Heterogeneous N2O5 uptake onto aerosol is the primary nocturnal path for removal of NOx (= NO + NO2) from the atmosphere and can also result in halogen activation through production of ClNO2. The N2O5 uptake coefficient has been the subject of numerous laboratory studies; however, only a few studies have determined the uptake coefficient from ambient measurements, and none has been focused on winter conditions, when the portion of NOx removed by N2O5 uptake is the largest. In this work, N2O5 uptake coefficients are determined from ambient wintertime measurements of N2O5 and related species at the Boulder Atmospheric Observatory in Weld County, CO, a location that is highly impacted by urban pollution from Denver, as well as emissions from agricultural activities and oil and gas extraction. A box model is used to analyze the nocturnal nitrate radical chemistry and predict the N2O5 concentration. The uptake coefficient in the model is iterated until the predicted N2O5 concentration matches the measured concentration. The results suggest that during winter, the most important influence that might suppress N2O5 uptake is aerosol nitrate but that this effect does not suppress uptake coefficients enough to limit the rate of NOx loss through N2O5 hydrolysis. N2O5 hydrolysis was found to dominate the nocturnal chemistry during this study consuming ~80% of nocturnal gas phase nitrate radical production. Typically, less than 15% of the total nitrate radical production remained in the form of nocturnal species at sunrise when they are photolyzed and reform NO2.
 The nitrate radical (NO3) and its reservoir partner dinitrogen pentaoxide (N2O5) are nocturnal trace gases present at large concentrations in polluted air masses. N2O5 is lost to heterogeneous uptake by aerosol. This heterogeneous uptake is responsible for the nocturnal removal of nitrogen oxides (NOx = NO + NO2), which can be a significant portion of the overall NOx removal budget [Brown et al., 2004; Dentener and Crutzen, 1993]. Heterogeneous N2O5 uptake can also result in halogen activation through production of nitryl chloride (ClNO2) which is photolyzed into atomic chlorine in the morning [Finlayson-Pitts et al., 1989; Osthoff et al., 2008; Thornton et al., 2010].
 The rate coefficient of the N2O5 heterogeneous loss (kN2O5) is proportional to the aerosol surface area density (A), the mean molecular speed of N2O5 (), and the N2O5 uptake coefficient (γ(N2O5)) as shown in equation (1), which is valid for small uptake coefficients such that gas phase diffusion to the particle surface does not limit the uptake [Fuchs and Sutugin, 1970].
 The uptake coefficient represents a reaction probability (i.e., the fraction of molecules which do not return to the gas phase after a collision with the surface).
 The N2O5 uptake coefficient typically depends on the aerosol composition and relative humidity and has been the subject of multiple laboratory studies and two recent reviews [Brown and Stutz, 2012; Chang et al., 2011]. The measured uptake coefficients on water droplets range from 0.01 to 0.06. On tropospheric aerosol which is not strongly acidic, N2O5 is ionized into aqueous nitrate (NO3−) and the cation NO2+. The competition between components of the aerosol that react with NO2+ determines the aqueous concentration of molecular N2O5 in the aerosol and subsequently, the portion of N2O5 which returns to the gas phase after accommodation. Any N2O5 which returns to the gas phase effectively reduces the uptake coefficient.
 Laboratory experiments have identified four mechanisms which affect the N2O5 uptake coefficient on tropospheric aerosol. First, numerous studies on inorganic salts and some organic substrates have found reduced uptake at low relative humidity and for solid particles [Hallquist et al., 2003; Hu and Abbatt, 1997; Thornton et al., 2003]. In these studies, the lower concentration of condensed water reduces the rate at which N2O5 ionizes. Second, Wahner et al. [1998b] have found that presence of nitrate (NO3−) in the aerosol reduces the uptake by an order of magnitude, and this result has been confirmed by Mentel et al. , Hallquist et al. , and Bertram and Thornton . Upon accommodation into the aerosol, N2O5 is ionized into NO3− and NO2+ as shown in reaction (R1).
 The accommodation and ionization set up an equilibrium between gas phase N2O5 and aqueous NO2+. Aerosol enhanced in nitrate will shift the equilibrium toward gas phase N2O5 and effectively reduce uptake coefficient. The suppression of the uptake coefficient by nitrate is called the “nitrate effect.” Third, Bertram and Thornton  have shown that aerosol chloride (Cl−) can reduce the suppression of uptake by nitrate. The nitrate suppression is reduced because the reaction of NO2+ with Cl− is favored over the reaction with NO3−. Fourth, several studies have shown reduced uptake of N2O5 on organic aerosol relative to aqueous aerosol [Badger et al., 2006; Cosman and Bertram, 2008; McNeill et al., 2006; Park et al., 2007]. Anttila et al.  have parameterized this effect in terms of an aerosol particle with an organic shell and an inorganic core. These organic coatings may reduce the availability of water on the aerosol surface and decrease the ionization rate of molecular N2O5.
 These laboratory results have rarely been tested against uptake coefficients determined from field measurements. There have been only four studies where uptake coefficients have been determined from ambient in situ measurements. Bertram et al.  directly measured the N2O5 loss rate coefficient in a flow tube reactor with ambient aerosol and in combination with aerosol surface area density measurements determined the uptake coefficient. These measurements in Seattle, Washington and Boulder, Colorado show a decrease in the uptake coefficient as the aerosol organic to sulfate ratio increased. Riedel et al. [2012a] have also measured ambient N2O5 uptake coefficients using a flow tube reactor and observed suppression of the uptake coefficient correlated with aerosol nitrate in La Jolla, California. Two aircraft studies have been used to determine N2O5 uptake coefficients in isolated plumes. Over New England and the Ohio River valley, Brown et al.  found the uptake coefficient to be variable; high on sulfate particles (~0.02) but an order of magnitude lower otherwise. A similar aircraft study in Texas found uptake coefficients to be low (average value of 0.003) but with too few determinations to parameterize a dependence on aerosol composition or relative humidity (RH) [Brown et al., 2009].
 All of the prior field determinations of γ(N2O5) have been for summertime or warm conditions. There are several important differences between winter and summer with respect to N2O5 uptake. First, longer nights during the winter allow for increased nocturnal NOx removal through the N2O5 pathway. Second, in summer, N2O5 chemistry represents a smaller fraction of total nitrogen oxide loss because it competes with nighttime NO3 chemistry during warm conditions as well as daytime photochemical reactions of NOx. In winter, by contrast, a much larger fraction of the reactive nitrogen loss proceeds through N2O5 [Davis et al., 2008; Dentener and Crutzen, 1993; Evans and Jacob, 2005; Macintyre and Evans, 2010]. Third, N2O5 heterogeneous uptake may differ substantially in winter due to a change in aerosol composition. Winter aerosols tend to have higher concentrations of nitrate and lower concentrations of organics, due to shifts in thermodynamic equilibrium of ammonium nitrate and reduced oxidation of volatile organic compounds, respectively [Zhang et al., 2007; F. Öztürk et al., Vertically resolved chemical characteristics and sources of submicron aerosols in a suburban area near Denver, Colorado, submitted to Journal of Geophysical Research: Atmospheres, 2013, hereinafter referred to as Öztürk et al., submitted manuscript, 2013]. Field investigations have not explored the influence of these factors on N2O5 uptake and reactive nitrogen loss. Here we present ambient, vertically resolved measurements of key nitrogen oxide species, including N2O5 and ClNO2, along with aerosol composition and relative humidity which are integrated into an iterative box model to determine the efficiency of winter N2O5 uptake at a polluted, midcontinental location. The influence of N2O5 hydrolysis on the overall nocturnal loss of nitrogen dioxide (NO2) is explored and compared with the daytime loss of NO2.
2 The Nitrogen, Aerosol Composition, and Halogens on a Tall Tower (NACHTT) Field Study
 The Nitrogen, Aerosol Composition, and Halogens on a Tall Tower (NACHTT) field study took place in the wintertime from 17 February through 14 March 2011. S. S. Brown et al. (The nitrogen, aerosol composition and halogens on a tall tower experiment, submitted to Journal of Geophysical Research: Atmospheres, 2013, hereinafter referred to as Brown et al., submitted manuscript, 2013) have provided an overview of the NACHTT field study including a description of all of the measurements, the climatology, and the scientific goals. Here we describe the instruments and measurements critical to this analysis and the measurement site.
