and 0.21, respectively. Modeled nocturnal nitrate (blue) is the total nitrate produced by heterogeneous chemistry in the box model, with the nocturnal production rate (µg m⁻³ per night) represented by the blue diamond. Preexisting nitrate (yellow) represents the nitrate present at sunset and is calculated as the difference between total measured nitrate from the aircraft (red diamond) and the model-predicted nitrate at the time of aircraft measurement (vertical black line). Assuming preexisting nitrate is constant overnight (i.e., no deposition or dilution) and constant values of γ(N₂O₅) and φ(ClNO₂), total nitrate expected at sunrise is represented by the gold diamond.

2.2.2 Model simplifications and uncertainties

For the UWFPS campaign, the box model was run in a similar manner to that described previously in McDuffie et al. (2018b), for nocturnal aircraft observations collected in the RL over the eastern US coast during the 2015 WINTER campaign. Due to more limited instrumentation during UWFPS than WINTER, a larger number of box model assumptions and simplifications were required, which are summarized below.

First, the wet SA density for the base case simulations was calculated by applying a hygroscopic growth curve as a function of RH (Fig. S2 in the Supplement) to the dry PM₁ SA measured by the UHSAS (details in Sect. S1.3 in the Supplement). The growth curve was derived with the Extended AIM Aerosol Thermodynamic Model (Wexler and Clegg, 2002), assuming pure NH₄NO₃ particles. Alternatively, estimating the growth factor from AMS measurements and estimates of aerosol organic density and the organic hygroscopicity constant (κ_Org) (described in Sect. S1.3; Jimenez et al., 2009; Mei et al., 2013; Cerully et al., 2015; e.g., Kuwata et al., 2012; Brock et al., 2016; Shingler et al., 2016) resulted in only a ∼3 % change in the total wet SA for night flights during UWFPS (Fig. S2). For the 1031 measurement periods (10 s each) with simultaneous values of γ(N₂O₅) and φ(ClNO₂), the median dry aerosol SA was 151.9 µm² cm⁻³, which increased to 353.1 µm² cm⁻³ when accounting for hygroscopic growth (Fig. S2). Additional uncertainties associated with hygroscopic growth and assumptions of constant SA are discussed below in Sect. 3.3.2.

Second, loss of the nitrate radical (NO₃) from its reaction with volatile organic compounds (VOCs) was assumed to occur with a single first-order rate constant ($k_{{\mathrm{NO}}_{\mathrm{3}}}$), calculated for each flight from a combination of historical ground-based VOC measurements and select VOC measurements from a PTR-MS at the UU site (see Sect. S1.2 for details; Atkinson and Arey, 2003). At night, NO₃ serves as one of the primary tropospheric oxidants for VOCs and can react with RO₂ and HO₂ radicals to contribute to nocturnal NO_x recycling (Vaughan et al., 2006). In this analysis, NO₃–VOC reactions were lumped and treated as a net NO_x sink with values of the first-order loss rate constant, $k_{{\mathrm{NO}}_{\mathrm{3}}}$, ranging from $\mathrm{1.5}\times {\mathrm{10}}^{-\mathrm{3}}$ to $\mathrm{9.5}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹ (NO₃ lifetime ∼ 100–1000 s). These rate constants are slightly larger than average values measured during the WINTER campaign ($\mathrm{1.3}\times {\mathrm{10}}^{-\mathrm{4}}$ to $\mathrm{4.6}\times {\mathrm{10}}^{-\mathrm{4}}$ s⁻¹) (McDuffie et al., 2018b) and within the range previously reported ($\mathrm{3}\times {\mathrm{10}}^{-\mathrm{5}}$ to $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{2}}$ s⁻¹) during winter 2012 at a ground site in Colorado (Wagner et al., 2013). Additional NO_x regeneration from reactions of NO₃ with HO₂ and RO₂ radicals was not included in this analysis due to a lack of radical measurements. An underprediction in $k_{{\mathrm{NO}}_{\mathrm{3}}}$ from these uncertainties would cause both an overprediction in the loss rate constant of N₂O₅ and the subsequent production of nitrate. While uncertainties in $k_{{\mathrm{NO}}_{\mathrm{3}}}$ can lead to large model uncertainties during summertime conditions (e.g., Phillips et al., 2016), NO₃–VOC reactivity is largely reduced during the winter season as a result of lower biogenic emissions and colder temperatures that favor N₂O₅ in its equilibrium with NO₃. Sensitivity studies discussed below showed 0.2 % changes in the median model-predicted nocturnal nitrate production rate associated with ±50 % changes in $k_{{\mathrm{NO}}_{\mathrm{3}}}$ (Table S4). The possibility of varying VOC reactivity with time was also investigated (Sect. S1.4.5) but resulted in a minimal (<0.1 %) impact on nitrate production results presented below. The potential for other rate constants to vary with time may additionally lead to increased variability in the results presented in Sect. 3.3.

Third, there are uncertainties in the assumptions regarding the start time and duration of each simulation. All simulations were initialized at 1.3 h prior to sunset, assuming no initial concentrations of N₂O₅ or ClNO₂. The presunset time of 1.3 h was derived for the WINTER campaign, based on the time when predicted daytime N₂O₅ concentrations (described in Sect. S1.4.4 and Brown et al., 2005) diverged from ambient observations when approaching sunset. This value was not recalculated for UWFPS simulations as daytime N₂O₅ calculations require measurements of j(NO₃) photolysis rates, which were not available during UWFPS. The median nocturnal nitrate production rate, however, changed by <0.3 % when this presunset time was varied between 0 and 2 h. Photolysis rates during this time were also calculated from those measured during the WINTER campaign (Sect. S1.4.3; Shetter and Müller, 1999). While WINTER photolysis rates may have been larger than those during Utah PCAP events, the median modeled nocturnal nitrate production rate showed a small sensitivity (<2.8 %) to ±40 % changes in these values (Sect. S1.4.3). Additional uncertainties in air age (i.e., simulation start time and duration), however, may still serve to overpredict N₂O₅ loss rates and nocturnal nitrate based on previous sensitivity studies (McDuffie et al., 2018b). A combination of these assumptions will lead to a greater uncertainty in model results near sunset, as discussed in Sect. 3.3.2.

Fourth, air parcel mixing and deposition of gas-phase nitric acid were not included in base case simulations. Additional simulations, described in Sect. S1.4.2, included deposition using a first-order nitric acid loss constant of $\mathrm{2.6}\times {\mathrm{10}}^{-\mathrm{6}}$ s⁻¹, calculated from a boundary layer height of 800 m; deposition velocity of 2.7 cm s⁻¹ (Zhang et al., 2012); and gas/particle nitrate fraction of 8 % from Franchin et al. (2018). The median nocturnal nitrate production rate increased by <8 % when this depositional loss of HNO₃ was included. In contrast, modeled nitrate production was most sensitive (−42.2 % reduction) to the addition of a first-order loss process, meant to simulate air parcel dilution and O₃ entrainment from vertical mixing between the RL and free troposphere (Table S4). Based on a previous analysis by Womack et al. (2019), the dilution rate constant was estimated to be $\mathrm{1.3}\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹ in the RL, with a possible range of 1.2 to 2.5 × 10⁻⁵ s⁻¹ (described in Sect. S1.4.1). Results from simulations that include dilution are discussed further in the final section.

