Effects of biogenic nitrate chemistry on the NO x lifetime in remote continental regions

We present an analysis of the NO x budget in conditions of low NOx (NOx = NO+ NO2) and high biogenic volatile organic compound (BVOC) concentrations that are characteristic of most continental boundary layers. Using a steady-state model, we show that below 500 pptv of NO x, the NOx lifetime is extremely sensitive to organic nitrate (RONO2) formation rates. We find that even for RONO 2 formation values that are an order of magnitude smaller than is typical for continental conditions significant reductions in NOx lifetime, and consequently ozone production efficiency, are caused by nitrate forming reactions. Comparison of the steady-state box model to a 3-D chemical transport model (CTM) confirms that the concepts illustrated by the simpler model are a useful approximation of predictions provided by the full CTM. This implies that the regional and global budgets of NOx, OH, and ozone will be sensitive to assumptions regarding organic nitrate chemistry. Changes in the budgets of these species affect the representation of processes important to air quality and climate. Consequently, CTMs must include an accurate representation of organic nitrate chemistry in order to provide accurate assessments of past, present, and future air quality and climate. These findings suggest the need for further experimental constraints on the formation and fate of biogenic RONO 2.


Introduction
Nitrogen oxides enter the atmosphere as a result of bacterial processes in soils, high temperature chemistry in lightning, and combustion of fossil fuels and biomass.Current estimates are that human creation of reactive nitrogen (both oxidized and reduced nitrogen) increased by over an order of magnitude from ∼ 15 Tg N yr −1 to ∼ 187 Tg N yr −1 between 1860 and 2005 (Galloway et al., 2008).This increase is one of the primary causes of air pollution, contributing directly to the production of urban ozone and secondary organic aerosol (e.g., Carlton et al., 2010;Pye et al., 2010;Pinder et al., 2012;Rollins et al., 2012).The increase in NO x also results in an increase in the global background of OH (e.g., Wild et al., 2001).This in turn affects air pollution by increasing the global background ozone concentration (e.g., Wild et al., 2001) and making it more difficult to reduce ozone in some cities (e.g., Zhang et al., 2008;Parrish et al., 2010).This increase in ozone also affects climate directly, and both NO x and ozone affect climate indirectly by their influence on the global lifetime of CH 4 (e.g., Fuglestvedt et al., 1999;Wild et al., 2001;Derwent et al., 2008;Fry et al., 2012).Several studies have shown that the net global impact of NO x emissions on climate forcing is highly dependent on the location and seasonal cycle of the emissions (e.g., Fuglestvedt et al., 1999;Derwent et al., 2008;Fry et al., 2012).Consequently, there has been a significant research effort to understand emissions of NO x from different sources such as fossil fuel combustion (e.g., van der A et al., 2008;Dallmann and Harley, 2010;Jaeglé et al., 2005), lightning (e.g., van der A et al., 2008;Hudman et al., 2007;Schumann and Huntrieser, 2007), biomass burning (e.g., van der A et al., 2008;Alvarado et al., 2010;Jaeglé et al., 2005;Mebust et al., 2011;Wiedinmyer et al., 2006), and soils (e.g., van der A et al., 2008;Bertram et al., 2005;Ghude et al., 2010;Hudman et al., 2010;Jaeglé et al., 2005).In contrast, the lifetime of NO x , knowledge of which is necessary determine concentrations from emissions, is not as well studied.
In the vicinity of emissions, the lifetime of NO x (defined here as concentration divided by loss rate) is a steeply nonlinear function of the concentration of NO x (Valin et al., 2011 and references therein).In the remote continental atmosphere, emissions are more uniformly distributed and NO x concentrations vary more slowly.Textbooks suggest that the chemical lifetime of NO x in these regions is largely set by its reaction with OH to produce HNO 3 .However, several analyses have quantified the effect of isoprene nitrate formation on the NO x budget, showing that isoprene nitrate formation is a major sink of NO x and implying a strong effect on NO x lifetime (e.g., Trainer et al., 1991;Horowitz et al., 2007;Ito et al., 2007;Wu et al., 2007;Paulot et al., 2012).
In this paper we investigate how changes in the formation rate of organic nitrates (RONO 2 ) affect the NO x budget in low NO x , high BVOC environments.Using a steady-state model we find that the instantaneous NO x lifetime, and consequently ozone production efficiency, is extremely sensitive to RONO 2 production even when production rates are an order of magnitude smaller than typical for continental conditions.Calculations using the WRF-Chem model (Weather Research and Forecasting model with chemistry) (Grell et al., 2005) with detailed RONO 2 chemistry added to the chemical mechanism, are shown to be consistent with the conceptual model; this indicates that the steady-state model is sufficient to serve as a guide for thinking about how changes in RONO 2 chemistry affect NO x .