 The study was located at the Boulder Atmospheric Observatory (BAO) in Weld County, Colorado. The BAO has a 300 m tower with an external elevator carriage capable of lifting ~1400 kg. Several instruments were placed in a temperature-controlled (nominally 25°C) enclosure mounted on the elevator for vertical profiling. The elevator ascended and descended at ~0.5 m/s and produced a vertical profile approximately every 10 min during continuous profiling. The height of the elevator was measured by counting the teeth of the elevator gear and was consistent with the measured global positioning system altitude. During the field study, profiling was done continuously, only limited by the weather and maintenance of the instruments and elevator. The elevator was not operated when the wind speed exceeded 12 m/s or ice was present on the elevator rails. The instruments were maintained daily, which typically resulted in an interruption of profiling that lasted 1–4 h.
 Five instruments were installed aboard the carriage elevator, and the measured species used in this analysis along with detection limits and accuracies are listed in Table 1. First, a cavity ringdown spectrometer measured nitrogen oxides and ozone [Wagner et al., 2011]. A 662 nm diode laser was used to measure the absorption from NO3, and a 405 nm diode laser was used to measure absorption from NO2. In separate channels, N2O5 was measured by thermal conversion to NO3, and NO and O3 were measured by chemical conversion to NO2. The inlet for the NO3 and N2O5 measurements consisted of 45 cm of 0.25 in. OD Teflon perfluoroalkoxy (PFA) tubing. A Teflon membrane (Pall Corp. R2PJ047, 2 µm pore size, 25 µm thickness) was used to remove aerosol from the sample stream and was replaced every 2 h by an automatic filter changer. Daily measurements of the N2O5 inlet transmission [Fuchs et al., 2008; Wagner et al., 2011] did not show a loss of N2O5 on the inlet surface. The transmission of NO3 through the inlet was not measured but was estimated to be 85% based on previous measurements of the loss of NO3 on Teflon tubing [Dubé et al., 2006] and validation experiments in an environmental simulation chamber [Dorn et al., 2013]. The inlet tubing and fittings were replaced daily. A separate inlet tube (45 cm of 0.25 in. OD Teflon PFA tubing) was used for the sampling of NO, NO2, and O3.
Table 1. Critical Measurements Used in This Analysis
CRDS, Cavity Ringdown Spectrometer; CIMS, Chemical Ionization Mass Spectrometer; UHSAS, Ultra High Sensitivity Aerosol Spectrometer; AMS, Aerodyne Aerosol Mass Spectrometer; GC-MS, gas chromatography mass spectrometer.
 Second, ClNO2 was measured using a chemical ionization mass spectrometer (CIMS) with the iodine anion as a reagent [Kercher et al., 2009]. The CIMS shared an inlet with the NO3 and N2O5 measurement which allowed the ClNO2 measurement to be calibrated relative to the N2O5 cavity ringdown measurement. N2O5 was added to the tip of the inlet daily. During calibrations, a NaCl salt bed was inserted into the sample stream, the N2O5 that was added to the inlet was converted to ClNO2 with unit yield [Riedel et al., 2012b], and the resulting ClNO2 mixing ratio was calibrated with the N2O5 measurement. When the salt bed was removed from the sample stream, the production of ClNO2 on the inlet surface was measured. The ClNO2 production on the inlet surface was always less than 5% of the N2O5 addition. The third instrument was another chemical ionization mass spectrometer that used acetate as the reagent ion and measured gas phase acids [Veres et al., 2008]. These measurements were not used in this analysis but are described in detail by T. C. VandenBoer et al. (Understanding the role of the ground surface in HONO vertical structure: High resolution vertical profiles during NACHTT, submitted to Journal of Geophysical Research: Atmospheres, 2013, hereinafter referred to as VandenBoer et al., submitted manuscript, 2013).
 Fourth, a compact time of flight aerosol mass spectrometer (C-ToF-AMS, termed “AMS” hereafter) was used to measure the nonrefractory composition of particles with physical diameters between 100 and 700 µm [Bahreini et al., 2009]. The AMS was calibrated with NH4NO3 before the field campaign and 5 times during the campaign. The aerosol encountered during the NACHTT campaign is described in detail by F. Öztürk et al. (submitted manuscript, 2013). Fifth, an optical particle counter (Ultra High Sensitivity Aerosol Spectrometer (UHSAS)—Droplet Measurement Technologies) shared an inlet with the AMS and was used to measure particle size distributions for particles with physical diameters between 70 nm and 0.8 µm [Cai et al., 2008].
 Both the AMS and the optical particle counter sampled from a common inlet behind a cyclone impactor that removed particles larger than 2.5 µm. The aerosol was heated and dried as it entered the instrument enclosure. The instrument enclosure was between 10°C and 30°C warmer than the ambient temperature, and the relative humidity in the aerosol inlet was typically less than 20%.
 In addition to instruments mounted on the elevator, several measurements were made from a fixed platform mounted on the main tower at a height of 22 m. From this platform, whole air samples were collected and were subsequently analyzed by a gas chromatography mass spectrometer (GC-MS) for speciated volatile organic compound (VOC) concentrations. Soluble trace gasses were also measured from the platform by a tandem mist chamber. A cascade impactor was used to collect filter samples of aerosol that were analyzed by ion chromatography and neutron activation.
 Filter-based radiometers (used to measure photolysis rates of O3, NO2, and NO3) were mounted at the top of a second scaffolding tower; 9 m tall and 15 m south of the main tower [Stark et al., 2007]. The hydroxyl radical (OH) was measured by conversion to isotopically labeled sulfuric acid and detection using a chemical ionization mass spectrometer [Tanner et al., 1997]. The OH measurement was housed in a trail near the base of the main tower and sampled directly through the trailer wall at a height of 2 m. Meteorological measurements (ambient temperature, wind speed and direction, relative humidity) were made aboard the movable elevator carriage as well as at fixed-height stations on the tower located 10, 100, and 300 m above ground.
 A map of the area surrounding the BAO tower is shown in Figure 1. The measurement site is surrounded by urban areas, most significantly the Denver metro area to the south. There are several large point sources of pollution emissions such as the Cherokee station power plant and Suncor refinery in Commence City, an industrial area 28 km south of the measurement site. The Wattenberg gas and oil field surrounds the measurement site and extends to the northeast. Typically, air masses observed at the BAO tower are strongly influenced by the Front Range urban area and have been shown to be affected by oil and gas production [Gilman et al., 2012]. Urban aerosol haze, known as the Denver brown cloud, is common at this site in winter time [Groblicki et al., 1981]. Periodic strong downslope winds from the west along the Rocky Mountain Foothills bring relatively clean continental background air to the site.
3 Iterative Box Model
 The N2O5 loss rate coefficient is determined using an iterative box model constrained by ambient vertically resolved measurements of N2O5, NO2, and O3 from the NACHTT field study. Simultaneous measurements of the submicron particle distribution and relative humidity are used to estimate the ambient aerosol surface area density and subsequently the N2O5 uptake coefficient.
 The source of ambient N2O5 is the reaction of ozone (O3) and nitrogen dioxide (NO2) that forms the gaseous nitrate radical (NO3) (R2). (Here we use the term “nitrate radical” to refer to neutral, gas phase NO3, and “nitrate” alone to refer to the aqueous anion NO3−.) NO3 then reacts with NO2 again to form N2O5(R3). N2O5 is thermally unstable and decomposes, setting up an equilibrium between NO3 and N2O5.
 During the daytime, NO3 and N2O5 are present in small concentrations due to removal of NO3 by photolysis and reaction with NO. The mixing ratios are typically not more than a few parts per thousand by volume (pptv) and then only under certain conditions [Brown et al., 2005]. However, during the night, the concentrations of NO3 and N2O5 can be significant. During NACHTT, the average nocturnal mixing ratios for NO3 and N2O5 were 5 and 140 pptv, respectively. The equilibrium partitioning between NO3 and N2O5 is determined by the NO2 concentration and the ambient temperature. N2O5 is favored by higher NO2 concentrations and lower temperatures. The average NO2 mixing ratio was 5.6 parts per billion by volume (ppbv), and a typical nighttime temperature was 0°C. For these conditions, the equilibrium ratio of N2O5 to NO3 is 102:1, using the equilibrium constant recommend by Sander et al. .
 NO3 is the primary atmospheric oxidant in urban influenced air during night and reacts (R4) with biogenic volatile organic compounds (VOCs) and sulfur compounds and some classes of highly reactive anthropogenic VOCs [Atkinson, 1991]. N2O5 is lost through heterogeneous reactions (R5) with aerosol with a loss rate coefficient described by equation (1).
