Among the numerous BVOC emitted into the troposphere, kinetic data for NO3 oxidation have been provided for more than 40 compounds. The most emitted/important BVOC have been subject to several kinetic studies, using both absolute and relative methods, which are evaluated to determine rate constants by IUPAC (Table 1). This is the case for isoprene, α-pinene, β-pinene, and 2-methyl-3-buten-2-ol (MBO). However, for isoprene, β-pinene, and MBO, rate constants obtained by different studies range over a factor of 2. For some other terpenes, only few kinetic studies have been carried out, with at least one absolute rate determination. This is the case for sabinene, 2-carene, camphene, d-limonene, α-phellandrene, myrcene, γ-terpinene, and terpinolene. For these compounds, experimental data agree within 30–40 %, except α-phellandrene and terpinolene for which discrepancies are larger. For other BVOC, including other terpenes, sesquiterpenes, and oxygenated species, rate constants are mostly based on a single determination and highly uncertain. For these compounds, further rate constant determinations and end-product measurements are essential to better evaluate the role of NO3 in their degradation. The ability to predict the NO3-BVOC rate constants using structure–activity relationships (SARs) has been improved. A recent study (Kerdouci et al., 2010; Kerdouci, 2014) presented a new SAR parameterization based on 180 NO3-VOC reactions. The method is capable of predicting 90 % of the rate constants within a factor of 2.

In general, NO3 reacts with unsaturated VOC by addition to a double bond (Wayne et al., 1991), though hydrogen abstraction may occur, most favorably for aldehydic species (Zhang and Morris, 2015). The location and likelihood of the NO3 addition to a double bond depends on the substitution on each end of the double bond, with the favored NO3 addition position being the one resulting in the most substituted carbon radical. In both cases, molecular oxygen adds to the resulting radical to form a peroxy radical (RO2). For example, the major RO2 isomers produced from isoprene and β-pinene oxidation via NO3 are shown in Fig. 2. The RO2 distribution for isoprene oxidation by OH has been shown to be dependent on the RO2 lifetime (Peeters et al., 2009, 2014), but no similar theoretical studies have been conducted on the NO3 system. Schwantes et al. (2015) determined the RO2 isomer distribution at an RO2 lifetime of ∼ 30 s for isoprene oxidation via NO3. More theoretical and experimental studies are needed to understand the influence of RO2 lifetime, which is long at night (∼ 50–200 s for isoprene; Schwantes et al., 2015), on the RO2 isomer distribution, as this distribution influences the formation of all subsequent products (Fig. 2).

The fate of RO2 determines the subsequent chemistry. During the nighttime in the ambient atmosphere, RO2 will isomerize or react with another RO2, NO3, or HO2. In order to monitor RO2 isomerization reaction products, RO2 lifetimes must be long in laboratory studies similar to the ambient atmosphere (e.g., Peeters et al., 2009; Crounse et al., 2011). The NO3 plus BVOC (NO3+ BVOC) reaction can be a source of nighttime HO2 and OH radicals (Platt et al., 1990). Reaction with NO is a minor peroxy radical fate at night (Pye et al., 2015; Xiong et al., 2015). Few laboratory studies have contrasted the fates of RO2 and their impacts on gas-phase oxidation and aerosol formation (Ng et al., 2008; Boyd et al., 2015; Schwantes et al., 2015). Boyd et al. (2015) examined how RO2 fate influences SOA formation and yields, and studied the competition between the RO2-NO3 and RO2-HO2 channels for β-pinene. Boyd et al. (2015) determined that the SOA yields for both channels are comparable, indicating that the volatility distribution of products may not be very different for the different RO2 fates. In contrast, the results from NO3 oxidation of smaller BVOC, such as isoprene, show large differences in SOA yields depending on the RO2 fate (Ng et al., 2008), with larger SOA yields for second-generation NO3 oxidation (Rollins et al., 2009).

The well-established gas-phase first-generation products from the major β- and δ-RO2 isomers formed from isoprene oxidation are shown in Fig. 2 (adapted from Schwantes et al., 2015). Some of the products are common between all the pathways, such as methyl vinyl ketone for the dominant β-RO2 isomer. However, some products are unique to only one channel (e.g., hydroxy nitrates form from RO2-RO2 reactions and nitrooxy hydroperoxides form from RO2-HO2 reactions). In this case, the overall nitrate yield and the specific nitrates formed from isoprene depend on the initial RO2 isomer distribution and the fate of the RO2. Furthermore, the distribution of gas-phase products will then influence the formation of SOA. For isoprene, the SOA yields from RO2-RO2 reactions are ∼ 2 times greater than the yield from RO2-NO3 reactions (Ng et al., 2008). The less well-established first-generation products from β-pinene oxidation are also shown in Fig. 2 (adapted from Boyd et al., 2015). There are still lingering uncertainties (shown in red) in the first-generation products formed from β-pinene oxidation. The product yields from the RO2+ HO2 channel are not well constrained, largely due to the unavailability of authentic standards. In Fig. 2, a carbonyl product is assumed to form directly from the RO2 + HO2 reaction instead of proceeding through an alkoxy intermediate consistent with theoretical calculations from different compounds (Hou et al., 2005a, b; Praske et al., 2015). This is also uncertain, as few theoretical studies have been conducted on large molecules like β-pinene. The identification of the carbonyl compound(s) produced from RO2 reaction with NO3, RO2, or HO2 is unknown. Hallquist et al. (1999) detected a low molar yield (0–2 %; Table 2) of nopinone from β-pinene NO3 oxidation. Further laboratory studies identifying other carbonyl products are recommended.

Given the limited number of studies that have considered the fate of the peroxy radical, generalizations cannot yet be made for all VOC. Indeed, more studies are needed to determine systematically how gas-phase products and SOA yields are influenced by reactions of RO2. More specifically, for all chamber experiments, constraining the fate and lifetime of RO2 is required to attribute product and SOA yields to a specific pathway. As shown in Table 2 in Sect. 2.2, the nitrate yields and SOA yields for NO3-induced degradation of many VOC vary significantly between different studies. This is likely, in part, a result of each experiment having a different distribution of RO2 fates, but may also arise from vapor wall losses.

In general, there are very few mechanistic studies for NO3 relative to other oxidants. Furthermore, the elucidation of mechanisms is limited by the fact that most studies provide overall yields of organic nitrates (without individual identification of the species) and/or identification (without quantification) due to the lack of standards.

For some particle-phase organics, the reaction with NO3 is at least as important as other atmospheric oxidants such as O3 and OH (Shiraiwa et al., 2009; Kaiser et al., 2011). The lifetime (τ) of a single component, liquid organic particle with respect to loss by reaction with NO3 at concentration [NO3] is partially governed by the uptake coefficient (γ) (Robinson et al., 2006; Gross et al., 2009): τliquid=2ρorgNADp3Morgc¯γ[NO3], where Dp is the particle diameter, ρorg and Morg are the density and molecular weight of the organic component, respectively, c¯ is the mean molecular velocity of gas-phase NO3, and NA is Avogadro number. Thus, defined, τ is the time required for all the organic molecules in a spherical (i.e., liquid) particle to undergo a single reaction with NO3.

Recent studies have shown that organic aerosols can adopt semi-solid (highly viscous) or amorphous solid (crystalline or glass) phase states, depending on the composition and ambient conditions (Virtanen et al., 2010; Koop et al., 2011; Renbaum-Wolff et al., 2013). Typically, the bulk phase diffusion coefficients of NO3 are ∼ 10-7–10-9 cm2 s-1 in semi-solid and ∼ 10-10 cm2 s-1 in solids (Shiraiwa et al., 2011). Slow bulk diffusion of NO3 in a viscous organic matrix can effectively limit the rate of uptake (Xiao and Bertram, 2011; Shiraiwa et al., 2012). Similarly, the solubility may be different in a concentrated, organic medium. If bulk diffusion is slow, the reaction may be confined to the near-surface layers of the particle or bulk substrate. The presence of organic coatings on aqueous aerosols was found to suppress heterogeneous N2O5 hydrolysis by providing a barrier through which N2O5 needs to diffuse to undergo hydrolysis (Alvarado et al., 1998; Cosman et al., 2008; Grifiths et al., 2009). Reactive uptake by organic aerosols is expected to exhibit a pronounced decrease at low RH and temperature, owing to a phase transition from viscous liquid to semi-solid or amorphous solid (Arangio et al., 2015). Therefore, the presence of a semi-solid matrix may effectively shield reactive organic compounds from chemical degradation in long-range transport in the free troposphere.

To get an estimate of the processing rate of BVOC-derived SOA, we have summarized the results of several laboratory studies to provide a rough guide to NO3 reactivity on different classes of organics that may be present in SOA (Fig. 3). A rough estimate of the reactivity of NO3 to freshly generated, isoprenoid-derived SOA, which still contains organics with double bonds (e.g., from diolefinic monoterpenes such as limonene), may be obtained by considering the data on alkenes and unsaturated acids, where the uptake coefficient is generally close to 0.1.

The classes of organics for which heterogeneous reactions with NO3 have been examined are alkanoic/alkenoic acids, alkanes and alkenes, alcohols, aldehydes, polyaromatic hydrocarbons (PAHs), and secondary organic aerosols. Laboratory studies have used either pure organic substrates, with the organic of interest internally mixed in an aqueous particle; as a surface coating, with the reactive organic mixed in a nonreactive organic matrix; or in the form of self-assembling monolayers. The surrogate surface may be available as a macroscopic bulk liquid (or frozen liquid) or in particulate form and both gas-phase and particle-phase analyses have been used to derive kinetic parameters and investigate products formed.

In the gas phase, the NO3 radical reacts slowly (by H-abstraction) with alkanes, more rapidly with aldehydes due to the weaker C-H bond of the carbonyl group, and most readily with alkenes and aromatics via electrophilic addition. This trend in reactivity is also observed in the condensed-phase reactions of NO3 with organics so that long-chain organics, for which non-sterically hindered addition to a double bond is possible, and aromatics are the most reactive. In very general terms, uptake coefficients are in the range of 1–10 × 10-3 for alkanes, alcohols, and acids without double bonds, 2–200 × 10-3 for alkenes with varying numbers of double bonds, 3–1000 × 10-3 for acids with double bonds again depending on the number of double bonds, and 100–500 × 10-3 for aromatics. These trends are illustrated in Fig. 3 which plots the experimental data for the uptake of NO3 to single-component organic surfaces belonging to different classes of condensable organics. Condensed-phase organic nitrates have been frequently observed following interaction of NO3 with organic surfaces (see below).

Uptake of NO3 to saturated hydrocarbons is relatively slow, with uptake coefficients close to 10-3. Moise et al. (2002) found that (for a solid sample) uptake to a branched-chain alkane was more efficient than for a straight-chain alkane, which is consistent with known trends in gas-phase reactivity of NO3. The slow surface reaction with alkanes enables both surface and bulk components of the reaction to operate in parallel. The observation of RONO2 as product is explained (Knopf et al., 2006; Gross and Bertram, 2009) by processes similar to those proceeding in the gas phase, i.e., abstraction followed by formation of peroxy and alkoxy intermediates which react with NO2 and NO3 to form the organic nitrate.

With exception of the data of Moise et al. (2002), the uptake of NO3 to an unsaturated organic surface is found to be much more efficient than to the saturated analogue. The NO3 uptake coefficient for, e.g., squalene, is at least an order of magnitude more efficient than for squalane (Xiao and Bertram, 2011; Lee et al., 2013). The location of the double bond is also important and the larger value for γ found for a self-assembling monolayer of NO3+ undec-10-ene-1-thiol compared to liquid, long-chain alkenes is due to the fact that the terminal double bond is located at the interface and is thus more accessible for a gas-phase reactant (Gross and Bertram, 2009). NO3 uptake to mixtures of unsaturated methyl oleate in a matrix of saturated organic was found to be consistent with either a surface or bulk reaction (Xiao and Bertram, 2011). The formation of condensed-phase organic nitrates and simultaneous loss of the vinyl group indicates that the reaction proceeds, as in the gas phase, by addition of NO3 to the double bond followed by reaction of NO3 (or NO2) with the resulting alkyl and peroxy radicals formed (Zhang et al., 2014b).

