Observational assessment of the role of nocturnal residual-layer chemistry in determining daytime surface particulate nitrate concentrations

This study discusses an analysis of combined airborne and ground observations of particulate nitrate (NO−3 (p)) concentrations made during the wintertime DISCOVER-AQ (Deriving Information on Surface Conditions from COlumn and VERtically resolved observations relevant to Air Quality) study at one of the most polluted cities in the United States – Fresno, CA – in the San Joaquin Valley (SJV) and focuses on developing an understanding of the various processes that impact surface nitrate concentrations during pollution events. The results provide an explicit case-study illustration of how nighttime chemistry can influence daytime surface-level NO−3 (p) concentrations, complementing previous studies in the SJV. The observations exemplify the critical role that nocturnal chemical production of NO−3 (p) aloft in the residual layer (RL) can play in determining daytime surface-level NO−3 (p) concentrations. Further, they indicate that nocturnal production of NO−3 (p) in the RL, along with daytime photochemical production, can contribute substantially to the buildup and sustaining of severe pollution episodes. The exceptionally shallow nocturnal boundary layer (NBL) heights characteristic of wintertime pollution events in the SJV intensify the importance of nocturnal production aloft in the residual layer to daytime surface concentrations. The observations also demonstrate that dynamics within the RL can influence the earlymorning vertical distribution of NO−3 (p), despite low wintertime wind speeds. This overnight reshaping of the vertical distribution above the city plays an important role in determining the net impact of nocturnal chemical production on local and regional surface-level NO−3 (p) concentrations. Entrainment of clean free-tropospheric (FT) air into the boundary layer in the afternoon is identified as an important process that reduces surface-level NO−3 (p) and limits buildup during pollution episodes. The influence of dry deposition of HNO3 gas to the surface on daytime particulate nitrate concentrations is important but limited by an excess of ammonia in the region, which leads to only a small fraction of nitrate existing in the gas phase even during the warmer daytime. However, in the late afternoon, when diminishing solar heating leads to a rapid fall in the mixed boundary layer height (BLH), the impact of surface deposition is temporarily enhanced and can lead to a substantial decline in surface-level particulate nitrate concentrations; this enhanced deposition is quickly arrested by a decrease in surface temperature, which Published by Copernicus Publications on behalf of the European Geosciences Union. 14748 G. Prabhakar et al.: Particulate nitrate formation in the wintertime drops the gas-phase fraction to near zero. The overall importance of enhanced late-afternoon gas-phase loss to the multiday buildup of pollution events is limited by the very shallow nocturnal boundary layer. The case study here demonstrates that mixing down of NO−3 (p) from the RL can contribute a majority of the surface-level NO−3 (p) in the morning (here, ∼ 80 %), and a strong influence can persist into the afternoon even when photochemical production is maximum. The particular day-to-day contribution of aloft nocturnal NO−3 (p) production to surface concentrations will depend on prevailing chemical and meteorological conditions. Although specific to the SJV, the observations and conceptual framework further developed here provide general insights into the evolution of pollution episodes in wintertime environments.


Introduction
Nocturnal processing of nitrogen oxides, NO x (= NO + NO 2 ), can strongly influence daytime air quality (Dentener and Crutzen, 1993;Brown et al., 2006c).At night, once photochemical reactions shutdown, NO x reacts with ozone (O 3 ) to form nitrate radical (NO 3 ) and dinitrogen pentoxide (N 2 O 5 ) (Reactions R1 through R3a).N 2 O 5 can react heterogeneously with airborne particles to form either nitric acid (HNO 3 ) (Reaction R4a) or, in the presence of particulate chloride, nitryl chloride (ClNO 2 ) (Reaction R4b, where Y ClNO 2 represents the molar yield of ClNO 2 with respect to the N 2 O 5 reacted).In the presence of basic species like ammonia (NH 3 ), HNO 3 can be neutralized to form particulate nitrate (NO −  3 (p) ).NO 3 radicals can alternatively react with volatile organic compounds (VOCs), which suppresses HNO 3 formation (Reaction R3b).Much research has focused on the influence of nocturnal NO x processing on the regional budgets of NO x and O 3 and on the oxidative capacity of the atmosphere during subsequent mornings (e.g., Brown et al., 2006b;Thornton et al., 2010;Wild et al., 2016).The corresponding impact of nighttime production of NO − 3 (g+p) , a key nocturnal sink for NO x , on local and regional air quality can be considerable (Lowe et al., 2015;Pusede et al., 2016) but is less often considered in detail.
The importance of nocturnal NO x chemistry to NO − 3 (p) production can be especially important in the winter.Relative to summer, nights in winter are longer, colder and more humid, and biogenic VOC emissions tend to be smaller.This allows for a larger fraction of NO 2 to be oxidized to HNO 3 via the N 2 O 5 hydrolysis pathway (Cabañas et al., 2001;Wagner et al., 2013), and colder temperatures favor partitioning of nitrate to the particle phase (Stelson and Seinfeld, 1982).In winter, nighttime HNO 3 production can more efficiently compete with daytime photochemically driven production due to the low photolysis rates and hydroxyl radical concentrations (Wagner et al., 2013;Pusede et al., 2016).Multiday pollution events (i.e., periods with elevated particulate matter, PM, concentrations) can occur when meteorological conditions inhibit dispersion, as is the case with the persistent cold air pool formation often found in valley regions (Whiteman et al., 2014;Baasandorj et al., 2017).During the daytime, sunlight-driven convection leads to an evolution of the near-surface temperature profile and causes the atmosphere to be reasonably well mixed up to some height (typically less than 1 km; cf.Fig. S1 in the Supplement).Radiative cooling in the late afternoon leads this mixed layer (ML) to decouple and separate into a shallow, near-surface-level nocturnal boundary layer (NBL) and a residual layer (RL) aloft, the behavior of which can be further modified by valley flows.
Nocturnal conversion of NO x to NO − 3 (p) can occur either in the NBL or the RL.Surface NO emissions can substantially limit direct production of NO −  3 (p) in the NBL by titrating O 3 , depending on the initial conditions.Nocturnal surface NO emissions do not directly influence the decoupled RL, with chemical production of NO − 3 (p) dependent on the NO x , O 3 and particulate matter in the mixed layer at the time of decoupling.Box and 3-D models have been previously used to assess the contribution of nocturnal processes in the RL to the daytime surface concentrations of particulate matter, especially NO − 3 (p) (Riemer et al., 2003;Curci et al., 2015).Yet, computational models often have difficulty in accurately predicting surface NO − 3 (p) in many regions, particularly in the winter season, despite good estimations of NO x emissions (Walker et al., 2012;Terrenoire et al., 2015), although this is not always the case (e.g., Schiferl et al., 2014).Here, airborne and ground measurements made over Fresno, CA, in the San Joaquin Valley (SJV) during the wintertime 2013 DISCOVER-AQ (Deriving Information on Surface Conditions from COlumn and VERtically resolved observations relevant to Air Quality; Appendix A) (Crawford and Pickering, 2014) study are used to further develop our understanding of the role that different factors play in determining surface-level NO − 3 (p) concentrations.Winters in Fresno are characterized by frequent multiday pollution episodes (Chow et al., 1999;Watson and Chow, 2002), when PM 2.5 (PM with aerodynamic diameter < 2.5 µm) mass concentrations exceed the 24 h National Ambient Air Quality Standard (NAAQS) of 35 µg m −3 (Fig. 1).Fresno is one of the largest cities in the San Joaquin Valley, which is largely an agricultural area and suffers from some of the worst air pollution in the United States (American Lung Association, 2014).Shallow daytime mixed layer heights and low wind speeds in winter lead to the accumulation of pollutants across the valley (San Joaquin Valley Air Figure 1.Time series of surface PM 2.5 concentration (µg m −3 ) measured in Fresno during the DISCOVER-AQ campaign for 1 h averages (light red dotted line) and for a running average (red line, smoothed over 24 h), along with the 1 h average NO − 3 (p) concentration (blue line).The vertical orange lines indicate the days on which airborne measurements were made.The horizontal dashed black line indicates the NAAQS 24 h standard of 35 µg m −3 for PM 2.5 .Pollution Control District, 2003).Previous observations in the SJV region have found a buildup of NH 4 NO 3 during pollution episodes (e.g., Chow et al., 2008).Approximately 30-80 % of the wintertime PM 2.5 mass in this region is ammonium nitrate (NH 4 NO 3 ), with a strong diurnal variability, and most other PM 2.5 is organic matter (Chow et al., 2006;Ge et al., 2012;Young et al., 2016;Parworth et al., 2017).During DISCOVER-AQ specifically, NO − 3 (p) was found to represent 28 % of non-refractory PM 1.0 (NR-PM 1 ; PM 1.0 , PM with aerodynamic diameter < 1 µm) mass on average (Young et al., 2016).
An important role for nocturnal NO − 3 (p) production in this region has been previously identified based on observations of long-term trends, the spatial and diurnal variability in NO −  3 (p) , and the chemical environment in and around Fresno.For example, Watson and Chow (2002) reported a sharp, early-morning (∼ 09:00 LT, local time) increase in surface NO − 3 (p) concentrations on many days of a severe pollution episode in 2000 and suggested that this behavior was consistent with mixing down of nitrate-rich air from the RL aloft.Young et al. (2016) and Parworth et al. (2017) observed similar behavior more than a decade later during DISCOVER-AQ in 2013.Pusede et al. (2016) characterized the relationship between long-term (multiyear) surface measurements of wintertime NO − 3 (p) and NO 2 in Fresno and Bakersfield and showed that the decline in NO − 3 (p) in the SJV over time (2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012) was predominately driven by reduced nocturnal NO − 3 (p) production in the residual layer.The balance between production, especially nighttime production, and daytime losses was identified by them as critical to understanding the multiday buildup during pollution events.Further, they concluded from DISCOVER-AQ aircraft measurements that much of the NO − 3 (p) production was localized over the cities given the sharp urban-rural gradients in NO − 3 (p) ; the spatial gradients in 2013 (from Pusede et al., 2016) seem to be sharper than gradients in 2000 (from Chow et al., 2006), likely reflecting the increasing localization of the NO −

