The lifetime of nitrogen oxides in an isoprene-dominated forest

The lifetime of nitrogen oxides (NOx) affects the concentration and distribution of NOx and the spatial patterns of nitrogen deposition. Despite its importance, the lifetime of NOx is poorly constrained in rural and remote continental regions. We use measurements from a site in central Alabama during the Southern Oxidant and Aerosol Study (SOAS) in summer 2013 to provide new insights into the chemistry of NOx and NOx reservoirs. We find that the lifetime of NOx during the daytime is controlled primarily by the production and loss of alkyl and multifunctional nitrates (6ANs). During SOAS, 6AN production was rapid, averaging 90 ppt h−1 during the day, and occurred predominantly during isoprene oxidation. Analysis of the 6AN and HNO3 budgets indicate that 6ANs have an average lifetime of under 2 h, and that approximately 45 % of the 6ANs produced at this site are rapidly hydrolyzed to produce nitric acid. We find that 6AN hydrolysis is the largest source of HNO3 and the primary pathway to permanent removal of NOx from the boundary layer in this location. Using these new constraints on the fate of6ANs, we find that the NOx lifetime is 11±5 h under typical midday conditions. The lifetime is extended by storage of NOx in temporary reservoirs, including acyl peroxy nitrates and 6ANs.


Introduction
The concentration and chemistry of nitrogen oxides (NO x ≡ NO + NO 2 ) in Earth's troposphere has a significant and non-linear effect on the oxidative capacity of the atmosphere.This in turn affects the production, composition, and aging of aerosols and the lifetime of greenhouse gases such as methane.Concentrations of NO x control the production of ozone, a respiratory health hazard, important oxidant, and greenhouse gas.In addition, the deposition of reactive nitrogen is an important source of nutrients in some ecosystems (e.g.Fowler et al., 2013).
Published by Copernicus Publications on behalf of the European Geosciences Union.P. S. Romer et al.: The lifetime of nitrogen oxides NO x is emitted by both anthropogenic and biogenic sources, including motor vehicles, power plants, forest fires, and soil bacteria (e.g.Dallmann and Harley, 2010;Mebust and Cohen, 2014;Hudman et al., 2012), and is temporarily or permanently removed from the atmosphere by chemical conversion to higher oxides of nitrogen.Across much of the globe, the balance of these sources and sinks is in a period of dramatic change, with large reductions of NO x emissions occurring in North America and Europe and significant increases occurring in Asia (e.g.Russell et al., 2012;Curier et al., 2014;Reuter et al., 2014).Understanding the effects of changes in NO x emissions on the concentration and spatial distribution of NO x requires detailed knowledge of the chemistry and transport of NO x and NO x reservoirs.These reservoirs are poorly understood and represent a significant uncertainty in analyses of NO x emissions and ozone production (e.g.Ito et al., 2007;Browne and Cohen, 2012;Mao et al., 2013).
The net chemical loss of NO x is difficult to directly observe.Observational methods for determining the lifetime of NO x are easiest to apply in the outflow of isolated emissions, where the declining concentration of NO x or the changing ratio of NO x to total reactive nitrogen (NO y ) provide clear evidence for NO x loss (e.g.Ryerson et al., 1998;Dillon et al., 2002;Alvarado et al., 2010;Valin et al., 2013).In rural and remote regions, emissions and concentrations of NO x and NO y are typically slowly varying over large distances (e.g.Browne et al., 2013), preventing the loss of NO x from being directly observable.Nor can the lifetimes found in plume studies be easily translated into an appropriate lifetime in the regional background.Short-lived NO x reservoirs such as peroxy acyl nitrate (PAN) can efficiently remove NO x in a plume, but act as a source of NO x in rural and remote regions (Finlayson-Pitts and Pitts, 1999).In addition, the non-linear interactions between NO x and OH make the lifetime of NO x in a fresh plume very different from its lifetime several hours downwind (e.g.Martinez et al., 2003;Valin et al., 2013).
To constrain the lifetime of NO x in rural and remote regions, observations of reactive nitrogen species must be combined with an understanding of the chemical transformations between NO x and its higher oxides.If the production, loss, and fate of these higher oxides are accurately understood, then the lifetime of NO x can be calculated by tracing the flow of reactive nitrogen through the system.Here, we evaluate the daytime lifetime of NO x in the rural southeastern United States, using measurements taken from 1 June-15 July 2013 as part of the Southern Oxidant and Aerosol Study (SOAS).In situ measurements of volatile organic compounds (VOCs), atmospheric oxidants, and a wide range of reactive nitrogen compounds are used to determine the production and loss rates for nitric acid, alkyl and multifunctional nitrates, and peroxy nitrates.These rates are used to assess the lifetime of NO x in this region.
2 The NO y family and the lifetime of NO x During the day, NO x is lost by associating with other radicals to produce higher oxides of nitrogen, primarily nitric acid, alkyl and multifunctional nitrates ( ANs = RONO 2 ), and peroxy nitrates ( PNs = R(O)OONO 2 ) (e.g.Day et al., 2003;Perring et al., 2010).The sum of these and other higher oxides such as N 2 O 5 and HONO are collectively known as NO z (NO z ≡ NO y − NO x ).
NO x is oxidized to produce the major daytime classes of NO z through Reactions (R1), (R2b), and (R3).