Consistent with reactivity trends for NO3 in the gas phase, the weakening of some C-H bonds in oxidized, saturated organics results in a more efficient interaction of NO3 than for the non-oxidized counterparts although, as far as the limited dataset allows trends to be deduced, the gas-phase reactivity trend of polyalcohol being greater than alkanoate appears to be reversed in the liquid phase (Gross et al., 2009). For multicomponent liquid particles, the uptake coefficient will also depend on the particle viscosity (Iannone et al., 2011) though it has not been clearly established if the reaction proceeds predominantly at the surface or throughout the particle (Iannone et al., 2011). The reaction products are expected to be formed via similar pathways as seen in the gas phase, i.e., abstraction of the aldehydic-H atom for aldehydes and abstraction of an H atom from either the O-H or adjacent α-CH2 group for alcohols prior to reaction of NO2 and NO3 with the ensuing alkyl and peroxy radicals (Zhang and Morris, 2015).

The efficiency of uptake of NO3 to unsaturated acids is comparable to that found with other oxidized, saturated organics (Moise et al., 2002) suggesting that the reaction proceeds, as in the gas phase, via abstraction rather than addition. Significantly larger uptake coefficients have been observed for a range of unsaturated, long-chain acids, with γ often between 0.1 and 1 (Gross et al., 2009; Knopf et al., 2011; Zhao et al., 2011a). γ depends on the number and position (steric factors) of the double bond. For example, the uptake coefficient for abietic acid is a factor of 100 lower than for linoleic acid (Knopf et al., 2011). The condensed-phase products formed in the interaction of NO3 with unsaturated acids are substituted carboxylic acids, including hydroxy nitrates, carbonyl nitrates, dinitrates, and hydroxy dinitrates (Hung et al., 2005; Docherty and Ziemann, 2006; McNeill et al., 2007; Zhao et al., 2011a).

The interaction of NO3 with condensed-phase aromatics and PAHs results in the formation of a large number of nitrated aromatics and nitro PAHs. Similar to the gas-phase mechanism, the reaction is initiated by addition of NO3 to the aromatic ring, followed by breaking of an N-O bond to release NO2 to the gas phase and forming a nitrooxy-cyclohexadienyl-type radical which can further react with O2, NO2, or undergo internal rearrangement to form hydroxyl species (Gross and Bertram, 2008; Lu et al., 2011). The uptake coefficients are large and comparable to those derived for the unsaturated fatty acids.

The literature results on the interaction of NO3 with organic substrates are tabulated in Table S1 in the Supplement, in which the uptake coefficient is listed (if available) along with the observed condensed- and gas-phase products.

The in situ formation of NO3 (e.g., electron transfer reactions between nitrate anions and other aqueous radical anions such as SOx-, sulfur-containing radical anions, or Cl2-) is generally of minor importance and the presence of NO3 in aqueous particles is largely a result of transfer from the gas phase (Herrmann et al., 2005; Tilgner et al., 2013). Concentrations of NO3 in tropospheric aqueous solutions cannot be measured in situ, and literature values are based on multiphase model predictions (Herrmann et al., 2010). Model studies with the chemical aqueous-phase radical mechanism (CAPRAM; Herrmann et al., 2005; Tilgner et al., 2013) predict [NO3] between 1 × 6 × 10-16 and 2.7 × 10-13 mol L-1. High NO3 concentration levels are associated with urban clouds, while in rural and marine clouds these levels are an order of magnitude lower. Since the NO3 concentrations are related to the NOx budget, typically higher NO3 concentrations are present under urban cloud conditions compared to rural and marine cloud regimes.

NO3 radicals react with dissolved organic species via three different pathways: (i) by H-atom abstraction from saturated organic compounds, (ii) by electrophilic addition to double bonds within unsaturated organic compounds, and (iii) by electron transfer from dissociated organic acids (Huie, 1994; Herrmann and Zellner, 1998). For a detailed overview on aqueous-phase NO3 radical kinetics, the reader is referred to several recent summaries (Neta et al., 1988; Herrmann and Zellner, 1998; Ross et al., 1998; Herrmann, 2003; Herrmann et al., 2010, 2015). Compared to the highly reactive and non-selective OH radical, the NO3 radical is characterized by a lower reactivity and represents a more selective aqueous-phase oxidant. The available kinetic data indicate that the reactivity of NO3 radicals with organic compounds in comparison to the two other key radicals (OH, SO4-) is as follows: OH > SO4- ≫ NO3 (Herrmann et al., 2015).

In Table S2, we list kinetic parameters for reaction of NO3 with aliphatic organic compounds as presently incorporated in the CAPRAM database (Bräuer et al., 2017). Typical ranges of rate constants (in M-1 s-1) for reactions of NO3 in the aqueous phase are 106–107 for saturated alcohols, carbonyls, and sugars; 104–106 for protonated aliphatic mono- and dicarboxylic acids, with higher values for oxygenated acids; 106–108 for deprotonated aliphatic mono- and dicarboxylic acids (higher values typically for oxygenated acids); 107–109 for unsaturated aliphatic compounds; and 108–2 × 109 for aromatic compounds (without nitro/acid functionality). The somewhat larger rate constants for deprotonated aliphatic mono- and dicarboxylic acids, unsaturated aliphatic compounds and aromatic compounds is related to the occurrence of electron transfer reactions and addition reaction pathways, which are often faster than H-abstraction reactions.

Many aqueous-phase NO3 reaction rate constants, even for small oxygenated organic compounds, are not available in the literature and have to be estimated. In the absence of SARs for NO3 radical reactions with organic compounds, Evans–Polanyi-type reactivity correlations are used to predict kinetic data for H-abstraction NO3 radical reactions. The latest correlation for NO3 reactions in aqueous solution based on 38 H-abstraction reactions of aliphatic alcohols, carbonyl compounds and carboxylic acids was published by Hoffmann et al. (2009): log⁡(kH)=(39.9±5.4)-(0.087±0.014)×BDE, where BDE is the bond dissociation energy (in kJ mol-1). The correlation is quite tight, with a correlation coefficient of R=0.9.

A direct comparison of the aqueous-phase OH and NO3 radical rate constants (k298K) of organic compounds from different compound classes is presented in Fig. 4, which shows that the NO3 radical reaction rate constants for many organic compounds are about 2 orders of magnitude smaller than respective OH rate constants. In contrast, deprotonated dicarboxylic acids can react with NO3 via electron transfer and have similar rate constants for OH reaction. Rate constants for OH and NO3 with alcohols and diols/polyols are well correlated (R2 values are given in Table S3), whereas those rate constants for carbonyl compounds and diacids have a lower degree of correlation.

Figure 4b shows a comparison of the modeled chemical turnovers of reactions of organic compounds with OH versus NO3 radicals distinguished for different compound classes. The simulations were performed with the SPACCIM model (Wolke et al., 2005) for the urban summer CAPRAM scenario (see Tilgner et al., 2013 for details) using the master chemical mechanism (MCM) 3.2/CAPRAM 4.0 mechanism (Rickard, 2015; Bräuer et al., 2017) which has in total 862 NO3 radical reactions with organic compounds.

Most of the data lie under the 1:1 line, indicating that, for most of the organic compounds considered, chemical degradation by OH is more important than by NO3, with a significant fraction of the data lying close to a 10:1 line, though OH fluxes sometimes exceed NO3 fluxes by a factor of 103-104. Approximate relative flux ratios (NO3 / OH) for different classes of organic are 10-1-10-2 for alcohols (including diols and polyols) and carbonyl compounds, 10-1-10-4 for undissociated monoacids and diacids, ∼ 1 (or larger) for dissociated monoacids, 10-2-> 10 for dissociated diacids, and 10-2-1 for organic nitrates. For carboxylate ions, NO3-initiated electron transfer is thus the dominant oxidation pathway. As OH-initiated oxidation proceeds via an H-abstraction, high NO3-OH flux ratios can be observed for carboxylate ions but not for protonated carboxylic acids.

Overall, Fig. 4b shows that, over a 4-day summer cycle, NO3 radical reactions can compete with OH radical reactions in particular for protonated carboxylic acids and multifunctional compounds. Nevertheless, aqueous NO3 radical reactions with organics will become more important during winter or at higher latitudes, where photochemistry as the main source of OH is less important. Finally, it should be noted that NO3 aqueous-phase nighttime chemistry will influence the concentration levels of many aqueous-phase reactants available for reaction during the next day.

Optical absorption spectroscopy has been the primary measurement technique for NO3. It usually makes use of two prominent absorption features of NO3 near 623 and 662 nm. Note that the dissociation limit of the NO3 molecule lies between the two absorption lines (Johnston et al., 1996); thus, illumination by measurement radiation at the longer wavelength band does not lead to photolysis of NO3. The room temperature absorption cross section of NO3 at 662 nm is ∼ 2 × 10-17 cm2 molec-1 and increases at lower temperature (Yokelson et al., 1994; Osthoff et al., 2007). Thus, at a typical minimum detectable optical density (reduction of the intensity compared to no absorption) and a light-path length of 5 km, a detection limit of 107 molec cm-3 or ∼ 0.4 ppt (under standard conditions) is achieved.

Initial measurements of NO3 in the atmosphere were long-path averages using light paths between either the sun or the moon (e.g., Noxon et al., 1978) and the receiving spectrometer (also called passive techniques because natural light sources were used) or between an artificial light source and spectrometer over a distance of several kilometers (active techniques; e.g., Platt et al., 1980). Passive techniques were later extended to yield NO3 vertical profiles (e.g., Weaver et al., 1996). In recent years, resonator cavity techniques allowed construction of very compact instruments capable of performing in situ measurements of NO3 with absorption spectroscopy (see in situ measurement techniques below).

An important distinction between the techniques is whether NO3 can be deliberately or inadvertently removed from the absorption path as part of the observing strategy. Long-path absorption spectroscopy does not allow control over the sample for obtaining a zero background by removing NO3 (Category 1). Resonator techniques (at least as long as the resonator is encased) allow deliberate removal of NO3 from the absorption path as part of the measurement sequence and may also result in inadvertent removal during sampling (Category 2).

For instruments of Category 1, the intensity without absorber (I0) cannot be easily detected. Therefore, the information about the absorption due to NO3 (and any other trace gas) has to be determined from the structure of the absorption, which is usually done by using differential optical absorption spectroscopy (DOAS) (Platt and Stutz, 2008), which relies on the characteristic fingerprint of the NO3 absorption structure in a finite wavelength range (about several 10 nm wide). Thus, a spectrometer of sufficient spectral range and resolution (around 0.5 nm) is required.

Instruments of Category 2 can determine the NO3 concentration from the difference (or rather log of the ratio) of the intensity with and without NO3 in the measurement volume. In this case, only an intensity measurement at a single wavelength (typically of a laser) is necessary, and specificity can be achieved through chemical titration with NO (Brown et al., 2001). However, enhanced specificity without chemical titration can be gained by combining resonator techniques with DOAS detection. It should be noted that the advantage of a closed cavity to be able to remove (or manipulate) NO3 comes at the expense of potential wall losses, which have to be characterized. Such instruments have the advantage of being able to also detect N2O5, which is in thermal equilibrium with NO3 and can be quantitatively converted to NO3 by thermal dissociation (Brown et al., 2001, 2002).