(p)
pollution to the urban centers as overall NO − 3 (p) concentrations in the region have decreased.Brown et al. (2006a) ob-served that the number concentration of accumulation mode particles (0.32-1.07 µm) often increased above the surface at 90 m a.g.l.compared to surface (7 m a.g.l.) measurements during night and suggested that this was due to the growth of smaller particles into the accumulation mode via NO − 3 (p) formation.They also observed that the concentration of NO −

(p)
at 90 m a.g.l.often increased at night, which is suggestive of in situ production.
The present study builds on this literature by examining the role that aloft nocturnal nitrate production, in concert with other processes, has in determining surface NO −

(p)
concentrations during the DISCOVER-AQ campaign that took place in January and February 2013 in the SJV.Our study combines aircraft and surface observations from DISCOVER-AQ (Fig. S2).During DISCOVER-AQ, two pollution episodes were observed during which PM 2.5 concentrations were elevated (Young et al., 2016).The analysis here focuses on the quantitative assessment of NO − 3 (p) concentrations during this first episode (14-22 January) in terms of the processes that govern the NO − 3 (p) diurnal behavior; the observed behavior during this first episode is qualitatively compared with that during the second episode (30 January-6 February) to examine the factors that contribute to episodeto-episode variability.On flight days, in situ measurements of the vertical profiles of particulate and gas concentrations above Fresno (and other SJV cities) were made three times: in the midmorning (∼ 09:30 LT), around noon and in the midafternoon (∼ 14:00 LT).These measurements allow for the assessment of the daytime evolution of the vertical distribution of PM and gases as well as characterization of the time-varying boundary layer height (BLH).They also allow for the determination of the overnight evolution of the PM vertical distribution, which can be used to characterize the factors that control NO − 3 (p) concentrations in the RL.The influence of processes occurring aloft on the temporal evolution of NO − 3 (p) surface concentrations is quantitatively evaluated for this case study using an observationally constrained 1-D box model.The box model accounts for both vertical mixing (entrainment) of air to the surface and for photochem-G.Prabhakar et al.: Particulate nitrate formation in the wintertime ical NO − 3 (p) production, as well as NO − 3 (p) loss processes.Ultimately, the observations and analysis further illustrate how daytime surface-level NO − 3 (p) concentrations depend on a combination of both nocturnal and daytime production of NO − 3 (p) , vertical mixing, altitude-dependent advection in the RL overnight, daytime entrainment of clean air from the free troposphere (FT) and evaporation-driven dry deposition.The model and observations are used to examine the relative importance of these different pathways during the case-study episode considered.This work adds to the existing literature by providing an observationally based, case-study demonstration of how nocturnal processes occurring aloft -in concert with other processes -exert a major control over the evolution of pollution episodes within the SJV specifically and likely in other regions as well.

Materials and method
Airborne in situ measurements (such as particle scattering; gas-phase concentrations; relative humidity, RH; and temperature) during the DISCOVER-AQ campaign were made by a suite of instruments onboard the P3-B NASA aircraft.The flight path flown during each of the three legs for each flight day is shown in Fig. S2.The aircraft measurements were complemented by a network of ground measurement sites, of which Fresno was one.At Fresno, continuous, in situ measurements of the chemical composition and physical properties of particulate matter were performed along with measurements of NAAQS-regulated pollutants (Young et al., 2016;Zhang et al., 2016;Parworth et al., 2017).Local conditions during DISCOVER-AQ were relatively cool (T avg = 7.9 • C) and dry (RH avg = 69 %) with frequent sunshine and no visible fog.All data are archived at the DISCOVER-AQ website (NASA Atmospheric Science Data Center).Details of all measurements made are provided in Appendix A and summarized in Table A1.

Vertical distribution of NO
The concentration and vertical distribution of NO − 3 (p) in the RL ([NO − 3 (p) ] RL ) in the morning serves as the initial condition constraint on what is mixed down to the surface as the day advances and the ML rises.Thus, knowledge of the vertical distribution of NO − 3 (p) in the RL near sunrise is needed to predict the temporal evolution of surface-level NO − 3 (p) during the daytime, as will be done below.Nighttime flights were not made during DISCOVER-AQ to allow for the characterization of the overnight evolution of the RL.However, the early-morning (∼ 09:30 LT) vertical profiles over Fresno allow for the characterization of the vertical structure of most of the RL near sunrise (∼ 07:10 LT), as the surface boundary layer height at this point is still quite shallow (∼ 50 m; see Appendix B for a description of the mixed boundary layer height determination method, Figs.B1-B2).Fast measurements of total NO − 3 (gas + particle, NO − 3 (g+p) ) were only available for a subset of flights (Pusede et al., 2016), and particulate-only NO − 3 measurements were not made with sufficient time resolution, less than about a minute, to allow for robust characterization of the NO − 3 (p) vertical profile.Therefore, NO − 3 (p) vertical profiles for each flight during Episode 1 are estimated from in situ measurements of dry particle scattering and the influence of water uptake on scattering, i.e., from the particle hygroscopicity, and are calibrated against the slower particle-into-liquid sampler (PILS) measurements (Appendix A, Fig. A1).The derived, observationally constrained NO − 3 (p) profiles based on the estimated NO − 3 (p) exhibit generally good correspondence with the sparser direct measurements of NO − 3 (g+p) , although on 1 of the 2 days available for comparison the total NO − 3 somewhat exceeds the estimated NO − 3 (p) below ∼ 75 m (Fig. 2).This indicates that the estimation method is reasonable, especially since most nitrate is expected to be in the particle phase (Parworth et al., 2017) given the high relative total ammonium (NH 3 + NH + 4 ) concentrations (Fig. 3).Only 4 out of 5 flight days during Episode 1 have been included in this analysis due to insufficient data on 16 January.