NO x can also be converted to NO z through reactions of the NO 3 radical.Although these reactions are most important at night, previous studies have shown that NO 3 chemistry can produce NO z during the day if concentrations of alkenes are high (e.g.Fuentes et al., 2007;Mogensen et al., 2015;Ayres et al., 2015).
The production and fate of different NO z species determine the lifetime of NO x .Some of these species are shortlived and re-release NO x back to the atmosphere within hours of being formed.If the lifetime for the conversion of an NO z species back to NO x is shorter than typical NO x lifetimes in the atmosphere, then NO x and these NO z species interact, and their concentrations will approach a steady-state ratio.As NO x is removed from the system, some of the shortlived NO z species dissociate, buffering the concentration of NO x .In this way, the presence of NO x reservoirs directly extends the lifetime of NO x .
One method to take this buffering into account when calculating the lifetime of NO x is to consider the sum of NO x and all NO z species with lifetimes to re-release of NO x shorter than the atmospheric lifetime of NO x .We define this sum as short-lived reactive nitrogen, or NO SL .The remaining forms of reactive nitrogen are defined as long-lived reactive nitrogen (NO LL ).The division between NO SL and NO LL depends on the lifetime of NO x .For the initial discussion in this manuscript, we use a provisional lifetime of 7 h to divide NO z species between NO SL and NO LL .This cutoff is in the middle of the range of NO x lifetimes found in plume studies (e.g.Ryerson et al., 1998;Dillon et al., 2002;Alvarado et al., 2010;Valin et al., 2013).The provisional cutoff chosen as a starting point does not affect the final results.
In areas well removed from large NO x sources, NO x and its short-lived reservoirs interconvert significantly faster than the rate of change of NO x .Under these conditions, the lifetime of NO x (τ NO x ) is equal to the lifetime of NO SL .If the conversion of NO LL to NO SL is negligible, then the lifetime of NO x can be calculated by Eq. (1).Throughout this paper, we use L(X) to indicate the gross loss rate of the compound or class of compounds X.
The relationship and interactions between NO SL and NO LL , and their typical compositions in the planetary boundary layer, are shown in Fig. 1.In the summertime at midlatitudes, peroxy nitrates typically release NO x within hours of being formed (LaFranchi et al., 2009), making them a component of NO SL .Under these same conditions, nitric acid typically converts back to NO x on timescales of 100 h or greater (Finlayson-Pitts and Pitts, 1999) and is a component of NO LL .The fate and lifetime of ANs, the third major component of NO z , remain poorly understood, making it uncertain whether ANs act as a component of NO SL or NO LL (Perring et al., 2013, and references therein).This is especially true for the multifunctional, biogenically derived nitrates that are the predominant component of ANs in forested areas (e.g.Beaver et al., 2012).
Recent studies of multifunctional nitrates suggest that the main daytime loss pathways of these species are deposition, reaction with OH, photolysis, and heterogeneous hydrolysis to produce nitric acid (e.g.Darer et al., 2011;Browne et al., 2013;Lee et al., 2014;Müller et al., 2014;Nguyen et al., 2015;Lee et al., 2016).These recent studies, combined with the extensive measurements made during SOAS, allow us to provide new constraints on the lifetime and fate of ANs and therefore to more accurately determine the lifetime of NO x .

Instrumentation and measurements
The primary ground site for SOAS was located in Bibb County, Alabama (32.90289 • N, 87.24968 • W) at the Centreville (CTR) long-term monitoring site in the SouthEastern Aerosol Research and CHaracterization (SEARCH) Network (Hansen et al., 2003).This location is 40 km southeast of Tuscaloosa (population 95 000), and 90 km southwest of Birmingham (population 210 000).Comparison with longterm measurements indicate that the summer of 2013 was cooler and cloudier than typical for previous summers (Hidy et al., 2014).Gas-phase measurements used in this study were located on a 20 m walk-up tower at the edge of the forest.Nitrate ion and meteorological parameters were measured in a clearing approximately 50 m away from the tower.
A nearly complete suite of reactive nitrogen species, including NO, NO 2 , PNs, ANs, HNO 3 , and NO − 3 , was measured during SOAS.NO was measured using the chemiluminescence instrument described in Min et al. (2014).The reaction of ambient NO with added excess O 3 formed excited NO * 2 molecules.A fraction of these fluoresce, and the emitted photons were collected on a red-sensitive photomultiplier tube (Hamamatsu H7421-50).Calibrations were performed every 2 h by diluting NO standard gas (5.08 ppm ± 5 % NO in N 2 , Praxair) to 3-20 ppb in zero air and adding it to the instrument inlet.The mixing ratio was corrected for enhanced quenching by water vapor (Thornton et al., 2000) using colocated measurements of relative humidity and temperature.
NO 2 , PNs, and ANs were measured via thermal dissociation laser induced fluorescence (TD-LIF), as described by Day et al. (2002).Ambient air was drawn into a multipass White cell, where a 532 nm Nd-YAG laser excited the NO 2 molecules, and their fluorescence signal was collected on a photomultiplier tube (Hamamatsu H7421-50).The same instrument was used to measure the sum of peroxy nitrates and the sum of alkyl and multifunctional nitrates by first passing the air through a heated oven, where the organic nitrates dissociated to form NO 2 .Organic nitrates present in the particle phase undergo evaporation and thermal dissociation in the heated ovens to form NO 2 .The TD-LIF measurement of ANs therefore includes alkyl and multifunctional nitrates in both the gas and particle phases, but does not include HNO 3 or particle-phase inorganic nitrate (Day et al., 2002;Rollins et al., 2010).All of the channels were calibrated by injecting NO 2 standard gas (5.03 ppm ± 5 % NO 2 in N 2 , Praxair) and corrected for enhanced quenching by water vapor.