Finally, the absolute uncertainty associated with each individual nocturnal nitrate production rate was calculated from the quadrature addition of the uncertainties associated with sensitivity tests described above and the NO₂, O₃, N₂O₅, and ClNO₂ measurements used as model fit parameters (<6 % for all tests). Production rates derived from model fits to observations as well as the absolute uncertainties associated with all 17 sensitivity tests are shown as a time series in Fig. S3. Dilution contributes 92 % of the total uncertainty (light blue in Fig. S3), on average. Both the base case results (black dots) and those from simulations including the effects of air parcel dilution are discussed in Sect. 3.3.3.

3 Results and discussion

3.1 PM_2.5 in Salt Lake Valley – winter 2017

To provide an overview of wintertime pollution events in the SLV, Fig. 4 shows a time series of total PM_2.5 mass (1 and 24 h averages) measured at the UDAQ Hawthorne (HW) site (Fig. 1) from 1 December 2016 to 22 February 2017. Additional time series of ground-based PM_2.5 measurements for all three Utah NAAs are provided in Franchin et al. (2018). The SLV data in Fig. 4 show four pollution events that exceeded the NAAQS during the 2016–2017 winter. Calculated from 24 h measurements, the four largest pollution events during December 2016 and January 2017 had daily PM_2.5 buildup rates that ranged from 3.7 to 15.6 µg m⁻³ d⁻¹ (see Fig. 4), encompassing the daily rates reported previously in the same valley (Whiteman et al., 2014; Silcox et al., 2012; Baasandorj et al., 2017). The last two major pollution events (10–22 January, event no. 3; and 25 January–5 February, event no. 4) overlapped with flights during UWFPS, shown by the gray shading in Fig. 4. Average non-refractory (NR) PM₁ aerosol mass fractions measured during these periods by the TO AMS showed that the aerosol was primarily composed of NH₄NO₃ (Fig. 4 pie charts). The sum of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ${\mathrm{NH}}_{\mathrm{4}}^{+}$ contributed to 76.6 % and 74.0 % of the total PM₁ mass measured during the last two pollution episodes (74 % average; Franchin et al., 2018), which agree with previous ground-based observations (e.g., Baasandorj et al., 2017) of past seasons. Nitrate alone contributed to an average 57 % and 58 % of the total aerosol mass during pollution episodes no. 3 and no. 4, respectively. During the relatively clean period sampled between 8 and 12 February 2017, the combined ${\mathrm{NH}}_{\mathrm{4}}^{+}+{\mathrm{NO}}_{\mathrm{3}}^{-}$ fraction decreased to an average of 57 %, with a larger relative contribution from aerosol organics. The remaining analyses here will focus on aircraft flights during the two late January pollution events (no. 3 and no. 4) to evaluate the contribution of nocturnal RL heterogeneous nitrogen chemistry to observed surface-level nitrate during pollution events.

Figure 4 Time series of total PM_2.5 mass (µg m⁻³) (1 and 24 h averages) for the 2016–2017 winter, measured at the Hawthorne (HW) UDAQ site in the SLV. Dashed black lines are daily PM_2.5 accumulation rates (rates given in Figure). The 24 h EPA national ambient air quality standard (NAAQS) for PM_2.5 (35 µg m⁻³) is shown by the dashed gray line. Gray shading indicates days when the TO aircraft was flying during UWFPS. Average aerosol mass fractions measured by the AMS aboard the TO are given in pie charts for polluted and clean conditions. Aerosol components are colored by nitrate (blue), ammonium (gold), sulfate (red), non-refractory chloride (pink), and organics (green).

3.2 Limiting and excess reagents for NH₄NO₃ aerosol

As NH₄NO₃ was the principal component of PM_2.5 during pollution events in the SLV (Fig. 4), the contribution from heterogeneous reactive nitrogen processes is dependent on whether NH₄NO₃ formation is limited by the availability of gas-phase NH₃ or HNO₃. Under ambient conditions, gas-phase NH₃ and HNO₃ are assumed to be in a thermodynamic equilibrium with their particulate equivalents (${\mathrm{NO}}_{\mathrm{3}}^{-}\left(\mathrm{p}\right)$ and ${\mathrm{NH}}_{\mathrm{4}}^{+}\left(\mathrm{p}\right)$). The limiting reagent can therefore be inferred from the ratio of total oxidized (${\mathrm{HNO}}_{\mathrm{3}}\left(\mathrm{g}\right)+{\mathrm{NO}}_{\mathrm{3}}^{-}\left(\mathrm{p}\right)$) to total reduced nitrogen (${\mathrm{NH}}_x={\mathrm{NH}}_{\mathrm{3}}\left(\mathrm{g}\right)+{\mathrm{NH}}_{\mathrm{4}}^{+}\left(\mathrm{p}\right)$), shown in Eq. (3). This ratio does not account for other aerosol components such as (NH₄)₂SO₄, NH₄HSO₄, and NH₄Cl but should generally represent the NH₄NO₃ aerosol system when particulate concentrations of sulfate and inorganic chloride are low, as was observed during UWFPS 2017 (Fig. 4 and Franchin et al., 2018). A nitrogen ratio greater than 1 indicates that oxidized nitrogen is in excess and NH₄NO₃ particle formation is limited by the presence of NH₃. Conversely, a ratio smaller than 1 indicates that formation is limited by the presence of HNO₃, which itself is limited by the oxidation rate of NO_x. In a HNO₃-limited system, NH₄NO₃ formation will be sensitive to changes in HNO₃ concentrations resulting from both day- and nighttime NO_x oxidation processes. Daytime NO_x oxidation rates during winter will depend on specific conditions but are generally slower, such that nighttime oxidation may play a dominant role (e.g., Wood et al., 2005; Kenagy et al., 2018).

$$\begin{array}{}\text{(3)}& \text{N Ratio}={\displaystyle \frac{{\mathrm{HNO}}_{\mathrm{3}}\left(\mathrm{g}\right)+{\mathrm{NO}}_{\mathrm{3}}^{-}\left(\mathrm{p}\right)}{{\mathrm{NH}}_{\mathrm{3}}\left(\mathrm{g}\right)+{\mathrm{NH}}_{\mathrm{4}}^{+}\left(\mathrm{p}\right)}}\end{array}$$

