The temperature dependence of the kinetic isotope effect (KIE) of β-pinene ozonolysis was investigated experimentally at 258, 273 and 303 K in the AIDA atmospheric simulation chamber. Compound specific carbon isotopic analysis of gas phase samples was performed off-line with a Thermo Desorption-Gas Chromatography-Isotope Ratio Mass Spectrometry (TD-GC-IRMS) system. From the temporal behavior of the δ13C of β-pinene a KIE of 1.00358 ± 0.00013 was derived at 303 K, in agreement with literature data. Furthermore, KIE values of 1.00380 ± 0.00014 at 273 K and 1.00539 ± 0.00012 at 258 K were determined, showing an increasing KIE with decreasing temperature. A parameterization of the observed KIE temperature dependence was deduced and used in a sensitivity study carried out with the global chemistry transport model MOZART-3. Two scenarios were compared, the first neglecting, the second implementing the KIE temperature dependence in the simulations. β-Pinene stable carbon isotope ratio and concentration were computed, with emphasis on boreal zones. For early spring it is shown that when neglecting the temperature dependence of KIE, the calculated average age of β-pinene in the atmosphere can be up to two times over- or underestimated. The evolution of the isotopic composition of the major β-pinene oxidation product, nopinone, was examined using Master Chemical Mechanism (MCM) simulations. The tested hypothesis that formation of nopinone and its associated KIE are the determining factors for the observed δ13C values of nopinone is supported at high β-pinene conversion levels.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
 The gas phase oxidative chemistry of volatile organic compounds (VOCs) contributes to tropospheric ozone production and secondary organic aerosol (SOA) formation, thus affecting human health and influencing the climate. A better understanding of VOC sources and processes is therefore needed for improved model predictions of future air quality and climate. This concerns in particular biogenic VOC (BVOC), whose emissions are globally estimated to be one order of magnitude higher than the anthropogenic VOC emissions [Guenther et al., 1995; Guenther, 1999; Müller, 1992; Piccot et al., 1992].
 Analysis and interpretation of stable isotope ratios is a useful tool in identifying and quantifying the sources of VOCs, as well as their physical and chemical processing in the atmosphere [Rudolph and Czuba, 2000; Rudolph, 2007]. In addition to concentration measurements of reactive gases and information gained from transport models or meteorology, knowledge of the isotopic composition reduces uncertainties in describing the origin and evolution of studied air masses.
 The stable isotope ratio of a sample is reported using delta notation, δ13C, describing the per mil (‰) deviation from a standard:
where 13Rsampl = [13C]sampl/[12C]sampl and 13Rstd = [13C]std/[12C]std are the isotope ratios for the sample and for the working standard, respectively. In the present work, final δ13C values are reported relative to the international reference Vienna Pee Dee Belemnite (VPDB) [International Union of Pure and Applied Chemistry (IUPAC), 1994].
 Oxidation as the major VOC degradation reaction in the atmosphere generally results in fractionation between the light and heavy isotopes. This is caused by the change in the oxidation reaction rate (k) when, instead of the pure 12C reactant, its 13C containing isotopologue is involved in the reaction. The kinetic isotope effect (KIE) describes this variation and is defined by
where 12k is the reaction rate of the pure 12C reactant and 13k is the reaction rate of the 13C containing isotopologue.
 Since the isotope fractionation effects are generally very small, the KIEs are converted, similar to delta values for stable isotope ratios, to per mil epsilon values, describing the relative difference of the reaction rate constants:
 The kinetic isotope effect of a reaction can be determined in laboratory studies from measurements of concentration and δ13C of a VOC as function of reaction time. Explicitly, the KIE value is deduced from the experimental data as a function of concentrations and isotope ratios at time t and t = 0 [Anderson et al., 2003] as follows:
 For atmospheric samples, the KIE value can be used to determine the average time passed since emission of a single species (tav) until observation [Rudolph and Czuba, 2000]:
where [Oxidant]av is the average concentration of the oxidant in the atmosphere, 0δ is the isotope ratio of the emission, tδ is the isotope ratio of the analyzed compound in the field sample and 12kox is the rate constant of the oxidation reaction. Having knowledge of the isotopically determined atmospheric age of an examined compound, tav, in addition to the mean concentration of the oxidant, the temporal and thus the spatial scale of the investigated process can be determined.