 An additional loss pathway for N2O5 is the possible homogeneous hydrolysis of N2O5 studied by Wahner et al. [1998a] which is neglected in this analysis because there is little absolute humidity during the winter time. Additionally, Brown et al.  found that observed N2O5 lifetimes and water vapor concentrations were consistent with a lower rate constant than recommended for the homogeneous hydrolysis reaction. This analysis assumes that all losses of N2O5 can be attributed to heterogeneous loss on aerosol surfaces.
 The equilibrium between NO3 and N2O5(R3) is established relatively quickly at ambient tropospheric temperatures and typical urban NO2 mixing ratios [Brown et al., 2003]. However, the loss rates of NO3 due to reactions with VOCs and the uptake of N2O5 by aerosol can be significantly slower than the forward and reverse reactions in (R3). The NO3 and N2O5 concentrations do not achieve steady state until there is balance between the nitrate radical production and losses of both NO3 and N2O5. In such cases the steady state analysis used by Brown et al. [2006, 2009] cannot be applied. Additionally, the NACHTT data set had vertical transects but not horizontal transects. Vertical transects at night include considerable meteorological variability that covaries with the NO2 levels, making the steady state analysis used by Brown et al. [2006, 2009] far more difficult even when the steady state approximation is valid. An alternate method of determining the N2O5 loss rate coefficient is to use an iterative box model that does not assume steady state but that requires knowledge of time zero (i.e., the time since emission of NOx into an air mass or the time since sunset). One analysis strategy would be to determine periods when the steady state approximation is valid and apply a steady state analysis to those times and the box model for all other cases. However, to determine when the steady state approximation is valid, it is necessary to run a box model and assume a reaction duration. For this analysis, we simply applied the box model to all cases including those for which the steady state approximation is valid. The reaction duration is assumed to be the time since sunset, which is appropriate for air masses unaffected by nocturnal emissions. The iterative box model used here is described briefly below and in more detail in Appendix A.
 The iterative box model begins with an air mass containing only O3 and NO2 which then react to form NO3 and N2O5 as described by reactions (R2) and (R3). The equilibrium cycling between NO3 and N2O5 is fast when NO2 concentrations are large (> 1 ppbv), reaction durations are long (> 1 h), and the temperature is low. The lifetime of NO3 with respect to N2O5 formation is 30 s at 0°C and 1 ppbv of NO2, and the lifetime of N2O5 with respect to thermal decomposition is 10 min at 0°C. In this box model, it is computationally advantageous to eliminate these fast reactions, allowing the time step in the box model to be larger. Specifically, the differential equation for NO2 contains two terms from the forward and reverse of reaction (R3) which describe the equilibrium cycling between NO3 and N2O5. When NO3 and N2O5 are in equilibrium, these two terms have nearly the same magnitude, and in the box model, they are replaced by an approximation which depends on only the O3 and NO2 concentration instead of the NO3 and N2O5 concentration (discussed in Appendix A). Without these equilibrium cycling terms and their dependence on NO3 and N2O5, the differential equations for O3 and NO2 can be numerically solved without knowledge of NO3 or N2O5 concentrations. Because the final (or measured) values of O3 and NO2 are known, the differential equations for O3 and NO2 can then be integrated backward in time starting with the measured concentrations of NO2 and O3.
 Once the initial O3 and NO3 mixing ratios are determined, the differential equations for N2O5 and NO3 (reactions (R4) and (R5)) are integrated forward in time to determine the final concentration of N2O5. An initial guess of 10−5 s−1 is used for the N2O5 loss rate coefficient. The box model concentration of N2O5 is then compared to the measured N2O5 concentration, and the N2O5 loss rate coefficient is iteratively adjusted using the secant method until the N2O5 concentration predicted by the box model agrees with the measured N2O5 concentration. Once the N2O5 loss rate coefficient is known, the uptake coefficient can be determined using equation (1).
 When applying the iterative box model to ambient data, additional chemistry not included in the iterative box model could affect the observed N2O5 concentration and bias the retrieved uptake coefficient. NO, the principal component of emitted NOx, reacts efficiently with NO3 and quickly converts the NO3/N2O5 reservoir into NO2, effectively resetting the zero time for the iterative box model. The uncertainty from NO emissions after sunset is minimized by excluding data when NO is observed above the detection limit and limiting the analysis to times when the nocturnal atmosphere is stable such that fresh NO emissions are confined to the surface layer.
 The potential temperature difference between the top (300 m) and bottom (10 m) of the tower is used to exclude air masses in which NO was not observed but was possibly affected by nocturnal emissions. When the potential temperature difference is large, the nocturnal atmosphere is stable and layered, the upward mixing from the surface is minimized, and air masses above the surface are less affected by nocturnal emissions. The iterative box model is only applied to data collected when the potential temperature difference is greater than 8°C and the elevator is at least 20 m above ground. The potential temperature difference of 8°C was chosen to eliminate retrieved uptake coefficients that were unphysical (> 1). This filtering by potential temperature does not eliminate all air masses affected by nocturnal emissions; in particular, emissions from warm combustion sources that are buoyant and rise through the nocturnal layers. These air masses would best be modeled using a reaction duration that is the transport time from the emission point to the measurement site. However, because the emission locations and emission times are not known (with the exception of two plumes), this uncertainty is accounted for by estimating the sensitivity of the retrieved uptake coefficient to the reaction duration and including that in the total uncertainty.
 The reaction duration (or zero time) used in the iterative box model is the time since sunset. Using sunset as the zero time can be inaccurate if there are nocturnal emissions as described above (a shorter reaction duration than the time since sunset) or if the photolysis of NO3 has slowed enough to let N2O5 accumulate before sunset [Geyer et al., 2003] (a longer reaction duration than the time since sunset). The median mixing ratio of N2O5 at sunset during NACHTT was 16 pptv and ranged from 60 to < 3 pptv (detection limit). Most nights, the integrated nitrate radical production was several parts per billion and the N2O5 produced before sunset was a small fraction of that total. To account for the uncertainty of the reaction duration, the iterative box model was also applied with a longer reaction duration of 125% and with a shorter reaction duration of 75%. If the N2O5 concentration has achieved steady state, the reaction duration has little effect on the retrieved uptake coefficient. However, this uncertainty can be significant when the N2O5 loss rate is slow and steady state has not been achieved. The amount of change in the retrieve uptake coefficient is used as the uncertainty from the reaction duration and added in quadrature to the uncertainty from NO3 reactivity that is discussed in the next section.
 The nocturnal production of nitrous acid, HONO, is also not included in the iterative box model. Unlike nocturnal NO emissions, HONO production is unlikely to affect the retrieved uptake coefficients. Nitrous acid is produced by a heterogeneous process that consumes NO2 throughout the course of the night [Kleffmann, 2007]. Several studies have found that the most significant surface for HONO production is the ground [Wong et al., 2011; Young et al., 2012], and because data used in this analysis do not include measurements below 20 m, HONO production on the ground surface should not affect the retrieve uptake coefficients significantly. If HONO production on aerosol surfaces were significant, the calculated concentration of NO2 used in the box model would be inaccurate. However, the analysis of T. C. VandenBoer et al. (submitted manuscript, 2013) found that during NACHTT aerosol uptake of NO2 is a very slow process, and HONO production can be neglected relative to reaction of NO2 with O3 for air masses above surface level.
3.1 NO3 Reactivity
 The measured concentrations of O3, NO2, and N2O5 can be used directly in this iterative box model; however, the NO3 reactivity or NO3 loss rate coefficient is estimated based on the VOC concentrations measured in the whole air samples. The NO3 loss rate coefficient is calculated using whole air samples, which were collected hourly at height of 22 m on the tower, together with laboratory-measured rate constants. When a species' concentration was below the instrumental detection limit, its concentration was assumed to be zero for the purposes of the NO3 reactivity calculation. The results of this calculation are shown in Figure 2. In each whole air sample, the concentrations of 82 species were measured, although only 42 with known rate constants were used to estimate the NO3 reactivity [Atkinson, 1991; Atkinson and Arey, 2003]. Among these, four species contributed most significantly to the NO3 reactivity (median mixing ratio and 90th percentile): 2 methyl 2 butene (6 and 16 pptv), styrene (3 and 10 pptv), delta limonene (1.5 and 6 pptv), and alpha pinene (1 and 4 pptv). Delta limonene and alpha pinene are biogenic VOCs and are typically observed at higher concentration during the summer, but even the small concentrations observed during NACHTT can affect the NO3 reactivity. Because the NO3 reactivity of the whole air samples typically varied by at least a factor of 10 over each night and their collection point was not colocated with the elevator-based measurements, the median NO3 reactivity from each night was applied to the entire night and 16th and 84th percentiles were used as the lower and upper uncertainties. The 16th and 84th percentiles were chosen because they correspond to ± 1 standard deviation of a normal distribution.