A time series of nitrogen ratios in the SLV between 17 January and 1 February is shown in Fig. 5a, calculated from 10 s averaged (AMS frequency) measurements of gas- and particle-phase compounds aboard the TO aircraft. Figure 5a shows that NH₄NO₃ particle formation in the SLV during pollution episodes was largely limited by HNO₃ (median ratio 0.77) but highly variable (range of 0.1–1.9) and time dependent, with the frequency of NH₃-limited conditions increasing throughout both late January pollution events. The color scale in Fig. 5a and the vertical profiles of average and 10th–90th percentile nitrogen ratios in Fig. 5b further show that the lowest nitrogen ratios corresponded to the lowest altitudes. This evidence of HNO₃ limitation near the ground is consistent with all previous ground-based observations that show exclusive HNO₃ limitation in the SLV (Kelly et al., 2013; Utah Division of Air Quality, 2014c). The increased frequency of NH₃-limited points throughout both pollution episodes (Fig. 5a), however, is opposite the trend predicted by Baasandorj et al. (2017), who suggested that observed surface-level oxidant depletion should lead to more HNO₃-limited conditions over time. Events of NH₃ limitation (excess HNO₃) during 2017, however, only occurred at the highest altitudes (panel b), and their increasing frequency with time (panel a) is consistent with these events reflecting negative NH₃ gradients away from the surface and/or the production of HNO₃ aloft from nocturnal N₂O₅ chemistry. The rate of HNO₃ production from nocturnal heterogeneous chemistry is expected to be maximized at higher altitudes, removed from NO emissions and O₃ titration at the surface (Fig. 2). Results here are also consistent with aerosol thermodynamic modeling studies by Franchin et al. (2018), who found that simulations of total PM₁ mass during UWFPS flights over the SLV were proportionally sensitive to 50 % reductions in total nitrate. Additional simulations by Franchin et al. (2018), however, also showed near 50 % PM₁ reductions with 50 % reductions in total ammonium (${\mathrm{NH}}_{\mathrm{3}}+{\mathrm{NH}}_{\mathrm{4}}^{+}$), indicating that 50 % ammonium reductions may be enough to shift the SLV from the HNO₃ to NH₃-limited regime. This is consistent with nitrogen ratios in Fig. 5 approaching and exceeding values of 1.

Figure 5 (a, top) Time series of the ratio of total oxidized (${\mathrm{HNO}}_{\mathrm{3}}+{\mathrm{NO}}_{\mathrm{3}}^{-}$) to reduced (${\mathrm{NH}}_{\mathrm{3}}+{\mathrm{NH}}_{\mathrm{4}}^{+}$) nitrogen between 16 January and 1 February 2017 (10 s averages), calculated from TO observations over the SLV. Individual nitrogen ratios are colored by aircraft altitude (m a.g.l.). Yellow and gray shading indicate times of day and night, respectively. (a, bottom) PM_2.5 mass (24 h average) measured at the HW ground site. (b) Vertical profile of oxidized-to-reduced nitrogen ratios from panel (a). Diamonds represent the average values in each altitude bin and gray shading shows the 10th–90th (light gray) and 25th–75th (dark gray) percentiles. The number of points in each bin is shown by the gray dashed line. The vertical black line illustrates a nitrogen ratio of 1.

3.3 Nitrate production via heterogeneous reactive nitrogen chemistry

The absolute amount of nitrate that is chemically produced from heterogeneous chemistry will depend on the production rates of the nitrate radical and gas-phase N₂O₅ (Sect. 3.3.1), the N₂O₅ aerosol uptake efficiency (Sect. 3.3.2), and the yields of ClNO₂ and HNO₃ (Sect. 3.3.2), which are quantified below. The final section (Sect. 3.3.3) presents forward-integrated box model simulations to further quantify the nocturnal nitrate production rate and estimate the contribution of this chemistry to NH₄NO₃ formation during January 2017 in the SLV.

3.3.1 Maximum instantaneous nitrate production rates

An upper-limit estimate of the instantaneous aerosol nitrate production rate from heterogeneous N₂O₅ chemistry is defined here as $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$. This rate can be calculated as 2 times the gas-phase production rate of the NO₃ radical ($P_{{\mathrm{NO}}_{\mathrm{3}}}$), given that the reaction between NO₂ and O₃ (Eqs. 4–6), rather than N₂O₅ uptake, is the rate-limiting step for nitrate formation (discussed below). In Eq. (4), $P_{{\mathrm{NO}}_{\mathrm{3}}}$ is calculated in units of molecules per cubic centimeter per second (molec. cm⁻³ s⁻¹) but is typically reported in units of ppbv h⁻¹ as shown here. The reaction kinetics in Eq. (5) between NO₂ and O₃ are from the 2008 IUPAC recommendation (IUPAC, 2008), ND is the number density of ambient air, and $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ in Eq. (6) is calculated after $P_{{\mathrm{NO}}_{\mathrm{3}}}$ has been converted to units of micrograms per cubic meter per hour (µg m⁻³ h⁻¹), as detailed in Sect. S2. This calculation estimates a maximum contribution of N₂O₅ heterogeneous chemistry to nitrate production as it assumes (1) N₂O₅ is produced quantitatively from NO₃ (i.e., no competing reaction of NO₃+VOC), (2) N₂O₅ is produced at the rate of NO₃ production (valid under cold conditions that shift the NO₃–N₂O₅ equilibrium to favor of N₂O₅), (3) N₂O₅ is efficiently taken up onto aerosol, and (4) aqueous-phase reactions form two molecules of HNO₃ for every molecule of N₂O₅ (i.e., φ(ClNO₂)=0).

$$\begin{array}{}\text{(4)}& {\displaystyle }\begin{array}{rl}{P}_{{\mathrm{NO}}_{\mathrm{3}}}\left[\mathrm{ppbv}{\mathrm{h}}^{-\mathrm{1}}\right]& ={\displaystyle \frac{k_{\mathrm{4}}\left[{\mathrm{O}}_{\mathrm{3}}\right]\left[{\mathrm{NO}}_{\mathrm{2}}\right]}{\mathrm{ND}\left[\mathrm{molec}.{\mathrm{cm}}^{-\mathrm{3}}\right]}}\cdot \mathrm{3600}\left[\mathrm{s}{\mathrm{h}}^{-\mathrm{1}}\right]\\ & \cdot \mathrm{1}\times {\mathrm{10}}^{\mathrm{9}}\left[\mathrm{ppbv}\right]\end{array}\text{(5)}& {\displaystyle }{k}_{\mathrm{4}}\left[{\mathrm{cm}}^{\mathrm{3}}{\mathrm{molecule}}^{-\mathrm{1}}{\mathrm{s}}^{-\mathrm{1}}\right]=\mathrm{1.4}\times {\mathrm{10}}^{-\mathrm{13}}{e}^{(-\mathrm{2470}/T)}\text{(6)}& {\displaystyle }{P}_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}\left[\mathrm{\mu }\mathrm{g}{\mathrm{m}}^{-\mathrm{3}}{\mathrm{h}}^{-\mathrm{1}}\right]=\mathrm{2}\cdot \left(P_{{\mathrm{NO}}_{\mathrm{3}}}\right[\mathrm{\mu }\mathrm{g}{\mathrm{m}}^{-\mathrm{3}}{\mathrm{h}}^{-\mathrm{1}}\left]\right)\end{array}$$

The value of $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ is expected to vary with altitude due to boundary layer dynamics and surface NO_x emissions that can deplete O₃ at night near the surface, as described previously in Baasandorj et al. (2017). The time series in Fig. 6a illustrates that the O₃ measured at HW was frequently absent at night during the third and fourth pollution events in January 2017. As surface-level O₃ was titrated overnight, ground-site data cannot provide direct information about $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ aloft in the RL. In the absence of vertical observations during pollution events in 2016, a previous analysis by Baasandorj et al. (2017) used late-afternoon measurements at the HW ground site to predict NO₃ production rates ($P_{{\mathrm{NO}}_{\mathrm{3}}}$) in the RL that varied from 0 up to ∼2 ppbv h⁻¹ (∼0–5 µg m⁻³ h⁻¹), but with values frequently <1 ppbv h⁻¹. These values correspond to instantaneous nitrate production rates ($P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$) of ∼0–10 µg m⁻³ h⁻¹, with typical values closer to 5 µg m⁻³ h⁻¹. Late-afternoon estimates from the same site during 2017 (dashed lines in Fig. 6, from Eq. 6) suggest smaller $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ rates in 2017 than in 2016, with values between 1 and 5 µg m⁻³ h⁻¹ during UWFPS pollution events (Fig. 6a).