Nitric acid was measured in the gas phase by chemical ionization mass spectrometry (CIMS), using CF 3 O − as the reagent ion (Crounse et al., 2006).The ions were quantified using a compact time-of-flight mass spectrometer, and the instrument was calibrated in the field using isotopically labeled nitric acid.Particle-phase inorganic nitrate (NO − 3 ) was measured using a Monitor for AeRosols and GAses (MARGA) (Allen et al., 2015).Ambient air was drawn through a rotating wet-walled denuder which collected water-soluble gasphase compounds.Particle-phase compounds were captured by a steam-jet aerosol collector downstream of the denuder.Water-soluble ions from both phases were then quantified via ion chromatography.This measurement of NO − 3 is designed to be specific to inorganic nitrate, and is not affected by ANs in the particle phase (Allen et al., 2015).The classification into NO SL and NO LL is based on typical summertime afternoon lifetimes.The measurement of HNO 3 represents nitric acid in the gas phase, while the measurement of NO − 3 represents inorganic nitrate in the particle phase.The measurement of ANs includes alkyl and multifunctional nitrates in both the gas and particle phase.
Measurements of reactive nitrogen species are summarized in Fig. 2. Concentrations of NO SL compounds (NO, NO 2 , and PNs) are shown in Fig. 2a.Afternoon concentrations of NO 2 and NO were typically around 220 and 50 ppt respectively.After sunset, NO dropped to near zero, and NO 2 began to increase.At sunrise, NO concentrations rapidly rose to over 200 ppt between 06:00 and 08:00 Central Standard Time (CST) while NO 2 decreased sharply.By 11:00, when the daytime boundary layer was well developed, the concentrations of NO and NO 2 returned to their typical afternoon values.Concentrations of PNs were 160 ppt at sunrise, increased to a maximum concentration of 300 ppt at 09:00 and declined slowly throughout the rest of the day.
Concentrations of HNO 3 and inorganic NO − 3 , components of NO LL , are shown in Fig. 2b.Both species increased slowly after sunrise and reached a maximum combined concentration of 300 ppt at 13:00, before declining to a combined concentration of 175 ppt at night.The total concentration of ANs in both the gas and particle phase, whose partitioning into NO SL and NO LL is not known, is shown in Fig. 2c.ANs averaged 150 ppt during the night and increased sharply after sunrise.After reaching a maximum of 250 ppt at 08:00, ANs declined slowly to a minimum concentration of 125 ppt at sunset.OH, HO 2 , and OH reactivity (OHR) were measured via fluorescence assay by gas expansion (FAGE) of OH.A 308 nm dye laser excited the OH radicals and their fluores- cence was detected by an electronically gated microchannel plate detector (Faloona et al., 2004).Calibration of the system was performed by in situ generation of OH radicals via photolysis of water vapor.Chemical zeroing was performed by periodically adding C 3 F 6 to the sampling inlet in order to quantify the interference from internally generated OH observed in previous field campaigns (Mao et al., 2012).HO 2 was measured in a second channel by adding NO to chemically convert HO 2 to OH.The amount of added NO was regulated such that HO 2 but not RO 2 was converted to OH (Fuchs et al., 2011).Total OH reactivity (OHR) was measured by drawing ambient air through a flow tube and mixing it with a fixed concentration of OH.At the end of the flow tube, the concentration of OH was measured.The OH reactivity is determined by the slope of the OH signal vs. reaction time (Mao et al., 2009).
Measured concentrations of OH peaked at 0.045 ppt and concentrations of HO 2 at 30 ppt during SOAS (Fig. 3, top panel).Both OH and HO 2 increased slowly throughout the morning and reached their maximum in the early afternoon.Concentrations then fell as the sun set, with OH usually dropping below 0.01 ppt by 19:00 The measured OH reactivity was high, reaching an afternoon peak of close to 25 s −1 (Fig. 3, bottom panel).OHR decreased throughout the night, reaching a minimum of 10 s −1 just before sunrise.
Measurements of ozone were made using a cavity ring down spectrometer (Washenfelder et al., 2011).O 3 was chemically converted to NO 2 by reaction with excess NO, and the resulting NO 2 was measured by cavity ring-down spectroscopy at 404 nm.The concentration of ozone increased from a minimum of 15 ppb at sunrise to a maximum of 38 ppb in the late afternoon (Fig. 3, middle panel).
Volatile organic compounds were measured primarily by gas chromatography-mass spectrometry (GC-MS).Samples were collected in a liquid-nitrogen cooled trap for 5 min, and then transferred by heating onto an analytical column, and detected using an electron-impact quadrupole massspectrometer (Goldan et al., 2004;Gilman et al., 2010).This system was able to quantify a wide range of compounds including alkanes, alkenes, aromatics, isoprene, and multiple monoterpenes.The sum of methyl vinyl ketone (MVK) and methacrolein (MACR) was measured using a proton transfer reaction time-of-flight mass spectrometer (PTR-TOF-MS) (Kaser et al., 2013).The interference in this measurement from the decomposition of isoprene hydroperoxides on instrument inlets (Rivera-Rios et al., 2014) is not corrected for, and increases the uncertainty in this measurement by approximately 20 %.