 When NO3 reactivity is low (~1 × 10−4 s−1) and the NO3 lifetime is in the range of a few hours, it is likely that species not measured during NACHTT, such as peroxy radicals (RO2), contribute significantly to the NO3 reactivity. For example, at a mixing ratio of 1 pptv, HO2 would consume NO3 with a first-order rate coefficient of ~1 × 10−4 s−1 [Hall et al., 1988], similar to the entire NO3-VOC reactivity on lower reactivity nights. Peroxy radical measurements during winter are sparse, although Fleming et al.  reported average total nighttime peroxy radical mixing ratios of 8–10 pptv at a coastal location in the UK during winter. Reactions of NO3 with RO2 are likely a small influence in this analysis since the equilibrium between NO3 and N2O5 strongly favors the latter. However, if N2O5 uptake were also very small due to low aerosol surface or small uptake coefficient, the NO3-RO2 reactions would be more significant.
 An additional loss pathway for NO3 is heterogeneous uptake on aerosol. Because the reported NO3 uptake coefficients are an order of magnitude smaller than those for N2O5 on most inorganic aerosols [Brown and Stutz, 2012] and the typical NO3 mixing ratio is also smaller, this pathway is estimated in previous studies to account for a very small fraction of the nitrate radical chemistry [Aldener et al., 2006; Wong and Stutz, 2010] and is neglected in this analysis. We note that NO3 heterogeneous uptake could be important if aerosol species such as polycyclic aromatic hydrocarbons were abundant [Gross and Bertram, 2008].
 The uncertainty in the uptake coefficient due to NO3 reactivity can vary greatly depending on conditions such as equilibrium ratio of NO3 and N2O5 and the approach to steady state. If the nitrate radical production rate and the N2O5 loss rate are sufficiently fast, even large changes in the NO3 reactivity have little effect on the retrieved uptake coefficient. However, when the nitrate radical production rate is slower, the uncertainty in the NO3 reactivity can have a larger effect. To account for this uncertainty, the box model was applied using three different NO3 reactivities at each data point; the median reactivity, 84th percentile reactivity, and the 16th percentile reactivity. In this data set, the equilibrium ratio of N2O5 and NO3 and the loss rates of N2O5 and NO3 strongly favor N2O5. Consequently, the lower limit of NO3 reactivity typically results in nearly the same uptake coefficient as the median value. However, the upper limit of NO3 reactivity at times makes the NO3 loss rate competitive with the N2O5 loss rate and reduces the retrieved uptake coefficient. The resulting uncertainty is skewed toward lower values of the uptake coefficient. In some cases the NO3 loss rate is greater than the nitrate radical production rate in which case the uncertainty includes zero, leading some data to provide only an upper limit to the uptake coefficient. Inclusion of peroxy radical reactions with NO3 (see above) would also skew the retrieved uptake coefficients lower and be of particular significance when the nitrate radical chemistry is proceeding slowly (low NO2 mixing ratio or low surface area density). The uncertainties due to the NO3 reactivity are added in quadrature to the uncertainty from the reaction duration and are displayed along with the retrieved uptake coefficient throughout this analysis.
3.2 Ambient Surface Area Density
 The ambient aerosol surface area density is also needed to convert the N2O5 loss rate coefficient to an uptake coefficient using equation (1). The optical particle counter aboard the elevator measured dry particle distributions for particles with diameters between 60 nm and 0.8 µm. The ambient surface area density is estimated by applying a calculated growth factor to the particle distribution measured at low relative humidity by the optical particle counter.
 The growth factor is estimated using the ISORROPIA II aerosol thermodynamics model [Fountoukis and Nenes, 2007] and the aerosol composition measured by the AMS aboard the elevator. The AMS reported the total nonrefractory mass of the dried aerosol and the mass of five components: sulfate, nitrate, ammonium, organics, and chloride. During NACHTT, the average aerosol mass loading was 4.6 µg/m3 and the average composition by mass was 19% sulfate, 39% nitrate, 14% ammonium, 27% organics, and < 1% chloride. The aerosol thermodynamics model only considers the inorganic components of the aerosol, so any contribution to the hygroscopicity from the organic portion was neglected. The model was set up to allow the aerosol to effloresce. For each datum reported by the AMS, the model calculated the mass of condensed water on the aerosol. The diameter growth factor was determined by taking the cube root of the ratio of wet aerosol mass to the dry aerosol mass. The estimated diameter growth factor is shown in Figure 3. For comparison, two growth factor parameterizations used in previous studies that reported N2O5 uptake coefficient are shown as well. Data with relative humidity greater than 90% have been excluded because of difficulty quantifying the growth factor and uncertainty in the relative humidity measurement. These data are shaded pink in Figure 3. Because the AMS reported aerosol composition data every 10 s, the growth factors calculated from these data were interpolated and applied to the particle size distributions which were measured every second.
 Both the measurement uncertainty from the optical particle counter and the uncertainty in the aerosol hygroscopicity contribute to the uncertainty in the ambient surface area density. For the dry particle size distributions measured by the optical particle counter, the number of particles and the particle diameters are both uncertain by ±10%. This leads to ±33% uncertainty in the dry surface area density. Any additional contribution to ambient surface area density from super-micron particles is not included in this estimate, and if the super-micron contribution is significant, then the retrieved uptake coefficients would be an upper limit for the actual uptake coefficient.
 The growth factor used here is based on the nonrefractory inorganic portion of the aerosol measured by the AMS and is 1.6 at 90% RH. Synthetic ammonium nitrate and ammonium sulfate (the majority of aerosol mass during NACHTT) have diameter growth factors of 1.75 and 1.7 at 90% RH, respectively [Hu et al., 2011], and are comparable to the growth factor calculated here. Some refractory aerosols such as NaCl (not detected by the AMS) have larger growth factors > 2.0 at 90% RH [Swietlicki et al., 2008]. Organic aerosol is typically less hygroscopic than ammonium nitrate and sulfate. Duplissy et al.  found that the growth factor at 90% RH on secondary organic aerosol increased from 1.25 to 1.6 as the aerosol aged. Fresh soot is hydrophobic and has a growth factor < 1.1 [Swietlicki et al., 2008]. Based on the aerosol composition during NACHTT (72% ammonium nitrate and sulfate and 28% organics), a conservative estimate of the uncertainty in the growth factor at 90% RH is ±20% and ranges from 1.3 to 1.9. The uncertainty in the growth factor is reduced at lower relative humidity.
 When the uncertainty in the diameter growth factor is squared and added in quadrature with the measurement uncertainty from the optical particle counter, the combined uncertainty in the ambient surface area is approximately a factor of 2 (i.e., −50% and + 200%) at 90% RH and is reduced to the measurement uncertainty from the optical particle counter (±33%) at 0% RH. The uncertainty in the ambient surface area density leads directly to a proportional uncertainty in the N2O5 uptake coefficient, through equation (1). Because this uncertainty is simply related to the surface area density and relative humidity, it is not shown in the figures and only stated in the text.
 The exclusion of data based on observed NO, potential temperature differences less than 8°C, RH greater than 90%, and periods when critical data were not reported (i.e., instrument zeroing, calibration, and maintenance) significantly reduce the amount of data available for use in this analysis. Data were collected for 25 days, yielding 323 h of data during the night. Filtering the data based on potential temperature difference was most restrictive and reduced the available data set to 14% of the total nighttime data. The potential temperature difference was only greater than 8°C on 9 out of 25 nights and then typically only for a few hours before sunrise. Subsequent filtering by NO mixing ratio, relative humidity, and missing data further reduce the amount of data analyzed to 7% of the total nighttime data or 85,440 one second data points.
3.4 Aerosol Nitrate Fraction
 One of the goals of this analysis is to correlate the N2O5 uptake coefficient with aerosol composition. At high relative humidity, water condensed on aerosol can be the majority of the aerosol mass and will strongly influence the concentration of other aerosol species, such as nitrate. When estimating the aerosol growth factor, the mass of water condensed on the aerosol is an intermediate product. This condensed water mass was added to the total dry mass measured by the AMS and used to determine the aerosol nitrate and sulfate mass fractions. If it is assumed that the aerosol is internally mixed and all the constituents are in the liquid phase, it would be possible to estimate the nitrate or sulfate concentration. However, because of the significant uncertainty in applying these assumptions uniformly across the entire data set, our alternate approach to avoid such uncertainties is to compare the N2O5 uptake coefficient with the nitrate and sulfate mass fraction, which are closer to the directly measured parameters.