Figure 6 (a) Time series of NO₂, O₃ (top), $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ (middle; see text for definition), and PM_2.5 (bottom) measured at the HW ground site during 16 January–6 February 2017. O₃ data during the middle January pollution event were corrected to account for a 4.5 ppbv offset in the HW measurements, as shown in Fig. S4. Aircraft flight times are shown by red shading. Dashed blue line shows the calculated $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ rates that would occur during the day if this mechanism were operative. Solid blue line assumes nitrate production from this mechanism during the day is zero. Late-afternoon $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ at the surface (dashed line) is roughly equivalent to the $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ expected in the RL at night. (b) Vertical profiles of O₃, NO₂, $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ (1 s data), and PM₁ (10 s data) measured from the aircraft on all night flights over the SLV. In each panel, light shaded regions show the 10th–90th percentile ranges, dark shaded regions are the 25th–75th percentile ranges, and the solid lines are the 50th percentile. Dashed black lines show the number of points at each altitude.

The bottom panels of Fig. 6b show the binned, vertical profiles of median, 25th, and 75th percentile instantaneous $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ values, along with aircraft observations of O₃, NO₂, and PM₁ for all UWFPS night flights (red shaded regions in Fig. 6a). The vertical profiles show a relatively uniform distribution of $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ with altitude through the lowest 600 m. The dashed black lines also show that the number of points in each altitude bin was weighted toward the 100–500 m altitude range. The median instantaneous $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ value in this polluted layer (0–600 m a.g.l., meters above ground level) was 1.6 µg m⁻³ h⁻¹ (N = 21 666). This value is at the low range of estimates of 1.6–5 µg m⁻³ h⁻¹ that are predicted from late-afternoon ground-based observations on each flight day (dashed line in the middle panel of Fig. 6a), following the method of Baasandorj et al. (2017).

Figure 7 Vertical profiles of NO₂, O₃, $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ (1 s data), and PM₁ (10 s data) measured from the TO aircraft during five box patterns, flown over the SLV urban core between 21:20 and 00:30 MST on 28 and 29 January. Percentiles and number of points at each altitude are shown as in Fig. 6. Square markers and error bars represent the median and 25th–75th percentile range of NO₂, O₃, $P_{{\mathrm{NO}}_{\mathrm{3}}^{-}}$, and PM_2.5 measured concurrently at the HW ground site.

Vertical profiles in Fig. 6b do not show evidence for a reduction in $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ or O₃ near the surface, as is expected for O₃ titration near the ground level (shown in panel a). The distribution in panel b, however, is affected by the location of the missed approaches/landings in the SLV (Salt Lake International and South Valley Regional airfields), which are further from the urban center of Salt Lake City than the HW ground site (see Fig. 1). Vertical profiles to the surface over urban Salt Lake City were not possible due to a lack of airfields for missed approaches. Instead, the SLV flights often executed box patterns over the eastern Salt Lake basin at several altitudes. Figure 7 shows the vertical distribution of $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ values from these boxes on 28–29 January between 21:20 and 00:30 local time, compared to $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ measured at the surface during the same interval. At 300 and 500 m a.g.l., the median (and interquartile range) $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ was 2.2 (2.1 to 2.4) and 1.9 (1.8 to 2.1) µg m⁻³ h⁻¹, while at 650 m, slightly above the most concentrated pollution layer, it was 0.5 (0.3 to 0.7) µg m⁻³ h⁻¹. The median value at the HW ground site, directly below the aircraft, was 0.02 (0.01 to 0.2) µg m⁻³. These plots demonstrate that $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ is typically low or zero at night near the surface within the urban area of Salt Lake City but large within the RL. Away from the urban area, the vertical distributions of $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ are also likely more uniform (Fig. 6b) due to the lack of O₃ titration within the nocturnal boundary layer. In the final section below, nightly integration of these instantaneous $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ values are compared to box model predictions of total nitrate.

3.3.2 Modeled uptake coefficients and production yields

Both the aerosol uptake efficiency of N₂O₅ (γ(N₂O₅)) and the production yield of ClNO₂ (φ(ClNO₂)) are highly variable, dependent on aerosol composition, and can impact the absolute amount of nitrate formed from nocturnal heterogeneous nitrogen chemistry. The nighttime formation of nitrate, however, is only limited by these processes when N₂O₅ uptake is inefficient and is instead limited by the oxidation rate of NO₂ (Reaction R4) (discussed above) at sufficiently large values of γ(N₂O₅).

As described in Sect. 2.2, an iterative box model was fit to observations of NO₂, O₃, N₂O₅, and ClNO₂ to quantify γ(N₂O₅) and φ(ClNO₂) during pollution events. For the SLV alone (N=1031), the distribution in Fig. 8 shows that γ(N₂O₅) values ranged 4 orders of magnitude from $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{3}}$ to >1 with two modes centered near 0.01 and 0.08. Values approaching or exceeding 1 are unphysical and suggest artifacts in the γ(N₂O₅) determinations for UWFPS (see below), at least for the largest values. Values of φ(ClNO₂) encompassed the entire possible range of 0 to 1 (Fig. 8). The medians for this subset were 0.076 and 0.220 for γ(N₂O₅) and φ(ClNO₂), respectively. For all UWFPS flights between 16 January and 1 February 2017, the median γ(N₂O₅) and φ(ClNO₂) values in the RL (N=2195) were 0.049 and 0.256, respectively, derived from box model fits to observations. These values are compared to multiple derivation methods further below.