VOC measurements at the site show that the OHR was dominated by reaction with biogenic compounds.Figure 3 shows the OH reactivity of individually measured compounds as a stacked area plot.In the daytime, isoprene accounted for nearly half of the total reactivity, while VOCs typically attributed to anthropogenic activities, including alkanes, aromatics, and simple alkenes, were responsible for less than 10 % of the measured OHR.Not included in Fig. 3 is the reactivity of VOCs whose reaction with OH does not lead to net loss of OH, and therefore does not contribute to the measured OHR.These compounds, primarily isoprene hydroperoxides (ISOPOOH) and C5hydroxyaldehydes (HPALD), have an average daytime reactivity of 2 s −1 .The sum of individual reactivities shows a similar diurnal pattern to the measured OHR, and accounts for 70-85 % of the total.Unknown biogenic emissions, small aldehydes and alcohols, and other 2nd and 3rd generation VOC oxidation products are all possible contributors to the missing reactivity (e.g.Di Carlo et al., 2004;Goldstein and Galbally, 2007;Pusede et al., 2014;Kaiser et al., 2016).Meteorological parameters including temperature and solar radiation were measured by Atmospheric Research and Analysis as part of SEARCH.
4 The production and loss of individual NO x reservoirs

Nitric acid
In the boundary layer, the production of nitric acid is typically followed by deposition and thus leads to the permanent removal of reactive nitrogen from the atmosphere.Nitric acid can undergo photolysis or reaction with OH to produce NO x , but these processes are slow (Burkholder et al., 1993;Atkinson et al., 2006), with an average calculated rate during SOAS of less than 0.2 ppt h −1 .Gas-phase nitric acid can also partition into aerosols.Nitric acid is long-lived in the particle phase and is typically lost by re-evaporation into the gas phase (e.g.Hennigan et al., 2008).The loss of ni-tric acid through deposition of aerosols is typically negligible compared to its gas-phase deposition (e.g.Zalakeviciute et al., 2012).Because nitric acid releases NO x so slowly, it is a component of NO LL .
The deposition velocity (v dep ) of HNO 3 in the gas phase was measured during SOAS by Nguyen et al. (2015).Around midday, when the boundary layer is well developed, the deposition velocity can be combined with the boundary layer height (BLH) to calculate a loss rate of using Eq.(2).

L(HNO
Using this method, we find the lifetime of nitric acid in the gas and particle phase to be 6 h at noon.In the late afternoon, changing boundary layer dynamics make this calculation of the loss rate inaccurate (e.g.Papale et al., 2006;Millet et al., 2015).The loss of nitric acid in the late afternoon was therefore calculated by fitting periods of consistent decay between 15:00 and 19:00 with an exponential curve.By fitting only the periods of consistent decay, we aim to select for periods where the production of nitric acid is at a minimum and the observed net decay of nitric acid is similar to its gross loss rate.Because nitric acid reversibly partitions between the gas and particle phases, the lifetime was calculated based on the concentration of nitric acid in both phases.The lifetime calculated using this method is 5 +3 −2 h, similar to the lifetime of nitric acid calculated using Eq. ( 2) at noon.
By combining the loss rate of nitric acid with the rate of change of its concentration, we can calculate an inferred production rate of nitric acid (Fig. 4).This inferred production rate for each hour is defined as the difference between the rate of change in the concentration of nitric acid and the loss rate.The rate of change was determined as the slope of a best-fit line of the concentration of nitric acid vs. time for each hour.
Since the calculation of the inferred production rate considers only the hour-to-hour change in nitric acid and not its gross concentration, the inferred production rate is not affected by distant nitric acid sources.We find very little (less than 15 %) variation in the concentration of NO x with wind direction and no correlation of the inferred production rate around noon with sulfate (a power plant tracer) or benzene (an urban tracer).As the transport time from these sources to the CTR site is significantly greater than 1 h, this result is not surprising.The changing boundary layer height could significantly impact the inferred production rate of nitric acid during the early morning, but it is likely unimportant at midday.
Also shown in Fig. 4 is the rate of nitric acid production from the reaction of OH + NO 2 (Reaction R1), using the rate constant measured by Mollner et al. (2010).The vertical bars for the inferred rate represent the combined effects of the uncertainty in both the fit of concentration vs. time and in the calculated nitric acid lifetime, as well as the day-to-day variations in the observations.The vertical bars shown for the production of nitric acid from the OH + NO 2 reaction in- clude both the systematic and random errors in the measurements of OH and NO 2 and in the rate coefficient, k OH+NO 2 , combined in quadrature.
Between 10:00 and 14:00, when photochemistry is most active, the inferred production rate is 3-4 times larger than the rate of Reaction (R1), a difference of approximately 30 ppt h −1 .The most likely explanation for the missing nitric acid production during this time is the heterogeneous hydrolysis of ANs.This reaction has been proposed as an important source of nitric acid over the Canadian boreal forest (Browne et al., 2013), and the hydrolysis of tertiary alkyl nitrates on atmospherically relevant timescales has been observed in several laboratory experiments (e.g.Darer et al., 2011;Liu et al., 2012;Rindelaub et al., 2015).If ANs are being converted to nitric acid, this process should appear as a sink in the budget of ANs.If other processes are responsible for the missing nitric acid source, these would not affect the budget of ANs.Only the conversion of ANs to nitric acid will lead to a missing source of nitric acid and a missing sink of ANs.

