Simulation of the diurnal variations of the oxygen isotope anomaly ( ∆ 17O) of reactive atmospheric species

. The isotope anomaly ( 1 17 O) of secondary atmospheric species such as nitrate (NO − 3 ) or hydrogen peroxide (H 2 O 2 ) has potential to provide useful constrains on their formation pathways. Indeed, the 1 17 O of their precursors (NO x , HO x etc.) differs and depends on their inter-actions with ozone, which is the main source of non-zero 1 17 O in the atmosphere. Interpreting variations of 1 17 O in secondary species requires an in-depth understanding of the 1 17 O of their precursors taking into account non-linear chemical regimes operating under various environmental settings. This article reviews and illustrates a series of basic concepts relevant to the propagation of the 1 17 O of ozone to other reactive or secondary atmospheric species within a photochemical box model. We present results from numerical simulations carried out using the atmospheric chemistry box model CAABA/MECCA to explicitly compute the diurnal variations of the isotope anomaly of short-lived species such as NO x and HO x . Using a simpliﬁed but realistic tropospheric gas-phase chemistry mechanism, 1 17 O was propa-gated from ozone to other species (NO, NO 2 , OH, HO 2 , RO 2 , NO 3 , N 2 O 5 , HONO, HNO 3 , HNO 4 , H 2 O 2 ) according to the mass-balance equations, through the implementation of various sets of hypotheses pertaining to the transfer of 1 17 O during chemical reactions. The model results conﬁrm that diurnal variations in 1 17 O of NO x predicted by the photochemical steady-state relation-ship during the day match those from the explicit treatment, but not at night. Indeed, the 1 17 O of NO x is “frozen” at night soon as the photolytical of NO drops ca. We introduce and quantify the diurnally-integrated isotopic signature (DIIS) of sources of atmospheric nitrate and H 2 O , which is of particular relevance to larger-scale simulations of 1 O where high computational costs cannot be afforded.


Introduction
Unraveling chemical mechanisms at play in the atmosphere requires finding creative ways to test the predictions of models which describe them. Most studies to date have relied on concentration measurements to validate model results. Over the past decades alternative isotopic approaches have demonstrated great capabilities in providing concentrationindependent information relevant to atmospheric processes (Laj et al., 2009;Monks et al., 2009). Of particular interest is the development of measurements of the isotope anomaly ( 17 O) of oxygen-bearing species (Thiemens, 2006). 17 O is defined as δ 17 O−0.52×δ 18 O, with δ x O=R x /R x VSMOW −1 (x =17 or 18) where R x refers to the x O/ 16 O elemental ratio in the species of interest and in Vienna Standard Mean Ocean Water (VSMOW), taken as a reference. Ozone (O 3 ) possesses a distinctive isotope anomaly inherited from nonmass dependent fractionation NMDF during its formation in the atmosphere (Marcus, 2008).
In contrast to conventional isotopic ratios which are strongly affected by isotopic fractionation, 17 O is fairly insensitive to mass-dependent fractionation. The vast majority of chemical reactions induce mass-dependent fractionation, which in general do not strongly modify 17 O. It can thus be reasonably assumed that 17 O is transferred as is during Published by Copernicus Publications on behalf of the European Geosciences Union. oxidation reactions in the atmosphere, although this consideration is sometimes challenged when dealing with species possessing small 17 O values (Kaiser et al., 2004). As a result, 17 O of a given species generally simply reflects the fractional importance in its elemental composition of oxygen atoms inherited directly or indirectly from ozone. This behavior has opened large possibilities to explore atmospheric oxidation mechanisms using 17 O signatures (Lyons, 2001;Michalski et al., 2003;Thiemens, 2006;Savarino et al., 2000;Savarino and Morin, 2011).
One area of intense research on the interpretation of 17 O signatures is the case of inorganic atmospheric nitrate (HNO 3 + particulate NO − 3 ), referred to as atmospheric nitrate (NO − 3 ) below. Indeed, atmospheric nitrate is the final oxidation product of nitrogen oxides (NO x =NO+NO 2 ), which are of primary importance for air-quality (Jacob, 1999;Finlayson-Pitts and Pitts, 2000;Brown et al., 2006). The development of sensitive methods to analyze the oxygen isotopic composition of nitrate (Michalski et al., 2002;Kaiser et al., 2007) makes it possible to obtain 17 O of atmospheric nitrate at weekly to sub-daily timescales in most environments. This has been used in the recent past to study the seasonal variations in NO x oxidation pathways in mid-latitudes (Michalski et al., 2003;Tsunogai et al., 2010) and polar Kunasek et al., 2008) regions, the nature of the sources of atmospheric nitrate in the Antarctic lower atmosphere McCabe et al., 2007;Frey et al., 2009), and more recently the global-scale variations in NO x sink reactions . 17 O of nitrate has also been used to identify long-term changes in the oxidative properties of the Earth atmosphere, from centennial (Alexander et al., 2004) to millenial