 A histogram of all of the uptake coefficients determined using the iterative box model is shown in Figure 4a plotted on a logarithmic scale. The red and the blue traces show histograms of the upper and lower uncertainty due to the NO3 reactivity and reaction duration. The distribution of uptake coefficients peaks at 0.015, and there is secondary peak at 0.04. The distribution ranges from 0.002 to 0.1. The peak of the distribution agrees with previous ambient determinations and laboratory experiments. However, the upper end of the distribution in Figure 4 does not agree with laboratory experiments such as Van Doren et al.  and Bertram and Thornton  in which the largest measured uptake coefficient was 0.06 and 0.035, respectively. In the NACHTT data set, the higher values of the uptake coefficient are correlated with low surface area densities and low NO3 reactivities as shown in Figure 4b. This disagreement at the upper end of the distribution may be due to missing contributions to the surface area density from super-micron particles or to the NO3 reactivity by peroxy radicals.
 A single profile of the N2O5 uptake coefficient is shown in Figure 5 along with measurements used to calculate it. This profile was collected on 5 March 2011 between 12:47 and 12:55 A.M. The profile is characterized by three distinct layers. The highest layer above 130 m is dry (RH = 40%) and has little aerosol mass or surface area density. The lower two layers (0–40 and 40–130 m) are much more humid, 80% and 90% RH, respectively. The aerosol composition in the two lower layers is also very similar and dominated by ammonium nitrate. The main difference in the aerosol between these two layers is the relative humidity and consequently the fraction of aerosol mass that is nitrate. In the lowest layer, the nitrate fraction is 18% and is diluted compared with the middle layer where the nitrate fraction is 32%. The two lower layers also have the same nitrate radical production rate of ~0.3 ppbv/h; however, the N2O5 concentration in the lowest layer is ~60 pptv and in the middle layer is greater than 300 pptv. As expected, the retrieved N2O5 uptake coefficient reflects this trend in the N2O5 concentration. In the lowest layer, the N2O5 uptake coefficient is near 0.04; however, in the middle layer, uptake coefficient drops below 0.01. The correlation between the uptake coefficient and the aerosol nitrate fraction suggests that in the middle layer, the N2O5 uptake is suppressed by nitrate.
 The upper layer in Figure 5 is very different from the lower layers, and the N2O5 chemistry is much slower. The nitrate radical production rate is ~0.12 ppbv/h and the surface area density is ~ 60 µm2/cm3. Because the reaction rates are much slower, the N2O5 concentration in the upper layer has not yet reached its steady state value and the iterative box model is much more sensitive to the uncertainty in NO3 reactivity and reaction duration. In the upper layer, the retrieved uptake coefficient is ~0.03, but the uncertainty includes values as low as 0.015. Because the nitrate fraction is similar in the upper and middle layer, it might be expected that the uptake coefficient would be suppressed similar to the middle layer. However, the aerosol in the upper layer has a different dry composition compared to the lower layers. Both sulfate and organic fraction of the aerosol is much larger than in the lower layers. High aerosol sulfate concentrations have been correlated with larger N2O5 uptake coefficients [Brown et al., 2006; Hu and Abbatt, 1997] while organics coatings can suppress the N2O5 uptake coefficient [Anttila et al., 2006].
 The anticorrelation between the N2O5 uptake coefficient and aerosol nitrate fraction is also clear in the 2 h before sunrise on 2 March as shown in Figure 6. The upper panel of Figure 6 shows the time series of the aerosol nitrate mass fraction and the times series of the N2O5 uptake coefficient (logarithmic scale). The gray-shaded background shows the height of elevator. The lower panel of Figure 6 shows the same data as in the upper panel, except here, the uptake coefficient is scattered against the nitrate fraction. Again, the uptake coefficient is anticorrelated with the nitrate fraction, indicating the role of nitrate in suppressing the uptake of N2O5.
 In the same manner as the 5 March profile, relative humidity controls the amount of condensed water on the aerosol and consequently the nitrate fraction during the 2 March time period shown in Figure 6. This is clearly seen in the profile shown in Figure 7 between 4:58 and 5:06 A.M. on 2 March. At 50 m, the uptake coefficient is 0.026 and the nitrate fraction is 0.3. The uptake coefficient decreases as the height increases (0.005 at 250 m), and the nitrate fraction rises to 0.45 at the top of the profile. The nitrate fraction of the dry aerosol is lower at the top of the profile than at the bottom. However, the condensed water fraction changes more dramatically, accounting for 40% of the aerosol mass at the bottom of the profile and near 0% at the top. The net result is a nitrate fraction that increases with height. The dependence of the retrieved N2O5 uptake coefficient with height is qualitatively consistent with suppression of this uptake by aerosol nitrate.
 Suppression of N2O5 uptake by nitrate can be seen throughout the entire data set in addition to the individual profiles described above. Figure 8 shows N2O5 uptake coefficient from all of the data used in this analysis scattered against the aerosol nitrate fraction. The data have been binned according to the nitrate fraction, and in each bin, the median, 5th, 16th, 84th, and 95th percentiles were calculated and displayed as boxes and whiskers. The uncertainty due to NO3 reactivity and duration for each individual data point is shown as pink bars. When the aerosol nitrate fraction is below 0.1, the median uptake coefficient was 0.04. However, when the nitrate fraction is greater than 0.25, the median uptake coefficient is reduced by at least a factor of 2.
 For comparison, the Bertram and Thornton  parameterization is also shown in Figure 8 along with its uncertainty. The parameterization requires the molarity of water and the molar ratio of nitrate to water. The water molarity used here was 30 mol/L, and a model aerosol consisting of only ammonium nitrate and water was used to convert the nitrate mass fraction to the molar ratio of nitrate to water. Neither of these assumptions has a strong effect on the magnitude of the uptake coefficient for conditions shown in Figure 8. Because this analysis is focusing on the nitrate effect, the chloride concentration in the parameterization was set to zero. Chloride was a minor component of submicron aerosol during NACHTT and was often below the AMS detection limit. Its influence, if present at higher concentrations, would be to reduce any suppression due to nitrate.
 The Bertram and Thornton parameterization predicts smaller uptake coefficients than the uptake coefficients retrieved by the box model. This could be due to either the errors in applying the iterative box model to the analyzed air masses (such as incorrect NO3 reactivity or nocturnal NOx emissions) or differences between the ambient aerosol and the synthetic aerosol used by Bertram and Thornton to develop the parameterization. One possible difference between the laboratory and ambient conditions is the temperature. Several laboratory studies have measured larger uptake coefficients at low temperatures [Griffiths and Cox, 2009; Hallquist et al., 2003; Van Doren et al., 1990]. The Bertram and Thornton parameterization was based on room temperature measurements at 25°C, whereas the average nocturnal temperature for the NACHTT data set is 1°C and a range of −6°C to 7.5°C included 90% of the analyzed data.
 In a complementary analysis, T. P. Riedel et al. (Vertically resolved ClNO2 and Cl2 measurements from a tall tower in a polluted continental setting: Insights into chlorine activation within urban or power plant plumes, submitted to Journal of Geophysical Research, 2013, hereinafter referred to as Riedel et al., submitted manuscript, 2013) have identified two power plant plumes in the NACHTT data set and studied ClNO2 production in these plumes. The N2O5 uptake coefficient was also estimated in each of these plumes and agreed with the uptake coefficient retrieved from the iterative box model.
 Correlations of derived uptake coefficients with aerosol nitrate were the most obvious feature of the NACHTT data set. Other correlations with, for example, the sulfate content, were not robust, in part because other components of the aerosol were smaller and tended to vary less than the nitrate content, which is the dominant component in the Denver urban area in winter. This work can also be contrasted with uptake coefficients determined from ambient aircraft measurements during summer conditions [Brown et al., 2006; Brown et al., 2009]. Both of these studies were based on the variation of NO3 and N2O5 steady state lifetimes with NO2 across discrete pollution plumes transected by the aircraft and resulted in a limited number of determinations. In the northeast U.S. in August 2004, uptake coefficients were shown to vary over the range 0.002–0.02, with the larger uptake coefficients associated with sulfate rich aerosol, and the smaller ones associated with mixed organic and sulfate aerosol. In Texas during October 2006, uptake coefficients were not clearly correlated with aerosol composition but had an average value of 0.003 with considerable scatter in the data that ranged from 4 × 10−4 to 0.019. Neither of these aircraft studies during the summer encountered large amounts of nitrate in the aerosol.