 The monoterpene β-pinene is one of the major biogenic VOCs emitted by forests, showing a high SOA formation potential via oxidation [Kanakidou et al., 2005] and thus, playing an important role in the aerosol-climate feedback mechanisms within the atmosphere. In this study, the KIE of β-pinene ozonolysis was determined during dark chamber experiments carried out at 258 K, 273 K and 303 K. Experimental results of the temporal evolution of nopinone isotopic composition, which is the main product of β-pinene ozonolysis, were investigated using a modified Master Chemical Mechanism (MCM). The determined KIE values were used to calculate in the model runs the rates of the β-pinene ozonolysis reactions involving a 13C isotope.
 Finally, a parameterization of the observed KIE temperature dependence was deduced and 3-D global simulations of the stable carbon isotope ratio and concentration of β-pinene were carried out to quantify the impact of the observed KIE temperature dependence of β-pinene ozonolysis on global scale.
2.1. Experimental Method
2.1.1. Experimental Conditions
 The β-pinene ozonolysis experiments were conducted at the AIDA (Aerosols Interaction and Dynamics in the Atmosphere) simulation chamber of the Karlsruhe Institute of Technology, Germany. The aerosol reactor, consisting of a cylindrical aluminum vessel of 84.5 m3 volume, is housed in a dark, thermally isolated chamber and can be operated in a temperature range between 183 K and 333 K. Three working platforms around the chamber facilitate the access to reactor flanges of various sizes. Details of the AIDA chamber are described by Saathoff et al. [2003, 2009]. The three β-pinene ozonolysis experiments described here were performed at temperatures of 258 K, 273 K and 303 K and ambient pressure (∼1000 hPa). Temperature and initial concentration of water and reactants are given in Table 1. The relative humidity ranged from 30 to 60%. Cyclohexane (99.5%, Merck) was used as scavenger for the OH-radicals generated during the β-pinene ozonolysis. Due to the high cyclohexane concentration (∼500 ppm) used in each experiment, the examined β-pinene oxidation was a pure ozonolysis reaction [Saathoff et al., 2009]. Prior to each experiment, the AIDA chamber was evacuated to typically 1 Pa total pressure, flushed two times with 10 hPa of synthetic air and filled to atmospheric pressure (∼1000 hPa) with humidified synthetic air (low hydrocarbon grade, Basi). Cyclohexane was added by flushing 9 L min−1 of synthetic air over a saturator. Ozone was generated by a silent discharge generator (Semozon 030.2, Sorbios) in mixing ratios of about 3% in pure oxygen and added to the chamber either directly or after dilution in a 1 L glass bulb with a flow of 5 L min−1 synthetic air. The β-pinene (99%, Aldrich) was evaporated up to pressures of ∼2 hPa into a 2 L glass bulb and flushed into the chamber with 10 L min−1 synthetic air for 2 min. The reaction started by injecting the β-pinene. The stirring fan on the bottom of AIDA chamber assured an overall homogeneous mixing of all reaction components within 1–2 min. For reference purposes, upon nearly complete consumption of the reactants, ∼20 ppb nopinone (98%, Aldrich), as major product of β-pinene ozonolysis, was added by flushing 8 L min−1 of synthetic air over a saturator containing nopinone at 50°C. In order to reach similar β-pinene lifetimes for all experiments, the concentrations of the reactants were varied according to Table 1.