Alkyl and multifunctional nitrates
Previous observational studies have found that the production of ANs is rapid in forested regions (e.g.Day et al., 2009;Beaver et al., 2012;Fry et al., 2013;Browne et al., 2013), but the subsequent fate of these biogenic nitrates is not well constrained.During the day, ANs are produced primarily from the reaction of organic peroxy radicals (RO 2 ) with NO.Most of the time, this leads to the formation of RO and NO 2 (Reaction R2a), but a fraction of the time produces an organic nitrate (Reaction R2b).The branching ratio k R2b /(k R2b + k R2a ) is designated α and varies with the structure of the R group, as well as the temperature and pressure. NO Organic peroxy radicals are produced in the daytime troposphere predominantly by the reaction of OH with VOCs and are lost through reaction with NO, HO 2 , and RO 2 , or through unimolecular isomerization.These radicals reach steady state within seconds, allowing the production of ANs via Reaction (R2b) to be calculated using Eq.(3).
The value f NO represents the fraction of RO 2 radicals that are lost by reaction with NO.This value was calculated separately for each measured VOC and is equal to the rate of Reactions ( R2b) and (R2a), divided by the sum of all RO 2 loss rates.Rate constants for the reaction of RO 2 radicals with NO, HO 2 , and other RO 2 radicals are taken from the Master Chemical Mechanism v3.2 (Saunders et al., 2003) for all species other than isoprene and methacrolein.The reactions of isoprene-derived RO 2 radicals are based on the LIM-1 scheme described by Peeters et al. (2014), with the rate of unimolecular isomerization scaled to match the rate of HPALD formation observed in chamber experiments by Crounse et al. (2011).For methacrolein, we include the isomerization rate described by Crounse et al. (2012).Unimolecular isomerization is not included for any other RO 2 species.Concentrations of RO 2 radicals are calculated iteratively at each point until they converge.
Values of k OH+R i and α i are taken from Atkinson and Arey (2003) and Perring et al. (2013) respectively, with the following exceptions.An α of 0.26 is used for α-pinene, following Rindelaub et al. (2015).An α of 0.12 is used for isoprene.This is in the middle of the range of branching ratios for isoprene (0.09-0.15) found in recent experiments (e.g.Paulot et al., 2009;Teng et al., 2015;Xiong et al., 2015).
The missing OH reactivity (Fig. 3) is included in this calculation as a generic VOC that forms RO 2 radicals that react with the same kinetics as CH 3 CH 2 O 2 and has a value of α of 0.005.This is an appropriate value if the missing reactivity is composed of small or highly oxygenated compounds (Perring et al., 2013).If the missing OH reactivity has a significant contribution from large hydrocarbons, then this value should be higher.
The daytime production of ANs also includes a minor contribution from the reaction of NO 3 with alkenes, via Reactions (R4) and (R5).
Concentrations of isoprene and monoterpenes were sufficiently elevated during SOAS that the reaction with these compounds is a significant fraction of the total daytime loss of NO 3 .Calculations following Ayres et al. (2015) indicate that this pathway produces ANs at an average rate of 10 ppt h −1 .The calculated total rate of AN production via Reactions ( R2b) and ( R5) is rapid, averaging approximately 90 ppt h −1 between 08:00 and 16:00 (Fig. 5).The oxidation of isoprene accounts for over three-quarters of the production of ANs, and monoterpenes account for an additional 15 %.Based on the uncertainty in each term in Eq. ( 3), the total systematic uncertainty in the production rate of ANs is estimated to be ±55 % (one sigma).The largest contribution to the total uncertainty comes from the calculation of f NO for isoprene.Reported uncertainties for the rate constants and radical concentrations involved in RO 2 loss (Boyd et al., 2003;Ghosh et al., 2010;Crounse et al., 2011;Peeters et al., 2014) combine to give an overall uncertainty of ±35 % in f NO for isoprene.Uncertainty in the values of alpha and the nature of the missing OHR are also significant contributions to the total uncertainty.The effects of boundary layer growth are not accounted for, but are unlikely to be important after 10:00 (e.g.Xiong et al., 2015).The 55 % uncertainty constrains the average ANs production rate to between 50 and 145 ppt h −1 .
Rapid production of ANs decreases the NO x lifetime only if it leads to the long-term removal of NO x from the atmosphere.This can occur either if the alkyl and multifunctional nitrates produced are themselves long-lived, or if they have short lifetimes but are lost primarily to deposition or to conversion to a different NO z species that is long-lived.Despite rapid production of ANs during the day, the diurnal cycle of ANs exhibits a decrease between 09:00 and 19:00 (Fig. 2c), implying that the ANs loss rate must be rapid.While ANs do not build up over the course of a day, their concentration is strongly correlated with their instantaneous production rate in the afternoon (Fig. 6).We interpret these two results to indicate that ANs are short-lived and near steady-state in the afternoon.A least-squares fit between AN production and concentration gives a slope of 1.7 h and an intercept of 40 ppt.If ANs are near steadystate, then the slope of this correlation is equal to the AN lifetime.The intercept of 40 ppt is interpreted as the largescale background of long-lived ANs during summertime at mid-latitudes.This background is likely composed of small monofunctional alkyl nitrates, since these compounds typically have lifetimes of days or weeks in the summertime troposphere (e.g Clemitshaw et al., 1997).Ethyl and isopropyl nitrate were measured by GC-MS during SOAS, and show a consistent concentration of ∼ 20 ppt, explaining 50 % of the intercept.Previous observations over North America suggest that the summed concentration of small monofunctional nitrates not measured during SOAS is likely also around 20 ppt in the southeastern United States, accounting for the other 50 % (e.g.Schneider et al., 1998;Blake et al., 2003;Russo et al., 2010).