5 Nocturnal NOx Loss
 Nocturnal loss of NO2 accounts for a significant portion of the total conversion of NO2 to HNO3 and the subsequent removal of emitted nitrogen oxides from the atmosphere. Nighttime NOx removal is especially important in the winter when the temperature is cooler (favoring N2O5 formation relative to NO3) and the nights are longer (favoring dark chemistry over photochemistry). The NACHTT data set and retrieved uptake coefficients represent an opportunity to quantify the total amount of NO2 removed during the night and to determine the amount of NO2 which is reformed at sunrise by photolysis of nocturnal species (NO3, N2O5, and ClNO2).
 Nocturnal removal of NOx proceeds primarily by nitrate radical production, N2O5 hydrolysis, and subsequent wet deposition. The nocturnal NOx removal rate can be quantified by considering the fraction of NO2 consumed by nitrate radical chemistry in each of four possible pathways. First, NO3 can be lost through reactions with VOCs. The second pathway is loss through N2O5 heterogeneous hydrolysis. When N2O5 is taken up on the aerosol, it typically reacts with water and forms two molecules of nitric acid. The third pathway is uptake to chloride-containing particles. Instead of forming nitric acid alone, one nitric acid and one nitryl chloride (ClNO2) molecule are formed. Because it is insoluble, the ClNO2 is repartitioned back into the gas phase, where it builds up in the atmosphere throughout the night and undergoes morning photolysis to atomic chlorine and NO2. The fourth pathway is for NO3 to undergo no further reactions except for cycling between NO3 and N2O5. At sunrise, this NO3 is photolyzed and the entire N2O5 reservoir thermally decomposes to reform NOx.
 Each of these pathways can be assigned a number representing the NO2 molecules removed from the atmosphere by each nitrate radical. The potential for removing NO2 is shown in Table 2. The reactions of NO3 with VOCs proceed by a variety of mechanisms, but for alkene reactions with NO3, they proceed via addition of NO3 to a carbon-carbon double bond, resulting predominantly in an organic nitrate product. A typically small fraction of the nitrogen is regenerated as NO2 in these reactions, though the organic nitrate versus NO2 yield depends strongly on the particular VOC. Some reactions, such as those of NO3 with aldehydes, lead to HNO3 production. For simplicity, reactions of NO3 with VOCs are assumed to lead to complete removal of reactive nitrogen. A more complete treatment of NO3 chemistry would not significantly alter the conclusions of this wintertime analysis, since NO3 reactions were the minor path for nighttime NOx loss.
Table 2. NO2 Removal Potential
Nitrate Radical Pathway
NO2 Removal Potential
Assuming unity yield of organic nitrates in NO3-alkene reactions that leads to complete removal of the reactive nitrogen and omitting reaction of NO3 with peroxy radicals that recycle NO2 with unit yield.
 Using the results of the iterative box model, it is possible to quantify the fraction of the nitrate radical production consumed by each of the four possible pathways. Once the N2O5 loss rate coefficient has been determined by the iterative box model, the reaction duration is extended from sunset to sunrise. The concentrations at sunrise along with the integrated losses of NO3 and N2O5 can be used to determine the partitioning between each of the possible pathways. To account for ClNO2 formation, reaction (R4) must split into two reactions ((R6) and (R7)).
 The summed rate for these reactions is the N2O5 loss rate determined using the iterative box model. The ratio of the rates of reactions (R6) and (R7)) is the ClNO2 yield. Because ClNO2 simply builds up throughout the night and undergoes no further reactions, the ClNO2 yield can be determined by comparing ClNO2 concentration with the integrated amount of N2O5 loss to aerosol uptake, as shown in equation (2). The integral is performed over the duration of the box model, which in this case is the time from sunset until the time when the concentration of ClNO2 is measured, yielding
 The ClNO2 yield calculated using equation (2) is more sensitive to the reaction duration than the N2O5 uptake coefficient. In the case where steady state is achieved, the uptake coefficient is insensitive to reaction duration; however, the integrated amount of N2O5 loss is directly proportional to the reaction duration. For air masses influenced by nocturnal emissions (such as a buoyant power plant plume), the ClNO2 yield would be underestimated and should be considered a lower limit. Figure 9 shows a histogram of the ClNO2 yields calculated using equation (2) and only includes the filtered data set to which the box model was applied. The majority of the ClNO2 yields are less than 10%. Because the ClNO2 concentrations were reported every 10 s, the calculated ClNO2 yield was interpolated to 1 s to match the other measurements (O3, NO2, N2O5, etc.).
 The ClNO2 yield has been estimated in two other analyses of the NACHTT data set. T. P. Riedel et al. (submitted manuscript, 2013) used a similar box model and measured ClNO2 concentration to describe ClNO2 production in two power plant plumes and found that yields of 40% and 80% fit each plume. Aside from these plumes, T. P. Riedel et al. (submitted manuscript, 2013) found that an average yield of 5% fits the remainder of the nocturnal data which is consistent with this analysis. A. H. Young et al. (Phase partitioning of soluble trace gases with size-resolved aerosols in near-surface continental air over northern Colorado, USA during winter, submitted to Journal of Geophysical Research, 2013, hereinafter referred to as Young et al., submitted manuscript, 2013) estimated the yield using the size-resolved aerosol composition and a ClNO2 yield parameterization. This method found the median yield was over 90% for all particle sizes. The discrepancy between the bottom-up (using aerosol composition) and top-down (using ClNO2 concentration) methods of estimating the ClNO2 yield have not been resolved.
 Calculated using the iterative box model, the fractions of the nitrate radical chemistry in each pathway as a function of the measured NO2 mixing ratio are shown in Figure 10. For the purpose of calculating the nitrate radical production and its loss pathways, the box model duration has been extended such that it runs from sunrise to sunset. In each panel of Figure 10, the red points indicate individual box model calculations. The black line shows the median value when binned according to NO2 mixing ratio. In Figure 10a, the integrated nocturnal nitrate radical production is displayed along with a histogram of NO2 mixing ratios. The integrated nitrate radical production depends strongly on the NO2 mixing ratio and reaches a maximum of ~6 ppbv when the NO2 mixing ratio is 25 ppbv. However, typical nitrate radical production is 1–2 ppbv at NO2 concentrations of 4 ppbv. The variation around the median nitrate radical production is due to variation in the ozone concentration. Figures 10b–10d show the fraction of nitrate chemistry in each of the four possible pathways. The largest portion of the nitrate radical chemistry is N2O5 hydrolysis shown in Figure 10c. It typically accounts for 80% of the nitrate radical production at NO2 mixing ratios between 4 and 30 ppbv. At NO2 mixing ratios less than 4 ppbv, the N2O5 hydrolysis fraction drops to 60%. The losses to NO3-VOC reactions (Figure 10b) are typically less than 10% but can be large when the NO2 concentration is low. The fraction of nitrate radical production which results in ClNO2 formation is shown in Figure 10d and is typically less than 10%, although there were a few data points associated with a direct emission of chloride when the ClNO2 yield was larger than 50%. The portion of the NO3 and N2O5 which did not react any further and was photolyzed at sunrise is shown in Figure 10e. This fraction was typically less than 10% at moderate NO2 levels.
 The nocturnal lifetime of NO2 with respect to nitrate radical production depends on the fraction of nitrate radical chemistry proceeding by each pathway, and some of the NO2 loss is returned when nocturnal species are photolyzed at sunrise. The net nocturnal NO2 loss can be quantified by the integrated nitrate radical production and an NO2 loss multiplier, η, defined in equations (3) and (4) using the NO2 removal potential of each pathway in Table 2. In equation (4), the fraction of nitrate radical chemistry in each pathway is represented as F.
 The NO2 loss multiplier has been calculated for each run of the box model calculation and is displayed in Figure 10f. The median is typically greater than 1.7 but drops to 1.4 at low levels of NO2. Some data points are dominated by NO3 reactivity at low levels of NO2 and the NO2 loss multiplier is close to one. If NO2 is recycled via NO3 reaction, either with peroxy radicals or with alkenes, the NO2 loss multiplier could be lower.
6 The Impact of the Nitrate Effect on Nocturnal NO2 Removal
 When the N2O5 uptake coefficient is suppressed by high aerosol nitrate, the effect on the NO2 loss multiplier can be categorized into three cases. First, we consider the case where all of the nocturnal nitrate radical production is consumed by N2O5 hydrolysis and the N2O5 concentration has risen to its steady state level. In this case, the N2O5 loss rate is the same as the nitrate radical production rate (O3 + NO2) and any changes in the N2O5 uptake coefficient are buffered by an increase or decrease in the N2O5 concentration. Reducing the loss rate coefficient (uptake coefficient) will not change the loss rate. Because the steady state N2O5 concentration will be larger, the amount of N2O5 and NO3 photolyzed at sunrise will be similarly larger. The increase in the amount of N2O5 recycled will reduce the NO2 loss multiplier; however, the change in uptake coefficient is buffered by changes in the N2O5 concentration.