Table 1. Temperature and Initial Concentration of Water, Ozone, β-Pinene and Nopinone for the Experiments, as well as Predicted β-Pinene Lifetimes Under the Given Conditions
2.1.2. Sampling and δ13C Analysis
 Gas phase samples were collected in pre-cleaned and evacuated Silcosteel gas canisters (Restek, Bellefonte, USA). The chamber was connected to the canisters via 6 mm PFA tubing. Ozone was removed by passing the samples through a heated Silcosteel capillary (120°C). Approximately 15 l of air were sampled by pressurizing the canisters to 2.5 bar. Blank probes for the clean chamber were taken for each experiment prior to reactant injection. Samples were collected at time intervals of 30 to 60 min. The gas phase isotopic composition was measured in the Institute for Energy and Climate Research of the Research Center Jülich within two days after samples were taken.
 Compound specific stable carbon isotope ratio analysis was carried out by using a setup optimized to measure gas phase samples. The system consists of a custom built cryo-sampling-thermal-desorption unit connected to a gas chromatograph coupled to an isotope ratio mass spectrometer via a combustion interface (TD-GC-IRMS).
 This setup was described in detail elsewhere [Iannone et al., 2007; Fisseha et al., 2009]. Briefly, the cryo-focusing system is custom designed (GERSTEL GmbH & Co. KG, Mülheim/Ruhr, Germany) to concentrate collected trace gases prior to separation. To this end, three successive cryo-trapping steps are used, leading to an optimal focusing of the VOCs. The first cryo-trap, a Silcosteel tube of 300 mm, 11 mm ID, packed with glass beads of 60–80 mesh, was operated at −170°C. Next, the VOCs from the samples were thermally desorbed at 240°C and transferred with helium carrier gas to two smaller cryo-traps. The focusing was achieved through alternatively cooling-heating of these cryo-traps, from −170°C to 250°C and from −80 to 250°C, respectively, at a rate of 12°C/s. Compounds were separated with an Agilent 6890 Gas Chromatograph equipped with a Rtx-1 fused silica column (105m × 0.32mm ID, film thickness 3 μm, Restek Corporation, Bad Homburg, Germany). For all measurements, the temperature program of the GC oven was holding 30°C for 5 min, ramping at a rate of 4°C/min to 200°C and holding there for 42.5 min. The separated VOCs were transferred into a combustion interface (quartz tube, packed with CuO) and oxidized at 850°C quantitatively to CO2 and water. The latter was removed in a cold trap at −100°C, whereas the CO2 was transferred to the isotope ratio mass spectrometer (Isoprime IRMS, GV Instruments, Manchester, UK) operated in continuous flow mode for stable carbon isotope ratio measurements.
 The ion currents at mass-to-charge ratios m/z 44, 45 and 46 were corrected for the contribution of 17O-containing isotopologues [Brand et al., 2010].
 For calibration purposes, isotopic measurements of standard mixtures were performed before, in between and after the sample analyses, by using two different TD-GC-IRMS setups: the gas phase setup, described above, and an aerosol particle setup, which is optimized for thermodesorption and transmission of the VOCs from aerosol filter samples to the GC. The systems have similar configuration, though the thermodesorbtion section of the latter one consists of a Thermal Desorption Unit (TDU, GERSTEL GmbH & Co. KG, Mülheim/Ruhr, Germany) mounted directly onto a Programmable Temperature Vaporizing Cooled Injection System (PTV-CIS).
 The standard mixtures contained n-nonane (Fluka, 99.5%), n-undecane (Merck, 99%), α-pinene (Aldrich, 99%) and nopinone (Aldrich, 98%). Bulk compounds diluted in n-hexane were injected directly in the TDU of the aerosol setup. Further measurements were carried out by injecting the standard solution in glass capillary tubes filled with silane-treated fine wool, which were thermo-desorbed in the TD tube of the gas phase setup. High purity CO2 (Messer, 100%) was calibrated against IAEA standards and used as a working reference gas to calculate the δ13C of the compounds. The δ13C values of individual compounds measured using both setups are given in Table 2. Within experimental errors, δ13C values derived from both systems show good agreement.