(p)
concentrations are nearly constant with altitude up to ∼ 400 m (the daytime boundary layer height) (Fig. 2b), whereas the early-morning NO − 3 (p) concentrations decrease steeply with altitude up to ∼ 350 m (Fig. 2a).Corresponding vertical profiles for NO, NO 2 , O 3 , relative humidity, temperature and total particle scattering are shown in Figs.S2 (early morning) and S3 (afternoon).Like NO − 3 (p) , all indicate substantial differences between the early-morning and afternoon profile shapes.This provides a strong indication that altitudespecific processes occur overnight that lead to a reshaping of the NO − 3 (p) vertical profile.At some altitudes the NO − 3 (p) in the early-morning RL is greater than the NO − 3 (p) measured in the previous afternoon, indicating net production, while at other altitudes the early-morning RL NO − 3 (p) is less than the previous afternoon, indicating net loss (Fig. 2).As noted by Pusede et al. (2016), there tend to be sharp concentration gradients in NO −  3 (p) and NO x between the city and surrounding areas, with lower concentrations outside the city.Thus, whether NO − 3 (p) at a given altitude increases or decreases overnight results from the competing effects of chemical production versus horizontal advection bringing in this (typically) cleaner air from outside the city.(In the absence of a strong jet aloft and no convective mixing, nighttime entrainment of cleaner FT air into the RL is expected to be considerably slower than horizontal advection.)Like NO − 3 (p) , the boundary layer is reasonably well mixed with respect to NO x , O 3 and particles at the time when decoupling of the RL occurs around 15:00 LT the previous day (Fig. S4  Figure 3.The gaseous fraction of total nitrate versus the molar ratio of total ammonia to total nitrate (ppb) under different environmental conditions (blue lines).The total ammonia is the sum of NH 3(g) measured on the P3-B close to ground (< 20 m a.g.l.) and NH + at ground level measured by PILS at approximately same time.The total nitrate is the NO − 3 (g+p) measured by TD-LIF close to ground (< 20 m a.g.l.).The gray dashed arrow indicates the observed range of molar ratio values during the campaign period.The total (gas + particle) ammonia is shown for reference (orange line).
atively minor vertical variation due to variations in temperature and RH alone (Fig. S5).In other words, without advective loss or dilution processes of either NO − 3 (p) or the precursor gases, it is expected that the NO − 3 (p) concentration would increase to a similar extent at all RL altitudes.
The substantial changes observed in the shape of the vertical profile overnight indicate that nighttime differential advection in the RL is a major factor in determining the shape of the morning NO − 3 (p) vertical profile during this pollution episode.Differential horizontal advection serves to directly export NO − 3 (p) from the urban area and import cleaner air from surrounding areas.Secondarily, as NO x concentrations are also lower outside of the Fresno urban area (Pusede et al., 2014), this differential advection will also influence the over-city concentrations of precursors gases (NO x and O 3 ; Figs.S3-S4) and consequently the altitude-specific nitrate production, with decreases likely.This is supported by surface-level measurements of NO x and O 3 made in Fresno and in the nearby and much more rural cities of Parlier (located 35 km SE of Fresno) and Madera (located 40 km NW of Fresno).The NO x and NO 2 concentrations are higher and the O 3 lower in Fresno compared to the surrounding cities throughout the day, and the instantaneous nitrate production rate ([NO 2 ][O 3 ]) is substantially higher in Fresno in the late afternoon, when decoupling occurs (Fig. S6).The important implication is that overnight advection both directly and indirectly alters the vertical NO − 3 (p) profile and decreases the over-city NO − 3 (p) concentrations in the morning, which will consequently serves to limit the extent of localized pollution buildup during events.The impact of overnight differential advection on reshaping the vertical distribution of NO − in the SJV (Bao et al., 2008).We suggest that a similar, but weaker, circulation may exist even in the winter, just at much slower wind speeds, and that this advection overnight is what leads to differential washout and the establishment of the particular vertical NO − 3 (p) concentration profiles in the RL.The concentration of NO − 3 (p) will likely be lowest in the early-morning RL at altitudes where horizontal advection has the greatest impact.Wind profiler measurements made in nearby Visalia, CA (65 km SE of Fresno), indicate that during the night (19:00-07:00) there was local maximum in the mean wind speed at ∼ 250 m, which is around the altitude at which the early-morning NO − 3 (p) concentration is minimum (Fig. 2a).Below 250 m there was a monotonic increase in the nighttime mean wind speed with altitude, with very slow speeds observed at the surface.Above 250 m the mean wind speed was relatively constant to ∼ 450 m, above which it increased with altitude.Explicit comparison between the vertical profiles of nighttime mean wind speed and the estimated early-morning NO − 3 (p) concentration indicates an inverse relationship (r = −0.98) between the two (Fig. S7).This is consistent with the idea that differential advection as a function of altitude overnight serves to shape the earlymorning concentration profiles.The wind direction at lower altitudes (∼ 150 m) was generally more variable than those at higher altitudes (285 or 450 m), with a general shift from more westerly at lower altitudes (but above the surface) to more northerly near the top of the RL (Fig. 4b).(Note that vector average wind speeds for each individual night were calculated and then a scalar average of these night-specific vector averages was calculated to give the episode average mean wind speeds.This averaging process emphasizes directional consistency of the winds on a given night, but not between nights.)The increase in NO − 3 (p) concentration at ∼ 400 m a.g.l. in the early-morning profile, especially noticeable on 21 January (Fig. S8), could result from a slowing of the winds near the top of the RL or from enhanced recirculation of pollutants at higher altitudes.Regardless of reason, this work indicates that the gradient between the local (above city) and regional NO − 3 (p) and precursor gases, evident in Pusede et al. (2016), is an important factor in determining the nighttime evolution of the RL vertical profile.Explicit characterization of the temporal evolution of the vertical structure of NO − 3 (p) within the nighttime RL would provide further insights into the altitude-specific processes that control the shape of the early-morning profile (and thus the concentration of NO − 3 (p) aloft that can be mixed to the surface in daytime).
The difference between the concentration of NO − 3 (p) at each altitude of the early-morning vertical profile and that at 15:00 LT on the preceding afternoon ( [NO − 3 (p) ] RL ) yields the net overnight NO − 3 production or loss in the RL.If it is assumed that the layer with the highest NO − 3 (p) is not influenced by advection, then the [NO − 3 (p) ] RL in this layer provides an estimate of the maximum chemical production (P NO − 3 ).This estimate of P NO − 3 is certainly a lower bound on actual nitrate formation given the assumption of no influence of horizontal advection, and this also does not account for produced nitrate that remains in the gas phase (although this is likely to be small).On average, the observations indicate that chemical production overnight in the RL leads to an approximate doubling over the initial NO − 3 (p) concentration, or 10-25 µg m −3 of NO − 3 (p) produced over the course of the night for this episode (Table S1 in the Supplement).Observed day-to-day variability in P NO − 3 likely results from day-to-day variations in precursor (NO x and O 3 ) concentrations and N 2 O 5 reactivity, as well as limitations of the assumption of no advection in this layer.To assess the reasonableness of this estimate of P NO 3 as a maximum production rate, values of the night-specific average rate coefficients for N 2 O 5 heterogeneous hydrolysis (k N 2 O 5 ) and associated uptake coefficients (γ N 2 O 5 ) needed to reproduce the observed P NO − 3 are back calculated based on the initial NO x , O 3 , and wet particle surface area, and assuming ClNO 2 formation is negligible (see Appendix C and Table S1).The derived k N 2 O 5 values range from 1.3 to 5.1 × 10 −5 s −1 with corresponding γ N 2 O 5 from 2.5 × 10 −4 to 4.8 × 10 −4 .These are smaller than values observed under water-limited conditions in other field studies (Brown et al., 2006c;Bertram et al., 2009) and lower than expected based on lab experiments (Bertram et al., 2009).γ N 2 O 5 values separately calculated from the particle composition measurements, following Bertram et al. (2009), are larger than the above backcalculated values, with γ N 2 O 5 ∼ 10 −3 , and more consistent with the literature.This suggests that the P NO − 3 is, in fact, a lower estimate and that the NO − 3 (p) concentration in even the lower layers of the RL is influenced by advection.Box model calculations using the (too low) back-calculated k N 2 O 5 and γ N 2 O 5 yield ∼ 15-42 % NO x conversion to HNO 3 overnight during this episode.If instead γ N 2 O 5 = 10 −3 is used, the calculated overnight conversion is somewhat larger, ∼ 52 %.Also, if k N 2 O 5 and γ N 2 O 5 were assumed to be sufficiently large such that they are not rate limiting the overnight conversion would increase further to ∼ 63 %.It should be noted that during this episode the surface O 3 overnight is essentially completely titrated away by 18:00 LT (Fig. 5).The reaction between NO 2 and O 3 (Reaction R1) is thus very slow and nighttime chemical production of NO − 3 (p) at the surface in the NBL is comparably small.