Compared to previous studies, the median γ(N₂O₅) over the SLV was twice as large as the mode derived with a similar model using data from the Nitrogen, Aerosol Composition, and Halogens on a Tall Tower (NACHTT) campaign near Denver, Colorado, in winter 2011 (Wagner et al., 2013). Similarly, the median was over 5 times larger than the median calculated using the same model from the 2015 WINTER campaign (McDuffie et al., 2018b). The largest values during UWFPS exceeded those from both WINTER and NACHTT studies, while the smallest values were also larger than either of the respective minimums. The two most common suppression mechanisms that lead to reductions in γ(N₂O₅) are associated with the presence of organic material and nitrate in the aerosol phase. Insoluble aerosol organics have been shown to suppress N₂O₅ uptake in previous laboratory studies (e.g., Griffiths et al., 2009; Thornton et al., 2003; McNeill et al., 2006; Thornton and Abbatt, 2005; Cosman et al., 2008; Badger et al., 2006; Folkers et al., 2003), and large organic mass fractions have been associated with γ(N₂O₅) reductions in past field studies (Bertram et al., 2009; McDuffie et al., 2018b). The average dry mass fraction of aerosol organics (i.e., organic mass/total dry aerosol mass) during the SLV pollution events was less than half of the average during the WINTER campaign (∼18 % vs. 40 %) and 40 % lower than the average during NACHTT (27 %, Wagner et al., 2013). Aerosol nitrate can also suppress uptake as soluble nitrate facilitates the reformation of gas-phase N₂O₅ (Bertram and Thornton, 2009; Griffiths et al., 2009), and nitrate mass fractions have been negatively correlated with γ(N₂O₅) in previous field studies (Wagner et al., 2013; Morgan et al., 2015; Riedel et al., 2012; Bertram et al., 2009; McDuffie et al., 2018b). The presence of sufficient aerosol water, however, can offset this nitrate suppression by promoting N₂O₅ aqueous solvation and reaction (e.g., Bertram and Thornton, 2009; Griffiths et al., 2009; Mentel et al., 1999; Wahner et al., 1998), resulting in increases in γ(N₂O₅) with the ratio of water to nitrate (McDuffie et al., 2018b). The average dry mass fraction of aerosol nitrate was much larger during UWFPS (60 %) than during NACHTT (30 %, Wagner et al., 2013) or WINTER (15 %, McDuffie et al., 2018b). High-humidity conditions during UWFPS (77 % average RH during pollution events) resulted in average aerosol water mass fractions (i.e., water mass/aerosol dry mass + water mass) near 70 %, as calculated with an aerosol thermodynamic model, described in Franchin et al. (2018). This higher RH likely contributed to efficient N₂O₅ uptake during UWFPS despite the presence of aerosol nitrate. In fact, the largest 25 % of UWFPS γ(N₂O₅) values exceed the largest value (0.175) that has been reported from recent field studies (Fig. 4 in McDuffie et al., 2018b).

Figure 8 (a) Histograms of γ(N₂O₅) determinations from the SLV during pollution events, calculated with the box model (green), steady-state approximation (pink), and parameterization from Bertram and Thornton (2009). (b) Histograms of φ(ClNO₂) determinations from the SLV during pollution events calculated with the box model (gold) and parameterization from Bertram and Thornton (2009) (gray).

The median φ(ClNO₂) value of 0.220 during the SLV pollution events was 4 times larger than during the NACHTT campaign (Riedel et al., 2013; Wagner et al., 2013) but within a factor of 2 larger than the median derived during WINTER over the US east coast (McDuffie et al., 2018a). The SLV median was also similar to medians reported from previous ground-based studies across North America (Mielke et al., 2016, 2011, 2013; Wagner et al., 2012; Thornton et al., 2010). Heterogeneous ClNO₂ production requires aerosol chloride (Reaction R6) (e.g., Behnke et al., 1997), and though a consistent geographic pattern in φ(ClNO₂) has not emerged from past studies (Fig. 2 in McDuffie et al., 2018a), heterogeneous chemistry in the vicinity of the Great Salt Lake appears to produce ClNO₂ with the same efficiency as comparable measurements near North American ocean coastlines. ClNO₂ production yields, however, remain smaller than those predicted based on measured aerosol composition, as discussed below.

While large γ(N₂O₅) and moderate φ(ClNO₂) values indicate efficient nitrate production from heterogeneous chemistry during UWFPS, these values may be upper and lower limits, respectively. As discussed in Sect. 2.1, limited observations of VOC and photolysis rates, as well as uncertainties in air age, and dilution may cause the $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and $k_{{\mathrm{ClNO}}_{\mathrm{2}}}$ values (and subsequent γ(N₂O₅) and φ(ClNO₂)) to be over- and underpredicted, respectively. This is more likely near sunset where the model has an increased sensitivity to assumptions in simulation start time (McDuffie et al., 2018b). Uncertainties in gas-phase measurements may also contribute to uncertainties in the model predictions, though the level of uncertainty associated with these parameters is small (Table S4). Additional uncertainties in $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and $k_{{\mathrm{ClNO}}_{\mathrm{2}}}$ may arise from model assumptions of constant temperature and RH (i.e., rate constants and surface area) overnight. While model sensitivities to these uncertainties cannot be directly quantified, the percent growth in SA from nitrate accumulation is estimated to be less than the uncertainty in the dry SA measurement (34 %). As modeled $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ values are also consistent with those derived from observations (discussed below), this source of uncertainty is not discussed further. Overall, while the box model has a large number of uncertainties and assumptions, predictions of nocturnal nitrate production, which are subject to uncertainties in both $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and $k_{{\mathrm{ClNO}}_{\mathrm{2}}}$, are not highly sensitive to sources other than dilution (Table S4).

Independent of the model fits of $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and $k_{{\mathrm{ClNO}}_{\mathrm{2}}}$, unphysically large γ(N₂O₅) values (>0.1 in Fig. 8) may alternatively be an artifact arising from an under-measurement of ambient aerosol SA. Low aerosol SA would bias high the γ(N₂O₅) calculation in Eq. (1) without influencing the model derivations of $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and $k_{{\mathrm{ClNO}}_{\mathrm{2}}}$. In this study, wet aerosol SA was calculated as described above by applying an RH-dependent growth factor curve to the measured dry PM₁ SA. Despite large concentrations of total dry SA (Fig. S2), an underprediction in the wet SA could arise from uncertainties in the hygroscopic growth curve or additional unmeasured SA from large particles (>1 µm). Both factors would be exacerbated by the high-humidity conditions encountered during UWFPS since large, hydrated particles would not be sampled efficiently by the aerosol inlet and hygroscopic growth curves are highly uncertain above ∼95 % RH (corresponding to 6.7 % of the SLV data). A third possible cause of under-measured SA is the presence of fog under high-humidity conditions. Fog is well known to promote rapid heterogeneous processes (Lelieveld and Crutzen, 1990) and is associated with surface areas that can be orders of magnitude larger than accumulation mode aerosol. For example, fog has been demonstrated to lead to rapid N₂O₅ loss at a ground site in Hong Kong, during November–December 2013 (Brown et al., 2016). It is therefore possible that unmeasured SA under high-humidity conditions could bias the calculated γ(N₂O₅) values high relative to values reported in previous literature. Any bias caused by aerosol SA, however, would not impact the model-derived $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ and $k_{{\mathrm{ClNO}}_{\mathrm{2}}}$ values that are used to calculate nocturnal nitrate production rates in the final analysis below.