Background
Daytime chemistry in the lower troposphere encompasses two chemical regimes: a low NO x (NO x = NO + NO 2 ) regime in which HO x (HO x = OH + HO 2 + RO 2 ) selfreactions (e.g., HO 2 + RO 2 ) dominate radical loss processes, and a high NO x regime in which radicals are lost through nitric acid production.Although low NO x chemistry has generally been synonymous with methane and carbon monoxide chemistry, recent field observations have shown that in the presence of high biogenic volatile organic compound (BVOC) concentrations, low NO x chemistry is significantly more complex than this textbook view.Most of these recent low NO x , high BVOC studies have focused on understanding the production and loss processes of HO x radicals (Lelieveld et al., 2008;Stavrakou et al., 2010;Stone et al., 2011;Taraborrelli et al., 2012;Whalley et al., 2011;Mao et al., 2012).Here, we focus on understanding the nitrogen radical budget under these conditions.
Chemical loss of NO x is generally considered to be dominated by nitric acid formation: Close to source regions, where NO x concentrations are high, NO x will also be lost through the formation of peroxy nitrates: It is well known that peroxy nitrates act as a NO x reservoir; they may be transported to rural and remote locations where they will dissociate, resulting in a net source of NO x downwind from the emissions.Chemical NO x loss also occurs via the formation of alkyl and multifunctional organic nitrates of the form RONO 2 from the minor branch of the NO and peroxy radical reaction: Measurements of total RONO 2 by thermal dissociation laser induced fluorescence (Day et al., 2002) have shown that RONO 2 account for a substantial fraction of oxidized nitrogen (NO y = NO + NO 2 + NO 3 + total peroxy nitrates + total alkyl and multifunctional nitrates + HNO 3 + 2*N 2 O 5 + HONO +...) in urban (Rosen et al., 2004;Cleary et al., 2005;Perring et al., 2010;Farmer et al., 2011) and rural (Murphy et al., 2006;Farmer and Cohen, 2008;Day et al., 2009;Perring et al., 2009a;Beaver et al., 2012) locations as well as downwind of the continents (Perring et al., 2010).Isoprene nitrates are thought to be a large fraction of the organic nitrates.Global modeling studies investigating the impact of isoprene-derived nitrates on NO x and O 3 have found large sensitivities in the net global and regional budgets of O 3 and OH to assumptions about formation, lifetime, and oxidation products of isoprene-derived nitrates (e.g., Horowitz et al., 1998Horowitz et al., , 2007;;von Kuhlmann et al., 2004;Fiore et al., 2005;Ito et al., 2007Ito et al., , 2009;;Wu et al., 2007;Paulot et al., 2012).Paulot et al. (2012) used a global CTM to calculate the impact of isoprene-derived nitrates on the NO x budget in the tropics and found that up to 70 % of the local net NO x sink is from the formation of isoprene-derived nitrates.
Recently, simultaneous field measurements of speciated multifunctional nitrates using chemical ionization massspectrometry (St. Clair et al., 2010) and measurements of total RONO 2 by thermal dissociation laser induced fluorescence provided the first opportunity for a comparison of the total RONO 2 measurement in a complex chemical environment.The sum of the individual compounds was ∼ 65 % of the total RONO 2 when only isoprene (first and second generation) and 2-methyl-3-buten-2-ol nitrates were included, and was almost closed when all nitrogen containing masses were included.The measurements confirmed that biogenic RONO 2 represent the vast majority of the total in a rural environment (Beaver et al., 2012).Recent measurements from the NASA Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) campaign See Table 2 a IUPAC Atkinson et al. (2004Atkinson et al. ( , 2006), b JPL 2011 (Sander et al., 2011), c MCM v3.2 (Jenkin et al., 1997; Saunders et al., 2003)  (1999).(Jacob et al., 2010) show that in the low NO x , high BVOC environment of the Canadian boreal forest, RONO 2 account for 18 % of NO y and often account for at least half of the instantaneous NO x sink (Browne et al., 2012).

Steady-state calculations
Here, we restrict our analysis to NO x concentrations less than 500 pptv.Discussion on the effects of RONO 2 chemistry at higher NO x concentrations can be found in Farmer et al. (2011) and are reviewed by Perring et al. (2012).These low NO x , high BVOC environments, such as boreal and tropical forests, are generally characterized by large expanses of relatively homogeneous emissions.Consequently, even while transport can be long-range, the lifetime of different species can be short relative to changes in sources and sinks.The lifetime of NO x is the ratio of the NO x concentration to the loss via formation of HNO 3 and RONO 2 .Although this lifetime may be similar to, or longer than, the length of a single day or night, since the transport pathways are over uniform environments, the air parcels still have sufficient time to approach steady-state with the sources and sinks of NO x .This does not affect the assumption of steady-state since the cycling reactions within the NO x family are fast.Simulations with a time-dependent box model also suggest that steadystate is applicable.