Vertical mixing, photochemical production and NO − 3 (p) sinks
The observed episode average-surface-level NO − 3 (p) concentration exhibits a distinct, rapid increase starting at ∼ 08:00 LT, then peaks around 10:00-11:00 LT and decreases fairly continuously after the peak, especially between 13:00 and 16:00 LT (Fig. 6a).For reference, time series of NO − 3 (p) during the pollution episode, along with CO, NO, NO 2 , O 3 , temperature, surface radiation and PM 1 , are shown in Fig. S9.Both Young et al. (2016) and Pusede et al. (2016) noted this increase, arguing it is a signature of nocturnal nitrate production.Here, we provide a more detailed examination of the specific influence of vertical mixing and nocturnal NO − 3 (p) production in the RL on the observed daytime variability in surface-level NO − 3 (p) using an observationally constrained one-dimensional box model (see Appendix D for details).In brief, the model accounts for time-dependent mixing between air in the mixed boundary layer and the RL, daytime photochemical production of nitrate, gas-particle partitioning of nitrate, entrainment of clean air from the free troposphere into the ML and loss of nitrate via dry deposition to calculate the time-dependent evolution of the surface-level NO − HNO 3 is calculated based on the oxidation of NO 2 by hydroxyl radicals, with wintertime concentrations estimated to peak around [OH] = 10 6 molecules cm −3 at noon in the region, with contributions from O( 1 D) + H 2 O (from O 3 photolysis), HONO photolysis and CH 2 O photolysis (Pusede et al., 2016).The OH concentration is assumed to scale linearly with the observed solar radiation (Fig. S10).
The average calculated daytime temporal evolution of surface NO − 3 (p) from the observationally constrained box model agrees reasonably well with the average of the surface observations from the 4 Episode 1 flight days considered (Fig. 7a).(The observed diurnal average in Fig. 6 uses all of the days from Episode 1, whereas in Fig. 7 only 4 flight days are included.This is because the initial early-morning NO − 3 (p) vertical profile is required as input to the model.)The model predictions for the individual flight days also exhibit generally good agreement with the NO − 3 (p) observations except in the late evening, which is discussed further below (Fig. S8).Specifically, the observationally constrained model also shows a rapid increase in NO − 3 (p) beginning at 08:00 LT, a peak around 10:00-11:00 LT and a gradual, time-varying decrease through the afternoon.
Consideration of the individual processes occurring in the model demonstrates that the vertical mixing down of 3 (p) occurs when even higher RL layers, where ] ML , are entrained.In other words, the temporal evolution of the surface-level NO − 3 (p) is linked to the shape of the early-morning vertical NO − 3 profile.Further, it should be noted that the exact model behavior is dependent on the timing of the CLASS-predicted boundary layer height increase, with the initial increase and timing of the surface-level NO − 3 (p) peak being particularly sensitive to the shape of the rise between 08:00 and 10:00 LT.Nonetheless, because the NBL is so shallow here, only ∼ 3-12 % of the daytime ML height, the surface concentration is strongly impacted by the concentrations in the RL and the initial (pre-08:00 LT) surface-level nitrate has control over daytime concentrations.Thus, the model results demonstrate that the observation of the large 10:00 LT peak in NO − 3 (p) is a clear indication of the strong influence of nocturnal processes occurring aloft -both chemical production and advection-driven local loss -on daytime surface concentrations.
As an extreme counterexample, if there were no NO − role in determining the daytime surface-level concentration of NO − 3 (p) , multiday buildup and the population exposure in this urban area.While it has previously been suggested that the morning increase in surface-level NO − 3 (p) is indicative of mixing down of NO − 3 (p) in the RL (Watson and Chow, 2002;Pusede et al., 2016;Young et al., 2016), the current study provides an explicit, observationally constrained demonstration of this effect and highlights the dual roles of chemical production and advective loss in the RL.
The time-evolving relative contributions of surface-level NO − 3 (p) from the NBL, the RL and photochemical produc- tion are individually quantifiable from the model for this episode (Fig. 7b).As the ML rises, the relative contribution of NO − radiation, the potential for enhanced production of OH (and subsequently NO − 3 (p) ) in the early morning via, for example, HONO photolysis is not accounted for in the model (Pusede et al., 2016).If this process were included, the increase in morning surface-level NO − 3 (p) would be even greater than is already calculated from mixing down of NO − 3 (p) in the RL.Since the observationally constrained model already predicts a somewhat larger peak at 10:00 LT for surface-level NO − 3 (p) concentrations compared to the observations, earlymorning photochemical production appears to have had a relatively limited influence on the morning surface-level NO − 3 (p) compared to mixing down of nocturnal NO − 3 (p) during this episode.
While vertical mixing and the shape of the NO − 3 (p) vertical profile are what predominately drive the morning temporal evolution in the surface-level NO − 3 (p) (especially the peak) for this episode, the afternoon behavior, especially between ∼ 13:00 and 16:00 LT, is shaped by the balance between photochemical production and loss via (i) dilution by entrainment of FT air and (ii) evaporation of NO − 3 (p) and subsequent dry deposition of HNO 3 gas, i.e., a gas-phase pump for NO − 3 (p) loss.Here, the relative importance of these loss pathways is considered.The latter process (gas-phase pump) has been previously considered by Pusede et al. (2016) while the former (FT entrainment) was not.Loss through dry deposition of NO − 3 (p) is negligible since deposition velocities for HNO 3 (v d = 1-10 cm s −1 ) are much larger than for particles (v d = 0.001-0.1 cm s −1 ) (Meyers et al., 1989;Horii et al., 2005;Farmer et al., 2013;Pusede et al., 2016).These loss mechanisms ultimately limit the extent of the pollution episode buildup.Once the daytime model ML reaches maximum height, entrainment into the ML of typically cleaner air from just above the ML (i.e., from the FT) occurs.The timeevolving entrainment rates are estimated from the CLASS model (Appendix C).
Considering the gas-phase pump, the warm (typically 290 K) and dry (RH = 40 % or less during the campaign) afternoon conditions enhance evaporation of NO − 3 (p) relative to nighttime and early-morning conditions, thereby increasing loss through dry deposition of HNO 3 gas in the afternoon (Pusede et al., 2016).However, total ammonia is in substantial excess (3.8-8.9 times NO − 3 (g+p) on a molar basis), with thermodynamic calculations indicating that the gasphase fraction of NO − 3 is < 0.15 during the daytime and near zero at night when it is colder and RH is higher (Fig. 3).These estimates of the gas-phase fraction of NO − 3 are similar to the observational measurements of Parworth et al. (2017), who determined the daytime and nighttime averages during the first episode were 0.08 ± 0.03 (1σ ) and 0.04 ± 0.05 (1σ ), respectively.Importantly, the gas-phase fraction here is substantially smaller than that estimated in Pusede et al. (2016), who found a daytime gas-phase fraction of 0.4 (median) and a 24 h average of 0.15.Consequently, the loss of nitrate via the gas-phase pump is less than in their analysis and suggests that the role of this pathway was likely overestimated.
The general influence of the gas-phase fraction on loss via dry deposition is shown in Fig. S11.In general, the results indicate that the gas-phase fraction has a strong influence on the loss of NO − 3 (p) due to HNO 3 deposition.Including both FT entrainment and dry deposition, the box model reasonably reproduces the observed afternoon decrease in surface-level NO −  3 (p) .This allows assessment of the relative importance of these two loss processes by turning them off one at a time (Fig. 7c).The calculations indicate that entrainment of clean FT air plays an important role in the afternoon surface concentration decline.Without entrainment, the model predicts that the afternoon NO − 3 (p) would be ∼ 18 % higher, leading to a double-humped daytime profile.Despite the relatively low gas-phase fraction, the gas-phase pump also contributes to the afternoon decline.The model results indicate that these two loss processes contribute approximately equally to the afternoon decline.There are, however, a few hours when the gas-phase pump is potentially of extreme importance.When the RL decouples and the surface mixed layer becomes quite shallow the rate of loss due to dry deposition is enhanced.This leads to a rapid decrease in surface-level NO − 3 (p) .Yet, the concurrent decrease in the NBL temperature and increase in RH and NH 3 enhances the partitioning of nitrate to the particle phase, thereby limiting the impact of this rapid decline over time.(In the model here, the decoupling is assumed to occur very rapidly while the temperature and RH changes are from observations and occur more gradually.If the decoupling were actually slower the influence of the gas-phase pump at this point in time would be reduced and the modeled decrease in NO − 3 (p) that occurs around 15:00-17:00 LT would be less than shown.) The model predicts that after decoupling and cooling occur the surface-level NO − 3 (p) will continue to decrease at ∼ 2 % h −1 overnight via the gas-phase pump, which is similar to the loss rate observed between midnight and 07:00 LT (Fig. 7a).If the gas-phase pump is turned off completely (i.e., the nitric acid deposition velocity is set to zero), there is an increase in the modeled NO − 3 (p) that begins at ∼ 15:00 LT (when decoupling occurs) and continues until 18:00 LT (Fig. 7c).This is a result of the continual decrease in temperature and increase in RH enhancing partitioning to the particle phase.Although not a focus of this study, on some days, there is a sharp increase in surface-level NO − wind speeds) that has higher surface concentrations.Regardless, while the reason for this nighttime increase in surface NO − 3 (p) remains unclear, the occurrence does not impact the analysis of the early-morning and daytime NO − 3 (p) behavior.The cumulative impact of the nocturnal production in the RL, daytime photochemical production and afternoon loss processes is that the NO − 3 (p) concentration at ∼ 15:00 LT, the point when decoupling of the RL occurs, is slightly higher than that at 08:00 LT during the episode.Therefore, there is a gradual net increase (average of 1.32 µg m −3 day −1 ) in surface-level NO − 3 (p) as the episode progresses, albeit with day-to-day variability (Fig. 6b).For comparison, the 24 h average-surface-level NO − 3 (p) increases by 0.66 µg m −3 day −1 .While decreasing NO x emissions and NO − 3 (p) production, especially nocturnal production (Pusede et al., 2016), is the most direct and reliable route towards decreasing surface NO − 3 (p) concentrations (Kleeman et al., 2005), decreases in NH 3 could theoretically also have some influence on NO − 3 (p) by increasing the efficiency of the gas-phase pump.However, this will only be the case if NH 3 decreases exceed decreases in NO x by at least a factor of 5 such that the ratio between the two is changed substantially and the gas-phase fraction is increased (Fig. 3).Such preferential targeting of NH 3 sources is therefore highly unlikely to be an efficient control strategy, at least for the SJV where the total ammonia-to-nitrate ratio is large.In regions where the NH + 4 (g+p) : NO − 3 (g+p) molar ratio is closer to unity, the nitrate partitioning is more sensitive to changes in this ratio and thus ammonia control could potentially prove effective.