To further evaluate the UWFPS γ(N₂O₅) and φ(ClNO₂) values, box model determinations are compared to two other derivation methods in Figs. 8 and S5. The first method calculates γ(N₂O₅) from observations of temperature, SA, NO₂, O₃, and N₂O₅, based on the steady-state approximation (γ(N₂O₅)_ss), described by Brown et al. (2003) and defined in Sect. S4.1. This method shows excellent agreement with box model results (Figs. 8 and S5). The steady-state method has been shown in previous analyses to overpredict γ(N₂O₅) values under cold, high-NO_x conditions, but only if the first-order rate constants for NO₃ and N₂O₅ loss ($k_{{\mathrm{NO}}_{\mathrm{3}}}$ and $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$) are modest (Brown et al., 2003). Both the steady-state and box model γ(N₂O₅) values are consistent with a rapid first-order loss constant of N₂O₅ (median $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}=\mathrm{1.1}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹), suggesting the steady-state approach is valid for SLV conditions. The corresponding median lifetime ($\mathrm{1}/k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$) of 14 min is, for example, much shorter than the lifetimes of 2–18 h calculated from a previous steady-state analysis of aircraft measurements over Texas in fall 2006 (Brown et al., 2009). Nevertheless, the color scale in Fig. S5 shows that the largest γ(N₂O₅) values (≥0.1) were exclusively derived for air sampled within 3 h of sunset (4.3 h simulation time), where previous analysis has shown the steady-state approximation to be least reliable. As Fig. S5 shows large values of γ(N₂O₅) from both the box model and the steady-state analysis during this time, there may be a common bias between the methods if these values are indeed too large.

The second method calculates both γ(N₂O₅) and φ(ClNO₂) using laboratory-derived parameterizations from Bertram and Thornton (2009) (BT09), based on the aerosol volume-to-surface-area ratio; N₂O₅ solubility (Fried et al., 1994); aerosol molarities of water, nitrate, and chloride; and laboratory-derived reaction rate constant ratios. Further details of each parameterization are provided in Sect. S4.2. These parameterizations have had mixed success in reproducing previous field-derived values (e.g., Bertram et al., 2009; Riedel et al., 2012; McDuffie et al., 2018a, b) but are commonly used to predict N₂O₅ uptake and ClNO₂ production on internally mixed inorganic aerosol when N₂O₅ chemistry is included in global models (e.g., Sarwar et al., 2014; Shah et al., 2018).

Results in Fig. S5 show that the median γ(N₂O₅) value predicted by the BT09 parameterization is within a factor of 2 of the box model median but that this parameterization does not reproduce the observed variability (Fig. 8). For φ(ClNO₂), the BT09 parameterization largely overpredicts model-derived values with a median of 0.66 relative to the model median of 0.22 (Fig. S5). This overprediction is consistent with all previous studies to compare parameterized and field-derived φ(ClNO₂) results (Wagner et al., 2013; Wang et al., 2017a, b; Ryder et al., 2015; Thornton et al., 2010; Riedel et al., 2013; Tham et al., 2018; McDuffie et al., 2018a). These results also suggest that the parameterization would need to be reduced by 68 % for agreement with the box model median, similar to the 74 %–85 % reduction required for agreement of this parameterization with the WINTER campaign median (McDuffie et al., 2018a). The possible presence of additional, refractory-phase chloride (i.e., NaCl, CaCl₂, and KCl) in the accumulation mode would increase the predicted γ(N₂O₅) and improve agreement with the box model but would further degrade the agreement of φ(ClNO₂).

Lastly, the empirical γ(N₂O₅) parameterization from McDuffie et al. (2018b) was applied to UWFPS data, though only an estimated range for the campaign median is presented due to uncertainties in the aerosol O:C ratio and aerosol organic density, both required for this calculation (discussed in Sect. S4.2). This parameterization models N₂O₅ uptake onto an aqueous inorganic particle with a resistive organic coating, with the coating thickness determined by the volume ratio of inorganic to total aerosol components (McDuffie et al., 2018b; Riemer et al., 2009; Anttila et al., 2006). By estimating a range of O:C ratios using the improved-ambient O:C ratio method from Canagaratna et al. (2015) and AMS organic m∕z 44 fraction (Fig. 6, Franchin et al., 2018), assuming an organic density of 1.3 g cm⁻³ (e.g., Kuwata et al., 2012) to estimate the organic-associated volume, and applying additional constants described in Sect. S4.2, this parameterization estimated a median γ(N₂O₅) between 60 % and 85 % lower than the box model. Though there are large uncertainties in the required parameters, these results suggest that during pollution events (1) aerosol organics are not surface active, (2) aerosol organics are not resistive toward N₂O₅, or (3) box model γ(N₂O₅) values are overpredicted due to missing SA (e.g., fog, Sect. 3.3.2) or other simplifying assumptions (e.g., dilution) discussed above.

Despite disagreement between the box model and parameterizations, the γ(N₂O₅) values predicted by all three methods are large enough, in combination with the large measured aerosol SA, to fall within the range where models of nighttime chemistry are insensitive to variation in uptake efficiency (e.g., Macintyre and Evans, 2010; Riemer et al., 2003; Wang et al., 2018). Under these conditions, the NO₂ gas-phase oxidation rate (i.e., $P_{{\mathrm{NO}}_{\mathrm{3}}^{-}}$), rather than N₂O₅ uptake, becomes the limiting factor to HNO₃ formation. As further evidence of this limitation, the median lifetime of NO₂ with respect to O₃ (${\mathit{\tau }}_{{\mathrm{NO}}_{\mathrm{2}}}=\mathrm{1}/\left(k_{\mathrm{1}}\left[{\mathrm{O}}_{\mathrm{3}}\right]\right))$ was 9 h while the lifetime of N₂O₅ (${\mathit{\tau }}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}=\mathrm{1}/k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$) was just 14 min, resulting in low N₂O₅ mixing ratios (median = 0.03 ppbv) during the SLV pollution events (Fig. S6). In addition, explicit box modeling of day- and nighttime chemical processes during UWFPS by Womack et al. (2019) also showed that the production of O_x,total ($={\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{3}}+\mathrm{2}\mathrm{•}{\mathrm{NO}}_{\mathrm{3}}+\mathrm{1.5}\mathrm{•}({\mathrm{HNO}}_{\mathrm{3}}+\text{particulate nitrate})+{\mathrm{ClNO}}_{\mathrm{2}}+\mathrm{3}\mathrm{•}{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+\text{others}$) was insensitive (<1.5 %) to order-of-magnitude changes in γ(N₂O₅). Short lifetimes of N₂O₅ relative to NO₂ and nitrate insensitivity to γ(N₂O₅) both indicate that nocturnal heterogeneous chemistry contributes to NH₄NO₃ formation but that absolute production is limited by gas-phase kinetics rather than aerosol composition and γ(N₂O₅). This insensitivity to γ(N₂O₅) provides confidence in the ability of the box model to predict the magnitude of nocturnal nitrate production in the SLV, regardless of uncertainties in γ(N₂O₅).