Another complication arises from the presence of water vapor and oxygen lines in the wavelength range of strong NO3 absorptions. To compensate for these potential interferences in open-path measurements (where NO3 cannot easily be removed), daytime measurements are frequently used as reference because NO3 levels are typically very low (but not necessarily negligibly low) (Geyer et al., 2003). Thus, a good fraction of the reported NO3 data (in particular, older data) represents day–night differences.

Measurements of the NO3 absorption structure using sunlight take advantage of the fact that NO3 is very quickly photolyzed by sunlight (around 5 s lifetime during the day) allowing for vertically resolved measurements during twilight (e.g., Aliwell and Jones, 1998; Allan et al., 2002; Coe et al., 2002; von Friedeburg et al., 2002). The fact that the NO3 concentration is nearly zero due to rapid photolysis in the directly sunlit atmosphere, while it is largely undisturbed in a shadowed area, can be used to determine NO3 vertical concentration profiles during sunrise using the moon as a light source (Smith and Solomon, 1990; Smith et al., 1993; Weaver et al., 1996). Alternatively, the time series of the NO3 column density derived from scattered sunlight originating from the zenith (or from a viewing direction away from the sun) during sunrise can be evaluated to yield NO3 vertical profiles (Allan et al., 2002; Coe et al., 2002; von Friedeburg et al., 2002).

Nighttime NO3 total column data have been derived by spectroscopy of moonlight and starlight (Naudet et al., 1981), the intensity of which is about 4–5 orders of magnitude lower than that of sunlight. Thus, photolysis of NO3 by moonlight is negligible. A series of moonlight NO3 measurements have been reported (Noxon et al., 1980; Noxon, 1983; Sanders et al., 1987; Solomon et al., 1989, 1993; Aliwell and Jones, 1996a, b; Wagner et al., 2000). These measurements yield total column data of NO3, the sum of tropospheric and stratospheric partial columns. Separation between stratospheric and tropospheric NO3 can be accomplished (to some extent) by the Langley plot method (Noxon et al., 1980), which takes advantage of the different dependence of tropospheric and stratospheric NO3 slant column density on the lunar zenith angle.

A large number of NO3 measurements have been made using the active long-path DOAS technique (Platt et al., 1980, 1981, 1984; Pitts et al., 1984; Heintz et al., 1996; Allan et al., 2000; Martinez et al., 2000; Geyer et al., 2001a, b, 2003; Gölz et al., 2001; Stutz et al., 2002, 2004, 2010; Asaf et al., 2009; McLaren et al., 2010; Crowley et al., 2011; Sobanski et al., 2016). Here, a searchlight-type light source is used to transmit a beam of light across a kilometer-long light path in the open atmosphere to a receiving telescope–spectrometer combination. The light source typically is a broadband thermal radiator (incandescent lamp, Xe arc lamp, laser-driven light source). More recently, LED light sources were also used (Kern et al., 2006). The telescope (around 0.2 m diameter) collects the radiation and transmits it, usually through an optical fiber, into the spectrometer, which produces the absorption spectrum. Modern instruments now almost exclusively use transmitter/receiver combinations at one end of the light path and retro-reflector arrays (e.g., cat-eye-like optical devices) at the other end. The great advantage of this approach is that power and optical adjustment is only required at one end of the light path while the other end (with the retro-reflector array) is fixed. In this way, several retro-reflector arrays, for instance, mounted at different altitudes, can be used sequentially with the same transmitter/receiver unit allowing determination of vertical profiles of NO3 (and other species measurable by DOAS) (Stutz et al., 2002, 2004, 2010).

Cavity ring-down spectroscopy (CRDS) and cavity-enhanced absorption spectroscopy (CEAS) are related techniques for in situ quantification of atmospheric trace gases such as NO3. These methods are characterized by high sensitivity, specificity, and acquisition speed (Table 3a), and they allow for spatially resolved measurements on mobile platforms.

In CRDS, laser light is “trapped” in a high-finesse stable optical cavity, which usually consists of a pair of highly reflective spherical mirrors in a near-confocal arrangement. The concentrations of the optical absorbers present within the resonator are derived from the Beer–Lambert law and the rate of light leaking from the cavity after the input beam has been switched off (O'Keefe and Deacon, 1988). CRDS instruments are inherently sensitive as they achieve long effective optical absorption paths (up to, or in some cases exceeding, 100 km) as the light decay is monitored for several 100 µs, and the absorption measurement is not affected by laser intensity fluctuations. For detection of NO3 at 662 nm, pulsed laser sources such as Nd:YAG pumped dye lasers have been used because of the relative ease of coupling the laser beam to the optical cavity (Brown et al., 2002, 2003; Dubé et al., 2006). Relatively lower cost continuous-wave (cw) diode laser modules that are easily modulated also have been popular choices (e.g., King et al., 2000; Simpson, 2003; Ayers et al., 2005; Odame-Ankrah and Osthoff, 2011; Wagner et al., 2011).

In a CEAS instrument (also referred to as integrated cavity output spectroscopy, ICOS, or cavity-enhanced DOAS, CE-DOAS), the spectrum transmitted through a high-finesse optical cavity is recorded. Mixing ratios of the absorbing gases are derived using spectral retrieval routines similar to those used for open-path DOAS (e.g., O'Keefe, 1998, 1999; Ball et al., 2001; Fiedler et al., 2003; Platt et al., 2009; Schuster et al., 2009).

CRDS and CEAS are, in principle, absolute measurement techniques and do not need to rely on external calibration. In practice, however, chemical losses can occur on the inner walls of the inlet (even when constructed from inert materials such as Teflon) or at the aerosol filters necessary for CRDS instruments. Hence, the inlet transmission efficiencies have to be monitored for measurements to be accurate (Fuchs et al., 2008, 2012; Odame-Ankrah and Osthoff, 2011). On the other hand, a key advantage of in situ instruments over open-path instruments is that the sampled air can be manipulated. Deliberate addition of excess NO to the instrument's inlet titrates NO3 and allows measurement of the instrument's zero level and separation of contributions to optical extinction from other species, such as NO2, O3, and H2O. Adding a heated section to the inlet (usually in a second detection channel) enables (parallel) detection of N2O5 via the increase in the NO3 signal (Brown et al., 2001; Simpson, 2003).

In addition, non-optical techniques have been used to detect and quantify NO3. Chemical ionization mass spectrometry (CIMS) is a powerful method for sensitive, selective, and fast quantification of a variety of atmospheric trace gases (Huey, 2007). NO3 is readily detected after reaction with iodide reagent ion as the nitrate anion at m/z 62; at this mass, however, there are several known interferences, including dissociative generation from N2O5, HNO3, and HO2NO2 (Slusher et al., 2004; Abida et al., 2011; Wang et al., 2014). There has been more success with the quantification of N2O5, usually as the iodide cluster ion at m/z 235 (Kercher et al., 2009), though accurate N2O5 measurement at m/z 62 has been reported from recent aircraft measurements with a large N2O5 signal (Le Breton et al., 2014).

Two groups have used laser-induced fluorescence (LIF) to quantify NO3 (and N2O5 through thermal dissociation) in ambient air (Wood et al., 2003; Matsumoto et al., 2005a, b). The major drawback of this method is the relatively low fluorescence quantum yield of NO3, and hence the method has not gained wide use.

Another technique that was demonstrated to be capable of measuring NO3 radicals at atmospheric concentration is matrix isolation electron spin resonance (MIESR) (Geyer et al., 1999). Although the technique allows simultaneous detection of other radicals (including HO2 and NO2), it has not been used extensively, probably because of its complexity.

Recently, a variety of in situ NO3 (Dorn et al., 2013) and N2O5 (Fuchs et al., 2012) measurement techniques were compared at the SAPHIR chamber in Jülich, Germany. All instruments measuring NO3 were optically based (absorption or fluorescence). N2O5 was detected as NO3 after thermal decomposition in a heated inlet by either CRDS or LIF. Generally, agreement within the accuracy of instruments was found for all techniques detecting NO3 and/or N2O5 in this comparison exercise. This study showed excellent agreement between the instruments on the single-digit ppt NO3 and N2O5 levels with no noticeable interference due to NO2 and water vapor for instruments based on cavity ring-down or cavity-enhanced spectroscopy. Because of the low sensitivity of LIF instruments, N2O5 measurements by these instruments were significantly noisier compared to the measurements by cavity-enhanced methods. The agreement between instruments was less good in experiments with high aerosol mass loadings, specifically for N2O5, presumably due to enhanced, unaccounted loss of NO3 and N2O5 demonstrating the need for regular filter changes in closed-cavity instruments. Whereas differences between N2O5 measurements were less than 20 % in the absence of aerosol, measurements differed up to a factor of 2.5 for the highest aerosol surface concentrations of 5 × 108 nm2 cm-3. Also, differences between NO3 measurements showed an increasing trend (up to 50 %) with increasing aerosol surface concentration for some instruments.

Analytical techniques to detect gaseous organic nitrates have been documented in a recent review by Perring et al. (2013). Sample collection techniques for organic nitrates include preconcentration on solid adsorbents (Atlas and Schauffler, 1991; Schneider and Ballschmiter, 1999; Grossenbacher et al., 2001), cryogenic trapping (Flocke et al., 1991) or collection in stainless steel canisters (Flocke et al., 1998; Blake et al., 1999), or direct sampling (Day et al., 2002; Beaver et al., 2012).

The approaches to the analysis of the organic nitrates fall into three broad categories. First, one or more chemically speciated organic nitrates are measured by a variety of techniques including liquid chromatography (LC) (Kastler et al., 2000) or gas chromatography (GC) with electron capture detection (Fischer et al., 2000), GC with electron impact or negative-ion chemical ionization mass spectrometry (GC-MS) (Atlas, 1988; Luxenhofer et al., 1996; Blake et al., 1999, 2003a, b; Worton et al., 2008), GC followed by conversion to NO and chemiluminescent detection (Flocke et al., 1991, 1998), GC followed by photoionization mass spectrometry (Takagi et al., 1981), GC followed by conversion of organic nitrates to NO2 and luminol chemiluminescent detection (Hao et al., 1994), CIMS (Beaver et al., 2012; Paulot et al., 2012), and proton transfer reaction MS (PTR-MS) (Perring et al., 2009). Second, the sum of all organic nitrates can be measured directly by thermal dissociation to NO2, which is subsequently measured by LIF (TD-LIF) (Day et al., 2002), CRDS (TD-CRDS) (Paul et al., 2009; Thieser et al., 2016), or cavity-attenuated phase shift spectroscopy (TD-CAPS) (Sadanaga et al., 2016). Finally, the sum of all organic nitrates can be measured indirectly as the difference between all reactive NOx except for organic nitrates and total oxidized nitrogen (NOy) (Parrish et al., 1993).

Recent advances in adduct ionization utilize detection of the charged cluster of the parent reagent ion with the compound of interest. This scheme is then coupled to high-resolution time-of-flight (HR-ToF) mass spectrometry. The combination of these methods allows the identification of molecular composition due to the soft ionization approach that minimizes fragmentation. Multifunctional organic nitrates resulting from the oxidation of BVOC have been detected using CF3O- (Bates et al., 2014; Nguyen et al., 2015; Schwantes et al., 2015; Teng et al., 2015) and iodide as reagent ions (Lee et al., 2014a, 2016; Xiong et al., 2015, 2016; Nah et al., 2016b).