Comparison between episodes
The above analysis focuses on observations made during one pollution episode, but there was a second pollution episode observed during DISCOVER-AQ (30 January-5 February 2013).The episode-averaged diurnal behavior of the surface NO − 3 (p) concentration for this second episode showed evidence of an early-morning increase, but the increase is not as sharp as the first episode (Fig. 9).Additionally, the dayto-day variability in the surface NO − 3 (p) was much greater during the second episode; on some days, there was minimal evidence of an early-morning increase but on others there was a substantial increase.The shapes of the early-morning vertical NO − 3 (p) profiles (around 09:30 LT) were notably different during Episode 2 on 2 of the flight days as well, as was the evolution of the profiles from morning to afternoon (Fig. S12).The afternoon mixed layer heights were much higher during Episode 2 than Episode 1, ranging from 600 to 700 m a.g.l.compared to 300-400 m a.g.l., respectively.The early-morning mixed layer heights were also higher during Episode 2 (∼ 170 m) compared to Episode 1 (around 70 m).During Episode 1, the surface-level winds exhibit a consistent shift in direction from easterly in the early morning (05:00-08:00 LT) to southerly in the later morning (09:00-12:00 LT), and the mean surface-level wind speed increased over this same period, from 0.31 to 0.82 m s −1 (Fig. 9).In contrast, during Episode 2 there was a lack of day-to-day consistency in the surface wind direction, especially during the early morning (05:00-08:00 LT), and there was a more substantial change in the mean surface-level wind speed from the early morning to later morning, from 0.32 to 1.12 m s −1 (Fig. 9).The Episode 2 mean nighttime aloft wind speeds were also overall lower and more constant with altitude, with little variability from 150 to 400 m.However, the wind speed did increase substantially from the surface to 150 m (Fig. S13).The aloft nocturnal winds during Episode 2 were somewhat more variable than Episode 1 winds in terms of the wind direction (Fig. 4 versus Fig. S13).
Overall, this increased day-to-day variability in both the surface NO − 3 (p) and wind behavior, as well as a difference in the evolution of the NO − 3 (p) vertical profiles from the early morning to late morning or early afternoon in Episode 2 compared to Episode 1, suggests that the meteorological conditions during the second episode were generally less conducive to simple interpretation using the mixing model discussed above.Instead, it seems that advection and export from the urban area were of increased importance during Episode 2, both overnight and especially in the earlyto-midmorning.The contrasting behavior between the two episodes suggests that while the observation of a sharp, earlymorning rise and peak in surface-level NO − 3 (p) (such as during the first episode) might be generally considered a strong indicator of the production of NO − 3 (p) in the RL, the absence of such a feature does not preclude an important role for nocturnal production aloft.

Production of NO −
3 (p) in the RL can vary widely based on initial concentrations of its precursor gases, as well as the rate of heterogeneous uptake of N 2 O 5 by particles.It may be that production of NO − 3 (p) via the N 2 O 5 hydrolysis pathway may be significant in the aloft RL in other regions with similar geographical and meteorological conditions, such as Salt Lake Valley, Utah (Kuprov et al., 2014;Baasandorj et al., 2017).However, in valley regions with lower NO x or O 3 the nocturnal P NO − 3 may be lower, thus limiting the importance of this pathway (Akira et al., 2005;Bigi et al., 2012).Among other factors, the extent to which nocturnal NO − 3 (p) formation occurs more so in the surface layer versus in layers aloft will depend importantly on the extent of NO x emissions at the surface (which titrate O 3 , suppressing particulate nitrate formation), the absolute and relative height of the nocturnal boundary layer (which affects the rate of HNO 3 deposition and the air volumes in which nitrate production occurs), and gradients in RH, T and NH 3 (Kim et al., 2014).
For example, Baasandorj et al. (2017)   NO − 3 (p) formation overnight, substantiated by direct measurements of N 2 O 5 , in addition to formation aloft.Nitratespecific diurnal profiles were not reported.In Shanghai, China, Wang et al. (2009) observed in fall 2007 that both O 3 and NO 2 remained elevated at night at the surface, with a concomitant increase in surface NO −  3 (p) .And in wintertime Seoul, Korea, Kim et al. (2017) observed relatively limited diurnal variability in O 3 and NO 2 concentrations measured at 60 m, with both remaining elevated throughout the night.However, they did not observe any notable buildup in NO −

(p)
overnight, but did observe an NO − 3 (p) increase and peak in the morning, as here.In contrast, in Fresno the nighttime surface O 3 levels during Episode 1 were nearly zero, suppressing surface NO − 3 (p) formation.This near-zero nocturnal O 3 is similar to observations by Kuprov et al. (2014) made a few years before Baasandorj et al. (2017) at one of the same valley floor sites in Utah, reflecting year-to-year differences.
Such differences can influence the extent to which a notable increase in NO − 3 (p) is observed to occur in the early morning as air is entrained from the residual layer to the surface.This is because if surface production and production in the residual layer are similar in magnitude the contrast between the two will be reduced and entrainment will appear to have a less apparent impact on the diurnal profile.However, because the effective volume of the residual layer is typically much larger than the nocturnal boundary layer (as is the case here), even without an observed increase in NO − 3 (p) at the surface in the morning the NO − 3 (p) produced in the residual layer can still dominate the overall NO − 3 (p) burden during the day.
Additionally, comparison between the Baasandorj et al. ( 2017) observations of late-afternoon surface NO 2 and O 3 (which reflect the initial conditions within the residual layer) with the Fresno observations indicates that differences can exist in how nocturnal production in layers aloft influences the buildup and sustaining of PM 2.5 in pollution episodes.They observed during a strong PM 2.5 episode a slow buildup of PM 2.5 followed by a plateau lasting multiple days.During this period, late-afternoon O 3 concentrations decreased over time while late-afternoon NO 2 was approximately constant (in the daily average).Consequently, the nitrate radical production rate in the residual layer, and thus the N 2 O 5 and NO − 3 (p) production rates, decreased over time in their study.In contrast, for Episode 1 here, the late-afternoon nitrate radical production rate increased over time across the episode (by 0.25 µg m −3 day −1 ), with only a moderate decrease in the daytime O 3 over time (Fig. S9).These differences reflect the different photochemical conditions between the regions and illustrate the coupling between the daytime photochemical conditions (i.e., O 3 production) and nighttime NO − 3 (p) formation above the surface.