Table 2. δ13C of Standards Measured Using Two TD-GC-IRMS Setups for Gas Phase and Aerosol Isotopic Analyses
Gas Phase Setup δ13C (‰)
Aerosol Setup δ13C (‰)
−43.0 ± 0.2
−42.9 ± 0.3
−26.2 ± 0.3
−26.6 ± 0.4
−27.3 ± 0.3
−27.1 ± 0.4
−30.0 ± 0.4
−29.7 ± 0.5
2.2. Application of the Master Chemical Mechanism in the Analysis of Isotopic Measurements
 A gas phase near-explicit chemical scheme provided by the Master Chemical Mechanism (MCM 3.1, http://mcm.leeds.ac.uk/MCM) describing the degradation of VOCs in the troposphere [Jenkin et al., 2003] was employed to interpret the observed time dependence of isotopic composition.
 Parts of the mechanism (a subset of 659 reactions with 99 compounds) were extracted by selecting β-pinene as primary VOC and its initial degradation products. For an explicit tracking of the β-pinene fraction containing 13C (referred to as 13β-pinene) and its oxidation products, a second set of reactions and compounds was added to get the following reaction system:
where R and P are reactants and products accompanied by their stoichiometric coefficients sr and sp, respectively. ki represent the reaction rate coefficients of reaction i. The superscripts indicate the presence of 12C only or 13C isotope in the considered compound. Due to the low abundance of the heavier isotope, the presence of doubly or higher substituted molecules was considered negligible. was solely used as the rate of 13β-pinene ozonolysis for the reactions 13β-pinene + O3 → 13C9H14O + 13CH2OO and 13β-pinene + O3 → 13C9H14OO + 13CH2O. Note that the superscript ‘13’ in the products only refers to the product originating from a 13C containing β-pinene and does not specify which product carries the 13C atom. The rates for the rest of reactions involving 13C isotope were considered equal to 12ki. This is legitimate since the aim of the study is to analyze the isotopic composition of β-pinene and nopinone during a pure ozonolysis reaction. differs from by the kinetic isotope effect (equation (2)). Note that within this approximate approach, possible differences of KIE for the different isotopomers are considered negligible, so the same KIE is used for all isotopomers.
 Additionally to the MCM reaction rates, the rate coefficient of 12β-pinene ozonolysis was employed as a function of temperature [von Hessberg et al., 2009]:
Some of the input parameters used to initialize the simulations for each experiment (temperature and initial concentration of β-pinene and ozone) are included in Table 1. The initial δ13C value of β-pinene injected into the chamber (−29.16‰) was used to initialize the concentration of the 13β-pinene. KIE was applied as derived from the experiments (see section 3.1) to calculate the rate constant
 The reaction system 6, preserving the masses of the stable isotopes in the course of the reactions, was solved at each integration step. Concentrations of both β-pinene and nopinone isotopologues (those containing only 12C and those containing at least one 13C atom) were determined. Subsequently, the δ13C values during the ozonolysis reaction were calculated as function of reaction time.
2.3. Modeling Stable Carbon Isotopes With MOZART-3
 MOZART-3 (Model for OZone And Related Tracers, version 3) is a global chemistry transport model, described in detail by Kinnison et al. . Tropospheric chemistry mechanisms including a limited representation of non-methane hydrocarbon chemistry and monoterpene oxidation, transport, tracer advection, convection and diffusion processes as well as dry and wet deposition are simulated within the model. Vertically, 60 hybrid layers reaching from the surface to 0.1 hPa and horizontally, a grid of 192 × 96 points (longitude/latitude), corresponding to a resolution of 1.875° × 1.895°, are used. The model time step is 15 min. 115 chemical species are involved in the simulations. α- and β-Pinene were added to the other species, representing together the monoterpene class C10H16. The system of chemical reactions consists of 71 photolysis, 219 gas phase and 21 heterogeneous reactions. The gas phase reactions have been updated to JPL-06 [Sander et al., 2006].