A lifetime of 1.7 h for the reactive component of ANs is roughly consistent with previous estimates.Perring et al. (2009) found a lifetime of 1.5-2.5 h for ANs in the southeastern United States, based on the correlation between ANs and formaldehyde.Multiple studies have also found evidence for rapid loss of ANs through particle-phase processing in the southeastern United States (e.g.Pye et al., 2015;Lee et al., 2016).This reactive component is likely composed of larger, multifunctional nitrates that can be lost rapidly by oxidation, deposition, or hydrolysis (Lee et al., 2014;Nguyen et al., 2015;Darer et al., 2011).
Because most ANs are short-lived, they do not serve as a permanent sink of NO x directly.To establish whether ANs are a component of NO SL or NO LL , the fate of ANs must be understood.Conversion of an alkyl nitrate to another alkyl nitrate does not affect the measurement of ANs and therefore does not contribute to the calculated 1.7 h lifetime.The only other NO y compounds produced by alkyl nitrate oxidation that have been observed in laboratory experiments are NO x and nitric acid (e.g. Lee et al., 2014;Darer et al., 2011).These two products are thought to arise from completely different mechanisms in the oxidation of ANs.NO x is produced either during the gas-phase oxidation of nitrates (Lee et al., 2014) or by the photolysis of carbonyl nitrates (Müller et al., 2014), while nitric acid is produced only by the heterogeneous hydrolysis of hydroxy-nitrates (Darer et al., 2011).The question of whether AN to nitric acid conversion is occurring is therefore equivalent to the question of whether deposition and the sum of all gas-phase loss processes are sufficient to explain the 1.7 h lifetime of ANs.If these processes cannot explain the short lifetime of ANs, then the unaccounted-for loss is likely due to heterogeneous formation of nitric acid.
An upper limit to the gas-phase oxidation rate of ANs can be calculated using measurements of ANs by assuming that all alkyl and multifunctional nitrates react with OH and O 3 at the same rate as isoprene hydroxy-nitrates and that these reactions all lead to loss of ANs.Over three-quarters of the ANs produced during SOAS were isoprene hydroxynitrates (Fig. 5), making the average loss rate of ANs close to the rate for isoprene hydroxy-nitrates.In addition, under low-NO x conditions, the most likely products of AN oxidation are either NO x or carbonyl nitrates (Lee et al., 2014).Studies by Müller et al. (2014) and Xiong et al. (2016) indicate that carbonyl nitrates are rapidly photolyzed to release NO x .If the photolysis rate is fast enough, then it is a reasonable approximation to treat ANs as releasing NO x every time they are oxidized.
Only ANs present in the gas phase are likely to undergo deposition or reaction with OH or O 3 .Observations during SOAS indicate that 20 % of ANs may be in the particle phase during the afternoon (Lee et al., 2016); however, even if we assume that all ANs are gas-phase, the rate of gas-phase oxidation plus the rate of deposition measured by Nguyen et al. (2015) during SOAS is insufficient to explain the loss of ANs in the afternoon (Fig. 7, filled areas).Since isoprene hydroxy-nitrates and most other first-generation nitrates must be further oxidized before undergoing photolysis, we do not include photolysis as a separate loss process in Fig. 7. Nitrates produced in the oxidation of compounds such as MVK and MACR can undergo photolysis without reacting with OH first, but these are a minor fraction of the total AN production rate (Fig. 5).
If the gap between the individual loss processes and the overall loss rate of ANs is attributed entirely to AN hydrolysis, then the rate of nitric acid production from ANs would be 65 ppt h −1 .This is two-thirds of the total AN production rate, and roughly equal to the calculated production rate of tertiary nitrates (Peeters et al., 2014;Rindelaub et al., 2015).Laboratory experiments have shown that, in general, tertiary nitrates undergo hydrolysis far faster than primary or secondary nitrates (Darer et al., 2011;Hu et al., 2011), making it likely that the rate of AN hydrolysis is similar to the rate of tertiary AN production.
While the simultaneous presence of a significant missing source of nitric acid and a missing sink of ANs supports the idea that AN to nitric acid conversion is occurring, the missing sink of ANs is approximately a factor of two larger than the missing source of nitric acid (Fig. 7, hatched area).The discrepancy between the two calculations of the AN hydrolysis rate could be accounted for by uncertainty in the measurements, in the calculated production rate of ANs, or in the calculated lifetime of nitric acid.As the data from SOAS are insufficient to determine which of these interpretations is correct, we use the average of the missing nitric acid production rate and the missing AN loss rate as our best estimate of the AN hydrolysis rate.