Total (organic plus inorganic) mass of particulate nitrates is routinely quantified using online AMS (Jayne et al., 2000; Allan et al., 2004), from which the mass of organic nitrates can be obtained by three techniques. First, the NO+ / NO2+ ratio (or NO2+ / NO+ ratio) in the mass spectra is used to distinguish organic from inorganic nitrates (Fry et al., 2009, 2013; Farmer et al., 2010; Xu et al., 2015b; Kiendler-Scharr et al., 2016). It is noted that the NO2+ / NO+ approaches zero in the case of low or nonexistent NO2+ signal, while NO+ / NO2+ gives large numbers. Second, positive matrix factorization (PMF) of data matrices including the NO+ and NO2+ ions in addition to organic ions (Sun et al., 2012; Hao et al., 2014; Xu et al., 2015b) is used. Third, the particulate inorganic nitrate concentration, as measured by an independent method such as ion chromatography, is subtracted from the total particulate nitrate concentration (Schlag et al., 2016; Xu et al., 2015a, b). A detailed comparison of these three methods is presented in Xu et al. (2015b). As the NO+ / NO2+ ratio in AMS data is dependent on instruments and the types of nitrates (inorganic and organic nitrates from different VOC oxidations), different strategies were developed when using this method to estimate particulate organic nitrates (Fry et al., 2013; Xu et al., 2015b).

A specialized inlet that selectively scrubs gaseous organic nitrates or collects particulate mass on a filter has been coupled to some of the techniques summarized in this section and utilized to observe particulate organic nitrates in the ambient atmosphere and laboratory studies. A TD-LIF equipped with a gas-scrubbing denuder (Rollins et al., 2010, 2012) and the filter inlet for gases and aerosols (FIGAERO) (Lopez-Hilfiker et al., 2014) at the front end of an iodide adduct HR-ToF-CIMS are examples (Lee et al., 2016; Nah et al., 2016b).

Owing to its ability to analyze polar organic compounds without a prior derivatization step, liquid chromatography coupled to MS (HPLC/MS) is well suited for the characterization of SOA compounds originating from the reactions of BVOC and NO3. Unlike in GC/MS methods, a soft ionization technique such as electrospray ionization (ESI) is utilized to ionize target analytes in the LC/MS technique. In the ESI/MS, target analytes are detected as a cation adduct of a target analyte (e.g., [M+H]+ or [M + Na]+) for a positive mode or a deprotonated form of a target analyte ([M-H]-) for a negative mode. As a biogenic SOA compound typically bears a functional group, such as a carboxylic group or a sulfate group, that easily loses a proton, the negative-mode ESI ((-)ESI) is commonly applied to detect SOA compounds. High-resolution MS such as TOF or Fourier transform ion cyclotron (FTICR) MS is commonly used to assign chemical formulas for SOA compounds unambiguously.

The LC/(-)ESI-MS technique played a crucial role in relating the formation of organosulfates (OS) and nitrooxy-organosulfates (NOS) to NO3-initiated oxidation of BVOC in laboratory-generated and ambient SOA. Since these earlier works, a number of studies have reported the presence of OS and/or NOS compounds in ambient samples (Table S4), though most studies do not connect these compounds explicitly to the NO3 oxidation of BVOC. It should be noted that the direct infusion (-)ESI-MS technique rather than LC/(-)ESI-MS is often used for the analysis of fog, rainwater, and cloud water samples as diluted liquid water samples can be injected into the ion source directly without a sample pretreatment procedure. However, caution is warranted for the direct infusion technique because it cannot separate isobaric isomers and it is susceptible to ion suppression, especially from the presence of inorganic ions in the samples.

Whilst the LC or direct infusion (-)ESI-MS techniques have been successfully applied for the detection of the oxidation products from NO3-BVOC reactions, the techniques have been less successful in quantifying these compounds, mainly due to the lack of authentic standard compounds. The synthesis of these compounds should be a priority for future studies.

Finally, total organic nitrate functional groups within the particle phase have been quantified in ambient air using FTIR of particles collected on ZnSe impaction disks (low-pressure cascade impactor, size segregated) or Teflon filters (PM1) (Mylonas et al., 1991; Garnes and Allen, 2002; Day et al., 2010). The organic nitrate content of particles can be quantified offline as well by collection on quartz fiber filters, extraction into solution (e.g., with water–acetonitrile mixtures), and analysis using standard wet chemistry techniques such as high-pressure liquid chromatography coupled to electrospray ionization mass spectrometry (HPLC-ESI-MS) (Angove et al., 2006; Perraud et al., 2010; Draper et al., 2015).

A few years after the first measurement of tropospheric NO3 (Noxon et al., 1980; Platt et al., 1980), it was recognized that the nitrate radical is a significant sink for BVOC, especially monoterpenes in terrestrial ecosystems and dimethyl sulfide (DMS) in maritime air influenced by continental NOx sources (Winer et al., 1984). The conclusion was based upon computer simulations using NO3 concentrations measured in field studies in the western US and Europe, and measured rate constants of NO3 with olefins. The scenarios in these simulations showed very low monoterpene concentrations in the early morning that were directly attributable to BVOC reactions with NO3. An analysis of NO3 formation rates at several urban and rural sites in Scandinavia (Ljungström and Hallquist, 1996) resulted in the conclusion that while nighttime urban loss of NO3 is dominated by reaction with NO, the loss in rural regions is likely dominated by reactive hydrocarbons, especially monoterpenes.

Due to the fast reactions of NO3 with BVOC, lifetimes of NO3 in biogenically influenced environments can be very short, making simultaneous detection of VOC and NO3 in biogenic regions very difficult. For this reason, several studies have inferred levels of NO3 and its role in processing BVOC using observational analysis and supporting modeling. In particular, the rapid decay of isoprene after sunset has received considerable attention. Measurements of BVOC ∼ 1–2 m above canopy level in a loblolly pine plantation in Alabama during the 1990 ROSE program (Goldan et al., 1995) were used to infer a nighttime NO3 mixing ratio of only 0.2 ppt and NO3 lifetime of only 7 s due to high levels of monoterpenes. The 4 h decay time of isoprene after sunset could not be accounted for by gas reactions with NO3 and O3 although the decrease in the α- / β-pinene ratio at night was consistent with known NO3 and O3 chemistry. As part of the North American Research Strategy for Tropospheric Ozone – Canada East (NARSTO-CE) campaign, measurements of BVOC were made in Nova Scotia in a heavily forested region (Biesenthal et al., 1998). A box-model simulation based on the observational analysis found that the short lifetime of isoprene at night (τ=1–3 h) could not be explained by the NO3 radical, which was estimated to be 0.1 ppt maximum at night due to low NOx and O3 levels and high monoterpene emissions. When OH yields from ozonolysis of BVOC were included in the model, this nighttime OH oxidant could partially account for the isoprene decay. During the Southern Oxidants Study (SOS) campaign in Nashville, TN (Starn et al., 1998), a chemical box model was used to show that rapid nighttime decays of isoprene were consistent with simulated NO3 but only when the site was impacted by urban NOx emissions. During the PROPHET study, measurements of VOC were made in a mixed forest approximately 10 m above the canopy surface (Hurst et al., 2001). Isoprene decays at night had an average lifetime of ∼ 2.7 h. Box modeling showed that O3 reactions as well as dry deposition were insufficient to account for the decay, and that the NO3 radical was a significant sink only after the majority of isoprene had already decayed. On some nights, oxidation by OH could account for all the decay but the decay rates were overpredicted. The authors concluded that vertical transport of isoprene-depleted air aloft contributes to the fast initial decay of isoprene, followed by nighttime OH, NO3, and O3 chemistry decay. Steinbacher et al. (2005) reported on surface measurements in the Po Valley at a site 200–300 m from the closest edge of a deciduous forest. Bimodal diurnal cycles of isoprene were observed with morning and evening maxima that were reproduced by a Eulerian model. Isoprene decay lifetimes of 1–3 h were partially explained by NO3 decay, although a dynamic influence on isoprene decrease seemed to be likely including horizontal and vertical dispersion. During the HOHenpeissenberg Photochemistry Experiment (HOHPEX) field campaign, BVOC were analyzed via 2-D GC at a site located on a hilltop above adjacent rural agricultural/forested area that is frequently in the residual layer at night (Bartenbach et al., 2007). For the reactive monoterpenes, a significant non-zero dependency of the concentration variability on lifetime was found, indicating that chemistry (as well as transport) was playing a role in determining the ambient VOC concentrations. The nighttime analysis gave an estimate of the NO3 mixing ratio of 6.2 ± 4.2 ppt, indicating it was a significant chemical factor in depletion of monoterpenes.

While the studies above made indirect conclusions about the role of NO3 in BVOC processing, field studies including direct measurements of NO3 are key to confirming the above findings. Golz et al. (2001) reported measurements of NO3 by long-path DOAS at an eucalyptus forest site in Portugal during the FIELDVOC94 campaign in 1994. The DOAS beam passed directly over the canopy at heights of 15 and 25 m, and as a result, they were unable to measure NO3 above the 6 ppt instrumental detection limit despite NO3 production rates of 0.4 ppt s-1. Rapid reaction with BVOC limited the NO3 lifetime to approximately 20 s such that NO3 reactions dominated other indirect losses, such as heterogeneous N2O5 uptake. Simultaneous measurements of NO3 and VOC during the Berliner Ozonexperiment (BERLIOZ) campaign in 1998 allowed one of the first assessments of the NO3 budget in comparison to OH and O3 oxidants (Geyer et al., 2001b). Surface measurements at this semi-rural location close to forests found the NO3 radical above detection limit (2.4 ppt) on 15 of 19 nights with a maximum of 70 ppt, a steady-state lifetime ranging from 20 to 540 s and N2O5 ranging from 2 to 900 ppt. The two most significant losses of NO3 were found to be its direct reaction with olefins (monoterpenes dominating) and indirect loss due to heterogeneous hydrolysis of N2O5. Over the study, it was possible for the first time to quantify the relative contribution of the NO3 radical to oxidation of VOC as 28 (24 h) and 31 % for olefinic VOC (24 h) compared to the total oxidation via NO3, OH, and O3. As part of the 1999 SOS study, NO3, isoprene, and its oxidation products were measured at a suburban forested site in Nashville, TN (Stroud et al., 2002). The nitrate radical measured at multiple beam heights by DOAS had maximum mixing ratios of 100 ppt that were generally found to anticorrelate with isoprene levels with significant vertical gradients on some nights. Early evening losses of isoprene were attributable to reaction with the NO3 radical. During the Pacific 2001 Air Quality Study (PACIFIC 2001) field campaign, NO3 was measured by long-path DOAS at an elevated forested site in the lower Fraser Valley of British Columbia with beam-path nighttime NO3 levels up to a maximum of 50 ppt (average of nighttime boundary layer and residual layer) (McLaren et al., 2004). Simultaneous analysis of carbonyl compounds in aerosol samples (Liggio and Mclaren, 2003) during the study found that only monoterpene oxidation products pinonaldehyde and nopinone (not reported) were enhanced in aerosol filters collected at night, evidence of the role of NO3 in nighttime oxidation of BVOC in the valley. In 2004 measurements of NO3 and N2O5 by CRDS, isoprene and its oxidation products were made on board the NOAA P-3 aircraft as part of the New England Air Quality Study (NEAQS) and International Consortium for Atmospheric Research on Transport and Transformation (ICARTT) campaigns in the northeast US (Brown et al., 2009). These studies found a very clear anticorrelation between isoprene levels after dark and NO3 mixing ratios, which varied as high as 350 ppt when isoprene was absent from the air mass. The loss frequencies (i.e., first-order loss rate constants) of NO3 were strongly correlated with the loss rate constant of NO3 with isoprene for lifetimes less than 20 min, clearly showing that isoprene was the most important factor determining the lifetime of NO3. It was also shown that more than 20 % of emitted isoprene was oxidized at night and that 1–17 % of SOA was contributed by NO3-isoprene oxidation. A number of recent studies have also investigated the role of NO3+ BVOC chemistry in more polluted areas. In many urban areas, the NO3+ BVOC chemistry occurs in parallel to heterogeneous NO3 / N2O5 chemistry and reactions of NO3 with anthropogenic VOC. Examples of such environments have been discussed in Brown et al. (2011, 2013) and Stutz et al. (2010) who presented observations in Houston, TX. Brown et al. (2011) and Stutz et al. (2010) found that up to 50 % of the NO3+ VOC reactions in Houston are driven by isoprene, with the other VOC emitted by industrial sources. Surprisingly, heterogeneous NO3 / N2O5 chemistry plays a minor role in Houston. Brown et al. (2011) also point out that the nocturnal VOC oxidation by NO3 dominates over that by ozone. Nocturnal NO3 formation rates were rapid and comparable to those of OH during the day. Crowley et al. (2011) compared NO3 chemistry in air masses of marine, continental, and urban origin at a field site in southern Spain. Under all conditions, NO3+ BVOC reactions (predominately α-pinene and limonene) contributed to the overall NO3 reactivity, confirming other observations that concluded that this chemistry is important in all environments where BVOC sources are present. In the southeastern US summer, this importance extends even through the daytime, when photolysis and NO reactions compete (Ayres et al., 2015). The NO3+ BVOC reaction rates observed in these studies imply a high production rate of SOA and organic peroxy radicals.