 The treatment of source specific isotope fractionation in MOZART-3 is described in detail by Stein and Rudolph . The emission inventories and other input data used for the model simulations have been created for the EU FP6 project GEMS [Hollingsworth et al., 2008]. Monthly anthropogenic and natural emissions originate from the RETRO project [Schultz et al., 2007]. RETRO ship emissions have been replaced by estimates based on the work by Corbett and Koehler , and East Asian anthropogenic emissions have been replaced by the REAS inventory [Ohara et al., 2007], though keeping the original RETRO seasonality. Biomass burning emissions are from the GFEDv2 inventory [van der Werf et al., 2006] giving actual wildfires with an 8-day resolution. The monoterpene emissions were split up as follows: 15% of the total monoterpenes were attributed to β-pinene [Spanke et al., 2001; Kanakidou et al., 2005], the rest of 85% was lumped together as α-pinene emissions. The simulations for this study were driven by ECMWF ERA-Interim reanalysis [Uppala et al., 2008; Dee and Uppala, 2009] meteorology for the period March to October 2004.
 For our special application, 12β-pinene and 13β-pinene were introduced as separate chemical species. The temperature dependence of the rate constant of 12β-pinene ozonolysis was implemented as from equation (7). The isotopologue 13β-pinene is emitted and undergoes the same reaction pathway as 12β-pinene in the course of the simulations. The reaction rate of 13β-pinene ozonolysis was calculated from equation (2) by using the determined KIE value.
3. Results and Discussions
3.1. Tracking of Stable Isotope Composition During β-Pinene Ozonolysis: Comparison Between Measurements and MCM Modeling
 The isotopic composition of β-pinene and nopinone (the major chromatographically separated compounds identified in the samples) was determined. The measurements of stable carbon isotope ratio and concentration of β-pinene were employed to calculate the ozonolysis KIE for each experiment. In turn, the experimentally obtained KIE values were employed in the initialization of MCM simulations. The progress of the isotopic composition of the major ozonolysis product, nopinone, was examined by comparing the measured values with the modeling output.
Figure 1 depicts the temporal evolution of the δ13C values after the β-pinene injection into the AIDA reaction chamber. In all cases, β-pinene became enriched in the heavier isotope 13C during the reaction. This behavior shows that β-pinene ozonolysis exhibits a normal kinetic isotope effect (KIE > 1), where the lighter isotope preferentially fractionates into the product. At 258 K, the δ13C value of β-pinene rises by 18.6‰ (from −28.9‰ to −10.3‰) in about 5 h after injection, compared with an increase by 15.8‰ at 273 K and 14.9‰ at 303 K respectively. For each temperature, the β-pinene lifetime was experimentally determined from measured concentrations. The resulting lifetimes of 1.18 h at 303 K, 1.29 h at 273 K and 1.36 h at 258 K, show good agreement with the predicted values (Table 1) with a maximum deviation of 3.7% at 258 K.
 In order to determine KIE, for each experiment a straight line was fitted to the experimental data according to equation (4). As can be seen in Figure 2, the slope of the regression line increases with decreasing temperature. According to equation (4), the slopes of the regression lines represent KIE/(1 − KIE); thus, KIE increases with decreasing temperature.
 The KIE calculated for each experiment as well as the corresponding ɛ values are summarized in Table 3.
Table 3. KIE and ɛ Values of β-Pinene Ozonolysis at Different Temperatures
1.00358 ± 0.00013
3.58 ± 0.13
1.00380 ± 0.00014
3.80 ± 0.14
1.00539 ± 0.00012
5.39 ± 0.12
 The average ɛ value for the β-pinene ozonolysis reaction at 303 K found in this work (3.58 ± 0.13‰) is higher than the value reported by Fisseha et al.  = 2.6 ± 1.5‰), though showing agreement within the range of uncertainty. Moreover, the experimentally determined ɛ value at 303 K is comparable with the ozonolysis ɛ value of other alkenes estimated from the inverse dependence of the kinetic isotope effect on carbon number (NC) [Rudolph, 2007]. According to that dependence, the predicted value for β-pinene with NC = 10 is 3.4 ± 0.1‰. To the best of our knowledge, no literature data is available up to now on at temperatures lower than room temperature.