Conclusion
This work combines surface and aircraft observations made during a pollution episode in 2013 to demonstrate that in the San Joaquin Valley (specifically Fresno, CA) production of NO − 3 (g+p) in the nocturnal residual layer can play a crucial role in determining daytime surface concentrations of particulate NO − 3 in winter, when photochemical production is relatively slow and morning boundary layers are extremely shallow.The influence of processes occurring in the aloft RL on NO − 3 (p) surface concentrations is evident in the NO − 3 (p) diurnal variability, specifically the occurrence of a midmorning peak in surface-level NO − 3 (p) .While the midmorning peak has been previously suggested as a signature of nocturnal nitrate production aloft (Watson and Chow, 2002;Brown et al., 2006a;Lurmann et al., 2006;Pusede et al., 2016;Young et al., 2016), the current study makes novel use of vertical profiles of NO − 3 (p) concentrations measured multiple times on individual days to quantitatively illustrate the importance of nocturnal processes on surface concentrations.The analysis shows that the NO − 3 (p) concentration in the morning-time mixed boundary layer can be dominated by nocturnally produced NO − 3 (p) ; vertical mixing in the early morning, which entrains air from the residual layer into the surface mixed layer, has a particularly large impact on the surface concentrations here due to the nocturnal boundary layer being exceptionally shallow.In the afternoon, photochemically produced nitrate contributes the majority of the total NO − 3 (p) burden for the episode examined but still with a substantial contribution from nocturnal production.The case study here illustrates that nocturnal NO − 3 (p) production can play a critically important role in the buildup and sustaining of pollution episodes in the SJV, supporting previous suggestions made, in part, on the basis of calculated chemical production values and an assessment of multiyear trends in the relationship between NO − 3 (p) and NO 2 (Pusede et al., 2016).
The current work also demonstrates that a difference exists between the shape of the typical vertical profiles of NO −   3 (p)   in the afternoon and early morning over Fresno.This difference is shown to very likely result from altitude-specific horizontal advection in the nocturnal RL leading to differential washout of NO − 3 (p) and precursor gases rather than from differences in chemical production rates.Consequently, there is a steep vertical gradient in NO − 3 (p) in the early-morning RL that, in turn, influences the temporal evolution of surfacelevel NO − 3 (p) during the day, especially in the early morning.Ultimately, differential advection is shown to have an important role in limiting the maximum surface-level concentration of NO − 3 (p) observed within the urban area during the day, which is a result of the urban-rural gradients being particularly steep (Pusede et al., 2016).Absent this overnight export of pollution from the city, nitrate pollution would build up during pollution events to a much greater extent.However, advection likely contributes to the buildup of NO − 3 (p) throughout the valley, outside of the cities.Daytime loss processes are also shown to help in limiting the multiday buildup of surface-level NO − 3 (p) .Afternoon entrainment of air from the cleaner free troposphere into the ML (and export of mixed layer air to the FT) is shown to be an important loss process for particulate nitrate.Janssen et al. (2012Janssen et al. ( , 2013) ) have similarly identified afternoon loss via FT entrainment as an important process shaping the diurnal variability of surface-level organic aerosol concentrations in forested areas that are dominated by organic aerosol.Loss of NO − 3 (p) via dry deposition of HNO 3 and subsequent evaporation of NH 4 NO 3 is found to contribute to afternoon particulate nitrate loss, but the effect is limited by the (relatively) high afternoon boundary layer and the small gas-phase fraction of nitrate (< 0.15).However, this gas-phase pump may have a substantial influence on the surface concentrations in the few hours just after decoupling of the RL occurs, when the boundary layer height is low and it is still sufficiently warm.Consistent with previous suggestions (Kleeman et al., 2005;Pusede et al., 2016), we conclude that control strategies for the region should focus on the reduction of concentrations of NO x and O 3 (the latter of which might require VOC controls) in the midafternoon, specifically around the time that the RL decouples from the surface layer, as this largely determines the production rate of nitrate in the aloft RL. www.atmos-chem-phys.net/17/14747/2017/Atmos.Chem.Phys., 17, 14747-14770, 2017 The P3-B was equipped with an array of instruments to measure both gas-and particle-phase properties.A TSI-3563 nephelometer provided total scattering from dry particles at 450, 550 and 700 nm and scattering at 550 nm by particles at 80 % RH (Beyersdorf et al., 2016).Gas-phase NH 3 was measured using a cavity ring-down spectroscopy with a Picarro G2103 (von Bobrutzki et al., 2010), using the NOAA aircraft NH 3 inlet and calibration scheme as in Nowak et al. (2010).Measurements of NO, NO 2 , NO x and O 3 were obtained through a four-channel chemiluminescence instrument (Brent et al., 2015).CO and CH 4 were measured with a differential absorption CO measurement (DACOM) spectrometer (Sachse et al., 1987).Total gas (HNO 3 ) + particle (NH 4 NO 3 ) nitrate was measured using thermal-dissociation laser-induced fluorescence (TD-LIF), where HNO 3 and volatilizable particulate nitrate are converted into NO 2 for detection (Day et al., 2002).While the TD-LIF instrument is not optimized for particle sampling, most of the particulate mass was in the submicron size range, and thus inertial losses will likely only lead to a small (if any) negative bias in the measured particulate nitrate (Pusede et al., 2016).Aerosol size distributions for 0.06-1.0µm diameter particles were measured with an ultra-high sensitivity aerosol spectrometer (UHSAS).The UHSAS uses an optical sizing method but is calibrated relative to the mobility diameter.The P3-B flew throughout the SJV for 10 days and performed vertical spirals over six sites across the valley, including Fresno.The location of these sites and the flight path are shown in Fig. S2.This same flight path was repeated three times every day between approximately 08:30 and 15:00 LT, with vertical profiles over Fresno at approximately 09:30-10:00 LT, 12:00-12:30 LT and 14:30-15:00 LT.This enables assessment of the evolution of the species-specific vertical profile during the day across the valley.Out of the 10 research flights during the campaign, only 8 of them have been used here due to gaps in the dataset.Four of these days are during the first pollution episode (18, 20, 21 and 22 January) and 4 are during the second pollution episode (30 and 31 January, and 1 and 4 February).
Observations of the light scattering coefficient at 550 nm (σ sca ) for dry and humidified particles (no size cutoff) made from the P3-B (Beyersdorf et al., 2016)  dent on particle composition, with higher hygroscopicity indicative of a higher particulate inorganic fraction and lower hygroscopicity indicative of a higher particulate organic fraction; the relationship between hygroscopicity and the inorganic fraction (or the organic fraction) is reasonably linear when the inorganic species are primarily ammonium sulfate and ammonium nitrate (Zhang et al., 2014), as these have similar hygroscopicities (Petters and Kreidenweis, 2007).The particulate nitrate concentration is much larger than the particulate sulfate concentration, as determined from both the surface and aircraft measurements (< 600 m a.g.l.), with nitrate-to-sulfate mass ratios of 8 and 16, respectively (both determined from PILS measurements).Thus, the observed hygroscopicity is primarily reflective of the particulate nitrate fraction (Parworth et al., 2017).More specifically, a linear relationship was observed between surface-level measurements of dry σ scat and PM 1.0 (black carbon (BC) + nonrefractory PM 1.0 ) mass concentrations in Fresno (slope = 2.83 m 2 g −1 , with intercept forced through zero; Fig. A1a).Only data points between 08:00 LT and 16:00 LT were included in determining this relationship to reflect the time period during which the airborne measurements were obtained.The observed relationship for dry, surface-level σ sca and NR-PM 1 is used to estimate the NR-PM 1 concentration during the vertical profiles from the aircraft dry σ scat measurements.The hygroscopicity (water uptake) of a particle depends on its chemical composition.Inorganic components, predominantly NO − 3 and ammonium in the wintertime SJV region (Young et al., 2016) are highly hygroscopic while organic components of PM 1 tend to have much lower hygroscopicity (Petters and Kreidenweis, 2007).Thus, measurements of the particle hygroscopicity can be used to estimate the ratio of inorganic to organic mass in the sampled PM (Massoli et al., 2009;Parworth et al., 2017).The average particle hy- where σ scat, wet and σ scat, dry are the scattering coefficients (in Mm −1 ) measured under wet (RH wet = 80 %) and dry (RH dry = 20 %) conditions, respectively.The parameter γ varies reasonably linearly with the particle inorganic mass fraction (Massoli et al., 2009).Therefore, an initial estimate of NO − 3 (p) concentrations at high time resolution, and thus as a function of altitude, is obtained from the equation [NO −3 (p) ] = γ .σ sca, dry /2.83.The factor of 2.83 has units of m 2 g −1 and comes from the σ scat versus NR-PM 1 relationship determined above.However, previous studies show some variability in the linear relationship between γ and inorganic mass fraction and, importantly, typically have slopes somewhat less than unity and nonzero intercepts, as is assumed in the above conversion (e.g., Massoli et al., 2009).Therefore, the low-time-resolution aircraft PILS NO − G. Prabhakar et al.: Particulate nitrate formation in the wintertime A2 Ground measurements Fresno (36.745 • N, 119.77 • W) was a "supersite" where comprehensive, continuous measurements of the chemical and physical properties of particulate matter were made.Chemical composition of non-refractory PM 1.0 was measured by a High-Resolution Time-of-Flight Aerosol Mass Spectrometer (HR-ToF-AMS) (Young et al., 2016).The soluble fraction of PM 3.0 was characterized using a particle-intoliquid sampler coupled to an ion chromatograph (Parworth et al., 2017).Gas-phase water-soluble species were collected at 5-7 h time resolution using an automatic-switching annular denuder system placed in front of the PILS and were analyzed offline with ion chromatography after extraction (Parworth et al., 2017).The combination of the denuder measurements and the particle measurements allowed for the determination of the gas-phase fraction of nitrate.Light extinction and light absorption coefficients were measured using the University of California (UC) Davis cavity ring-down photoacoustic spectrometer, and scattering coefficients were determined by the difference (Cappa et al., 2012;Lack et al., 2012).Refractory black carbon concentrations were measured using a single particle soot photometer (Schwarz et al., 2006).In situ gas-phase measurements of NO, NO 2 and O 3 , along with environmental factors (T and RH) were made by the California Air Resources Board.Particle size distributions were measured using a scanning mobility particle sizer (size range: 10-800 nm) and an aerodynamic particle sizer (700 nm-6 µm).Measurements included in the current study are listed in Table A1.
Additionally, a radiosonde was used to obtain vertical profiles of pressure, temperature and humidity over nearby Huron (36.203 • N, 120.103 • W) twice a day -once in the morning around 08:00 LT and again in the evening at 16:00 LT.Diurnal measurements of the surface heat flux and friction velocity were determined from measurements made with a sonic anemometer at Huron.Measurements of wind speed and wind direction as a function of altitude at nearby Visalia, CA, are from the National Oceanic and Atmospheric Administration (NOAA) Profiler Network (https://www.esrl.noaa.gov/psd/data/obs/instruments/WindProfilerDescription.html).rameters are constrained by observations from nearby Huron of the nocturnal boundary layer height, the morning inversion strength (∼ 08:00 LT), the sensible surface heat flux, the friction velocity and the lapse rate through the residual layer, as well as by an estimate of the subsidence rate based on Trousdell et al. (2016).The model inputs are adjusted to ensure that the modeled ML growth agrees reasonably well with the observations from the P3-B over Fresno (Fig. B2).The resulting average entrainment velocities in the afternoon (13:00-16:00 LT) from the CLASS model agree well with independently determined entrainment rates based on afternoon decline in SO 2− 4 (p) for the Episode 1 days.Since SO 2− 4 (p) is effectively nonvolatile and since photochemical production via oxidation of SO 2 is relatively slow, the decline in SO 2−  4 (p) in the afternoon can be attributed solely to the dilution from entrainment of "clean" FT air since the influence of the gas-phase pump is small.After 15:00 LT the boundary layer is assumed to linearly drop over a 1 h period to the NBL height observed at 08:00 LT the same day.A relatively rapid (∼ 1 h) decline in the mixed layer height is consistent with wintertime observations of diurnal BLH profiles (Bianco et al., 2011).
The sensitivity of the box model to the boundary layer growth predicted by the (observationally constrained) CLASS model has been examined.An alternative boundary layer growth profile was estimated by fitting the observed P3-B ML heights using a sigmoidal function (Fig. B3).The general shapes of the CLASS and sigmoidal profiles are similar, although the sigmoidal profile exhibits a somewhat faster rise.Entrainment of FT air in the afternoon for the sigmoidal growth profile was accounted for using the average entrainment rates estimated from the observed SO 2− 4 (p) loss rates and assuming that entrainment begins at noon, when the BLH was near the maximum.The same linear decrease in the BLH starting at 15:00 LT was assumed.The use of this alternative model yields a diurnal NO − 3 (p) profile for Episode 1 that is very similar to that obtained using the CLASS model (Fig. B3).This indicates that the general behavior of the diurnal surface NO − 3 (p) profile is not particularly sensitive to the treatment of the boundary layer rise and that the results obtained here are robust.specific average rate coefficients for N 2 O 5 heterogeneous hydrolysis (k N 2 O 5 ) is obtained through consideration of the initial concentrations of precursor gases and the observed maximum overnight increase in the RL NO − 3 (p) , P NO − 3 .More specifically, a 1-D box model including nocturnal gasphase chemistry and heterogeneous reaction of N 2 O 5 with particles was run iteratively to determine an average k N 2 O 5 for the night (19:00-08:00; 13 h) such that it reproduced the observed P NO − 3 .The observed chloride at Fresno was small (1 % of PM 1.0 ) during the episode, and thus formation of nitryl chloride (ClNO 2 ) can be reasonably neglected (Young et al., 2016).Since the boundary layer is fairly wellmixed in the afternoon, surface-level observations of NO x , O 3 , NO − 3 (p) , particle wet surface area and temperature at 15:00 LT on the preceding day were used as initial conditions.Based on back-calculated k N 2 O 5 values, night-specific values of the heterogeneous N 2 O 5 uptake coefficient (γ N 2 O 5 ) were determined from where ω is the mean molecular speed of N 2 O 5 (256 m s −1 ), S a is the wet particle surface area and γ is the N 2 O 5 heterogeneous uptake coefficient (Brown et al., 2006c).The wet particle surface area was calculated from the observed dry particle size distributions, particle hygroscopicity and RH.The resulting back-calculated k N 2 O 5 values from Eq. (C1) were in the range 1.3-5.1 × 10 −5 s −1 .The corresponding back-calculated γ N 2 O 5 values were in the range 2.5 × 10 −4 to 4.8 × 10 −4 (Table S1), which as noted in the main text are somewhat smaller than values observed under water-limited conditions in other field studies and lower than expected based on lab experiments (Bertram et al., 2009).
A second estimate of the γ N 2 O 5 values is calculated from the particle composition following Bertram et al. (2009).The calculated γ N 2 O 5 values depend on the particle water content (specifically, the ] and thus RH) and the chloride fraction.The composition-calculated γ N 2 O 5 values (∼ 10 −3 ) are larger than the above back-calculated values and more consistent with the literature although on the lower side of previous measurements (Brown et al., 2006c;Bertram et al., 2009).That the back-calculated γ N 2 O 5 values are smaller than the γ N 2 O 5 calculated from the composition, which is likely a consequence of the P NO − 3 being an under-estimate relative to the true overnight production in the RL.This is because the observed P NO − 3 is taken as the difference between the previous afternoon and early-morning NO − 3 (p) concentration in the aloft RL layer having the maximum morning concentration.This does not account for the influence of advection, which is most likely going to reduce the morning NO − 3 (p) relative to if there were no advection.