time scales.
While including the isotopic composition of long-lived tracers (e.g. CO 2 , N 2 O etc.) into global biogeochemical models of the carbon and nitrogen cycle has proved extremely successful (e.g., Hoag et al., 2005), embedding the 17 O of short-lived reactive compounds into atmospheric photochemical models has only recently gained increased attention (Lyons, 2001;Michalski et al., 2003;Zahn et al., 2006;Dominguez et al., 2009;Gromov et al., 2010;Michalski and Xu, 2010). Current hope within the "atmospheric geochemistry community" is that 17 O data can help solve atmospheric chemistry issues such as ascertaining the relative role of heterogeneous reactions in NO x sink mechanisms (i.e. what is the exact role of N 2 O 5 hydrolysis; Brown et al., 2006). However, inferring quantitative atmospheric information from 17 O of nitrate requires assessing precisely its controls and to include them into a consistent modeling framework. In the last few years, several models have been proposed to study the spatio-temporal variations of 17 O and relate them to spatio-temporal variations of the fractional contribution of NO x sink reactions. The pioneering work of Lyons (2001) set the stage for the first model study of the seasonal variations of 17 O of atmospheric nitrate by Michalski et al. (2003). Further implementations of 17 O into atmospheric chemistry models were proposed in the following years, from 0-D box-modeling Dominguez et al., 2009;Michalski and Xu, 2010) to the 3-D chemical transport model GEOS-Chem (Kunasek et al., 2008;Alexander et al., 2009).
This study revisits some assumptions, hypotheses and approaches previously introduced in the literature (e.g. Michalski et al., 2003;Morin et al., 2007Morin et al., , 2008Kunasek et al., 2008;Alexander et al., 2009) and puts them within a consistent framework and perspective that makes it easier to understand and implement in existing atmospheric chemistry models. Limitations of the various assumptions that have been used so far are highlighted and critically evaluated. The overarching goal is to provide a rationale behind assumptions and simplifications that have to be used in large scale model implementation in order to reduce computing costs. The CAABA/MECCA atmospheric chemistry box model (Sander et al., 2011) was used to explicitly calculate the time evolution of the 17 O of short-lived reactive species at each time step. Model runs were performed in a few simple cases to demonstrate the usefulness of such assessments and provide the basis of future analogous studies. Finally, recommendations are given for the implementation of simplifying assumptions into large-scale atmospheric chemistry models.
2 General framework

The general "mass-balance" equation
The general "mass-balance" equation (also termed the "continuity equation") governing the temporal evolution of the concentration of a given species in a given air parcel is given by: where P i and L j represent source and sink rates (in cm −3 s −1 ) of the species X, respectively. Its atmospheric concentration, denoted [X], is expressed in cm −3 . Sources and sinks include both chemical reactions within the parcel and fluxes at its boundaries. Atmospheric chemistry models are mostly driven by reaction kinetics, so that the chemical components of P i and L j are simply expressed as a reaction rate constant (usually referred to as k values) times the relevant atmospheric concentrations (Jacob, 1999;Finlayson-Pitts and Pitts, 2000). The implementation of 17 O into the mass balance Eq. (1) follows from mass conservation applied to the oxygen isotope anomaly. Of course, this rather simple method would not apply to isotopic enrichment (δ) values, because isotopic fractionation has to be fully taken into account for every reaction considered (Gromov et al., 2010). The key assumption behind the modeling approach is that sink reactions do not  (Kaiser et al., 2004). The 17 O mass-balance equation reads: where 17 O(X) represents the 17 O of the species X and 17 O i (X) is the isotope anomaly that is transferred to X through the production channel P i of the species X. It is estimated as a function of the 17 O value of the precursors involved in a given production channel for species X, using a mass-balance approach based on the counting of the oxygen atoms transferred throughout a given production channel. Non-mass dependent fractionation induced by a specific reaction can also be taken into account in the equation above. Solving numerically the system of equations formed by Eqs. (1) and (2) for all relevant atmospheric species simultaneously yields the time evolution of the concentration and 17 O of each atmospheric species. This is generally not computationally affordable for large-scale modeling studies such as Alexander et al. (2009). The computation can be carried out for limited periods of time using box models.

Isotopic exchange reactions
Not only chemical production and destruction impact the 17 O of a given species. Isotopic exchange reactions can also modify it. Their main characteristic is that they have no impact on the chemical budget of a species (i.e., Eq. (1) is not changed), but they have an impact on the isotopic massbalance Eq. (2). The magnitude of an isotopic exchange reaction can be expressed in a similar manner to chemical production or destruction fluxes. In what follows, the rate of the k isotopic exchange reaction is referred to as E k ; the ultimate 17 O value that would be attained in species X if the isotopic exchange with the species Y k fully proceeds is noted 17 O(Y k ). Implementing this into Eq. (2) yields:

Steady-state approximation
A very commonly used simplification in atmospheric chemistry models is the so-called "photochemical steady-state (PSS)" approximation. This simply assumes that the photolytical lifetime of a given species is sufficiently short that the short-term variations of its concentration are negligible, i.e. d dt [X]≈0. In other words, a near-perfect balance between sources and sinks for a given species is assumed. Implementing this assumption into the isotopic mass-balance Eq.
(2), and taking into account that, at PSS, i P i = j L j yields:

Atmospheric nitrate
Atmospheric nitrate is formed homogeneously and heterogeneously in the atmosphere through the following reactions (Jacob, 1999;Finlayson-Pitts and Pitts, 2000): Here, RH represents a generic hydrocarbon. Dry and wet deposition are the main sinks of atmospheric nitrate, controlling its atmospheric lifetime which is on the order of days to weeks (Finlayson-Pitts and Pitts, 2000). A straightforward rearrangement of Eq.
(2) yields the equation governing the time evolution of 17 O of atmospheric nitrate: where τ is the atmospheric lifetime of atmospheric nitrate. 17 O i NO − 3 values can be calculated for each nitrate production channel (Michalski et al., 2003;Morin et al., 2007Kunasek et al., 2008): As will be demonstrated below, both the mixing ratio and the 17 O of nitrate precursors vary diurnally. For instance, OH plays a significant role only during the day, and 17 O(NO 2 ) exhibits a strong diurnal variation with a minimum during the day and a maximum at night. Clearly, only the daytime 17 O(NO 2 ) values matter for the OH+NO 2 nitrate production channel, since during the night this reaction is suppressed. To account for the fact that the isotopic signature of a given production channel has to be scaled with its strength, we define the diurnally-integrated isotopic signature (DIIS) of the nitrate source, denoted 17 O i NO − 3 , as follows: DIIS values quantify the overall 17 O inherited from a given source reaction, taking into account the scaling of diurnal variations in its strength with the associated 17 O it transfers. Additionally, DIIS is a useful metric to quantify the impact of various environmental settings or hypotheses pertaining to isotopic transfer on the ultimate 17 O of atmospheric nitrate.
In the case where the atmospheric lifetime of a given secondary species is significantly longer than one day, DIIS values can be used to infer the seasonal variations of 17 O from the following equation, virtually assuming that steady-state applies: Equation (11) takes into account that both P i and 17 O i NO − 3 values change seasonally or as a function of environmental conditions. This method was implicitly used originally by Michalski et al. (2003) to study the seasonal variations of 17 O(NO − 3 ) in coastal California. While correct at the seasonal scale to study seasonal variation of nitrate as far as its lifetime is significantly larger than several days, this method does not adequately address variations of 17 O(NO − 3 ) at temporal scale smaller than its atmospheric lifetime (Michalski and Xu, 2010), because sink reactions (both physical and chemical) must then be explicitly taken into account, as shown by Eq. (5).