Daytime
Here, we use a simplified representation of daytime chemistry (Table 1) where P (HO x ) represents primary HO x production from all sources including O( 1 D) + H 2 O, photolysis of species such as H 2 O 2 and HCHO, and any others.We assume that 80 % of HO x production results in OH and the remainder in HO 2 (from HCHO photolysis).In addition to CO and CH 4 chemistry, we include a lumped VOC that reacts with OH to form a lumped peroxy radical (RO 2 in Table 1).When this lumped RO 2 species reacts with NO, it either propagates the radicals (R3b) or forms an organic nitrate (R3a).The fraction of the time that an organic nitrate is formed R3a/(R3a + R3b) is referred to as the branching ratio (α).For specific molecules, α increases with increasing carbon number, lower temperature, and higher pressure (Arey et al., 2001).
For the other RO 2 reactions, we assume that the RO 2 species behaves like a primary or secondary peroxy radical.Following the MCM protocol, the RO 2 + RO 2 reaction then results in 1.2 alkoxy radicals (Jenkin et al., 1997).In the model, the alkoxy radical either instantaneously isomerizes or decomposes (i.e., we ignore the reaction with O 2 ) to produce a peroxy radical that is lumped with CH 3 O 2 (i.e., no formation of organic nitrates upon reaction with NO).The RO 2 + CH 3 O 2 reaction follows the same assumptions resulting in 0.6 CH 3 O 2 and 0.6 HO 2 .The RO 2 species undergoes an isomerization reaction with products of OH and HO 2 .This reduced complexity is designed to mimic the low NO x chemistry of isoprene (e.g., Peeters et al., 2009;Peeters and Müller, 2010;Crounse et al., 2011Crounse et al., , 2012)).
For illustrative purposes, we use the mean conditions sampled during ARCTAS at low altitude and removed from recent biomass burning influence (Table 2) as inputs to the model.We run the model at specified NO concentrations until the radicals (RO 2 , CH 3 O 2 , HO 2 , OH, and NO 2 ) are in Values of α equal to 0 %, 0.1 %, 1 %, 5 %, and 10 % are used to illustrate a range of conditions that vary from remote conditions removed from the continents (α = 0 % and α = 0.1 %) to areas influenced primarily by BVOCs (e.g., monoterpenes, isoprene) with high RONO 2 formation (α = 5-10 %).
It should be noted that the α value in the steady-state model is different from what has been referred to in the literature as the "effective branching ratio" (Rosen et al., 2004;Cleary et al., 2005;Perring et al., 2010;Farmer et al., 2011).The effective branching ratio refers to the average branching ratio of the entire VOC mixture (including CO, CH 4 , etc) and is therefore smaller than the branching ratio of the RO 2 species.Observations suggest that the effective branching ratio for VOC mixtures for urban regions ranges from 4-7 % (Cleary et al., 2005;Farmer et al., 2011;Perring et al., 2010;Rosen et al., 2004).The effective branching ratio for the situations calculated here ranges from 0.06-8.74% and is dependent on NO x due to changes in the ratio of CH 3 O 2 to RO 2 with NO x (Table 3).Full details regarding the calculation of α eff and discussion of how it varies with NO x can be found in Appendix A.

Nighttime
Nighttime chemical loss of NO x occurs via NO 3 reactions with alkenes that have organic nitrate products, heterogeneous hydrolysis of N 2 O 5 , and reactions of NO 3 with aldehydes.The latter two loss processes both result in the formation of HNO 3 .We consider a nighttime VOC mix that consists of three VOCs: isoprene, α-pinene, and acetaldehyde.
Since there is no suitable ARCTAS data to constrain the nighttime concentrations of alkenes and aldehydes, we use output from the WRF-Chem model to guide our choice of input concentrations (Table 5).We choose a lower estimate of 400 pptv of alkenes (which we split evenly between isoprene and α-pinene) and a mid-range concentration of 2 ppbv of acetaldehyde.In this choice of isoprene and α-pinene we do not mean to imply that this is the exact speciation of the BVOCs.Rather we choose these two alkenes to act as example species since they have different reaction rates and organic nitrate yields.Varying the split between these two See Table 5 a JPL 2011 (Sander et al., 2011) b JPL 2011 calculated from . c IUPAC (Atkinson et al., 2006).BVOCs has no significant impact on our conclusions.We also note that although isoprene is primarily emitted during the day, it is possible to have isoprene emitted near sunset persist into the night (e.g., Brown et al., 2009).
The reaction of NO 3 with alkenes results in an NO 3 -alkene adduct that either retains or releases the nitrate functionality upon reaction with other radicals.We use the parameter β to represent the fraction that retains the nitrate functionality.Recent measurements of organic RONO 2 yields for the reaction of biogenic VOC with NO 3 suggest that β for isoprene is ∼ 65-70 % (Rollins et al., 2009;Perring et al., 2009b), ∼ 40-45 % for β-pinene (Fry et al., 2009), and ∼ 30 % for limonene (Fry et al., 2011).Due to experimental difficulties, most chamber studies of this type are carried out under conditions where the ratio of RO 2 to HO 2 is greatly enhanced relative to the ambient atmosphere.Since the β value depends on which radical the nitrooxy peroxy radical reacts with, these organic nitrate yields are not strictly applicable to ambient measurements.We use these chamber results as a guide and assign a β value of 30 % for α-pinene, and 70 % for isoprene.
We run the model using two different lifetimes of N 2 O 5 (3 h and 5 h) with respect to heterogeneous hydrolysis.Assuming a reactive uptake coefficient of 0.01, these lifetimes correspond to aerosol surface areas of approximately 144 and 87 µm 2 cm −3 for the lifetimes of 3 h and 5 h, respectively.Both these surface areas and the reactive uptake coefficient used here are likely upper limits for a remote environment.With this simplified representation of the chemistry of these VOCs and the inorganic reactions of NO x and O 3 shown in Table 4, we calculate the loss of NO x to HNO 3 and to RONO 2 by prescribing the NO 2 concentration and assuming NO 3 and N 2 O 5 are in instantaneous steady-state.