C2 Reactions with VOCs
Not considered above is the reaction of the NO 3 radical with VOCs.NO 3 radicals react rapidly with alkenes and more slowly with alkanes and other species.NO 3 reaction with VOCs can lead to hydrogen abstraction and direct formation of HNO 3 , especially for reactions with alkanes.For alkenes and aromatics, NO 3 reaction typically proceeds via NO 3 addition and formation of organic nitrates.The latter would suppress formation of particulate inorganic nitrate but can serve as an important source of particulate organic nitrate (Kiendler-Scharr et al., 2016).Organic nitrate formation has been observed as an important source of summertime organic aerosol in Bakersfield, CA (also in the SJV) (Rollins et al., 2012).VOC concentrations and reactivity are likely much lower during the colder winter compared to the warmer summer (Pusede et al., 2014), and thus reaction of VOCs with NO 3 radicals is likely significantly suppressed.The concentrations of a broad suite of VOCs were measured via whole air canister sampling during DISCOVER-AQ.These measurements can be used to assess the potential influence of NO 3 reaction with VOCs on HNO 3 and NO − 3 (p) formation.The nitrate reactivity towards each VOC is calculated as k VOC + NO 3 • [VOC], where the k VOC + NO 3 is the VOC-specific rate coefficient and [VOC] is the VOC concentration (Ng et al., 2017).Average afternoon VOC concentrations are used, which should be representative of the initial concentrations in the RL.The VOCs are ranked according to their reactivity with NO 3 .The top 20 VOCs are 3 (p) measurements (pink circles) (Parworth et al., 2017).
instantaneous BLH) is assumed to remain unchanged from the early-morning-observed profile.The vertical NO − 3 (p) profile is updated to that observed during the second flight once the BLH (from the CLASS model) reaches the ML height observed around noon.
NO 2 +OH → HNO 3 ; k OH = 2.8×10 −11 cm −3 molecule −1 s −1 (DR1) The OH concentration at a given time step was assumed to scale with the solar radiation flux (SR) as where the maximum daytime OH concentration is assumed to be [OH] max = 1 × 10 6 molecules cm −3 , after Pusede et al. (2016).The rate coefficient for condensation of HNO 3(g) onto suspended particulates, k cond , was calculated based on collision theory (Seinfeld and Pandis, 2006) as where the summation is over particle size, D p, i is the mean particle diameter in the size bin i (m) and dN i is the number concentration in the size bin i (m −3 ).The term β i is the sizedependent Fuchs correction in the continuum regime given by where Kn = λ/D p, i and λ is the gas mean free path (65 nm).The parameter D is the diffusion coefficient of HNO 3 gas in air (cm 2 s −1 ) given by De Andrade et al. (1992): where T is ambient temperature (K).The corresponding evaporation rate coefficient (k evap ) is determined as where K eqm is the instantaneous (temperature and RHdependent) equilibrium partitioning coefficient for ammonium nitrate.The rate coefficient for loss of gas-phase HNO 3 or NO − 3 (p) from dry deposition, k dep (s −1 ), is where v d is the deposition velocity (cm s −1 ) and BLH is the time-dependent boundary layer height.The HNO 3(g) deposition velocity has been shown to vary linearly with wind speed (Ma and Daggupaty, 2000).Here, it was assumed that v d = 1 + 9 • ws − ws min ws max − ws min , (D10) where ws is the observed wind speed and where ws min and ws max are the minimum and maximum values observed.The bounds of Eq. (C10) (lower limit v d = 1 cm s −1 and upper limit 10 cm s −1 ) were chosen to span previously observed ranges.While the accuracy of the empirical Eq. (C10) is not known, we note that use of a constant v d of 0.07 cm s −1 does not change the box model output substantially (Fig. S14).Of course, if the actual v d were lower than estimated here, the influence of dry deposition on NO − 3 (p) concentrations would be decreased.The NO − 3 (p) deposition velocity was assumed to be 0.01 cm s −1 , which is consistent with the much slower deposition of particles than soluble gases such as HNO 3 .Dry deposition occurred both during the daytime and nighttime.