Hydrogen peroxide (H 2 O 2 )
Hydrogen peroxide is a key atmospheric oxidant which plays a major role for in-cloud oxidation of S(IV) (Finlayson-Pitts and Pitts, 2000;Alexander et al., 2005). Savarino and Thiemens (1999a) demonstrated that it possesses a small but significant 17 O signature, which has then been used to study the partitioning between various S(IV) oxidants in the atmosphere (Savarino et al., 2000;Alexander et al., 2005). H 2 O 2 is mostly formed through the self reaction of HO 2 : The 17 O inherited by H 2 O 2 during the above reaction is equal to 17 O(HO 2 ). Indeed, Zhu and Lin (2001) have shown that the most likely mechanism for the self reaction of HO 2 involves a six-member-ring intermediate through headto-tail association, which implies that the two oxygen atoms in H 2 O 2 originate from a single one HO 2 radical out of the two reactants. The concept of DIIS applies to H 2 O 2 in a manner analogous to atmospheric nitrate (see above). Since Reaction (R5) is the sole significant H 2 O 2 production pathway, and because the atmospheric lifetime of H 2 O 2 is generally larger than one day, the application of Eq. (11) is trivial and shows that seasonal variations of 17 O(H 2 O 2 ) can directly be inferred from variations of 17 O HO 2 +HO 2 (H 2 O 2 ) at first order.

Material and methods: numerical experiments on 17 O of short-lived species
In this study, we focus on the time evolution of the 17 O of short-lived atmospheric reactive species such as HO x (= OH + HO 2 ), NO x (= NO + NO 2 ) and RO 2 . For simplicity, in this initial study we restrict our analysis to gas-phase reactions and exclude halogen, sulfur and carbonaceous chemistry, to focus on the highly non-linear NO x -HO x /RO x -O 3 chemistry first. The impact of diurnal variations of 17 O of short-lived species on secondary species such as atmospheric nitrate and H 2 O 2 is explored through the estimation of diurnally-integrated isotopic signature (DIIS) of these species. This series of 51 reactions (including 14 photolysis reactions) represents a subset of the chemical mechanism implemented in MECCA (Sander et al., 2011) suited for simplified analysis in the remote marine boundary layer. The complete listing of the reactions considered is given as an online supplement to this article. Note that this article mostly seeks to illustrate the basic concepts and equations introduced in Sect. 2, and the impact of performing various hypotheses to propagate the 17 O of ozone throughout atmospheric reactions. This is why heterogeneous reactions leading to the formation of atmospheric nitrate are not explicitly included in the model, because doing so would render the illustration of the main concepts unnecessarily tedious. We concentrate on gas-phase reactions, which provide illustrations of the main behaviors described here, and leave the explicit inclusion of heterogeneous chemistry in the model for a follow-up study comparing observed and simulated diurnal variations Schematic representing the isotopic mass-balance equation including one isotopic exchange reaction. Arrows represent production (or destruction) fluxes. The flux is given by the P , L and E terms, while the corresponding transferred 17 O value is given in brackets. The solid box represent the chemical budget of the species X, while the dashed box takes into account the full isotopic budget of the species X. The scheme illustrates that isotopic exchange reactions have no impact on the chemical budget of a given species X.

17 O(H 2 O) and 17 O(O 2 )
Because they represent large oxygen reservoirs with a negligible isotope anomaly, we assume in what follows that 17 O of water vapor (H 2 O) and molecular oxygen (O 2 ) are constant, with a value of insignificantly different from 0‰ Luz, 2003, 2005), in comparison to the 17 O of the species dealt with below. Indeed, 17 O(O 2 ) = −0.3‰ (Barkan and Luz, 2003), while 17 O(H 2 O) ranges between −1.0 and 0.0‰ (Barkan and Luz, 2005). This simplification is generally made in modeling studies dealing with 17 O(NO − 3 ) (Michalski et al., 2003;Alexander et al., 2009), and allows to focus on and interpret the changes in 17 O of reactive and secondary species attributable to chemical transfer of 17 O from ozone.