 The second case occurs when the NO3 and N2O5 loss rates are competitive and steady state is achieved. When the N2O5 concentration rises due to the decreased uptake coefficient, the NO3 concentration also rises and the fraction of nitrate radical production that is lost through the NO3 reactivity pathway increases. Because NO3 reactivity removes less NO2 than does N2O5 hydrolysis, the NO2 loss multiplier is reduced.
 The third way that a reduced uptake coefficient can affect the NO2 loss rate is by increasing the time taken for the N2O5 and NO3 concentrations to achieve steady state, which reduces the fraction of nitrate radical production going through both the NO3 reactivity and the N2O5 hydrolysis pathways. This effect can be important when the N2O5 lifetime is a few hours but not if it is only a few minutes.
 The box model was used to investigate the impact of the nitrate effect on nocturnal NO2 loss by artificially turning the nitrate effect off and on. This is done by doubling and halving the uptake coefficient in the box model corresponding to the magnitude of the median nitrate effect observed in this analysis.
 The first regime described above is most representative of the NACHTT data set where most of the nitrate radical production is consumed by N2O5 hydrolysis. However, at low NO2 mixing ratios, there are data points where the NO3 reactivity is important or steady state is not achieved. In these cases the nitrate effect can be important.
 The upper panel of Figure 11 shows the NO2 loss multiplier for the cases where the uptake coefficient is increased (red) and decreased (black). The median from the unmodified case is shown in blue. At an NO2 mixing ratio of 5 ppbv, the unmodified NO2 loss multiplier is 1.7. Doubling the uptake coefficient increases the NO2 loss multiplier to 1.8 (i.e., a 6% increase) and halving the uptake coefficient reduces the NO2 loss multiplier to 1.5 (12% decrease). For lower (higher) NO2 mixing ratios, the effect is larger (smaller).
 The middle panel of Figure 11 shows the fractional change in the N2O5 loss rate. When the uptake coefficient is increased/decreased, the loss rate normalized by the unmodified loss rate is shown in black/red. Because changes in the uptake coefficient are buffered by the N2O5 concentration, the median N2O5 loss rate does not change dramatically. The median loss rate is within 10% of the unmodified loss rate except at low NO2 mixing ratios. However, there are data points at low NO2 mixing ratios where the N2O5 loss rate is either halved or doubled. The lower panel of Figure 11 shows the fraction of nitrate radical production which remains as N2O5 and NO3 at sunrise. When NO2 is 5 ppbv, the median recycled fraction is 11%, 7.5%, and 5% for the halved, unmodified, and doubled uptake coefficient, respectively. This calculation would be much more sensitive to a large reduction in γ(N2O5), such as the order of magnitude decreases attributed to organic aerosol during summertime.
7 Daytime NO2 Loss
 The primary daytime sink of NOx is the conversion of NO2 to HNO3 by the reaction of NO2 with the hydroxyl radical (OH), which is photochemically generated.
 Photochemical formation of peroxyacyl nitrates (PAN) [Roberts, 2007] and organic nitrates [Day et al., 2003] also create long-lived nitrogen species and are local or permanent sinks for NOx, especially during winter when thermal dissociation of PAN is slow. Here we only consider the primary daytime pathway and compare with the nighttime loss of NOx that proceeds mainly through NO2 oxidation by O3 and subsequent N2O5 hydrolysis.
 The relative importance of daytime and nighttime mechanisms varies with season. During winter, the short days and cooler temperatures favor nocturnal loss via N2O5 hydrolysis, while longer summer days and higher OH concentrations favor daytime oxidation by OH. Using the retrieved N2O5 uptake coefficients and the daytime hydroxyl radical concentration, the importance of each NO2 removal process can be estimated and compared during the NACHTT study.
 The hydroxyl radical (OH) concentration was measured near the base of the BAO tower 2 m above the ground. The OH measurements were available only during the first half of the field study from 17 February 2011 to 27 February 2011. A diurnal average of OH measurements is shown in Figure 12, where the average daily peak concentration was 2 × 106 molecules/cm3, and the typical daily peak was between 1 and 6 × 106 molecules/cm3. These concentrations are consistent with other midlatitude wintertime measurements in urban environments [Heard et al., 2004; Kanaya et al., 2007; Ren et al., 2006]. In a separate analysis of the OH measurements from the NACHTT field study, S. Kim et al. (The primary and recycling sources of OH during the NACHTT-2011 campaign, submitted to Journal of Geophysical Research: Atmospheres, 2013) found the OH concentration near the ground was influenced by photolysis of HONO near the surface, and in the absence of HONO, the modeled OH concentration would be a factor of 7 lower. HONO has a strong vertical gradient near the ground and could affect the OH concentration up to a height of 50 m (T. C. VandenBoer et al., submitted manuscript, 2013). In the absence of HONO above the surface layer, the OH concentration is likely to have been lower. However, because there is considerable uncertainty in OH concentration above the surface layer where the measurement was made, a range of concentrations is used to calculate the daytime NO2 loss. The average measured concentration at 2 m height (2 × 106 molecules/cm3) is used as the upper end of the range and the modeled OH concentration in the absence of HONO (3 × 105 molecules/cm3) is used as the lower end of the range.
 To estimate the daytime loss of NO2, it is also necessary to consider the influence of NOx on the OH concentration. Our approach is to use the NOx dependence from the Ehhalt and Rohrer  parameterization shown in equation (5). Ehhalt and Rohrer  have parameterized the OH concentration as a function of NO2 mixing ratio, and the photolysis rates of O3 and NO2. Because the parameterization was developed for summertime conditions in Germany with high solar insolation, biogenic VOC emissions, and relative humidity, its absolute value is not applicable to the conditions of NACHTT. However, the parameterization does provide a simplified dependence of both NO2 and photolysis rates, which we take advantage of here by scaling it to match the upper and lower limits of the OH concentration.
 The daytime conversion of NO2 to HNO3 can then be determined by integration over the course of the day and then compared to the nighttime loss of NO2. The nighttime loss of NO2 is shown in Figure 13 as a function of NO2 concentration and colored by the observed O3 mixing ratio. This nighttime loss was calculated using the iterative box model and is the product of the integrated nitrate radical production (Figure 10a) and the NO2 loss multiplier (Figure 10e). The spread in the nocturnal data is primarily due to the variation of the O3 concentration and the subsequent variation in the nitrate radical production rate. The daytime NO2 loss is calculated by integrating the rate of reaction (R8) using the upper and lower limits for the OH concentration. The average NO2 mixing ratio during NACHTT was 5.6 ppbv, and at this NO2 mixing ratio, the lower daytime NO2 loss was 0.6 ppbv while the upper end of the range was 4.5 ppbv. The nocturnal loss ranged from 2.2 to 4.4 ppbv.
 Oxidation of NOx is the main source of nitrate that forms ammonium nitrate aerosol, the primary aerosol component of wintertime urban haze known as the Denver Brown Cloud in this location (Neff ; (F. Öztürk et al., submitted manuscript, 2013); (A. H. Young et al., submitted manuscript, 2013)). If the OH concentration is lower above the surface layer, this analysis suggests nighttime oxidation through N2O5, rather than photochemical conversion through OH, is the primary mechanism for wintertime NO2 oxidation and the subsequent aerosol production.
 During wintertime in a polluted environment, the N2O5 uptake coefficient was determined from ambient measurements using an iterative box model. The retrieval of the uptake coefficient was possible in the wintertime conditions because N2O5 hydrolysis dominated the nitrate radical chemistry and because the strong nocturnal layering isolated the analyzed air masses from nocturnal NO emissions. To perform a similar analysis in the summer, direct measurements of NO3 reactivity and more precise NO measurements would be necessary.
 The range of retrieved uptake coefficients was broadly in agreement with laboratory measurements on synthetic aerosol. However, under conditions of low surface area density and low NO3 reactivity, the retrieved uptake coefficients were significantly larger than laboratory measurements. The discrepancy is possibly due to unmeasured VOC species that would contribute to the NO3 reactivity or contributions by super-micron particles to the surface area density.