There are many factors that motivate understanding organic nitrate in the particulate phase through field deployment of a variety of instrumentation, much of which is described in other sections of this review. Nitrogen-containing organic fragments (not necessarily organic nitrates) have been identified in atmospheric particles using mass spectrometric techniques (Reemtsma et al., 2006; Farmer et al., 2010; O'Brien et al., 2014). Total atmospheric organic nitrates, as well as organic nitrates segregated by phase, also have been measured in the atmosphere using techniques such as TD-LIF, CIMS, etc. (Day et al., 2003; Beaver et al., 2012). Given these observations and the propensity of organic nitrate compounds to partition to the condensed phase to create SOA (Rollins et al., 2013), it is critical to determine the level of organic nitrates that reside specifically in the atmospheric aerosol phase under typical ambient conditions and to identify the chemical and physical processes that determine their concentrations. It is also important to note that formation of SOA that contains organic nitrate groups has the potential to sequester NOx, thereby influencing the cycling of atmospheric oxidants.

Organic nitrates in urban PM that were identified using functional group analyses such as FTIR spectroscopy have been attributed to emission of nitrogen-containing primary organic aerosol or to involvement of reactive nitrogen compounds in SOA formation chemistry (Mylonas et al., 1991; Garnes and Allen, 2002; Day et al., 2010). Other more advanced techniques, such as TD-LIF enhanced with the ability to separate phases or techniques to obtain high-resolution mass spectra (HR-ToF-AMS), have been utilized to quantify the amount of organic nitrate in particles in areas less likely to be influenced strongly by BVOC emissions, such as urban areas or areas influenced by oil and gas operations (Lee et al., 2015). Of specific interest here, however, are observations of organic nitrate PM in areas with a significant influence of BVOC, especially if co-located measurements allow for insight into the role that NO3 plays in the initial BVOC oxidation step. As such, we focus here on online measurements and on measurements that allow specific attribution to BVOC-NO3 reactions. Such measurements broadly can be categorized by region of sampling: the eastern United States (US), the western US, and Europe. Figure 5a summarizes average mass concentrations of submicrometer particulate organic nitrates (NO3,org) and particulate inorganic nitrates (NO3,inorg) in different months at multiple sites around the world. Figure 5b summarizes the corresponding percentage (by mass) of submicrometer particulate organic nitrate aerosols in ambient organic aerosols. Detailed information and measurements for each site are provided in Table S5.

The first reports of aerosol organic nitrates in the southeastern (SE) US resulted from composition analysis of four daily PM filter samples from four Southeastern Aerosol Research and Characterization (SEARCH) network sites during summer 2004. Filters were analyzed for polar compounds, with particular focus on organosulfates, using offline chromatographic–MS methods (Gao et al., 2006; Surratt et al., 2007, 2008). Several nitrooxy organosulfates were identified, but the only one quantified (1–2 % of organic mass) was associated with α-pinene photooxidation or reaction with NO3. Several of the nitrooxy organosulfates were likely the same as products from BVOC-oxidant–NOx-seed systems based on comparison to spectra collected from chamber studies.

Brown et al. (2013) examined several nighttime aircraft vertical profiles in Houston (October  2006 during the Texas Air Quality Study 2006) that showed increases of total nitrate aerosol (and increases in AMS m/z 30 to m/z 46 ratio, the unit mass resolution approximation for NO+ / NO2+, indicative of organic nitrates; Farmer et al., 2010) and oxygenated organic aerosol (OOA). The OA versus carbon monoxide (CO) slopes at lower altitudes were consistent with SOA sources from NO3-BVOC reactions, with a combination of observations and zero-dimensional modeling showing 1 to 2 µg m-3 SOA formation from NO3-BVOC oxidation overnight with formation rates of 0.05 to 1 µg m-3 h-1.

More recently, during the summer Southern Oxidant and Aerosol Study (SOAS; mixed, semi-polluted forest) in Alabama (2013), an unprecedented suite of instruments quantified particle-phase organic nitrates using five different online methods: HR-ToF-AMS (NO+ / NO2+), HR-ToF-AMS – PiLS (particle-into-liquid sampler) ion chromatography (PiLS-IC), HR-ToF-AMS (PMF), TD-LIF (denuded), and iodide CIMS. Total particle-phase nitrates increased throughout the night and peaked in early/mid-morning. Xu et al. (2015b) systematically evaluated the three AMS-related methods in estimating ambient particulate organic nitrate concentrations. Analysis presented in Xu et al. (2015a, b) using the HR-ToF-AMS – PiLS-IC method showed that organic nitrate functional groups comprised ∼ 5–12 % of OA mass and correlated with PMF-derived less-oxidized oxygenated OA (LO-OOA). Two-thirds of the LO-OOA was estimated to be formed via NO3-BVOC chemistry (dominantly monoterpenes, ∼ 80 %), with the balance due to ozone (O3)-BVOC chemistry. Organic nitrates were calculated to comprise 20–30 % of the LO-OOA factor. Ayres et al. (2015) used a measurement-constrained model for nighttime that compared NO3 production/loss to total organic nitrate (HR-ToF-AMS NO+ / NO2+, TD-LIF) formation to calculate a molar yield of aerosol-phase organic nitrates of 23–44 % (organic nitrate formed per NO3-BVOC reaction) that was dominated by monoterpene oxidation. They noted that the estimated yield was low compared to aggregated aerosol-phase organic nitrate yields, possibly due to rapid nitrate losses not considered in the model. Organic nitrate hydrolysis in the particle phase is one potential loss pathway, although recent laboratory studies suggest this process is slow for NO3+β-pinene SOA (Boyd et al., 2015). Also, particle-phase organic nitrates were observed to contribute 30–45 % to the total NOy budget. Lee et al. (2016) quantified speciated particle-phase organic nitrates using iodide CIMS (88 individual C4-C17 mono/dinitrates). A large fraction was highly functionalized, with six to eight oxygen atoms per molecule. Diurnal cycles of isoprene-derived organic nitrates generally peaked during daytime, and monoterpene-derived organic nitrates peaked at night or during early/mid-morning. Using an observationally constrained diurnal zero-dimensional model, they showed that the observations were consistent with fast gas–particle equilibrium and a short particle-phase lifetime (2–4 h), again possibly due to hydrolysis if the field-derived lifetimes for particle-phase organic nitrates can be reconciled with recent laboratory studies (Boyd et al., 2015). The sum of the CIMS particle-phase organic nitrates (mass of nitrate functional groups only) was correlated with the two total aerosol organic nitrate AMS-based methods (R2=0.52, 0.67) with slopes of 0.63 and 0.90 (Lee et al., 2016). The CIMS sum was also correlated with the total measured with the TD-LIF method (R2=0.55); however, since the TD-LIF measurements were ∼ 2–4 times higher (depending on period) than the AMS-based methods, the CIMS versus TD-LIF slope was substantially lower (0.19). Reasons for the differences between the total organic nitrate measured by different methods have been investigated but remain unclear.

A seasonal and regional survey of particle-phase organic nitrates is reported by Xu et al. (2015b) using a HR-ToF-AMS and an aerosol chemical speciation monitor (ACSM) (Ng et al., 2011) at four rural and urban sites in the greater Atlanta area (2012–2013) and in Centreville, AL (summer 2013 only, SOAS). They show strong diurnal cycles during summer, peaking early/mid-morning, and cycles with similar timing but smaller magnitude during winter. The concentrations were slightly higher in summer, which was attributed to compensating effects of source strength and gas–particle partitioning. Shallower boundary layers during winter also may have played a role in making the summer and winter concentrations more similar (Kim et al., 2015).

Fisher et al. (2016) report a broad regional survey of particle-phase (and gas-phase) organic nitrates (HR-ToF-AMS NO+ / NO2+) during summertime for the Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC4RS) aircraft campaign (August–September, 2013, SE US only) as well as the ground-based SOAS measurements. A substantial vertical gradient was observed in particle-phase organic nitrates, with concentrations decreasing by several-fold from the boundary/residual layer into the free troposphere. Consistent with SOAS ground observations, 10–20 % of observed boundary layer total (gas plus particle) organic nitrates were in the particle phase for the aircraft measurements.

In addition to the measurements made in the SE US, characterization of aerosol organic nitrates has been performed in New England. As part of the New England Air Quality Study (NEAQS) in summer 2002, Zaveri et al. (2010) observed evolution of aerosols in the nocturnal residual layer with an airborne quadrupole (Q)-AMS in the Salem Harbor power plant plume. The aerosols were acidic and internally mixed, suggesting that the observed nitrate was in the form of organic nitrate and that the enhanced particulate organics in the plume were possibly formed from NO3-initiated oxidation of isoprene present in the residual layer.

Significant work on understanding ambient organic nitrate formation from BVOC-NO3 has been performed in California. During the California Research at the Nexus of Air Quality and Climate Change (CalNex) field campaign from mid-May through June 2010, Rollins et al. (2012, 2013) measured particulate total alkyl and multifunctional nitrates (pΣANs) with TD-LIF at a ground site in Bakersfield, California. They attributed the increase in pΣAN concentrations at night to oxidation of BVOC by NO3 forming SOA, with an estimated 27 to 40 % of the OA growth due to molecules with nitrate functionalities. On average, 21 % of ΣANs were in the particle phase and increased with OA, which was fit to a volatility basis set in which pΣANs / ΣANs increased from ∼ 10 % at < 1 µg m-3 and plateaued at ∼ 30 % by ∼ 5 µg m-3. At the same site, using PMF analysis of FTIR and HR-ToF-AMS measurements, Liu et al. (2012a) showed that the organic nitrate-containing biogenic SOA condensed onto 400 to 700 nm sized primary particles at night. As part of the Carbonaceous Aerosol and Radiative Effects Study (CARES) in June 2010, Setyan et al. (2012) observed enhanced SOA formation due to interactions between anthropogenic and biogenic emissions at a forest site in the foothills of the Sierra Nevada mountains, approximately 40 km downwind of Sacramento. While nitrate accounted for only ∼ 4 % of the particle mass measured by a HR-ToF-AMS, it was attributed potentially to organic nitrates based on the much higher NO+ / NO2+ ion ratio than observed in pure ammonium nitrate.