Daytime
We compute the lifetime of NO x with respect to chemical loss to RONO 2 and nitric acid using Eq.(1): For NO x concentrations less than 500 pptv when α = 0 %, HNO 3 formation is the sole mechanism for NO x loss, and the NO x lifetime is longest at low NO x and decreases as NO x increases (Fig. 1).This decrease is roughly proportional to 1/[OH] (not shown) which, at low NO x concentrations, increases as NO x concentrations increase due to an increase of OH recycling from HO 2 + NO.As α increases, the NO x lifetime decreases, most significantly at the lowest NO x concentrations.At 100 pptv NO x , for α values in the range expected in remote forested regions, RONO 2 production results in a NO x lifetime of less than 8 h (α = 5 %) and less than 5 h (α = 10 %), compared to a NO x lifetime of greater than one day (∼ 27 h) for α = 0 %.The lifetime of NO x peaks near NO x concentrations of ∼ 20 pptv (α = 1 %) to ∼ 210 pptv (α = 10 %) for α values of at least 1 % (Fig. 1).This reflects the dependence of RONO  as roughly proportional to 1/[RO 2 ].As NO x increases, the change in RO 2 with NO x slows, and the OH term becomes more important.The resulting maximum in NO x lifetime depends on the weighting of the RO 2 term (the α value) and shifts to higher NO x concentrations as α increases (Fig. 1).
The relative effects of HNO 3 versus RONO 2 formation on NO x lifetime are shown in Fig. 2, where the fraction of NO x loss to RONO 2 is shown versus NO x .The fraction of NO x loss to RONO 2 is significant at NO x below 100 pptv-even if α is as low as 1 %.That fraction decreases as NO x increases.
For the α = 5 % and α = 10 % cases that are expected to be typical of BVOC emissions from forests, RONO 2 production represents more than half of the NO x loss at NO x concentrations below ∼ 400 pptv and ∼ 950 pptv, respectively.Consequently, in remote regions with high BVOC emissions where we expect NO x concentrations of ∼ 20-300 pptv, RONO 2 formation accounts for over 50 % of the instantaneous NO x loss.It is notable that even for the α = 1 %, which is similar to the measured value for ethane of 1.2 % ± 0.2 % (Atkinson et al., 1982), ∼ 31 % of NO x loss is due to RONO 2 at 100 pptv NO x and ∼ 15 % of NO x loss at 500 pptv NO x .We note that the total VOC reactivity of 2 s −1 that we use in these calculations is much too high for ethane to affect the RONO 2 yield (∼ 370 ppbv of ethane are required to have a reactivity of 2 s −1 ).Since the importance of RONO 2 decreases with decreasing VOC reactivity, we expect that RONO 2 formation would be low in pure ethane, CO, CH 4 chemistry.However, only ∼ 740 pptv of isoprene (α ∼ 10 %) is needed to achieve a reactivity of 2 s −1 and 74 pptv of isoprene with a reactivity of 0.2 s −1 would have the effect of α ∼ 1 %.Even a small addition of isoprene or other highly reactive BVOC will result in a reactivity and α in the range of these calculations.
The exact numbers presented in Figs. 1 and 2 are sensitive to the parameters chosen for HO x production, VOC reactivity, and peroxy radical reaction rates.We have tested the effects of much slower or faster peroxy radical self reaction rates, the effect of increasing the peroxy radical isomerization rate by an order of magnitude, and the effects of varying the HO x production and non-methane VOC reactivity.We find that the basic structure of our results, that organic nitrate formation is an important NO x loss under low NO x conditions, is insensitive to wide variations in the assumed parameters.

Nighttime
The nighttime formation of RONO 2 from NO 3 chemistry also has important implications for the chemical loss of NO x , especially since the branching ratio for RONO 2 formation is much higher for NO 3 chemistry and N 2 O 5 is present at very low concentrations due to low concentrations of NO 2 .We calculate the NO x lifetime at night with respect to the formation of RONO 2 and HNO 3 using Eq. ( 2) and Eq.(3) respectively. (2) For NO x concentrations less than 500 pptv, the NO x lifetime with respect to RONO 2 formation is just under 40 h and is essentially invariant with respect to assumptions regarding the N 2 O 5 lifetime to hydrolysis and acetaldehyde concentrations (Fig. 3a).The lifetime shows relatively little sensitivity to reasonable changes in alkene concentration since any increase in alkenes decreases the steady-state NO 3 concentration.The NO x lifetime with respect to nighttime production of HNO 3 is much longer (at least several days -not shown) even for N 2 O 5 hydrolysis lifetimes as short as 10 min.As a result, the fractional loss of NO x to RONO 2 dominates, always accounting for at least ∼ 95 % of the fractional NO x loss (Fig. 3b).Furthermore, increasing the HNO 3 production through the aldehyde + NO 3 reaction by increasing the acetaldehyde concentration by a factor of 3 (to 6 ppbv) results in minor differences.Even if we replace acetaldehyde with pinonaldehyde (which reacts an order of magnitude more quickly), the fraction of NO x loss to RONO 2 is high: at 100 pptv NO x it is ∼ 92 % for pinonaldehyde concentrations of 2 ppbv and 80 % for 6 ppbv pinonaldehyde (for a N 2 O 5 lifetime of 180 min).
Since the lifetime is controlled by the production of RONO 2 , the lifetime is highly sensitive to the assumed value of β; as β increases and the loss of NO x through NO 3 reactions becomes more efficient, the NO x lifetime will be limited by the NO 2 + O 3 rate.Under this condition, the NO x lifetime is where F is a number between 1 (loss through NO 3 dominates) and 2 (loss through N 2 O 5 dominates).Under low NO x conditions F will be close to 1 and the lifetime has a limiting value at high BVOC or high β of ∼ 12 h.