Figure 4 .
Figure 4. (a) Vertical profile of the average nighttime (19:00-07:00) horizontal winds over Visalia, CA (65 km SE of Fresno), and the surface (10 m) wind in Fresno for flight days during Episode 1 (18, 20, 21 and 22 January).The length of the arrows corresponds to the wind speed and the direction to the average wind direction, with the measurement height indicated by the circle on the tail of the arrow.(b) Corresponding wind roses for (b1) the surface, (b2) 125-175 m, (b3) 225-345 m and (b4) 400-500 m.The length of each arc corresponds to the normalized probability and the colors indicate the wind speed (m s −1 ; see legend).Data are from the National Oceanic and Atmospheric Administration, Earth System Research Laboratory, Physical Sciences Division Data and Image Archive (https://www.esrl.noaa.gov/psd/data/obs/datadisplay/,accessed 3 June 2017).

Figure 5 .
Figure 5.Diurnal profiles for ozone (blue), NO 2 (brown), NO (green), and the product of O 3 and NO 2 (gray) for the first pollution episode.

14754G.Figure 6 .
Figure 6.(a) Average diurnal profile (solid line) of surface NO − 3 (p) for all days of Episode 1.The shaded area indicates the 1σ standard deviation.The solid black line is a linear fit (r 2 = 0.99) to the data between 13:30 and 15:30 LT.(b) Time series (solid blue line) of surfacelevel NO − 3 (p) during Episode 1.The circles indicate the daytime peak values.The linear fit (red line) to the daytime NO − 3 (p) peaks suggest an increase of 1.32 µg m −3 day −1 .
[NO − 3 (p) ] RL and the shape of the [NO − 3 (p) ] RL vertical profile predominately control the morning-time evolution of the surface NO − 3 (p) during this episode (Figs. 7 and 8).The particularly steep rise in the surface-level NO − 3 (p) in the morning results from the combination of the NBL height being exceptionally shallow (only ∼ 20 m) and the NO − 3 (p) in the lowaltitude region of the RL being greater than the NO − 3 (p) in the early-morning NBL.The peak and turnover in surfacelevel NO − PhotochemistryInitial surface 400 300 200 100 0Mixed layer height (m a.g.l.)24:00 18:00 12:00 06:00 00:00 Time of day (h)

Figure 8 .
Figure 8. Model predictions of the diurnal variation in surface-level NO − 3 (p) under (a-c) different assumptions regarding the NO − 3 (p) concentration and vertical variability in the early-morning RL or (d) without daytime photochemical production of NO −3 (p)  .In all panels the blue curve shows the observations and the green curve shows the full observationally constrained model results (identical to Fig.6) for the average of the 4 flight days in Episode 1.For (ac), the assumptions were as follows:(a) the [NO − 3 (p) ] RL is equal to zero; (b) the [NO − 3 (p)] RL is constant with altitude and equal to the NO − 3 (g+p) at 15:00 LT in the previous afternoon, corresponding to a case of zero net production or loss; (c) the [NO − 3 (p) ] RL is constant with altitude and equal to the maximum observed[NO −  3 (p) ] in the early-morning RL profile.
observe at their valley wall and valley floor sites in wintertime Utah that O 3 concentrations near the surface remain well-above zero even during pollution episodes, thus allowing for surface-level www.atmos-chem-phys.net/17/14747/2017/Atmos.Chem.Phys., 17, 14747-14770

Figure 9 .
Figure 9. Panels (a, b): diurnal variation in the surface-level particulate nitrate concentration during (a) the first episode and (b) the second episode.The solid black lines are the average profile over the episode and the colored lines are for individual days.Panels (c, d, e, f): wind roses for surface-level (10 m) winds in Fresno for the early morning (05:00-08:00 LT) during (c) Episode 1 and (d) Episode 2 and for the late morning (09:00-12:00 LT) during (e) Episode 1 and (f) Episode 2. //doi.org/10.5067/Aircraft/DISCOVER-AQ/Aerosol-TraceGas).

Figure
Figure A1.(a) Total particle scattering at 550 nm (Mm −1 ) versus PM 1.0 mass (submicron black carbon (BC) + non-refractory PM 1.0 (NR-PM 1 )) concentration (µg m −3 ) observed at ground level in Fresno.The solid red line is the orthogonal distance regression fit including data only during the daytime (black circles) between 08:00 LT and 16:00 LT; slope = 2.83 mm 2 µg −1 .(b) NO − 3 (p) concentration measured by PILS on P3-B aircraft versus that estimated from scattering using the relation NO − 3 (p) = γ • σ sca, dry /2.83.The solid red line is the linear fit to the data, with slope = 0.78.The dashed black line is the 1 : 1 line.

Figure B2 .
Figure B2.Evolution of the ML height with time (starting at 08:00 LT) on the 4 flight days in Episode 1.The observational constraints are shown as black circles, where the first point comes from nearby balloon sonde measurements and the last three from the P3-B vertical profiles.

Figure B3 .
Figure B3.Average modeled surface NO − 3 (p) (solid lines) using the CLASS model output (green) and a sigmoid fit to the observed ML heights (blue).The ML heights used in the model are shown in dashed lines.

Figure C1 .
Figure C1.Model results showing the influence of including NO 3 + VOC reactions on HNO 3 production via the heterogeneous hydrolysis of N 2 O 5 , as a function of the heterogeneous oxidation rate.The red line shows the ratio between the HNO 3 produced via N 2 O 5 hydrolysis when reactions with VOCs are considered and when they are not.Reaction of NO 3 with VOCs reduces the HNO 3 formed via hydrolysis.The blue line shows the ratio between the total HNO 3 produced from either N 2 O 5 hydrolysis or NO 3 + VOC reactions when reactions with VOCs are considered and when they are not.

Figure
Figure D1.(a) Time series of NH 3(g) (µg m −3) measured with the denuder at the surface (green squares) and at the lowest altitudes by the chemical ionization mass spectrometer onboard P3-B aircraft (yellow triangles).(B) The nitrate gas-phase fraction estimated by ISORROPIA (blue squares) and the observed fraction determined from the denuder HNO 3(g) and PILS NO − 3 (p) measurements (pink circles)(Parworth et al., 2017).

Table A1 .
Summary of instruments deployed and measurements on ground and on aircraft made during the DISCOVER-AQ campaign.