During the Rocky Mountain Biogenic Aerosol Study field campaign in Colorado's Front Range (rural coniferous montane forest) (BEACHON-RoMBAS) from July to August 2011, Fry et al. (2013) observed aerosol-phase organic nitrates by optical spectroscopic (denuded TD-LIF) and mass spectrometric (HR-ToF-AMS, NO+ / NO2+) instruments. The two methods agreed well on average (AMS/TD-LIF slope of 0.94–1.16, depending on averaging method) with a fair correlation (R2=0.53). Similar to studies in other forested environments, the organic nitrate concentration was found to peak at night. The organic nitrate concentration was positively correlated with the product of the nitrogen dioxide and O3 mixing ratios but not with that of O3 alone; this suggested nighttime NO3-initiated oxidation of monoterpenes as a significant source of nighttime aerosol organic nitrates. The gas–particle partitioning also showed a strong diurnal cycle, with the fraction in the particle phase peaking at ∼ 30 % at night and decreasing to a broad minimum of ∼ 5 % during daytime, which suggests a change in composition in addition to thermodynamic partitioning effects.

Iinuma et al. (2007) analyzed ambient aerosol samples collected on filters in a Norway spruce forest in northeastern Germany during the BEWA campaign (Regional biogenic emissions of reactive volatile organic compounds from forests: process studies, modeling, and validation experiments) and compared the results to those from chamber studies. The filter extracts were analyzed using LC-ESI-ToF-MS in parallel to ion trap MS. Several nitrooxy organosulfates with significant mass in the BEWA ambient samples were enhanced in the nighttime samples relative to the daytime samples. Their abundance in the nighttime samples strongly suggests that NO3-monoterpene chemistry in the presence of sulfate aerosols has an important role in the formation of these nitrooxy organosulfate aerosols.

A similar study by Gómez-González et al. (2008) focused on isoprene through LC-multidimensional MS (MSn) analysis of filter samples from both chamber studies and ambient summer day/night PM2.5 samples from K-Puszta, Hungary, a mixed deciduous/coniferous forest site. Although not the focus of the study, they confirmed the presence of significant quantities of nitrooxy organosulfates that were enhanced in the nighttime samples over the daytime samples.

Initial online evidence of the production of organic nitrate aerosols in Europe was provided by Allan et al. (2006) when studying nucleation events driven by BVOC oxidation in Hyytiälä, a (boreal) forested region in Finland. The Q-AMS m/z 30 to m/z 46 ratio (the unit mass resolution approximation for NO+ / NO2+ ratio) was frequently found to be very high, ∼ 10, for a distinct organic Aitken mode that became apparent late in the afternoon and increased at night. They hypothesized that the excess m/z 30 (NO+) signal was associated with organic nitrates, although could not rule out amine contributions. During the same field study, Vaattovaara et al. (2009) applied two tandem differential mobility analyzer methods to study the evolution of the nucleation- and Aitken-mode particle compositions at this boreal forest site. The results showed a clear anthropogenic influence on the nucleation- and Aitken-mode-particle compositions during the events and suggested organic nitrate and organosulfate aerosol was generated from monoterpene oxidation. Also, it was shown that organic nitrate was enhanced in aerosol exposed to elevated temperatures, implying low volatility of organic nitrates (Häkkinen et al., 2012).

More recently, Hao et al. (2014) used a HR-ToF-AMS on a tower in Kuopio, Finland, 224 m above a lake surrounded by a mixed forest of mostly coniferous (pine and spruce) mixed with deciduous trees (mostly birch) to measure submicron aerosol composition. The site also was influenced by urban emissions. A particular focus of the study was to separate organic and inorganic nitrate using PMF. They found that ∼ 37 % of the nitrate mass at this location and time could be allocated to organic nitrate factors, the rest being inorganic nitrate. The organic nitrate aerosol was segregated into two organic factors, less-oxidized OOA (LO-OOA), and more-oxidized OOA (MO-OOA) (previously called SV- and LV-OOA, respectively); the majority (74 %) of the organic nitrate was found to be in the more volatile LO-OOA factor. Based on meteorology, the air mass source of the organic nitrate aerosol was from a sector with residential and forested areas. Again, the organic nitrate aerosol showed a diurnal trend that was highest at night.

An analysis of AMS data taken across Europe within EUCAARI and EMEP intensive measurement campaigns (Kulmala et al., 2011; Crippa et al., 2014) has recently shown high organic nitrate contributions to total measured PM1 nitrate (Kiendler-Scharr et al., 2016). The spatial distribution and diurnal pattern of particulate organic nitrate indicate a gradient of concentration. High concentrations are found in source regions with NOx emissions and during the night. Low concentrations are found in remote regions and during the day. EURAD-IM simulations for Europe show an increase of SOA by 50 to 70 % when considering SOA formation by NO3 oxidation with maximum ground-level concentrations of SOA from NO3 oxidation in the range of 2 to 4 µg m-3 (Li et al., 2013; Kiendler-Scharr et al., 2016).

Taken together, the observations of particle-phase organic nitrates in the US and Europe suggest that particle-phase organic nitrates (formed substantially via NO3-BVOC chemistry) are ubiquitous, especially in, but not limited to, summer. Their formation appears to play an important role in SOA formation, which can potentially be underestimated due to short particle-phase lifetimes. Regions with widespread NOx and BVOC emissions and a humid climate may create optimal conditions for a rapid life cycle of particle-phase organic nitrates.

Organic nitrates are produced from the reactions of VOC with OH followed by NO as well as with NO3, and both of these pathways are represented in chemical mechanisms albeit at varying levels of detail. The use of the term “model” below refers to the treatment of BVOC + NO3 chemistry in lumped chemical mechanisms. The products formed from the OH-initiated (typically daytime) versus NO3-initiated (typically nighttime) chemistry may or may not be treated separately.

The NO3-BVOC reactions result in an RO2 that reacts with NO3, other RO2, HO2, or NO. RO2-NO reactions for NO3-initiated chemistry are relatively unimportant due to rapid reaction of NO with NO3 at night (Perring et al., 2009), but they are included in models. Unimolecular rearrangements of the NO3-initiated RO2 radical are not currently considered in models (Crounse et al., 2011). The products of the initial NO3-BVOC reaction may retain the nitrate group, thus forming an organic nitrate or releasing nitrogen as NO2. The branching between organic nitrate formation and N recycling is parameterized in models. Table 4 summarizes the gas-phase organic nitrate yields for isoprene and monoterpene oxidation by NO3 in a number of currently available chemical mechanisms. The yields represent the first-generation yields since products may react to form further organic nitrates or release NO2. The organic nitrate yield values span from 0 (e.g., SAPRC07 isoprene) to 100 % (e.g., MCM isoprene). Although GEOS-Chem v10-01 does not consider gas-phase monoterpene chemistry, the model has recently been updated to consider a 10–50 % yield of organic nitrates from the monoterpene-NO3 reaction independent of the nitrate-RO2 fate but dependent on monoterpene identity (Fisher et al., 2016). Differences in the organic nitrate yield from NO3 oxidation result from a number of causes including treatment of RO2 fate, assumptions about decomposition versus retention, and prioritization of functional group identity.

Some models parameterize the yield of organic nitrates as a function of RO2 fate while others, such as the carbon bond-based (CB) mechanisms, treat all RO2 fates the same. The MCM v3.3.1 also considers the yield of isoprene organic nitrates to be independent of RO2 fate, but monoterpene organic nitrate yields are variable between 0 and 100 % depending on RO2 fate. Differences in organic nitrate formation, due to treating the organic nitrate yield as a function of RO2 fate, may vary with atmospheric conditions. Reactions with both HO2 and RO2 are significant at night (Xie et al., 2013; Pye et al., 2015). RO2-NO3 may be important in urban areas or locations where BVOC concentrations are not so high as to deplete NO3 (Rollins et al., 2012).

Mechanisms differ in their assumptions about whether or not the organic nitrates from NO3-initiated chemistry release NO2 or retain the nitrate group. An example of this difference in treatment of organic nitrates can been seen in the reactions of nitrated peroxy radicals with different radicals (NO, HO2, RO2) predicted by SAPRC07 and MCM. MCM predicts greater loss of the nitrate group, while SAPRC tends to retain it, leading to either < 5 % (MCM) or > 50 % (SAPRC) organic nitrate yields.

In order to predict accurately the fates of RO2 and yield of organic nitrates, models must also include information on RO2 reaction rate constants. Some mechanisms use the same set of RO2 rate constants for all hydrocarbons. However, the MCM (Jenkin et al., 1997; Saunders et al., 2003) indicates that the RO2-HO2 rate constant should vary with carbon number (n) and predict k = 2.91 × 10-13 exp(1300/T) [1-exp⁡(-0.245n)] molec-1 cm3 s-1. The MCM RO2-RO2 rate constant varies between 2 × 10-12 cm3 molec-1 s-1 (based on C1-C3 primary RO2 with adjacent O or Cl) and 6.7 × 10-15 cm3 molec-1 s-1 for tertiary alkyl RO2 (based on t-C4H9O2). RO2-NO3 and RO2-NO rate constants are estimated as 2.3 × 10-13 and 9.0 × 10-12 cm3 molec-1 s-1 at 298 K.

AQMs and chemistry–climate models typically cannot handle the complexity associated with tracking each individual VOC and all its possible reaction products. As a result, surrogate species are often used to represent classes of compounds (e.g., CB05, which uses the designation NTR to indicate organic nitrates). This mapping can cause yields of organic nitrates to be falsely low in a mechanism if other functional groups are prioritized over nitrate in the mapping of predicted products to mechanism species. Compared to the other mechanisms in Table 4, SAPRC07 monoterpenes tend to have very low organic nitrate yields as a result of prioritization of peroxide and non-nitrate functional groups. If nitrate groups were prioritized, SAPRC07 would more closely resemble the “other monoterpene” yields from SAPRC07tic. In addition, the diversity across mechanisms in the RO2-HO2 monoterpene organic nitrate yields would be reduced such that they would all indicate > 50 % organic nitrate yields and all but the CB mechanisms would predict a 100 % yield of organic nitrates from RO2-HO2. The RO2-HO2 pathway is relatively unstudied in laboratory conditions due to difficulties in maintaining sufficient concentrations of both NO3 and HO2 radicals (Boyd et al., 2015; Schwantes et al., 2015).

Nitrate radical oxidation can lead to significant amounts of SOA on global and regional scales. Due to a lack of information on the identity and volatility of later-generation BVOC + NO3 products, most models parameterize SOA formation separately from gas-phase chemistry using either the Odum two-product (Odum et al., 1996) fit, volatility basis set (VBS) (Donahue et al., 2006) fit, or fixed yield (Table 5). Based on the understanding of SOA pathways at the time, Hoyle et al. (2007) found that up to 21 % of the global average SOA burden may be due to NO3 oxidation, and Pye et al. (2010) predicted ∼ 10 % of global SOA production was due to NO3. Regional contributions to SOA concentrations can be much higher (Hoyle et al., 2007; Pye et al., 2010). Nitrate radical reactions themselves are estimated to account for less than 3 % of isoprene oxidation and less than 2 % of sesquiterpene oxidation globally; however, they account for 26 % of bicyclic monoterpene oxidation (Pye et al., 2010). Representations of monoterpene-NO3 SOA are more widespread in chemistry–climate models than other BVOC-NO3 SOA parameterizations due to the relatively early recognition of its high yields (e.g., Griffin et al., 1999) and relative importance for SOA. Inclusion of SOA from isoprene-NO3 is more variable as reflected in Table 5.