17 O(O 3 )
Although several atmospheric reactions induce non-mass dependent fractionation (Brenninkmeijer et al., 2003;Thiemens, 2006) and thus may contribute significantly to the non-zero 17 O values of several atmospheric species, the overwhelming source of non-zero 17 O in the lower atmosphere is ozone (O 3 ). As repeatedly mentioned in the recent literature (e.g. Morin et al., 2007;Michalski and Bhattacharya, 2009;Alexander et al., 2009;Dominguez et al., 2009), the tropospheric value of 17 O(O 3 ) is controversial. In addition, ozone is isotopically asymmetrical (Janssen, 2005;Marcus, 2008), meaning that the 17 O borne by its terminal and central atoms are different. Furthermore, oxy-gen atoms of O 3 are not chemically equivalent in terms of reactivity during bimolecular reactions. We define 17 O(O ⋆ 3 ) as the 17 O value which is transferred along with the terminal O atom of ozone. The motivation for this choice is two-fold. Firstly, terminal oxygen atoms generally have a greater probability of being transferred than the central oxygen atom , and this probability even equals 1 for the following reactions: O 3 +Ag metal , O 3 +NO − 2 (Liu et al., 2001;Michalski and Bhattacharya, 2009), O 3 +NO 2 (Peìro-Garcìa and Nebot-Gil, 2003, Berhanu andBhattacharya, personal communication, 2011). Secondly, we note that atmospheric direct measurements of 17 O(O ⋆ 3 ) are now possible using the reaction O 3 +NO − 2 as a chemical probe (Michalski and Bhattacharya, 2009;Vicars et al., 2011).
We note that, although this is not entirely consistent with the full range of experimental observations and their theoretical implications, this equation is equivalent to considering that 17 O resides exclusively on the terminal oxygen atoms of ozone (Michalski and Bhattacharya, 2009).
Consistent with the modeling studies carried out hitherto (Michalski et al., 2003;Morin et al., 2008;Kunasek et al., 2008;Alexander et al., 2009;Dominguez et al., 2009;Michalski and Xu, 2010), we use a constant value of 17 O(O 3 ) of 30‰, which falls within the 25-35‰ range generally found in the literature (see Brenninkmeijer et al. (2003) or Morin et al. (2007)  ) exhibit significant diurnal variations, the quantitative results provided below for illustration purposes would need to be revised, but the underlying concepts exposed here would remain valid. In this case, only an explicit modeling framework as described here would then be suitable to compute the 17 O values of reactive and secondary atmospheric species. In this work, bimolecular reactions involving ozone are: Ab initio calculations on the mechanism of the reaction NO 2 +O 3 reveal that it proceeds through the abstraction of the terminal O atom of ozone (Peìro-Garcìa and Nebot-Gil, 2003). In addition, the transfer of 17 O through reaction NO 2 +O 3 has been recently studied in the lab and it was also concluded that only the terminal O atom of ozone is transferred (Berhanu and Bhattacharya, personal communication, 2011). We also assume that the OH+O 3 reaction proceeds exclusively through the transfer of the terminal O atom of ozone. We thus apply 17 O(O ⋆ 3 ) as the isotopic signature of these reactions. Considering a 17 O(O 3 ) value of 30‰, this corresponds to 17 O(O ⋆ 3 ) = 45‰. In the case of the reaction NO+O 3 , we apply the 17 O transfer rate determined experimentally by Savarino et al. (2008): With a 17 O(O 3 ) value of 30‰, this corresponds to a 17 O NO+O 3 (NO 2 ) value of 42‰. The fact that the 17 O(O 3 ) transferred through this reaction is lower than through reactions described before stems from the fact that not only the terminal, but also the central oxygen atom of ozone reacts with NO, as described in detail by Savarino et al. (2008). Lastly, in the case of reaction HO 2 +O 3 this is irrelevant to the value of 17 O(OH) because the oxygen atom in OH stems from HO 2 , not ozone.

17 O(RO 2 )
In this study we explicitly separate HO 2 from other peroxy radicals, denoted RO 2 where R represents a carbonaceous chain, because the chemical budget of HO 2 and RO 2 is very different. While reactions involving ozone contribute to the budget of HO 2 , the only source of RO 2 is the reaction between O 2 and a R radical. Since 17 O(O 2 )=0‰ (see above), this immediately implies that 17 O(RO 2 )=0‰ under all tropospheric conditions.

Overview of the sets of hypotheses regarding the 17 O transfer throughout chemical reactions
Below we present the various sets of hypotheses (numbered Cases 1 to 6) implemented to compute the time evolution of 17 O of the species of interest using various assumptions in terms of 17 O transfer.

Case 1: NO x photochemical steady-state (PSS)
and basic hypotheses -OH, HO 2 : 17 O of both species is equal to 0‰.
-NO, NO 2 , NO 3 : The 17 O of these species is calculated using PSS: as defined by Michalski et al. (2003) and demonstrated in Morin et al. (2007). It follows from PSS that 17 O(NO) = 17 O(NO 2 ). 17 O(NO 3 ) is given as:

Case 2: explicit NO x
In this case, the time evolution of 17 O of NO, NO 2 and NO 3 is computed explicitly. This means that the PSS approximation is not used at all regarding the computation of the 17 O of these species. Table 2 presents the chemical reactions for which the 17 O i (X) is different than in Case 1 (PSS NO x ). The decomposition of N 2 O 5 and HNO 4 through photolysis or thermal decomposition is treated as follows. Our base hypothesis is that the photolysis and thermal decomposition of HNO 4 proceed without scrambling of its isotopic composition upon dissociation. The case of N 2 O 5 is more complex and is illustrated by Fig. 2. Upon dissociation or photolysis of N 2 O 5 , the 17 O of NO 2 and NO 3 formed is given by the following equations, based on the assumption that the two N−O bonds of the dimer have an equal probability to break: represent the 17 O of the two dimers making up N 2 O 5 , i.e. NO 2 and NO 3 , respectively.

Case 3: explicit HO x
In this case, in addition to the hypotheses of Case 2 (explicit NO x ), the 17 O value of HO 2 is allowed to vary in time and is computed explicitly. This also induces non-zero values of 17 O(H 2 O 2 ), through reaction HO 2 +HO 2 . Table 3 presents the chemical reactions for which the 17 O i (X) is different than in Case 1 (PSS NO x ) and 2 (explicit NO x ). Note that in Case 3 17 O(OH) is assigned a value of to 0‰. Note that, strictly speaking, the O atoms in HO 2 are chemically not equivalent, because one is bonded to the H atom while the other one is not. This opens the possibility that the intramolecular distribution of 17 O within HO 2 is not statistically distributed, in a manner somewhat equivalent to ozone, as first noted by Savarino and Thiemens (1999b). For the sake of simplicity, we consider here that the 17 O of HO 2 can be represented as a single value, implicitly assuming that the intramolecular distribution of HO 2 is statistical.

Additional tests
In addition to the three main cases presented above, three additional tests were performed. They all are based on Case 3 (explicit NO x and HO x ), i.e. they can all be independently compared to Case 3.

Case 4: NMDF H+O 2
In this case, we take into account that reaction H+O 2 →HO 2 induces non-mass dependent fractionation of oxygen isotopes. The effect is assumed to be on the order of 1‰, according to Savarino and Thiemens (1999b). In practice, any HO 2 produced through this channel is thus attributed a 17 O value of 1‰.