Twenty-four hour average lifetime
The average NO x lifetime will be a combination of the nighttime and daytime sinks.However, the NO x lifetime at night is much longer than the daytime value except at α = 0 % where the two are nearly equal.Under the range of NO x concentrations studied here, the nocturnal lifetime is dominated by organic nitrate formation and is essentially invariant with NO x concentration.Thus, the shape of the NO x lifetime curve will be similar to the shape of the daytime lifetime curve (Fig. 1), however the curve will be shifted to longer lifetimes due to the slower loss at night.

Ozone production efficiency
Since the production of RONO 2 reduces the NO x lifetime, it will reduce the number of ozone molecules produced per NO x removed (the ozone production efficiency-OPE) (Fig. 4).OPE is calculated using Eq. ( 5): At 100 pptv NO x OPE decreases from ∼ 110 for α = 0 % to ∼ 19 for the α = 10 % case.The shape of the OPE versus NO x curve also changes with α; the slope of the OPE versus NO x line decreases in steepness as α increases.The shallow slope of OPE versus NO x for the higher α cases occurs because both ozone production and NO x loss depend on RO 2 .
For the low α cases, NO x loss depends primarily on OH concentration, which, as discussed earlier, decreases as NO x decreases.Since the RO 2 concentration increases as NO x decreases, this results in a high OPE at low NO x .NO x reservoirs, such as peroxy nitrates, transport NO x from high NO x , low OPE environments (urban areas) to areas downwind at lower NO x and high OPE. Figure 4 suggests that if this downwind area is over the continents, that the OPE may be significantly lower than the traditional textbook view of low NO x chemistry would assume.This high sensitivity of OPE to the RONO 2 formation potential also suggests that small errors in RONO 2 representation may lead to larger errors in the calculated ozone burden.
As will be discussed further in Sect.7, some fraction of RONO 2 return NO x to the atmosphere after oxidation and consequently have a similar impact as other NO x reservoirs such as the peroxy nitrates discussed above (with the important distinction that the NOx is returned to the atmosphere after oxidation -not just after thermal decomposition).The impact of this has been discussed by Paulot et al. (2012) who show that increases in the NO x recycling from isoprene nitrates in the tropics increases ozone downwind of the continents.Since this is not a steady-state process, we are unable to represent using our steady-state model and instead use the 3-D chemical transport model to investigate this effect (Sect.6).Under conditions where the return of NO x to the atmosphere from RONO 2 is important, Eq. ( 5) should be rewritten as: Here k RONO 2 loss represents the total effective first order loss rate of RONO 2 and δ refers to the fraction of this loss that returns NO x to the atmosphere (rather than removing through processes such as deposition).It is important to note that accounting for this process simply by decreasing the α value is incorrect since the amount of NO x returned will depend strongly on the history of the airmass and will not necessarily be representative of the local chemistry.For instance, one could imagine a forested region where there is a transition region from isoprene to monoterpene emissions.In this situation, transported isoprene nitrates may release NO x in the monoterpene region.Due to the different properties of monoterpene nitrates and isoprene nitrates (e.g., vapor pressure, oxidation rates, deposition rates), simply decreasing the monoterpene nitrate formation will result in an inaccurate representation of the chemistry that will induce errors in calculations of ozone and SOA.Alternatively, the speciation of RONO 2 production may be constant, but the atmospheric conditions may change (e.g., the transition from day to night) that would result in the same species of nitrates having different integrated effects on atmospheric chemistry.The value of OPE in the atmosphere has often been estimated using the correlation between NO z (NO z = NO y -NO x ) and O 3 , however, this is a difficult comparison due to the different lifetimes of O 3 and NO z , as well as the variability in lifetimes of the different NO z components.These problems are more significant in the boundary layer of remote environments where there are large contributions of peroxy nitrates and HNO 3 to NO z .However, measurements from a forest in northern Michigan suggest an OPE of ∼ 22 for NO x concentrations around 300 pptv (Thornberry et al., 2001) The net chemical loss is defined as the sum of the net chemical loss to different classes of NO y including RONO 2 , RO 2 NO 2 , and HNO 3 (full details can be found in Appendix B).If the net chemical loss is less than zero for any particular class, the net loss is set to zero.The results are sorted by the effective α eff value as calculated using Eq.(A2).
OPE value that lies between our α = 5 % and α = 10 % values expected for a forested environment.