 The KIE experimental data can be well fitted by a mono-exponential-plus-constant function dependent on temperature (Figure 3):
For the achieved measurement precision of 0.13‰ (see Table 3), the results obtained by using the regression equation (8) indicate that a change in KIE with temperature is experimentally not distinguishable at temperatures higher than 284 K. This conclusion is consistent with the work of Anderson , who showed that for a series of VOC oxidation experiments carried out at temperatures higher than 288 K, no significant KIE temperature dependence could be established within their measurement precision. Note that applying equation (8) outside the temperature range within which experiments were performed may result in uncertainties, specifically for temperatures lower than 258 K.
 The δ13C values of gas-phase nopinone vary between −30.3‰ and −25.1‰ (Figure 1). Similar to the β-pinene, gas-phase nopinone became overall heavier during the ozonolysis reaction, but the increase of nopinone δ13C values in the course of the experiments was only very slight. The isotopic composition of the first generation oxidation product nopinone depends on factors involved in both, its chemical formation and removal processes, together with their associated KIEs. First, assuming that KIE in β-pinene ozonolysis reaction forming nopinone primarily determines the nopinone δ13C composition, a nopinone δ13C value lower than the precursor δ13C value by the KIE is expected at early stages. Additionally, after full oxidation of all β-pinene existing in the system, nopinone δ13C value should be equal to the initial δ13C value of β-pinene. Second, chemical and condensational loss processes should influence the evolution of nopinone isotopic composition. Since OH radicals were efficiently scavenged during the experiments, chemical loss of nopinone can be excluded from the factors controlling its isotopic composition. Finally, condensational processes during oxidation reactions should not significantly affect δ13C evolution. Fisseha et al.  report an average fractionation of 2.3‰ for the partitioning of nopinone in the aerosol in an experiment using no OH scavenger. Irei et al. [2006, 2011] show that for toluene oxidation, only the first reaction step determines the isotopic composition, thus fractionation due to partitioning into particulate matter can be neglected.
 To explore the controlling factors of the measured temporal evolution of nopinone isotopic composition, the hypothesis is tested that the nopinone formation from β-pinene ozonolysis with its determined KIE is dominating the δ13C evolution of nopinone. To this end, MCM simulations were carried out, as described in section 2.2. The runs were initialized with the experimentally obtained KIE values (Table 3). Figure 4 shows measured and modeled δ13C values of β-pinene and nopinone as function of the fractional conversion of β-pinene.
 The MCM curves show that, as the reaction progresses, δ13C of β-pinene increases. The δ13C of the nopinone produced from the β-pinene ozonolysis rises too. The difference between the initial and final δ13C values of nopinone is yet smaller than for the β-pinene. At the beginning of the reaction, the modeled δ13C values of β-pinene and nopinone differ by the exact amount dictated by the KIE. Since the reaction is assumed to be a closed system, where only one product forms and is not removed, the δ13C value of the nopinone at the end of the reaction is equal to the initial δ13C value of β-pinene [Schmidt et al., 2004]. Note that the assumption of no effective nopinone loss occurring in the course of the experiments will affect nopinone gas-phase concentrations and, by that, the δ13C of the modeled nopinone. The semivolatile nopinone is known to partition into the secondary organic aerosol formed during β-pinene ozonoloysis [Pathak et al., 2008; Hohaus et al., 2010], yet associated with a small isotope fractionation (see above). Therefore, for the δ13C modeling, nopinone partitioning between gas and particle phase was neglected.
 Within the error range, good agreement between measured and predicted δ13C values of nopinone was found at high degree of β-pinene processing. Discrepancies between modeled and measured nopinone δ13C exist for early stages of the reaction (see Figure 4). Overall, the observed isotopic composition of nopinone is mainly driven by the chemical processes involved in its formation and the associated KIE. For high degrees of β-pinene processing nopinone loss processes can be neglected.