Case 5: Scrambling upon the decomposition of HNO 4
In this case, it is assumed that the thermal decomposition and photolysis of HNO 4 induce a scrambling of its oxygen atoms. Table 4 presents the chemical reactions for which the 17 O i (X) is different than in Case 1 (PSS NO x ) for the species produced upon the thermal decomposition of HNO 4 .
where values for k R10 were measured by Dubey et al. (1997). In this study, the sole chemical reaction considered inducing non-zero 17 O values in OH is the reaction between O( 1 D) and H 2 O. Mass-balance states that 17 et al., 2007). Under most conditions prevailing in the lower troposphere in mid-latitudes, 17 O(OH) = 0‰ (Michalski et al., 2003). However, under cold conditions the isotopic exchange reaction can compete with its OH chemical sinks , which are mostly OH+CH 4 and OH+CO (Finlayson-Pitts and Pitts, 2000). When Case 6 is tested, 17 O(OH) is assigned a value calculated from Eq. (14) and the mixing ratio of CO, CH 4 and H 2 O and the relevant kinetic rate constants.

MECCA
The chemistry module MECCA (Model Efficiently Computing the Chemistry of the Atmosphere) is embedded in the CAABA (Chemistry As A Box-model Application) boxmodel (Sander et al., 2011). It uses an adaptative time resolution mathematical method to solve the stiff set of equations describing the evolution of the chemical composition of the portion of atmosphere hypothetically contained in a closed box.

Isotopic equations
The MECCA chemistry module, like all atmospheric chemistry models, solves the continuity equation for all considered species and all reactions simultaneously: Considering that the model provides the necessary data at a time step t, it follows that at the next time step t+ t: Atmos. Chem. Phys., 11, 3653-3671, 2011 www.atmos-chem-phys.net/11/3653/2011/ The same applies to the isotopic continuity equation (Eq. 2), so that: By combining Eqs. (15) and (3.3), 17 O(X)(t+ t) can be inferred as a function of the relevant chemical and isotopic data at time t. This simple explicit approach was implemented in a computer program separate from MECCA, which takes as input a data file containing the variables dealt with in Eqs. (15) and (3.3) at each time step, and processes them according to the different cases described above in terms of 17 O i (X) to compute the time evolution of 17 O of each relevant species. One major issue that has to be considered when using this simple approach pertains to the comparison of the chemical lifetime of a species X and the time-step of the integration of Eqs. (15) and (3.3). Indeed, if the lifetime of X is shorter than the time step considered, then the total chemical production or destruction during a given time step t may exceed the amount of species X dealt with in the box (or grid-cell). This causes immediate failure of the integration procedure. The time step of the isotopic calculations performed here was chosen accordingly. A time resolution of 10 s was found to be sufficient to avoid integration issues such as described above. More integrated approaches, fully embedded into the boxmodel itself, have been developed and avoid such shortcomings (see e.g., Gromov et al., 2010). However, for the sake of the present study, and taking advantage of the easiness of manipulating 17 O through simple mass-balance equations, we preferred the implementation presented above for this study.

Presentation of MECCA model runs
Our base-run corresponds to atmospheric settings typical of the remote, mid-latitude (45 • N) boundary layer during springtime. Photolysis rate coefficients are calculated by the model (Sander et al., 2005). The model run is started on 1 April, at a temperature of 293 K, a relative humidity of 81%, with a starting NO 2 mixing ratio of 20 pmol mol −1 . Initial values for the mixing-ratio of main atmospheric species follow: CH 4 , 1.8 µmol mol −1 ; CO, 70 nmol mol −1 ; H 2 O 2 , 600 pmol mol −1 ; HNO 3 , 5 pmol mol −1 ; HCHO, 30 pmol mol −1 , O 3 , 25 nmol mol −1 . The model accounts for dry deposition of NO 2 , HNO 3 , N 2 O 5 and H 2 O 2 . In contrast, no emissions into the model box are considered during the model run. After a spin-up time of 1 day, sufficient to initialize the mixing ratio of short-lived species, the time evolution of the mixing ratio and isotope anomaly of short-lived species is analyzed during 36 h, corresponding to the time frame between 24 and 60 h from the start of the model run. In lack of emissions of primary species into the box considered, this suffices to identify and study the main features of the diurnal variations of the mixing ratio and 17 O of shortlived species while not suffering from the inherent limitations of box-modeling experienced when longer time periods are considered (Sander et al., 2005). We concentrate our in-depth analysis on this one model run, which shows many different interesting features of the diurnal variations of 17 O of short-lived species and their sensitivity of the various assumptions tested through Cases 1 to 6. The intricacy and the highly non-linear coupling between HO x and NO x including their 17 O requires careful attention to decipher the causes for the variation of 17 O. The relevance of the conclusions reached from this analysis is assessed using other model runs undertaken under different atmospheric conditions. Indeed, atmospheric chemical processes depend in particular on temperature, time of the year and latitude (through their control of incoming solar radiation) and the chemical regime of the atmosphere. Figure 3 shows the evolution of the mixing ratio of O 3 , HO x and NO x /NO y (NO y refers to sum of NO x and its reservoir species: NO 3 , N 2 O 5 , HONO, HNO 3 , HNO 4 ) simulated by MECCA under the conditions of the base model run presented in Sect. 3.4. Negative time corresponds to the abovementioned spin-up time period. Note that the time axis is the same for all the plots exhibiting time series in this article. The model results show typical variations in the mixing ratio of the species of interest, notably with peak values of OH, HO 2 and NO reached during the day. The NO x /NO y partitioning changes diurnally, with species such as NO 3 and N 2 O 5 present mostly during the night, and species such as HNO 4 , HONO present mostly during the day. H 2 O 2 is produced during the day, and undergoes dry deposition which leads to a reduction of its mixing ratio during the night. The mixing ratio of ozone remains quasi-constant during the time period studied, illustrating that the simulation reproduces the chemical steady-state prevailing in the remote, mid-latitude boundary layer. As a straightforward corollary of the above paragraph, it appears that in this simulation the OH+NO 2 and HNO 4 hydrolysis are mostly daytime nitrate production pathways, while NO 3 +RH and N 2 O 5 hydrolysis proceed only at night, when significant amounts of NO 3 and N 2 O 5 are present. Note that this study does not aim at disentangling complex aspects of the daytime chemistry of N 2 O 5 revealed by recent field campaigns (e.g., Brown et al., 2006). H 2 O 2 is only produced during the day, when HO 2 maximizes. Figure 4 exemplifies such opposed behavior and illustrates the concept behind diurnally-integrated isotopic signature (DIIS) of the nitrate and hydrogen peroxide sources. From the analysis of this figure, it appears obvious that the nighttime 17 O values of HO 2 have no impact on the 17 O of H 2 O 2 produced. Only daytime 17 O values are worth discussing in this case.  -under the environmental conditions tested, whether isotopic exchange between OH and H 2 O is considered has no significant impact on all the reaction pathways considered. This simply indicates that 17 O(OH)=0‰ under these environmental conditions.