Boreal forest: comparison to a 3-D chemical transport model
We compare the steady state calculations described above to the WRF-Chem 3-D chemical transport model simulations carried out using a domain that includes a large fraction of Canada where we expect low NO x concentrations coupled with high BVOC emissions from the boreal forest to have a strong effect on NO x lifetime.Details regarding the WRF-Chem model simulations can be found in Appendix B.
The WRF-Chem model allows us to account for the effects from NO x reservoirs with long lifetimes relative to changes in sources and sinks (i.e.ones for which transport plays an important role in determining concentration) such as: formation and decomposition of peroxy nitrates and the release of NO x from oxidation and photolysis of RONO 2 .We define the NO x lifetime with respect to the net chemical loss of NO x .In this formulation the NO x lifetime depends both on local chemistry as well as the decomposition of transported NO x reservoirs.If the net chemical loss to any class of species (e.g., peroxy nitrates, RONO 2 , nitric acid) is less than zero, then that species has zero contribution to the chemical loss of NO x at that NO x concentration.Figure 5 shows the NO x lifetime to net chemical loss as a function of NO x , binned by the effective α value calculated using Eq.(A2).In the calculation Fig. 6.WRF-Chem results for (A) fractional net NO x loss to organic nitrates, (B) fractional net NO x loss to HNO 3 , and (C) fractional net NO x loss to peroxy nitrates.The net chemical loss is defined as the sum of the net chemical loss to different classes of NO y including organic nitrates, peroxy nitrates, and nitric acid (full details can be found in Appendix B).If the net chemical loss is less than zero for any particular class, the net loss is set to zero.The results are sorted by the effective α eff value as calculated using Eq.(A2).
of α eff we assume that the ozone production rate defined in Eq. ( A3) is equivalent to Eq. ( 7): We note that the WRF-Chem results we report use 24-h averaged data to calculate α eff .This allows us to sort the airmasses by their RONO 2 production rates; however, the exact value of α eff differs slightly from what would be calculated using only the daytime data.Within the domain, we find examples of airmasses with α eff ranging from ∼ 0.4-8 %.Both the full 3-D calculations (Fig. 5) and the box model (Fig. 1) show the same general dependence of the lifetime on α: a dependence that due to the dominance of RONO 2 formation as a NO x sink, is roughly proportional to 1/α.The most notable difference between the two is that the NO x lifetime from the 3-D calculations decreases more steeply as NO x increases than it does for the steady-state results.This is due to an increase in the loss due to peroxy nitrate formation (Fig. 6c) as NO x increases, an effect that is not represented in the steady-state model which assumed peroxy nitrates were at steady-state and thus could be ignored.
The fractional net NO x loss to RONO 2 , peroxy nitrates, and HNO 3 is shown in Fig. 6.The NO x concentrations predicted by WRF-Chem cover the range of ∼ 30-250 pptv.Although this range represents a small fraction of the global variation of NO x concentrations, it is a typical range for the majority of remote continental regions.However, the chemistry in this regime is highly sensitive to the NO x concentration and, as shown in both Fig. 2 for the steady state model and in Fig. 6 for the WRF-Chem model, large changes in the fractional composition of the products of the NO x loss reactions are predicted.In both calculations the fraction of net NO x loss to RONO 2 (Fig. 6a) approaches unity as NO x decreases and as the effective α value increases.Interestingly, the WRF-Chem predictions for the fractional net NO x loss to HNO 3 shows only a slight increase as a function of NO x (Fig. 6b) and the decrease in fractional NO x loss to RONO 2 is compensated by an increase in the net NO x loss to peroxy nitrates when NO x is greater than ∼ 50-80 pptv (Fig. 6c).We note that a plot of the fractional instantaneous gross loss when only RONO 2 and HNO 3 are considered (which is a direct comparison to Fig. 2), does show the fractional contribution of HNO 3 increasing with increasing NO x (not shown).The fractional net NO x loss to peroxy nitrates exhibits little variation with respect to α eff , indicating that peroxy nitrates are acting to buffer NO x .A full investigation of this effect, however, would require a larger NO x range and attention to the effects of temperature and transport.Many of these aspects of peroxy nitrate chemistry have been discussed previously (Sillman and Samson, 1995).We note that due to the thermal instability of peroxy nitrates, the importance of peroxy nitrates as a NO x reservoir will be highly dependent on temperature and we expect large differences between seasons and between boreal and tropical forests.In no regime does peroxy nitrate chemistry change the conclusion that the lifetime of NO x is controlled by RONO 2 production rates at low NO x concentrations.