3.2. Temperature Dependence of KIE and Its Application in Ambient Atmospheric Studies of VOCs
 In order to test the effect of an increasing KIE at lower temperature on global isotope distribution and the inferred photochemical age, the temperature dependence of KIE was implemented in 3-D simulations of the stable carbon isotope ratio and concentration of β-pinene. A sensitivity study was carried out with the global chemistry transport model MOZART (Model for Ozone And Related Tracers, version 3):
 1. Under the base case scenario (‘_0’), no temperature dependence of KIE was considered;
 2. Under the temperature dependency scenario (‘_T’) the temperature dependence of KIE (equation (8)) was implemented in the calculations.
 For case ‘_T’, 13k_T was calculated at each model step, taking into account the temperature dependence of KIE (equations (2), (7) and (8)). For case ‘_0’, a parallel simulation was carried out, neglecting the temperature dependence of β-pinene ozonolysis KIE.
 Among all simulations, the near surface results from 1 April 2004, 15:00 UT are presented. Special emphasis is put on the boreal needleleaf forests, which cover a broad swath of land, typically north of 50° north latitude to beyond the Arctic Circle (after the International Global Biosphere Programme IGBP classification [Friedl et al., 2002]). Boreal biogenic VOC emissions are dominated by monoterpenes and among them, β-pinene emissions are significant [Tarvainen et al., 2005, and references therein]. Note that maximum differences between the two model runs are expected when choosing early spring for the analyses. At that time of the year, low temperatures still prevail in the boreal zone, thus intensifying the divergence in the β-pinene isotopic composition calculated using the test versus the base case. The temperature on 1 April 2004 varies between 250 K and 280 K, with median value of 265 K. Furthermore, high monoterpene emissions are reached soon after bud burst in March/April [Hakola et al., 2001].
 As indicated in section 1, average atmospheric age tav can be derived basing on known source isotopic composition and KIE. As a consequence, the differences in β-pinene isotopic composition generated by taking into account the temperature dependence of KIE, compared with the ‘_0’ base case, will result in a modified calculated tav. The model output data sets from the sensitivity runs ‘_T’ and ‘_0’ are depicted in Figure 5a in form of
This relative value describes how much a determined tav can differ from its real value when ignoring the KIE temperature dependence in the atmospheric calculations and can be expressed by using equation (5) as follows:
The variation with the temperature of the terms Xδ, referring to the isotopic fractionation of the examined compound from emission to observation, and Xɛ, involving the KIE of the chemical degradation, will determine the sign and magnitude of Δreltav, as discussed in further detail below. The extent of Xδ is controlled by two factors, temperature and age of observed air masses. Near the source, the fractionation is small at any temperature, thus Xδ ≈ 1. Temperature dependence of Xδ becomes important for old air masses, in which the 13C enrichment of reactants is higher at low temperature (Figure 4). The lower the temperature, the higher tδ_T − 0δ in comparison with tδ_0 − 0δ. According to this, Xδ in old air masses is equal to unity at room temperature and higher than 1 at lower temperature. Other than Xδ, Xɛ is always lower or equal to unity and depends on temperature alone. At room temperature, ɛ_T is similar to ɛ_0, therefore Xɛ ≈ 1. At lower temperature, ɛ_T is higher than ɛ_0 (Figure 3); hence Xɛ is lower than 1. All these temperature-dependent changes of Xδ and Xɛ as well as the resulting overall relative change in atmospheric age Δreltav are summarized in Table 4. Summing up, at low temperature and for fresh air masses (i.e., close to the source) Δreltav is negative. At low temperature but in older air masses, the tav deviation can be either negative or positive, depending on the concurrence between Xɛ and Xδ. Finally, Δreltav is positive in old air masses at higher temperature.
Table 4. Sign and Magnitude of tav Deviations Depending on Temperature and Age of the Observed Air Massesa
See text for a detailed discussion of the temperature dependence of Xδ and Xɛ.