SOA from BVOC-NO3 reactions traditionally has been parameterized on the initial hydrocarbon reaction assuming semivolatile products and an Odum two-product approach (e.g., Chung and Seinfeld, 2002). This treatment is often implemented in parallel to the gas-phase chemistry, meaning that later-generation products leading to SOA are not identified. Information is still emerging on the fate of organic nitrates, and that information is just beginning to be included in models. Hydrolysis of particle-phase organic nitrates is one such process more recently considered with impacts for both O3 and PM in models (Hildebrandt Ruiz and Yarwood, 2013; Browne et al., 2014; Pye et al., 2015; Fisher et al., 2016).

The influence of BVOC nighttime oxidation on the nitrogen budget remains unclear. Current modeling efforts have mainly focused on the nighttime oxidation of isoprene, which is dominated by isoprene-NO3 reaction. This pathway is initialized via addition of NO3 to one of the double bonds, as discussed in Sect. 2.1.2. Due to the additional stabilization from alkoxy radical and nitrate functional groups (Paulson and Seinfeld, 1992), the yield of first-generation organic nitrates is relatively high (62–78 %; Table 2); they may react with NO3 again to produce secondary dinitrates (Perring et al., 2009; Rollins et al., 2009, 2012). Assuming little NOx is recycled from these organic nitrates, most models suggest that nighttime oxidation of isoprene by NO3 contributes significantly to the budget of organic nitrates (von Kuhlmann et al., 2004; Horowitz et al., 2007; Mao et al., 2013; Xie et al., 2013). Two recent studies (Suarez-Bertoa et al., 2012; Müller et al., 2014), however, suggest fast photolysis of carbonyl nitrates with high efficiency of NOx recycling, which could lead to release of NOx in the next day. Further modeling is required to investigate the importance of nighttime isoprene oxidation on the nitrogen budget.

Very little modeling effort has been dedicated to the influence of nighttime terpene oxidation on the nitrogen budget, mainly due to the lack of laboratory data on oxidation products and their fate. In contrast to isoprene, terpene emissions are temperature sensitive but not light sensitive (Guenther et al., 1995), leading to a significant portion of terpene emissions being released at night. The high yield of organic nitrates and SOA from the terpene-NO3 reaction (Fry et al., 2009, 2011, 2014; Boyd et al., 2015) provides an important sink for NOx at night, likely larger than for isoprene-NO3 over the eastern US (Warneke et al., 2004). Recent laboratory experiments suggest that aerosol organic nitrates can be either a permanent or temporary NOx sink depending on their monoterpene precursors (and hence nature of the resulting RO2) as well as ambient RH (Boyd et al., 2015; Nah et al., 2016b). In order to understand the impact of terpenes on nighttime chemistry, a fully coupled model of terpene-NOx chemistry will be required, as monoterpenes can be the dominant loss process for NO3 and N2O5 at night (Ayres et al., 2015).

While a significant portion of nitrogen is emitted at night (Boersma et al., 2008), the impact of nighttime chemistry on the initiation of the following daytime chemistry has received little attention in regional and global models. Different treatments of NO3 chemistry can result in 20 % change in the following daytime O3 concentration, as shown by a 1-D model study (Wong and Stutz, 2010) and box model simulations (Millet et al., 2016). This impact can be further complicated by uncertainty in emissions of BVOC and model resolutions. For example, a recent study by Millet et al. (2016) shows that in a city downwind of an isoprene-rich forest, daytime O3 can be largely modulated by the chemical removal of isoprene throughout the night. Such local-scale events may only be captured by a very high-resolution model with detailed characterization of emission sources. It is important to assess this impact on a global scale using 3-D chemistry models, owing to the profound coupling of boundary layer dynamics and chemistry. Quantifying the impact of BVOC-NO3 chemistry on NOx fate is important given the long-standing problem in current global and regional AQMs of a large overestimate of O3 over the eastern US in summer (Fiore et al., 2009).

Recent field campaigns (SOAS, SEAC4RS, EUCAARI, EMEP) have allowed for the attribution of SOA to NO3 oxidation to provide model constraints not previously available. Pye et al. (2015) and Fisher et al. (2016) implemented updated BVOC + NO3 chemistry in CMAQ and GEOS-Chem, respectively, to interpret data in the SE US during the summer of 2013 (SOAS and SEAC4RS). Model predictions of gas-phase monoterpene nitrates (primarily NO3 derived) were higher than the sum of C10H17NO4 and C10H17NO5 (Nguyen et al., 2015) by a factor of 2–3 (Fisher et al., 2016) and 7 (Pye et al., 2015), consistent with a significant fraction of the monoterpene nitrates being highly functionalized (Lee et al., 2016). The studies identified particle-phase hydrolysis as an important modulator of particulate organic-nitrate concentrations and organic nitrate lifetime. The GEOS-Chem simulation reproduced the particle-phase organic nitrate diurnal cycles (SOAS), boundary layer concentrations, and gas–particle partitioning reasonably well; however, it underestimated concentrations in the free troposphere, possibly due to measurement limitations and/or the implementation of rapid uptake followed by hydrolysis of all gas-phase organic nitrates in the model, which may not be valid for non-tertiary organic nitrates (Fisher et al., 2016).

Previous sections have detailed the reactions of BVOC with NO3 and the need to include this chemistry to represent more accurately processes that control O3 and SOA formation. But applying that information in a way that can be used for air quality studies presents a serious challenge. As highlighted in Sect. 2.6.1, the chemical mechanisms currently being used in AQMs are limited in their representation of NO3-BVOC chemistry, largely lumping all monoterpenes together, and with no agreement on yields. The lack of detail in current mechanisms is reflected in the variety of methods by which SOA formation from BVOC-NO3 chemistry is estimated (Sect. 2.6.2).

Typically, the NO3-BVOC chemistry is implemented in AQMs into the existing system of organic and inorganic chemical reactions that occur in the atmosphere. Because there may be hundreds or thousands of different chemical reactions occurring simultaneously and the computational efforts required to solve those on a 3-D grid are onerous, the chemical mechanisms used in AQMs are typically condensed to a certain extent. The greatest challenges in modeling the reactions initiated by NO3 and BVOC in AQMs are (1) deciding how much detail must be included to accurately represent the chemistry; (2) estimating intermediate reactions and/or products when direct experimental observations are not available; (3) integrating the new reactions into existing chemical mechanisms; and (4) validating the complete schemes against observational data.

Including all of the attack pathways and isomers that are formed in the reactions of NO3 and BVOC and their subsequent products rapidly becomes an intractable problem, as the number of species and reactions produced from a VOC grows exponentially with the number of carbons in the compound (Aumont et al., 2005), resulting in an estimate of almost 400 million products from a single C10 hydrocarbon. Even restricting the chemistry solely to the RO2 formed from α-pinene, β-pinene, and limonene via addition of NO3 to the double bond results in 861 unique product species and 2646 reactions as estimated from the MCM (http://mcm.leeds.ac.uk/MCM-devel/home.htt; Saunders et al., 2003). In comparison, the chemical mechanisms used in AQMs typically consider a total of 100–200 species and less than 400 reactions to model the entire gas-phase chemistry occurring in the troposphere. One challenge is to find a balance between complexity and computational efficiency that involves both deriving complete mechanisms as well as condensing them to the extent possible.

The second major challenge is that many of the chemical pathways must be estimated given the limited experimental measurements of intermediate reaction rate constants and products. Structure–activity predictions have been used heavily in the past, but these have been formulated for a limited number of compounds. Their predictions become less accurate as the complexity of the molecule increases (Calvert et al., 2015). When heterogeneous reactions play a significant role in the transport and fate of reaction products, as they do in monoterpene chemistry, the challenge becomes even greater. With recent research, new product structures that contribute to SOA have been identified (Boyd et al., 2015). However, these are not covered by existing predictive theory, and these new pathways must be characterized, including reaction rate constants, co-reactants, and products. Physical parameters of all of these new species, such as solubility, radiative properties, emission rates, and deposition velocities also are required, but data are often unavailable for these or even comparable species.

The last challenge is integrating the chemistry within the rest of the chemistry occurring in the atmosphere. The major chemical mechanisms used in AQMs today were developed primarily to address episodes of elevated O3 under conditions of high NOx and have been evaluated for this purpose. Thus, the mechanisms often do not lend themselves well to predicting the chemistry of complex VOC or other air quality endpoints (Kaduwela et al., 2015). Minor pathways with respect to O3 formation have been removed from the mechanisms to reduce the computational burden, but these pathways may be important for formation of SOA. In addition, the detailed chemistry of multistep alkoxy and peroxy radical chemistry is condensed into a single step in some mechanisms, but identifying whether these radicals react with NOx or HOx or isomerize is critical for predicting the types of organic molecules that are formed. As described in Sect. 2.6, existing mechanisms include the capability for a limited number of nitrates, and in many cases the links to facilitate expansion to more detailed representations are missing.

Significant work must be done to allow modelers to implement this new information in AQMs and thus use this updated knowledge to develop improved predictions of future air quality. One approach is to focus on key chemicals of interest, derive mechanisms that are suitable for specialized applications, and append these on to existing frameworks (for example, Xie et al., 2013). The longer-term view requires a more comprehensive approach that draws on the development of community archives that can better accommodate rapidly changing information and better represent the interactions of biogenic with anthropogenic chemistry. Here, we put forward our recommendations for future work in the following areas:

Development of tools for the semi-automated production of the reaction pathways and products of later-generation products resulting from alternate pathways of radical reactions with BVOC. These tools should be able to incorporate experimental data when available. In conjunction with the automated development, we require advanced methods for condensing these large mechanisms into computationally feasible reaction schemes.

Generally speaking, once detailed mechanisms are developed, they are evaluated through some form of benchmarking. Systematic strategies for mechanism evaluation include validation of highly detailed mechanisms unable to be run in 3-D models against benchmark data from well-characterized simulation chamber experiments (Jenkin et al., 1997; Aumont et al., 2005) and the incorporation of these mechanisms into box or 1-D models to validate radical and short-lived species against field campaign observations. Less-detailed air quality (AQ) mechanisms can then be compared to these reference mechanisms by way of sensitivity experiments in idealized modeling studies – often aimed at assessing the sensitivity in O3 to changing NOx and VOC emissions (Archibald et al., 2010; Squire et al., 2015). AQ mechanisms are often also then re-evaluated against chamber and/or field experiment data before they are implemented into 3-D models and then undergo evaluation against extensive measurements in the residual layer.

One of the greatest challenges in the BVOC-NO3 system is that current nighttime measurements are mainly collected from surface sites, which are confined to a shallow surface layer at night and not representative of the whole nighttime boundary layer. The impact of nighttime chemistry on daytime ozone and nitrogen/aerosol budget would require careful investigation of nighttime chemistry in the residual layer, which contains > 80 % of air masses at night.

Moreover, the benchmarking activities mentioned above and the development process discussed in Sect. 3.5.1 are not well aligned. A more unified approach that identifies some key mechanistic problems and identifies strategies to evaluate them is required in order to make improved progress on simulating the changing composition of the atmosphere.

Uncertainties in AQM predictions also arise from the representation of physical sub-grid-scale processes. The ones particularly relevant for the NO3-BVOC chemistry include, but are not limited to, the following.

The spatial distribution of BVOC and NOx precursors is highly variable, but the current AQMs neglect these heterogeneities and assume perfect mixing within grid cells of typically 3–10 km in the horizontal. At those resolutions, models are unable to resolve the localized surface emission sources and the microscale structure of boundary layer turbulence, and therefore cannot resolve spatial heterogeneities in chemistry, partitioning, and mixing of chemicals, which are essential for predicting the concentrations of secondary pollutants.

Typically, the freshly emitted monoterpene species have a tendency to accumulate in the shallow nighttime boundary layer (typically < 200 m), and can react with NO3 if available. However, often NO3 is located in the residual layer that is decoupled from the nighttime boundary layer (NBL), and the BVOC + NO3 reactions would depend on the model's ability to mix the two layers. Thus, mixing within and out of the boundary layer provides a key challenge for modeling the impacts of BVOC-NO3 chemistry, as the measured gradients of NO3 and BVOC are very strong in the vertical (e.g., Brown et al., 2007b; Fuentes et al., 2007).