Discussion
In the past few years it has become increasingly apparent that our understanding of atmospheric chemistry in low NO x , high BVOC environments is limited.Most of the work in this chemical regime (e.g., Lelieveld et al., 2008;Peeters and Müller, 2010;Stavrakou et al., 2010;Stone et al., 2011;Taraborrelli et al., 2012;Whalley et al., 2011), however, has focused on the HO x budget with little to no discussion on other controlling factors, including the nitrogen budget.Uncertainties in the HO x budget, particularly regarding the fate of RO 2 and the production of OH, impact the NO x budget via the changes in the concentrations of RO 2 , HO 2 , and OH which, in turn, change the absolute values of RONO 2 and HNO 3 production.However, the work presented here shows that in these low NO x , high BVOC environments the fate of NO x also has important consequences on atmospheric chemistry.In particular we show that the formation of RONO 2 accounts for the majority of the instantaneous NO x sink, resulting in decreased NO x lifetime and decreased OPE relative to chemistry dominated by CO and CH 4 .Thus, it is clear that although there are significant uncertainties associated with this chemical regime, it is necessary to consider both the HO x and NO x budgets.
One of the most important uncertainties regarding the impact of RONO 2 chemistry on regional and global scales is the extent to which these molecules serve as permanent versus temporary NO x sinks; a value which, in general, is not well known.For instance, if we assume that RONO 2 predominately serve as temporary NO x sinks that transport NO x to areas with higher OPE (e.g., areas with lower NO x or areas at the same NO x but lower α), we expect an increase in the ozone burden as a result of accounting for RONO 2 chemistry.In contrast, if the RONO 2 are lost primarily through deposition, they may increase nitrogen availability in the biosphere.Since many areas are nitrogen limited, introduction of nitrogen will also affect the carbon storage capacity of an ecosystem (e.g., Holland et al., 1997;Thornton et al., 2007Thornton et al., , 2009;;Bonan and Levis, 2010).A recent study observed the direct foliar uptake of RONO 2 and subsequent incorporation of the nitrogen into amino acids (Lockwood et al., 2008), indicating that (at least some) RONO 2 will affect plant growth.
In order to improve our understanding of the impact of RONO 2 on atmospheric chemistry, particularly on the global and regional NO x and HO x budgets, laboratory studies on the formation of RONO 2 (particularly for biogenic species other than isoprene), oxidation, physical loss, and oxidation products are necessary.Of particular importance is improving the constraints on the extent to which organic nitrates act as permanent versus temporary sink of NO x .This requires measurement of: the oxidation rates and products, dry and wet deposition velocities, and secondary organic aerosol formation and processing for various biogenic organic nitrates.These laboratory measurements must be supplemented by field measurements spanning NO x concentrations from near zero to a few ppbv.In one such analysis, we use measurements from the ARCTAS campaign (Browne et al., 2012).However, a thorough understanding will require measurements in environments with different classes of BVOC emissions (e.g., pine forests which are dominated by monoterpenes (α ∼ 18 %) and oak forests which are dominated by isoprene (α ∼ 10 %)).These field measurements will provide constraints on how the importance of RONO 2 versus nitric acid changes as a function of NO x and will test the representation of RONO 2 chemistry in condensed chemical mechanisms.
It is interesting to consider how incorporation of improved RONO 2 chemistry into condensed chemical mechanisms may impact our understanding of both preindustrial and future climates.For instance, it is likely that during the preindustrial era when NO x concentrations were lower, that RONO 2 formation was a more important NO x sink than it is today.Model predictions of preindustrial climate often predict larger ozone concentrations than the semi-quantitative measurements of the late 19th/early 20th century indicate (e.g., Mickley et al., 2001;Archibald et al., 2011).Although there may be problems with the ozone measurements or with the emissions estimates used in the models, this may also indicate that models are missing a NO x sink in the preindustrial era.As shown in Fig. 4, we calculate that the OPE is very sensitive to the assumed branching ratio, indicating that a small error in RONO 2 formation may have a large effect on the ozone burden.
In industrialized countries, NO x emissions are currently decreasing due to air quality control measures (e.g., van der A et al., 2008;Dallmann and Harley, 2010;Russell et al., 2010Russell et al., , 2012)).Coupling this decrease in NO x with the increase in biogenic VOC emissions expected in a warmer climate, suggests that RONO 2 chemistry will begin to play a more important role in NO x termination in urban and suburban areas.As discussed in Sect.4.1, the crossover from RONO 2 to nitric acid accounting for over 50 % of NO x loss occurs at ∼ 400 pptv for a 5 % branching ratio and at ∼ 950 pptv for a 10 % branching ratio.Past studies have constrained the effective branching ratio in urban areas at 4-7 % (Cleary et al., 2005;Farmer et al., 2011;Perring et al., 2010;Rosen et al., 2004), which suggests that to predict ozone in future climates, it will be necessary to correctly simulate RONO 2 chemistry in order to understand regional pollution and air quality.