 As can be seen in Figure 5a, negative values of Δreltav in the Asian boreal zone suggest strong fresh monoterpene emissions at lower temperature (case1 in Table 4), contrasting to the European part, where the Xδ term becomes dominant because of the older air masses, thus leading to slightly positive Δreltav. This observation might be explained by the unlike structure of the vegetation. The western part of the boreal zone is dominated by ‘evergreen needleleaf forests (IGBP 1),’ while the eastern part is covered by ‘deciduous needleleaf forests (IGBP 3),’ the latter showing higher monoterpene emission potential in the budding season. These areas are continuously supplied with significant freshly emitted monoterpenes, therefore negative Δreltav values predominate. Very old air masses, characterized by strong Xδ term can be detected over the oceans. Examining the magnitude of Δreltav, relative deviations in determined β-pinene tav of up to 30% in the Asian and North American boreal zone can arise. There are also smaller areas in central Sweden, Eastern Finland and Eastern Canada, where the calculated tav might be even two times over- (case 1 in Table 4) or underestimated (case 3 in Table 4). Neglecting the temperature dependence of KIE in evaluations of the average atmospheric age of a species may therefore play an important role in the interpretation of the VOCs atmospheric processing. The simulations also indicate very low concentrations of OH radicals prevailing in the boreal early spring. Therefore, the atmospheric residence time of β-pinene is more strongly controlled by its reaction with ozone. Taking this into account, median β-pinene lifetime of 52.7 h in the boreal forests are computed (Figure 5b). Note that for room temperature and typical atmospheric O3 concentration levels, β-pinene lifetime is about 1.1 days [Atkinson and Arey, 2003]. Given the aforementioned considerations, neglecting the temperature dependence of KIE, the absolute β-pinene average age tav, isotopically determined, is over- or underestimated by up to one day in the calculations (Figure 5c).
 This study reports for the first time values for temperatures lower than room temperature. The values of β-pinene ozonolysis at 273 K and 258 K are 3.80 ± 0.14‰ and 5.39 ± 0.12‰, respectively. At 303 K, the value of 3.58 ± 0.13‰ shows agreement with results of Fisseha et al. . It supports also the inverse KIE dependence on the carbon number [Rudolph, 2007] being an apt method to estimate the KIE of VOC oxidation reactions.
 According to these findings, KIE increases with decreasing temperature. The KIE temperature dependence of β-pinene ozonolysis can be described as follows:
Considering measurement error, the KIE temperature dependence becomes significant at temperatures lower than 284 K. Such temperatures are commonly found in the boreal needleleaf forests, which are a major source of β-pinene. The KIE temperature dependence was hence implemented in global modeling calculations of β-pinene stable carbon isotope ratio and concentration, with emphasis on boreal zones. The simulations carried out with the global chemistry transport model MOZART-3 show that ignoring the temperature dependence of KIE in the calculations might lead to noticeable over- or underestimation of the β-pinene atmospheric average age in the investigated regions. The consequence might be an inaccurate interpretation of the spatial scale of studied processes. Since the BVOC emissions are constrained by low temperature, we expect severe effects from KIE temperature dependence in case of VOCs with emissions independent of temperature. Future experiments should explore the effect of temperature on KIE in oxidation reactions of anthropogenic and biogenic VOCs, covering the full range of temperatures relevant for the troposphere.
 Furthermore the use of a simplified MCM to predict δ13C values of the major β-pinene oxidation product, nopinone, shows that the tested hypothesis that the chemical formation of nopinone and the related KIE are the determining factors in the evolution of its isotopic composition can be applied at high degrees of β-pinene processing. Early stages of the reaction may involve nopinone loss processes that affect its isotopic composition and this should be explored in future experiments.
 We thank Jochen Rudolph (York University, Toronto) for fruitful discussions and valuable suggestions. We also gratefully acknowledge the AIDA scientific team for constant advice and assistance during the measurement campaign. This work was supported by the EU within the EUROCHAMP project. We thank Angelika Heil for providing us with IGBP Moderate resolution Imaging Spectroradiometer (MODIS) Land Cover data.