Using this average, the rate of AN hydrolysis to produce nitric acid is 45 ppt h −1 between 10:00 and 14:00.When this is combined with the loss of ANs by deposition, 55 % of the ANs produced lead to the permanent removal of NO x from the atmosphere.Using the hydrolysis rate calculated from only the nitric acid budget or only the ANs budget changes this fraction to 35 or 75 %.The remaining locally produced ANs are assumed to re-release NO x back to the atmosphere through oxidation and photolysis.
Based on the lifetime and fate calculated here, locally produced ANs have a lifetime to re-release of NO x of just under 4 h, making them part of NO SL .At the same time, de-position and the rapid conversion of reactive multifunctional nitrates to nitric acid means that the formation of ANs leads to the significant removal of NO SL , and therefore NO x , from the atmosphere.

Peroxy nitrates
Peroxy nitrates are produced through the association of a peroxy acyl radical with NO 2 (Reaction R3).While non-acyl peroxy radicals can also associate with NO 2 , the product is extremely unstable and decomposes within seconds in the summertime boundary layer.Peroxy nitrates are primarily lost by thermal dissociation to form NO 2 and a peroxy acyl radical.This acyl radical can either react with NO 2 to reform a peroxy nitrate, or react with NO or HO 2 to form an acyloxy radical or a peracid.The lifetime of peroxy nitrates therefore depends on the temperature and the relative concentrations of NO 2 , NO, and HO 2 (LaFranchi et al., 2009).Rate constants from Orlando and Tyndall (2012) and Atkinson et al. (2006) for the reactions of peroxy acyl nitrate and acyl peroxy radical were used to calculate the lifetime of peroxy nitrates during SOAS.
During the day, peroxy nitrates re-release NO x on timescales of 1-2 h and are a component of NO SL .The production of peroxy nitrates therefore does not contribute to the net loss of NO SL , but still affects the lifetime of NO SL by adjusting the amount of NO x available for reactions that produce ANs or nitric acid.At SOAS, the ratio of peroxy nitrates to NO x is typically around 0.7 at midday.
There are other loss processes of peroxy nitrates.The reaction of OH with methacryloyl peroxy nitrate (MPAN) is rapid, but MPAN is typically a minor component of total peroxy nitrates (LaFranchi et al., 2009).The deposition rate of peroxy nitrates was not measured during SOAS, but previous measurements in a ponderosa pine forest estimate the deposition velocity to be between 0.5 and 1.3 cm s −1 (Wolfe et al., 2009;Min et al., 2012).Using this range of deposition velocities gives a total deposition loss rate of peroxy nitrates of 5 ± 3 ppt h −1 in the afternoon.
5 The photochemical lifetime of NO x and NO SL The measured concentrations and calculated production and loss rates of each individual NO z species can be combined to determine the lifetime of NO SL .This lifetime depends on the distribution of NO z between NO SL and NO LL and the chemical transformations between these two classes.If a 7 h lifetime to re-release of NO x is used as the provisional dividing line between NO SL and NO LL , then in the afternoon NO SL was composed of NO x , PNs, and the reactive component of ANs.As discussed earlier, both peroxy nitrates and ANs have lifetimes to re-release of NO x of less than 4 h.During the same time, NO LL was composed of nitric acid and unreactive ANs.We interpret the y intercept in the correlation between AN production and concentration (Fig. 6) to represent a 40 ppt background of unreactive ANs, likely composed of small monofunctional nitrates.We treat all ANs greater than this constant background as short-lived.
The lifetime of NO SL can then be calculated as τ NO SL = [NO SL ]/L(NO SL ).The individual processes that lead to loss of NO SL and their average value between 10:00 and 14:00 during SOAS are shown in Fig. 8.The loss of short-lived reactive nitrogen is dominated by the hydrolysis of ANs to produce nitric acid.This single process accounts for 65 % of the total NO SL loss.
NO SL is also converted to NO LL during SOAS through the association of OH and NO 2 to produce nitric acid and the production of small, unreactive alkyl nitrates.The deposition of both peroxy nitrates and ANs, as well as the uptake of NO x by plants, also leads to the loss of NO SL .Based on the deposition velocity of NO x over vegetation measured by Breuninger et al. (2013), the rate of NO x uptake was calculated to be approximately 1 ppt h −1 .A 50 % uncertainty in the AN hydrolysis rate, combined in quadrature with the uncertainties from the other NO SL loss processes, gives the overall uncertainty in the NO SL loss rate of ±25 ppt h −1 .
When combined with the average concentration of NO SL of 700 ppt during this same time period, the lifetime of NO SL , and therefore the photochemical lifetime of NO x , is calculated to be 11 ± 5 h.This calculated lifetime of NO SL is used as the cutoff between NO SL and NO LL .Changing the cutoff from our provisional value of 7 to 11 h does not change the partitioning of NO y between these two classes.
The long lifetime of NO x calculated here is qualitatively consistent with the partitioning of NO y during SOAS.The concentration of NO SL is approximately twice as large as NO LL during the afternoon (Fig. 2).In the absence of large fresh emissions of NO x , this implies that the conversion of NO SL to NO LL must be slow, in agreement with our calculations.More quantitative calculations of the NO x lifetime P. S. Romer et al.: The lifetime of nitrogen oxides using the ratio of NO SL to NO LL or NO x to NO y have been developed for analyses of plumes (e.g.Kleinman et al., 2000;Ryerson et al., 2003) but are not adaptable to this data set.