Overview of the diurnally-integrated isotopic signatures (DIIS) values for atmospheric nitrate and hydrogen peroxide sources
-Isotopic scrambling during the thermal and photolytical decomposition of and HNO 4 leads to lowering the DIIS value of all reaction pathways, except for H 2 O 2 production.

Representation of diurnal variations of 17 O(NO 2 )
As shown on Fig. 4a, 17 O(NO 2 ) exhibits diurnal variations with a maximum during the night and a minimum during the day, consistent with previous expectations . Figure 5 compares the results obtained using permanent photochemical steady-state (Case 1, NO x PSS) and explicitly computed (Case 2, NO x explicit, see Sect. 3.2.2). During the day, both calculations show a minimum at noon, on the order of 28‰. This is explained by the fact that during the day, the contribution of the NO+RO 2 and NO+HO 2 to the production of NO 2 peaks at noon, when peroxy radicals reach their maximum values (see Fig. 3). Owing to the short lifetime of NO 2 during the day, the result of the computation based on PSS is fully consistent with the explicit computation. This explains why 17 O OH+NO 2 NO − 3 is the same under Case 1 and Case 2 (PSS and explicit NO x , respectively, see Table 5), because this pathway operates only during the day, when 17 O(NO 2 ) has the same value in both cases.
The major difference between the two simulations occurs at night. Indeed, while the result from PSS leads 17 O(NO 2 ) to reach values above 41‰ at night (i.e., on the order of 17 O NO+O 3 (NO 2 )), the result from the explicit calculation does not exceed 39‰ at night, except for a limited period of time at dawn. The explanation for this behavior follows: at dusk, the 17 O(NO 2 ) is fixed by the PSS conditions which prevail just before PSS recycling of NO x becomes insignificant. At this point, NO 2 becomes relatively inert and its 17 O does not vary anymore. As evidenced by Fig. 5, nighttime 17 O(NO 2 ) corresponds to the 17 O(NO 2 ) value computed at PSS when the lifetime of NO 2 is on the order of 10 min. It is then "frozen" until the dawn comes, along with the restart of photochemical activity. The difference between the two calculations lies between 2 and 3‰ under the conditions of the base model run. This explains why DIIS values for the   The addition of non-mass dependent fractionation through the H+O 2 reaction, which is the dominant HO 2 production reaction, results in elevating the 17 O(HO 2 ) value by roughly the magnitude of the isotopic fractionation constant.
Combining the explicit calculation of the time evolution of 17 O(HO 2 ) with the inclusion of non-mass dependent fractionation occurring during the H+O 2 reaction leads to daytime 17 O(HO 2 ) values on the order of 2‰.
We note that the corresponding 17 O HO 2 +HO 2 (H 2 O 2 ) values for either Case 3 or 4 (explicit NO x and HO x and NMDF H + O 2 , respectively), 1.1 and 1.8‰, respectively, are consistent with the experimental results of Savarino and Thiemens (1999a) values ranging between 0.9 and 2.0‰, under coastal conditions in California.

Impact of isotopic scrambling during the thermal and photolytical decomposition of HNO 4
Case 5 tests the hypothesis where thermal decomposition and photolysis leads to isotopic scrambling between O atoms in molecules making up HNO 4 (see Table 4). Under such conditions, it is observed that the 17 O of HO 2 increases, while 17 O of NO x generally decreases. This behavior is reflected in the DIIS values of the relevant reactions (see Table 5). Detailed investigation of the reasons for this result reveals that much of the effect proceeds through the thermal decomposition of HNO 4 , especially at dusk when HNO 4 thermal decomposition is on the order of its formation rate due to reduced photochemical activity lowering the amount of HO 2 . Through slow but steady cycles of formation/decomposition, HNO 4 temporarily bridges the pool of oxygen atoms within NO x and HO x , leading to lowering the 17 O of NO x and increasing the 17 O of HO x in a significant manner (see Fig. 6). In the following, we do not further discuss the impact of the hypothesis of Case 5, although model results are also given for this case.

Sensitivity to atmospheric conditions
This section presents the results obtained under different conditions than in the base model run. For the sake of brevity, and since the physico-chemical reasons behind the observed behavior are similar to the phenomena described above, we focus our attention on DIIS values, which provide an efficient metric to compare model runs carried out under different environmental conditions.