3.3.3 Modeled nocturnal nitrate production rates and contribution of heterogeneous chemistry to total NH₄NO₃ aerosol accumulation rates

As described in Sect. 2.2 and shown in Fig. 3, the box model simulates the amount of total nitrate (${\mathrm{HNO}}_{\mathrm{3}}+{\mathrm{NO}}_{\mathrm{3}}^{-}$) produced from heterogeneous chemistry over the course of a single night. This amount of nitrate, in units of µg m⁻³ per night, is in addition to any nitrate present at sunset from the previous day (e.g., Fig. 3). Figure 9 shows the distribution of nightly nitrate production predicted by base case simulations (N=1031), ranging from ∼0 to 31 µg m⁻³ nitrate per night, with a median of 9.9 µg m⁻³ nitrate per night.

Figure 9 Histograms of nocturnal nitrate production rates (µg m⁻³ per night) predicted by base case simulations and simulations incorporating a first-order dilution loss process with rate constant $k_{\mathrm{dilution}}=\mathrm{1.3}\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹.

In addition to evidence from the previous section, comparisons between the base case results and integrated $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ values from Sect. 3.3.1 also suggest that nocturnal nitrate production is limited by the rate of NO₂ oxidation rather than the efficiency of N₂O₅ aerosol uptake. Based on the calculations in Sect. 3.1, upper-limit $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ values, integrated over an average 14 h night and reduced to account for a φ(ClNO₂) value of 0.2, ranged from <0.5 to >40 µg m⁻³ per night, with a median of 20.2 µg m⁻³ per night (N = 21 666). To more directly compare with box model results, the subset of points with simultaneous γ(N₂O₅) determinations had a median of 10.6 µg m⁻³ per night, which is slightly larger but agrees well with the box-model-predicted median of 9.9 µg m⁻³ per night. As described in Sect. 3.3.1, the $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ calculation assumes efficient N₂O₅ uptake and only considers nitrate production to be limited by gas-phase kinetics. Observed agreement between the integrated $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ values and box-model-predicted production rates therefore suggests that nitrate production may be largely limited by gas-phase oxidation rather than multiphase processes. As a result, the large variability in predicted nitrate production rates is reflective of the variability in the observed NO₃ radical production rates (Fig. 6).

Uncertainties associated with base case production rates are discussed in Sect. 2.2.2 and shown as a time series in Fig. S3. Air parcel dilution associated with the vertical entrainment of air from the free troposphere (Sect. S1.4.1) was the largest source of uncertainty (Table S4, Fig. S3). This process was not included in base case simulations, though mixing/dilution has been observed and predicted in analyses of WINTER nighttime flights (Kenagy et al., 2018; McDuffie et al., 2018b). Estimating the impact of dilution by including a single first-order dilution rate constant (k_dilution) of $\mathrm{1.3}\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹ reduced the median nocturnal nitrate production rate by 42 % to 5.7 µg m⁻³ per night and resulted in a smaller range of production rates (∼0 to 16 µg m⁻³ per night) relative to base case simulations in Fig. 9. As described in Womack et al. (2019) (and in Sect. S1.4.1), a single first-order dilution rate constant of $\mathrm{8}\times {\mathrm{10}}^{-\mathrm{6}}$ s⁻¹ was derived for pollution event no. 4 in the SLV by fitting a box model to best reproduce the day-to-day buildup of observed O_x,total between 28 January and 1 February at the UU ground site. In the model described by Womack et al. (2019), this rate constant was then scaled up by 40 % when simulating the nocturnal RL in order to maintain constant dilution and account for the reduced volume relative to the mixed daytime boundary layer. While dilution/entrainment rates may vary from day to night, the method of Womack et al. (2019) represents the single number that would best represent the average rate. The same procedure is followed here with a resulting k_dilution value of $\mathrm{1.3}\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹, which is ∼60 % lower than k_dilution from the WINTER campaign, derived from observations of NO_y ($=\mathrm{NO}+{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{NO}}_{\mathrm{3}}+\mathrm{2}\mathrm{•}{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+{\mathrm{ClNO}}_{\mathrm{2}}+{\mathrm{RONO}}_{\mathrm{2}}\mathrm{\dots }$) overnight in a single RL air parcel over the eastern US coast (McDuffie et al., 2018b). As processes relevant to RL dilution were not directly measured during UWFPS, there are uncertainties associated with this k_dilution estimation. For instance, based on the modeled surface albedo in Womack et al. (2019), k_dilution could have reproduced observed O_x,total mixing ratios with scaled values ranging between $\mathrm{1.2}\times {\mathrm{10}}^{-\mathrm{5}}$ and $\mathrm{2.5}\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹ (Fig. S10, Womack et al., 2019). This particular range of loss rate constants predicts median nitrate production rates in the SLV between 3.6 and 6.1 µg m⁻³ per night.

Modeled nitrate production rates are further compared in Fig. 10 to the average daily accumulation of surface-level nitrate aerosol during pollution event no. 4 at the HW ground site. This ground-based accumulation rate (red diamond in Fig. 10a) was taken as the slope of the 24 h average PM_2.5 observations at HW (scaled by 0.58; average ${\mathrm{NO}}_{\mathrm{3}}^{-}$ fraction from Fig. 4) during the first 6 d of event no. 4, before it began to degrade on 1 February 2017 (Fig. 10b). Only data from event no. 4 are assessed here as this was the only PCAP sampled with the aircraft on multiple nights. Figure 10a shows this average, 24 h surface accumulation rate of 4.6 µg m⁻³ d⁻¹ (red diamond) compared to the 10th–90th percentile distributions, medians, and averages of the nocturnal production rates predicted by base case box model simulations (gray) and simulations including the effects of 24 h dilution (blue), described below.

Figure 10 (a) For pollution event no. 4, comparison of model-predicted nocturnal nitrate production (µg m⁻³ d⁻¹) for base case simulations (gray), simulations with 24 h of dilution (blue), and the average daily nitrate buildup observed at HW (red). Dilution cases are for simulations that incorporate nocturnal dilution rate constants of $\mathrm{1.2}\times {\mathrm{10}}^{-\mathrm{5}}$ (L), $\mathrm{1.3}\times {\mathrm{10}}^{-\mathrm{5}}$ (M), and $\mathrm{2.5}\times {\mathrm{10}}^{-\mathrm{5}}$ (H) s⁻¹, scaled by 60 % during the day. Box-and-whisker plots show the 10th–90th percentile distributions of each set. Upper-limit (UL) values assume morning mixing between equivalent nitrate concentrations produced in the RL and NBL. Lower-limit (LL) values assume morning mixing with no nitrate production in the NBL. The red diamond shows the ground-based buildup rate, calculated from 24 h averaged data at HW in panel (b). (b) Observed concentrations and average daily buildup rate of nitrate aerosol mass (total mass ⋅ 0.58) at HW during event no. 4.