This NO x lifetime is longer than the lifetime of NO x calculated in fresh plumes, where observational studies have found lifetimes of 5-8 h (e.g.Ryerson et al., 1998;Alvarado et al., 2010;Valin et al., 2013).These studies focus solely on the chemistry of NO x rather than NO SL and recognition of the buffering effect of organic nitrates would extend the lifetimes found in these studies.In addition, the average noontime concentration of OH observed during SOAS was up to a factor of 5 lower than values typically observed in urban areas (e.g.Mao et al., 2010;Rohrer et al., 2014).Lower concentrations of OH slow the rate of atmospheric oxidation, leading to longer lifetimes of NO x .
If lower OH and the production of NO x from peroxy nitrates were the only differences between polluted areas and the regional background, then the lifetime of NO x during SOAS would be significantly longer than 10 h.However, the production of ANs is extremely rapid and the deposition and hydrolysis of these species accounts for the majority of the NO x removal in this rural region.The VOC mixture present in the southeastern United States leads to very high values of OH reactivity and α, both of which enhance the production of ANs.High concentrations of VOCs also lead to lower OH concentrations and slower production of nitric acid by Reaction (R1).Moving from urban centers to rural or remote regions is therefore also a move from nitric acidto AN-dominated NO x chemistry.Changes to our understanding of the production and fate of alkyl and multifunctional nitrates will therefore have a large impact on predictions of the lifetime of NO x and NO SL , with subsequent impacts on the concentration and distribution of NO x across a region.

Conclusions
Measurements in a low-NO x , high-VOC region provide new insights into the lifetime and chemistry of NO x and NO SL in rural areas.NO SL is found to have an average lifetime of 11 ± 5 h, longer than the lifetimes of NO x observed in plume studies, which do not account for buffering by short-lived NO z species.The long lifetime of NO SL makes it relatively evenly distributed across the region and allows small inputs of NO x to sustain the concentrations of NO SL observed during SOAS.
The long daytime lifetime of NO SL found here indicates that NO x emitted on one day will persist into the night where NO 3 is often the most important oxidant (Brown and Stutz, 2012).Depending on the chemistry taking place, NO SL could either be efficiently removed from the atmosphere at night, or remain in the atmosphere until the next day.To fully understand the transport and distribution of NO x across a region the daytime chemistry of NO x discussed here must be com-bined with additional analyses of the nighttime chemistry of NO x and NO y (e.g. Brown et al., 2009;Crowley et al., 2011;Ayres et al., 2015).
The production and loss of ANs are found to be the most important variables in controlling the lifetime of NO SL .
ANs were observed to have a lifetime of under 2 h during the afternoon.This estimate is in line with many previous estimates of AN lifetimes, and indicates that ANs are an important short-lived NO x reservoir.Observations of both nitric acid and ANs during SOAS provide strong evidence that both gas-phase oxidation to produce NO x and particle-phase hydrolysis to produce nitric acid are important chemical loss processes for ANs.Comparison of the nitric acid and AN budgets indicate that between 30 and 70 % of the alkyl and multifunctional nitrates produced are converted to nitric acid.Further laboratory and field studies are necessary to better constrain this percentage and to understand the mechanisms that control it.
The vast majority of these ANs are formed during the oxidation of biogenic hydrocarbons, while much of the NO x is emitted by anthropogenic activities.In this way, the formation of ANs represents an important anthropogenicbiogenic interaction, where the oxidation of biogenic VOCs serves to remove anthropogenic pollution from the atmosphere.In rural and remote regions, the interactions between NO y , HO x , and VOCs are complex and bi-directional.As NO x emissions decrease, ANs will likely become an even more important part of the NO y budget, making it increasingly important that their chemistry and loss be taken into consideration when calculating the lifetime and fate of NO x .

Figure 1 .
Figure 1.A schematic representation of the chemistry of NO SL and NO LL , showing the typical components of both classes.

Figure 2 .
Figure 2. Diurnal cycle of measured reactive nitrogen species during SOAS.Reactive nitrogen species are classified as likely components of NO SL (a), likely components of NO LL (b) or unknown (c).The classification into NO SL and NO LL is based on typical summertime afternoon lifetimes.The measurement of HNO 3 represents nitric acid in the gas phase, while the measurement of NO − 3 represents inorganic nitrate in the particle phase.The measurement of ANs includes alkyl and multifunctional nitrates in both the gas and particle phase.

Figure 3 .
Figure 3.Diurnal cycle of OH, HO 2 , O 3 and VOCs during SOAS.The top plot shows the concentration of OH and HO 2 ; the middle plot shows the concentration of O 3 ; the bottom plot shows the OH reactivity.

Figure 4 .
Figure 4. Production rates of nitric acid during SOAS calculated from the reaction of OH + NO 2 (black) and inferred from the concentration and deposition rate of nitric acid (blue).The vertical bars show the systematic and random uncertainty in the calculated rates, as described in the text.

Figure 6 .
Figure6.The concentration of ANs vs. their production rate during the afternoon (12:00-16:00).The black squares show the median in each bin, and the shaded grey area the interquartile range.A linear fit gives a slope of 1.7 h.

Figure 7 .
Figure 7. Loss rates and fates of ANs during SOAS.The black line shows the loss rate of ANs based on the difference between the calculated production rate and the observed change in concentration.The shaded areas show the rates of known ANs loss processes, and the hatched area shows the missing nitric acid source.