Impact of seasonal variations
Using the same chemical mechanism and the same initial chemical composition of the boundary layer, model runs were performed at different times of the year, i.e. starting from 1 January with a temperature of 283 K and 1 July with a temperature of 303 K to see whether seasonal variations in environmental conditions (temperature and actinic flux) can modify the conclusions reached above for the springtime model run, started on 1 April with a temperature of 293 K. The photochemical activity increases monotonically from the winter to summer model runs, as expected (chemical data not shown).
The model shows that the DIIS of daytime nitrate production channels ( 17 O OH+NO 2 NO − 3 and 17 O HNO 4 hydrol NO − 3 ) are most dependent on the season, due to their strong ties to photochemical activity, which controls 17 O of NO 2 and HNO 4 through photochemical steady state during the day. The 17 O OH+NO 2 NO − 3 varies In contrast, the DIIS of nighttime nitrate production channels exhibits a stronger dependence upon the isotopic assumption (as detailed in Sect. 4.1.3), but shows little seasonal variations. The biggest variation is between Case 1 (PSS NO x ) and Case 2 (explicit NO x ), the former leading to an overestimation ranging from 1.5 to 2.0‰, from winter to summer for both N 2 O 5 hydrolysis and NO 3 +RH. The 17 O NO 3 +RH NO − 3 and 17 O N 2 O 5 hydrol NO − 3 both vary within about 1‰ seasonally, and remain on the order of 40 and 33‰ year-round, respectively.
Last, 17 O HO 2 +HO 2 (H 2 O 2 ) values show little seasonal variation (less than 0.1‰). They remain consistently on the order of 1‰ when only the OH+O 3 reaction is responsible for 17 O transfer from O 3 to HO 2 . They increase to around 1.7‰ when non-mass dependent fractionation of 1‰ is considered throughout the reaction H+O 2 → HO 2 . The only major change occurs in Case 5, i.e. considering scrambling during the thermal decomposition and photolysis of HNO 4 .
Under the conditions experienced for our base model run, the isotopic exchange reaction between OH and H 2 O does not lead to 17 O(OH) values significantly different from 0. This explains why the DIIS values for Case 6 (OH + H 2 O isotopic exchange) are very similar to that of Case 3 (explicit NO x and HO x ). This effects becomes significant only at lower temperatures (see Morin et al., 2007) and is further explored in Sect. 4.2.2.

Higher latitude and colder conditions
A simulation was carried out under springtime Arctic conditions, i.e. a latitude of 80 • N and temperature of 253 K, starting from 1 April. The results of this comparison is shown in terms of DIIS values in Table 7.
The DIIS values of daytime nitrate production channels show a strong difference between Arctic and mid-latitude conditions. With the exception of Case 6 (OH + H 2 O isotopic exchange), the Arctic 17 O OH+NO 2 NO − 3 values are ca. 5.5‰ higher than at mid-latitudes, which simply stems from reduced photochemical recycling under reduced insulation prevailing in the Arctic and colder temperatures. It is noteworthy that under Arctic conditions, owing to the lower temperatures prevailing, the value of 17 O OH+NO 2 NO − 3 is 2‰ higher under Case 6 (OH + H 2 O isotopic exchange) than under other cases (except Case 5). The diurnal variations of 17 O(NO 2 ) is similar for Case 2 (explicit NO x ) and Case 6 (OH + H 2 O isotopic exchange) under Arctic conditions, demonstrating that all of the difference observed stems from the fact that 17 O(OH) amounts ca. 6‰ under Arctic conditions and Case 6, consistent with the initial estimates provided by Morin et al. (2007). In summary, the impact of colder and more boreal environmental conditions is mostly seen for the DIIS of daytime nitrate production, upon which photochemical conditions and the 17 O of OH have a direct impact. The DIIS of nighttime nitrate production channels as well as H 2 O 2 seem to be fairly insensitive to these factors.

Higher initial NO x mixing ratio
A further simulation was carried out under springtime midlatitude conditions (45 • N, 293 K), with an initial NO x mixing ratio of 2 nmol mol −1 instead of 20 pmol mol −1 in the base run. The results in terms of DIIS are shown in Table 8. The impact of performing the PSS approximation to compute 17 O of NO x is similar, i.e. there is no impact on daytime nitrate production pathways and H 2 O 2 . It is more visible in the case of nighttime nitrate production pathways, although the difference between Case 1 (PSS NO x ) and Case 2 (explicit NO x ) for nighttime nitrate production pathways is smaller than under the conditions of the base model run.
Atmos. Chem. Phys., 11, 3653-3671, 2011 www.atmos-chem-phys.net/11/3653/2011/ We compare here our results to the implementation of 17 O(NO − 3 ) into the GEOS-Chem chemistry transport model, which was recently carried out by Alexander et al. (2009). In this work, 17 O(NO x ) was computed under the hypothesis of photochemical steady-state. For the sole daytime nitrate production channel considered (OH+NO 2 ), 17 O(NO 2 ) was estimated using the α value (see Sect. 3.2.1) computed using accumulated reaction rates between 10:00 and 14:00 solar time. For nighttime nitrate production channels, Alexander et al. (2009) used the photochemical steadystate formalism using NO 2 production rates accumulated between 00:00 and 02:00 solar time. We compute the 17 O inherited by atmospheric nitrate through the OH+NO 2 and NO 3 +RH using the algorithm of Alexander et al. (2009) presented above, and compare it to the corresponding DIIS val-ues. The results are given in Table 9. We find that the algorithm introduced by Alexander et al. (2009) underestimates the isotopic signature of the OH+NO 2 channel by 1‰ under springtime conditions, because it ignores contributions of this channel before 10:00 and after 14:00, when 17 O(NO 2 ) is relatively higher than during noontime but the OH+NO 2 reaction proceeds significantly. The underestimates ranges between 0.5 and 1.5‰ when the comparison extends to other seasons and latitudes considered in the model runs. Alexander et al. (2009) also overestimate the isotopic signature of the NO 3 +RH channel by 1.6‰, due to the fact that they use PSS equations to derive 17 O(NO y ) at night, which has been proven above to cause significant overestimation of the DIIS of nighttime nitrate production channels.
We strongly suggest that DIIS values are implemented in large-scale modeling frameworks, such as GEOS-Chem, to avoid performing such errors. To facilitate this, we provide below a method to implement this concept within a model such as GEOS-Chem, using the formalism of Alexander et al. (2009) These three equations can be generalized as follow: rather than computing the instantaneous isotopic signature of each nitrate source considered, under PSS conditions, let us examine their diurnally integrated isotopic signature. It is possible to compute the α value matching the DIIS values explicitly computed, using the formalism of Eqs. (17), (18) and (19): The then defined effective α, denoted α, are specific to each nitrate production pathways, and can serve to expand the formalism defined at PSS to account for the fact that PSS does not hold to quantitatively compute the isotopic signature of atmospheric nitrate sources. Such effective α values can then be implemented in a model like GEOS-Chem . Indeed, in this model implementation, the isotopic signatures of nitrate production channels were computed at a daily time resolution (B. Alexander, personal communication 2011). α NO 2 +OH is conceptually equivalent to α day as defined in Alexander et al. (2009) because this pathway proceeds during the day. Likewise, Alexander et al.
(2009) defined a α night value which holds for N 2 O 5 hydrolysis and the NO 3 + RH reactions. In the cases tested, our study indicated that α NO 3 +RH has the same value as α N 2 O 5 hydrol , justifying the use of a single α value for "nighttime" nitrate production channels. The α values extracted from data in Table 9 for the OH + NO 2 channel are equal to 0.73 and 0.69 for the explicit calculation and Alexander et al. (2009), respectively. For the NO 3 + RH channel, the α values are equal to 0.93 and 0.99, respectively. The errors in terms of DIIS, as detailed above, translate in errors in terms of α.
In practice, the issue associated with the computation of α NO 2 +OH in GEOS-Chem can easily be solved as follows: rather than computing α values over an arbitrary time window which causes a systematic underestimation at least on the order of 0.04 in terms of α, we recommend to extend the temporal range of integration to the full length of the day (i.e., from 00:00 to 24:00 solar time), and scale the instantaneous PSS α values with the rate of reaction OH + NO 2 . Indeed, we have shown that 17 O OH+NO 2 NO − 3 values computed using PSS approximations match the DIIS values obtained through the explicit modeling of 17 O of NO x and NO y . The issue with the nighttime nitrate production channels should be solved without resorting to using photochemical steady state equations at night, since we have shown that this leads to systematically erroneous results and is based on a scientific oxymoron. The model results show that 17 O NO 3 +RH NO − 3 and 17 O N 2 O 5 hydrol NO − 3 do not vary significantly over night. This behavior stems from the fact that the main driver of change of 17 O of nitrate precursors, that is photochemical cycling between NO x , HO x and ozone is inactive at night, thereby "freezing" the 17 O signature of most reactants until dawn. Given the low sensitivity of DIIS values, and thus α values, for nighttime nitrate production channels to environmental conditions such as temperature, actinic flux and NO x levels, a conservative approach may be to use a fixed value of 0.94 for the α of NO 3 +RH and N 2 O 5 hydrolysis, respectively. Indeed, this value corresponds to the middle of the range covered (within 0.02, minimum in summer and maximum in winter) by our model runs, spanning a wide range of atmospheric and environmental conditions.