Conclusions
Recent field measurements have indicated that low NO x , high BVOC chemistry is significantly more complex than the textbook view of low NO x chemistry being controlled by methane and carbon monoxide.Most of the work on low NO x , high BVOC chemistry has focused on the implications for the HO x budget.In this paper we analyze how the NO x lifetime responds to changes in RONO 2 production under these conditions.We find that production of RONO 2 accounts for the majority of the instantaneous NO x sink in low NO x , high BVOC environments in both a steady-state model and a 3-D chemical transport model.Furthermore, the NO x lifetime and OPE are highly sensitive to RONO 2 production.These findings suggest that proper representation of RONO 2 formation and NO x recycling are necessary for accurate calculation of past, present, and future ozone concentrations and the corresponding climate effects.(Goliff and Stockwell, 2010;Stockwell et al., 2010) with substantial modifications to the RONO 2 and isoprene chemistry.The isoprene chemistry is based on Paulot et al. (2009a, b) and uses ozonolysis rates of isoprene-derived nitrates from Lockwood et al. (2010).The formation of a hydroperoxyaldehyde (HPALD) from the 1,6 H-shift of isoprene peroxy radicals is included using the rate constant measured by Crounse et al. (2011).Photolysis of HPALD is the same as assumed in Stavrakou et al. (2010) with the assumption that one OH is generated.Loss of HPALD also occurs through reaction with OH and is assumed to regenerate OH (Peeters and Müller, 2010).When the first generation isoprene-derived nitrates react with OH between 0 % and 65 % of the nitrogen is returned as NO x .The exact amount of NO x returned depends on whether the isoprene nitrate peroxy radical reacts with HO 2 (with an assumed 100 % yield of a multi-functional nitrate) or with NO or other peroxy radicals (to return between ∼ 34 % and ∼ 65 % of the nitrogen as NO x ).Ozonolysis of the first generation nitrates is assumed to return 32.7 % (for β-hydroxy isoprene nitrates) or 44.5 % (for δ-hydroxy isoprene nitrates) of the nitrogen as per MCM v3.2 (Jenkin et al., 1997;Saunders et al., 2003).Based on Geiger et al. (2003) the NO 3 + isoprene reaction forms an organic nitrate that is oxidized by OH to return 0 % of the NO x .There are no reactions between NO 3 and the isoprene-derived nitrates in the chemical mechanism.Monoterpene derived nitrates are oxidized to form HNO 3 ; all other nitrates are assumed to release NO 2 with 100 % efficiency when oxidized by OH.
Photolysis of RONO 2 is assumed to release NO 2 with 100 % efficiency except for the photolysis of the peroxide nitrate formed from reaction of an isoprene nitrate peroxy radical with HO 2 .As per MCM v3.2, we assume that photolysis results in OH and an alkoxy radical which then decomposes.We assume that ∼ 1/3 of the alkoxy radicals will release NO 2 when they decompose.Photolysis crosssections of RONO 2 were calculated using FAST-JX 6.5 (Bian and Prather, 2002) and include enhancement from carbonyl groups (Barnes et al., 1993) and reductions from hydroxy groups (Roberts and Fajer, 1989) where appropriate.Dry deposition rates of RONO 2 follow Ito et al. (2007) and there is no wet deposition for any species.
The monoterpene chemistry includes two lumped monoterpenes: α-pinene to represent low-reactivity monoterpenes and limonene to represent high reactivity monoterpenes.The nitrate yield from the reaction of the α-pinene peroxy radical with NO is set to 18% (similar to that measured by Nozière et al. (1998)) and is set to 22% for the limonene peroxy radical reaction (based on Leungsakul et al. (2005)).The α-pinene-derived nitrate is assumed to be a mix of both unsaturated (yield of 0.12) and saturated (yield of 0.06) nitrates while the limonene-derived nitrate is assumed to be unsaturated.Oxidation rates by OH are calculated using weighted averages of the MCM v3.2 rates for α-pinene and β-pinene (50-50 mixture) for the saturated nitrate and from limonene for the unsaturated nitrate.The ozonolysis rate of the unsaturated nitrate is calculated using the EPA Estimation Program Interface (EPI) Suite v4.1 (available at http://www.epa.gov/opptintr/exposure/pubs/episuite.htm)(US EPA, 2011).All the oxidation reactions are assumed to form a more highly functionalized nitrate that has the same chemical properties as HNO 3 .The oxidation of the monoterpenes by NO 3 forms two nitrooxy-peroxy radicals.One of these primarily decomposes (formed 90% of the time for α-pinene and 29% of the time for limonene) while the other primarily reacts to form a nitrate.We assume that the nitrates formed from these reactions are split 70/30 between saturated/unsaturated nitrates.
There is no heterogeneous hydrolysis of N 2 O 5 in the WRF-Chem model, however this should be a small NO x sink under low NO x conditions and we anticipate no significant change to the results if heterogeneous N 2 O 5 hydrolysis were included.
2 production on RO 2 concentrations.At low NO x concentrations, RO 2 concentrations change rapidly as a function of NO x , resulting in the NO x lifetime curve behaving approximately www.atmos-chem-phys.net/12

Fig. 1 .Fig. 2 .
Fig. 1.Steady-state model results of NO x lifetime to chemical loss versus NO x concentration.

Fig. 3 .
Fig. 3. Steady state model calculation of NO x lifetime at night to (A) RONO 2 formation and (B) fractional NO x loss to RONO 2 at night in the steady-state model.

Fig. 4 .
Fig. 4. Steady-state model results for ozone production efficiency (OPE) versus NO x concentration.

Fig. 5 .
Fig. 5. WRF-Chem predication of the NO x lifetime to net chemical loss over Canada (north of 53 • N) averaged over two weeks in July.The net chemical loss is defined as the sum of the net chemical loss to different classes of NO y including RONO 2 , RO 2 NO 2 , and HNO 3 (full details can be found in Appendix B).If the net chemical loss is less than zero for any particular class, the net loss is set to zero.The results are sorted by the effective α eff value as calculated using Eq.(A2).

Table 1 .
Reactions and rate coefficients used in the steady-state modeling of daytime chemistry.

Table 2 .
Parameters used in the daytime steady-state model.The value of the parameters (except for NMVOC + OH) are based on the mean ARCTAS measurements from less than 2 km pressure altitude and excluding data with recent anthropogenic or biomass burning influence.

Table 3 .
Effective α value at various NO x concentrations.These are calculated using Eq.(A2).

Table 4 .
Reactions and rate coefficients used in the steady-state modeling of nighttime chemistry.

Table 5 .
Parameters used in the nighttime steady-state model.