Comparing modeled RL chemical nitrate production to the observed ground-based accumulation rate can provide an estimate for the fractional contribution of N₂O₅ uptake to total particulate nitrate production in the SLV. Direct comparison is difficult, however, as the 24 h ground-based accumulation rate includes contributions from photochemistry and nocturnal formation in the RL and nocturnal boundary layer (NBL) and is impacted by dilution and mixing processes. For example, the amount of nocturnally produced nitrate at the surface will depend on mixing between the NBL and RL during morning boundary layer expansion (Fig. 2). In Fig. 10a, the median base case prediction without dilution or mixing (gray, 8.6 µg m⁻³ per night) was nearly twice as large as the 24 h average accumulation rate observed at the surface during the same event (4.6 µg m⁻³ per night, red). Therefore, to more directly compare box model predictions and ground-based observations, Fig. 10a also shows the results from two simulations that include upper- and lower-limit estimates of loss from nocturnal and daytime dilution. For both scenarios, the nighttime (0–14 h) k_dilution value of $\mathrm{1.3}\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹ (blue) was applied to all modeled species as described above. At sunrise, morning mixing between the NBL (taken as 40 % by volume) and RL (taken as 60 % by volume) was then estimated using the assumed volume ratio between the two layers and assuming either equivalent nocturnal nitrate production in both layers (upper limit) or no production in the NBL (lower limit). Nocturnal production in the NBL is expected to be suppressed relative to the RL due to O₃ titration (e.g., Fig. 6 here and Fig. S6 in Womack et al., 2019), making the assumption of equivalence an upper-limit estimate to nocturnally produced nitrate at the surface after morning mixing. The upper-limit case required no reduction of the model-predicted nitrate concentrations at sunrise (e.g., Fig. 9), whereas these concentrations were instantaneously reduced by 40 % for the lower-limit case. To account for daytime dilution in the remaining ∼10 h, morning concentrations for both cases were further diluted with the daytime boundary dilution rate constant from Womack et al. (2019) ($\mathrm{8}\times {\mathrm{10}}^{-\mathrm{6}}$ s⁻¹), described above and in Sect. S1.4.1. For a single 24 h period, this resulted in a net median of 2.4 to 3.9 µg m⁻³ nitrate produced from nocturnal heterogeneous N₂O₅ uptake for the lower and upper-limit cases, respectively. When considering the entire possible range of dilution rate constants from Womack et al. (2019), the median values from both cases were between 1.1 and 4.2 µg m⁻³ d⁻¹, as shown in Fig. S7.

Comparison of modeled rates to the observed surface buildup of 4.6 µg m⁻³ d⁻¹ suggests that, on average, nitrate produced from heterogenous chemistry can account for at least 50 % of the nitrate accumulation observed at the surface. This result is qualitatively consistent with an observational analysis by Pusede et al. (2016), who determined that nocturnal heterogeneous chemistry was the main source of regional aerosol nitrate during wintertime pollution events in the San Joaquin Valley. The lower-limit estimate, however, is also similar to a box model analysis of this same event by Womack et al. (2019), who found roughly equal contributions between photochemical and nocturnal nitrate production pathways, highlighting that photochemical nitrate production is also occurring during these events. Therefore, while results in Fig. 10a (including dilution) predict a median nocturnal fractional contribution of 52 %–85 % (ranging between 24 % and 91 %; Fig. S7), confirmation and further quantification of this result will require additional, vertically resolved measurements of aerosol composition, gas-phase precursors, and physical parameters, as well as more sophisticated modeling of these multiday pollution accumulation events with 3-D chemical transport models.

4 Summary and conclusions

Aerosol- and gas-phase measurements collected during the 2017 UWFPS campaign showed multiple pollution events that exceeded PM_2.5 standards in the SLV, the most populated region in the state of Utah. During these events, aerosol particles were largely composed of NH₄NO₃, which forms from the reaction between gas-phase NH₃ and HNO₃. While NH₃ is emitted from surface sources, HNO₃ is chemically formed from the oxidation of NO_x emissions. This oxidation can occur through daytime reactions with the photochemical OH radical or through nocturnal heterogeneous reactions involving NO₃ and N₂O₅. The contribution of nocturnal chemistry to PM_2.5 formation in the SLV is dependent on whether NH₄NO₃ formation is NH₃ or HNO₃ limited, as well as the NO₃ production rate, N₂O₅ uptake efficiency, ClNO₂ and HNO₃ production yields, and loss processes such as air parcel dilution.

Vertically resolved measurements of gas- and particulate-phase oxidized and reduced nitrogen in the SLV showed that NH₄NO₃ formation during pollution events was nearly always HNO₃ limited but that oxidized and reduced nitrogen approached equivalence as pollution events progressed. This reagent balance analysis is consistent with aerosol thermodynamic modeling presented in Franchin et al. (2018), which predicted that all three major valleys in the Wasatch region were sensitive to nitrate reductions and that the SLV was also sensitive to NH₃ reductions. Both observation- and modeling-based analyses agreed that NH₄NO₃ formation in the RL was largely HNO₃ limited during pollution events, providing the possibility of a large contribution from nocturnal heterogeneous chemistry to HNO₃ and PM_2.5 mass.

Analysis of vertically resolved, calculated nitrate production rates (an upper-limit estimate due to heterogeneous HNO₃ formation, $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$) and results from an observationally constrained chemical box model suggest that nocturnal chemistry is an efficient mechanism for PM_2.5 production in the SLV during pollution events. Nitrate production rates had a median of 1.6 µg m⁻³ h⁻¹, while values of γ(N₂O₅) and φ(ClNO₂) had medians of 0.076 and 0.220, respectively, during pollution events. Values of γ(N₂O₅) were larger than previous field-based determinations (e.g., McDuffie et al., 2018b) and those predicted from the Bertram and Thornton (2009) parameterization but were in agreement with values derived using the N₂O₅ steady-state approach. The median φ(ClNO₂) value was larger than that derived from aircraft observations over the eastern US coast but was simultaneously overpredicted by 68 % by the Bertram and Thornton (2009) parameterization, which uses measurements of aerosol chloride and aerosol water estimations.

While the box model has uncertainties associated with limited available measurements and model assumptions, the large measured aerosol SA, efficient N₂O₅ uptake coefficients, and moderate ClNO₂ yields resulted in nightly modeled nitrate production rates that were largely insensitive to specific values of derived parameters. Agreement between base case modeled nightly nitrate production (9.9 µg m⁻³ per night) and that calculated from $P_{{\mathrm{NO}}_{\mathrm{3}}^{-},max}$ values (10.6 µg m⁻³ per night) alternatively suggests that nitrate production is more sensitive to gas-phase NO₂ oxidation rates than γ(N₂O₅), providing confidence in the model's predictions of nocturnal nitrate. Of the parameters tested, the model was most sensitive to loss through air parcel dilution, with a 42 % reduction to 5.7 µg m⁻³ nitrate per night when including a nocturnal k_dilution rate constant of $\mathrm{1.3}\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹. When considering the possible effects of 24 h dilution, model simulations predicted a reduced median of 2.4–3.9 µg m⁻³ nitrate d⁻¹, corresponding to 52 %–85 % (median) of the net aerosol nitrate accumulation that was observed at a SLV ground site. Due to model uncertainties and sensitivities to dilution, further quantification of this result will require additional vertically resolved measurements and photochemical/3-D modeling analyses. These results, however, highlight the importance of nocturnal chemistry in the formation of PM_2.5 in the SLV and can provide constraints for regulatory models of PM_2.5 that are used to assess control strategies in this populated nonattainment area.