Implication for 17 O(H 2 O 2 )
An interesting implication of our work is the fact that under all tested environmental conditions, the model predicts non-zero 17 O(H 2 O 2 ) even without invoking non-mass dependent fractionation through the H+O 2 reaction, as evidenced by Savarino and Thiemens (1999a). This significant 17 O(H 2 O 2 ), on the order of 1‰, stems from the OH+O 3 reaction and could be used in the future to probe the level of photochemical activity of a given air parcel through measurements of 17 O(H 2 O 2 ) either in the gas-phase or in rainwater, as suggested by Savarino and Thiemens (1999b).

Open questions
Two untested assumptions of this work are the hypothesis that 17 O(O 3 ) remains constant throughout the day, and that the thermal decomposition and photolysis of HNO 4 does not lead to any isotopic scrambling between the two molecules making up these dimers. The assumption related to the diurnal variations of 17 O(O 3 ) can now be addressed using field measurements carried out using a chemical probing method based upon the NO − 2 + O 3 reaction (Michalski and Bhattacharya, 2009;Vicars et al., 2011). As indicated above, should 17 O(O 3 ) exhibit significant diurnal variations, several quantitative results provided above for illustration purposes would become obsolete -note that the same would apply to all model studies carried out so far, which all assume diurnally invariant 17 O(O 3 ) (e.g. Michalski et al., 2003;Morin et al., 2008;Kunasek et al., 2008;Dominguez et al., 2009;Michalski and Xu, 2010;Alexander et al., 2009 Luz, 2003, 2005), the 17 O of O 2 and H 2 O are expected to be small and should affect negligibly the discussion presented above. We have also chosen to not propagate experimental and theoretical uncertainties associated with the 17 O transfer rate of 17 O(O 3 ) along with chemical reactions mostly for clarity reasons, to rather focus on the overall methodological aspects of the explicit modeling of the 17 O transfer through a full photochemical mechanism.

Conclusions
This study addresses in detail the question of the impact of diurnal variations of 17 O of short-lived reactive species on secondary species such as atmospheric nitrate and H 2 O 2 . Using a state of the art photochemical box model, the time evolution of 17 O of NO x , NO y and HO x is computed under various sets of hypotheses pertaining to the method of computing the 17 O values, reflecting different levels of simplifying approximations. Most of the conclusions of this article are drawn from model simulations carried out under clean atmospheric conditions in mid-latitudes ; their broader relevance and robustness is however assessed using model simulations carried out under cold and boreal conditions, and under a 100-fold increase in initial NO x mixing ratio.
The primary goal of this study was to demonstrate that using a detailed box-modeling study to assess the isotopic signature of various nitrate and H 2 O 2 production pathways is feasible and provides relevant information to larger-scale modeling studies. In the meantime, essential features of the coupling between chemical reactions and the 17 O of key atmospheric species were described and are most likely also valid under different environmental contexts. Taking this study as an initial step, the model could rather easily be extended to account for gas/particles interactions, which are of primary importance for the budget of NO x , and to simulate 17 O values of secondary species such as atmospheric nitrate and H 2 O 2 under atmospheric contexts as different as over continents (urban polluted, tropical etc.) and under polar conditions including more complex and realistic chemical mechanisms. We believe that the present study provides the necessary framework for carrying out this work under conditions that will make it usable by larger-scale modeling studies, or for the interpretation of short-term intensive measurement campaigns using a modeling tool analogous to CAABA/MECCA. Supplement related to this article is available online at: http://www.atmos-chem-phys.net/11/3653/2011/ acp-11-3653-2011-supplement.pdf.