A large focus on model evaluation has been on the impacts of higher horizontal resolution (Jang et al., 1995). It has been shown in several cases that owing to the complex interplay of chemical families, the sensitivity of the chemical system is not captured at lower resolution (e.g., Cohan et al., 2006). However, very little work has focused on the role of improvements in vertical resolution, despite the fact that inter-model differences in properties like the height of the boundary layer vary by over a factor of 2 in some cases (e.g., Hu et al., 2010). Moreover, the NBL is not well mixed, so evaluation of nocturnal physics requires more than just evaluating the NBL height.

Typically, parameterizations have been applied to anthropogenic emission sources (e.g., aircraft plumes, urban plumes) and not to biogenic sources. Partly, this is a result of the differences in the source terms, anthropogenic emissions often being well represented as point sources in space, whereas biogenic emissions are often large area sources. However, as the emissions of BVOC are often very species specific, and observations highlight large spatial variability over small areas (e.g., Niinemets et al., 2010), the adoption of the anthropogenic plume parameterizations to BVOC emissions could lead to improvements in model performance.

One approach is the plume-in-grid (PiG) parameterization (Karamchandani et al., 2002). This aims to solve the problem of sub-grid-scale chemical processes by implementing ensembles of Gaussian puffs within the AQM (e.g., Vijayaraghavan et al., 2006). Other approaches include hybrid Eulerian–Lagrangian models (Alessandrini and Ferrero, 2009). These differ from the PiG models by simulating large numbers of stochastic trajectories that can make use of variable reactive volumes to simulate their diffusion into background air masses simulated on Eulerian grids.

Global models have generally used a different approach to the problem of plumes. Broadly, following one of the two paradigms (Paoli et al., 2011) to (i) modify the emissions of the reaction mix (using so-called effective emissions or applying emission conversion factors) and (ii) modify the rates of reaction (effective reaction rates).

The number of chamber studies investigating NO3 chemistry is small compared to the number of studies for photochemical oxidation and ozonolysis. In most of the studies, gas-phase oxidation products and SOA yields from the oxidation of BVOC have been measured. Studies include the investigation of SOA from monoterpenes (Wangberg et al., 1997; Griffin et al., 1999; Hallquist et al., 1999; Spittler et al., 2006; Fry et al., 2009, 2011; Boyd et al., 2015; Nah et al., 2016b), methyl butenol (Fantechi et al., 1998a, b), and isoprene (Rollins et al., 2009; Ng et al., 2010; Schwantes et al., 2015). A few more studies investigated gas-phase reaction kinetics, including the reactions of NO3 with aldehydes (Clifford et al., 2005; Bossmeyer et al., 2006), amines (Zhou and Wenger, 2013), or cresol (Olariu et al., 2013). As a consequence of the small number of studies, the oxidation mechanisms of organic compounds by NO3 and the yields of oxidation products in the gas phase and particle phase have larger uncertainties. The well-controlled oxidation environments in chamber experiments, coupled with complimentary gas-phase and particle-phase measurements (online and offline), allow for elucidating detailed oxidation mechanisms under varying reaction conditions (Ng et al., 2008; Boyd et al., 2015; Schwantes et al., 2015). Identification of gas- and particle-phase reaction products from NO3-BVOC chemistry within controlled chamber environments can also greatly aid in the interpretation of field data in which multiple oxidants and BVOC are present. Future chamber experiments will naturally take advantage of new advanced gas–aerosol instrumentation and aim to constrain the formation yields of gas-phase oxidation products and establish a fundamental understanding of aerosol formation mechanisms from NO3-BVOC under a wide range of oxidation conditions.

Although chamber studies allow separating processes driven by chemistry and physics from transport processes that occur in the real atmosphere, careful characterization of the behavior of NO3 in chambers as well as the organic products of the NO3 oxidation remains a research priority. Yields of gas-phase oxidation products can be influenced by chamber-specific loss processes (surface loss on the chamber wall) and SOA yields can be impacted by both direct loss of particles and loss of species that can condense on particle or chamber wall surfaces (McMurry and Grosjean, 1985; Loza et al., 2010; Matsunaga and Ziemann, 2010; Yeh and Ziemann, 2014; Zhang et al., 2014a, 2015; Krechmer et al., 2016; La et al., 2016; Nah et al., 2016a; Ye et al., 2016). The extent to which vapor wall loss affects SOA yields appears to be dependent on the VOC system, from relatively small effects to as high as a factor of 4 (Zhang et al., 2014a; Nah et al., 2016a). Studies on the effects of vapor loss on SOA formation from BVOC + NO3 are limited. With minimal or no competing gas–particle partitioning processes, substantial vapor wall loss of organic nitrates has been observed in experiments not specific to NO3 oxidation (Yeh and Ziemann, 2014; Krechmer et al., 2016). However, the use of excess oxidant concentrations and rapid SOA formation in BVOC + NO3 experiments (hence, shorter experiments) could potentially mitigate the effects of vapor wall loss on SOA yields in chamber studies (Boyd et al., 2015; Nah et al., 2016a). In light of the developing understanding of this issue, an important consideration for the design of any future systematic chamber studies is the influence of vapor wall loss on SOA formation from nitrate radical oxidation under different reaction conditions, such as peroxy radical fates, relative humidity, seeds, oxidant level, chamber volume, etc.

As discussed above, the fate of peroxy radicals directly governs the product distribution in the NO3-BVOC system, including SOA yields and composition. Dark reactions of peroxy radicals differ significantly from their photochemical analogs, and are directly related to the development of mechanistic understanding in the NO3-BVOC system. There is a need to systematically investigate reaction products and SOA formation from NO3-BVOC reactions under different peroxy radical reaction regimes, but this aspect has only recently become a focus of chamber studies (Ng et al., 2008; Boyd et al., 2015; Schwantes et al., 2015). Rapid formation of highly oxygenated organic nitrates has been observed in laboratory studies of β-pinene + NO3 and α-pinene + NO3; these products could be formed by unimolecular isomerization of peroxy radicals or autoxidation (Nah et al., 2016b). The importance of this peroxy radical reaction channel in NO3-BVOC chemistry warrants further studies. Future chamber studies will need to be explicit in their specification of the peroxy radical chemistry regime that is investigated in a particular experiment, and will need to relate that regime to the conditions of ambient nighttime atmosphere.

Recent field studies have shown that organic nitrates formed from NO3-BVOC are important components of ambient OA. However, the reactivity in both gaseous and condensed phases of these biogenic nitrates, in particular of polyfunctional nitrates, has been subject to few studies and requires better characterization to evaluate the role of these compounds as reservoirs/sinks of NOx. Field results suggest that the fate of organic nitrates in both the gas and aerosol phase have variable lifetimes with respect to hydrolysis. The difference in the relative amount of primary/secondary/tertiary organic nitrates (which hydrolyze with different rates) from nitrate radical oxidation versus photochemical oxidation needs to be constrained. Most of the hydrolysis studies thus far are conducted in bulk, except for a few recent studies on monoterpene organic nitrates (e.g., Boyd et al., 2015; Rindelaub et al., 2015). The solubility of multifunctional organic nitrates in water and the extent to which hydrolysis occurs in aerosol water warrant future studies. The effect of particle acidity on hydrolysis might also be important for organic nitrates formed in different BVOC systems.

While there are extensive studies on photochemical aging of ozonolysis SOA, studies on photochemical aging of NO3-initiated SOA and organic nitrates are extremely limited. A recent study shows that the particle-phase organic nitrates from NO3+β-pinene and NO3+α-pinene reactions exhibit completely different behavior upon photochemical aging during the night-to-day transition, and act as permanent and temporary NOx sinks, respectively (Nah et al., 2016b). With the ∼ 1-week lifetime of aerosols in the atmosphere and the majority of NO3-BVOC organic nitrates that are formed at night, the photochemical fates of these organic nitrates could impact next-day NOx cycling and ozone formation. Therefore, there is a critical need to understand the multigenerational chemistry and characterize the evolution of organic nitrates over its diurnal life cycle, including aging NO3-initiated SOA and organic nitrates by photolysis and/or OH radicals.

The optical properties, especially in the short wavelength region, of NO3-derived SOA may be most conveniently measured during coordinated chamber studies that also include detailed measurements of gas-phase oxidation chemistry and aerosol composition. Such studies could also serve to isolate the specific optical properties of NO3-BVOC-derived aerosol to obtain better optical closure in the interpretation of field data. Field studies that include aerosol optical properties measurements in conjunction with other instrumentation can help quantify the bulk organic nitrate abundance and identify organic nitrate molecular composition in the SOA.

The discussion above shows that recent advances in analytical instrumentation are key to the developing science of NO3-BVOC chemistry. Chamber studies provide an excellent opportunity for the comparison and validation of such instrumentation. State-of-the-art and developing instruments for measurement of NO3 and N2O5 were compared approximately a decade ago (Fuchs et al., 2012; Dorn et al., 2013). These instruments have improved and proliferated since that time, and further validation studies are needed. Measurements of total and speciated gas and aerosol-phase organic nitrates, as well as other oxygenated compounds that result from NO3-BVOC reactions, have not been the subject of a specific intercomparison study. Their comparison and validation will be a priority in future coordinated chamber studies.

Because of the need for a better understanding of NO3 oxidation and because of the challenges of chamber studies, investigating NO3 chemistry, coordination between studies carried out in different chambers, and between chamber and field studies, can augment efforts of single or stand-alone chamber studies. Coordinated studies that would include several chambers could increase the accuracy and reliability of results and quantify realistic errors associated with product yield estimates. This can be achieved by determining the same quantities in similar experiments in different chambers. Studies could benefit from complementary capabilities and properties of chambers. Chambers that typically operate at higher concentration ranges, and therefore increased oxidation rates, are suitable to perform a larger number of experiments that are useful for screening experiments and a series of experiments with systematic variations of chemical conditions. Other chambers are suited to perform experiments at atmospheric reactant concentrations. Experiments in these chambers may take place on a longer timescale, for example, a scale characteristic of the duration of at least one night. Analytical instrumentation and capability also differs considerably among chambers, so that coordinated chamber studies can make use of the determination of complementary quantities such as product yields of different organic compounds and characterization of various properties of particles for the same chemical system. For instance, it would be invaluable to conduct coordinated studies where a variety of instrument techniques are used to measure total and speciated gas- and particle-phase organic nitrates, as well as aerosol physical and chemical properties in the same chamber.

Substantial insights into aerosol sources, formation, and processing can be gained from coordinated laboratory chamber and field studies. Laboratory chamber experiments provide the fundamental data to interpret field measurements. The analysis of field data in turn can provide important insights for constraining chamber experiment parameters so that the oxidation conditions in chambers can be as representative as possible of those in the atmosphere. Two recent sets of experiments serve as examples of this approach. Fundamental chamber studies on β-pinene+NO3 in the Georgia Tech Environmental Chamber (GTEC) facility under conditions relevant to the SE US provided constraints on the contribution of monoterpenes + NO3 to ambient OA during the 2013 SOAS campaign (Boyd et al., 2015; Xu et al., 2015a). The Focused Isoprene eXperiment at California Institute of Technology (FIXCIT) chamber study following SOAS advanced the understanding of isoprene oxidation chemistry relevant to the SE US (Nguyen et al., 2014). It is important not to consider fundamental laboratory studies as isolated efforts, but they should be an integrated part of field studies. Similarly, having the modeling community involved in early planning stages of laboratory and field studies will greatly aid in the identification of critically needed measurement data.