 The analysis is consistent with suppression of N2O5 uptake by aerosol nitrate. Vertically resolved measurements sampled several nocturnal layers that had a range of relative humidity, which played a crucial role controlling the amount of water condensed on the aerosol and hence, the aerosol nitrate fraction that determines the magnitude of the uptake coefficient suppression. Aerosol nitrate mass fractions of 30% were observed to suppress the uptake coefficient by a factor of two. The magnitude of the suppression was smaller than that observed on synthetic aerosol by Wahner et al. [1998b] and Bertram and Thornton . The quantitative disagreement between laboratory measurements of the nitrate effect and ambient data could be due to a temperature difference but also reflects the need for more detailed understanding of ambient aerosol composition coincident with the suppressed N2O5 uptake.
 Using the retrieved uptake coefficient, the box model duration was extended to sunrise to examine the nocturnal NO2 loss. During NACHTT, the average NO2 mixing ratio was 5.6 ppbv. At this level, N2O5 hydrolysis typically accounted for 77% of nitrate radical chemistry and for each nitrate radical produced 1.7 NO2 molecules were removed from the atmosphere. At sunrise, ~13% of the nitrate radical production was in the form of NO3, N2O5, or ClNO2, and reformed NO2 as the nocturnal species was photolyzed during the morning.
Appendix A: Iterative Box Model
 The measured concentration of N2O5 can be directly predicted using a box model only if the N2O5 loss rate coefficient is known. However, if the box model is sufficiently constrained such that the N2O5 loss rate coefficient is the only adjustable parameter, then the value of the loss rate coefficient can be adjusted iteratively until the N2O5 concentrations matches the measured concentration.
 The box model used above includes five reactions describing the production and loss of NO3 and N2O5 ((R9)–(R13)). The rate constants for the first three reactions ((R9)–(R11)) are known, and the recommended rate constants from National Aeronautics and Space Administration-Jet Propulsion Laboratory are used here [Sander et al., 2011]. The loss rate coefficient for NO3 reactions with VOCs (R12) is determined from ambient measurements of VOC and laboratory-measured rate coefficients. The N2O5 loss rate coefficient (R13) is determined by iterating the box model.
 A coupled set of four differential equations (A5)–(A6) describes the time evolution of each of the four species in reactions (R9)–(R13)).
 Because cycling between NO3 and N2O5 is fast and is established quickly in high NOx conditions, one differential equation can be eliminated by assuming NO3 and N2O5 are in equilibrium [Brown et al., 2003]. This also allows for a larger time step to be used in the box model. With the assumption of equilibrium, NO3 and N2O5 can be represented by a single variable, nocturnal nitrogen, NN, such that [NN] = [N2O5] + [NO3]. The equilibrium constant (Keq) can then be used to calculate the concentrations of each species (A5)–(A6).
 The differential equations for NO3 and N2O5 are then combined into a single equation (A7) and the terms describing the equilibrium cycling cancel.
 Nominally, the assumption of equilibrium between NO3 and N2O5 also simplifies the differential equation for NO2(A2), where the second and third terms cancel. However, here the assumption of equilibrium leads to an error which accumulates as the equations are integrated. For each molecule of NO3 that is produced and lost through NO3 reactions with VOCs, one molecule of NO2 is lost. However, for each molecule of N2O5 lost through heterogeneous chemistry, two molecules of NO2 are lost. The loss of an additional molecule of NO2 is accounted for by a small difference in the second and third terms of equation (A3). This difference can be accounted for by assuming the difference between the terms is proportional to the nitrate radical production and that proportionality constant s is constant in time (A8).
 This physical meaning of s is the ratio of nitrate radical production which goes through N2O5 (either as N2O5 or lost through uptake) to the total nitrate radical production. Using equation (A4), the difference can be expressed in terms of N2O5.
 To determine the value of the proportionality constant s, equation (A9) is integrated from start of the box model to an arbitrary time t2.
 Because s is constant the respect to time, it can be pulled out of the integral. Then, equation (A10) can be solved for s and the cumulative nitrate radical production in the denominator can be replaced by the cumulative loss of O3.
 This definition of s intuitively makes sense as the ratio of the N2O5 concentration plus cumulative N2O5 lost to the cumulative nitrate radical production. It varies between 0 and 1 according to the amount of NO3 or N2O5 chemistry. Even though it has explicit time dependence stated in equation (A11), it is averaged over from the start of the box model to time t2. After making these simplifications, the box model consists of three differential equations (A12), (A13), (A14).
 Because the final concentrations are known it would be convenient to integrate these equations backward in time and iterate the N2O5 loss rate coefficient until the N2O5 concentration was zero at sunset. However, because the ambient N2O5 concentration could be in steady state, several different start times would yield the same final N2O5 concentration and it is unlikely the iterations would converge.
 An alternate method of integrating these equations is to do it in two steps. First, the equations for O3 and NO2 are integrated backward in time to sunset. Then, the equation for nocturnal nitrogen can be integrated forward from sunset until the time of the measurements starting with an N2O5 concentration of zero at sunset. The box model will then predict a final N2O5 concentration. The N2O5 loss rate coefficient can then be iterated until the predicted N2O5 concentration matches the measured concentration.
 The model depends on the N2O5 loss rate coefficient in two places: in the equations for nocturnal nitrogen (A14) and a weaker dependence in s(t) (A11). To help the model converge to a solution, the loss rate coefficient is varied in two steps. Initially, s(t) is taken to be 1, and the O3(t) and NO2(t) are calculated backward in time. Then, the nocturnal nitrogen is calculated and loss rate coefficient is adjusted until the final N2O5 concentration is matched. Then, a new s(t), O3(t), and NO2(t) are calculated using equation (A11) and N2O5 concentrations from the previous iteration. The process is continued until loss rate coefficient changes less than 1%. If the number of iterations of the first step exceeds 30 or the second step exceeds 10, the calculation is stopped and the datum is marked as nonconvergent. Typically, the calculation converges in with 5 iterations in the first step and 3 in the second step. The average time taken depends on the initial guess, the duration of the calculation, and the time step used. For the NACHTT data set, this calculation was implemented using the Igor Pro data analysis software package. The calculation took ~5 ms for each hour of duration on a notebook computer using a time step of 30 s and an initial guess of 10−5 for the N2O5 loss rate. The script used for this calculation is included in the supporting information.
 One complication of using the iterative box model is the possibility that there are multiple solutions or more than one loss rate coefficient that produces the same final N2O5 concentration. This possibility was investigated numerically for loss rate coefficients between 10−7 s−1 and 1 s−1, and multiple roots were not found.
 For some input conditions, the iterative box model will return a negative N2O5 loss rate coefficient. This nonphysical result means the nitrate radical production rate and/or reaction time is not large enough to produce the final N2O5 concentration. This situation frequency occurs when calculating uncertainties. Either the lower limit of the reaction duration or the upper limit NO3 reactivity is used, and a negative N2O5 loss rate is required to produce the final N2O5 concentration. In this case, the iterative box model is considered to have not converged, or if the error bars are being calculated, a value of zero is used for the lower limit of the loss rate coefficient.
 This method of retrieving the N2O5 loss rate coefficient was checked by using the full differential equations for the box model (A1)–(A4). The final concentrations were then fed into the iterative box model and N2O5 loss rate coefficient retrieved. An example of the iterative box model is shown in Figure A1. The upper panel shows the value of the loss rate coefficient for each iteration. The middle and lower panels show the NO2 and N2O5 mixing ratios as a function of reaction duration for each iteration and for the box model using the full differential equations. In this case the losses are dominated by N2O5, and s(t) (A11) is nearly equal to one, which is close to the initial guess. Because s(t) does not change much between the initial guess and the final iteration, the NO2 mixing ratios do not change much with each iteration. However, the N2O5 mixing ratio does change significantly as the model converges. For these conditions, the box model converged in 9 iterations.
 The accuracy of the iterative box model was tested over a range of initial conditions. The reaction duration, N2O5 loss rate coefficient, initial NO2, and temperature were varied. Then, loss rate coefficient was retrieved using the iterative box model. A comparison of the results is shown in Figure A2. Except for initial NO2 mixing ratios less than 100 ppt, the retrieval was accurate to better that 1%. Because the change in the loss rate coefficient must only be less the 1% for the retrieval to stop iterating, this level of agreement is expected. For small mixing ratios of NO2, cycling between NO3 and N2O5 takes a long time to establish equilibrium and the assumption of equilibrium used in the retrieval is not valid. Therefore, the disagreement at low NO2 mixing ratio is expected.
 We would like to thank everyone who helped make NACHTT possible and specifically Gerd Hübler, Dan Wolfe, Bruce Bertram, and Eric Williams for organizing site logistics and the elevator operation. This work is supported by the NOAA's Health of the Atmosphere Program and Atmospheric Chemistry, Carbon Cycles, and Climate Program.