Atmospheric Chemistry and Physics Discussions Interactive comment on “ Hydrogen isotope fractionation in the photolysis of formaldehyde ”

Commentary on Hydrogen Isotope Fractionation in the Photolysis of Formaldehyde There is clearly a great deal of hard work behind this paper which concerns a critical step in the photochemistry of the atmosphere. I suggest that the paper would be more useful to the readers of ACP if the following points were to be addressed. The terms ’incomplete photolysis’ (R1) and ’complete photolysis’ (R2) are defined in the introduction, referring to the H + HCO and CO + H2 product channels in formaldehyde photolysis respectively. This terminology is confusing, because the experimental procedure relies on the complete photolysis of an HCHO sample to products, presumably involving some amount of both the ’complete’ and ’incomplete’ pathways. These

duces H 2 that has virtually the same isotopic ratio as that of the parent CH 2 O. These findings imply that there must be a very strong concomitant isotopic enrichment in the radical channel (CH 2 O + hν → CHO + H) as compared to the molecular channel (CH 2 O + hν → H 2 + CO) of the photolysis of CH 2 O in order to balance the relatively small isotopic fractionation in the competing reaction of CH 2 O with OH. Using a 1-10 box photochemistry model we calculated the isotopic fractionation factor for the radical channel to be 0.22(±0.08), which is equivalent to a 780(±80)‰ enrichment in D of the remaining CH 2 O. When CH 2 O is in photochemical steady state, the isotopic ratio of the H 2 produced is determined not only by the isotopic fractionation occurring during the photolytical production of H 2 (α m ) but also by overall fractionation for the removal

Introduction
Formaldehyde (CH 2 O) is a key carbonyl compound in the atmosphere. Its abundance varies over a wide large range from sub-ppb levels to ∼100 ppb depending largely on local sources (Warneck, 1999). Its turnover is large and it is a source of molecular hy-in situ production of CH 2 O by photochemical oxidation of volatile organic compounds appears to be the dominant source on a global scale (Carlier et al., 1986;Warneck, 1999). In remote oceanic areas (Wagner et al., 2002;Weller et al., 2000), in the free troposphere (Frost et al., 2002), and in the stratosphere, only the photochemical oxidation of CH 4 serves as the major source. Apart from the importance of the rather 10 simple CH 2 O molecule in the Earth's atmosphere and far beyond, it is also subject to fundamental research regarding for instance the exact processes during its photolysis (e.g., Moore and Weisshaar, 1983;Townsend et al., 2004 "Incomplete" photolysis (R1) produces HO 2 radical by the rapid reaction of hydrogen (H) and formyl (CHO) radicals with atmospheric oxygen (O 2 ), which can lead to the that the D enrichment of H 2 is much stronger than the concomitant enrichment for CH 4 acompanying its destruction by OH, O( 1 D), and Cl radicals. This means that the D enrichment of H 2 occurs not only by the fractionation in the reaction of H 2 with oxidizing radicals (OH, Cl, O( 1 D)) but is also due to the chain reactions leading from CH 4 to H 2 (Rhee et al., 2006a). Gerst and Quay (2001) discussed potential reactions that may 10 lead to the D enrichment along the photochemical chain reactions of CH 4 . However, the detailed mechanism by which the D content of H 2 is accumulated has not yet been elucidated due to the lack of measurements for isotopic fractionation factors at each reaction step and branching, all of which are fundamentally difficult to determine.
To address this question, as a first step we investigated the isotopic fractionation 15 occurring during the photolysis of CH 2 O by which H 2 is produced for the conditions at Earth's surface. In spite of its crucial role in the isotope budget of H 2 , as well as CO, in the atmosphere, the isotopic fractionation occurring during photolysis of CH 2 O has been rarely investigated in the past (Crounse et al., 2003;Feilberg et al., 2005;Feilberg et al., 2007b). Since CH 2 O is a relatively "long-lived" intermediate in the photochemical 20 chain reactions between CH 4 and H 2 , the results will provide essential insight into understanding the accumulation of D in H 2 produced.

Experiments
Formaldehyde (CH 2 O) was prepared by purifying para-formaldehyde (Merck) in a vacuum system following the method of Spence and Wild (1935). Solid para-formaldehyde 25 was heated under vacuum at ∼420 K. For purification the evaporating CH 2 O and impurities were forced through a set of glass U-tubes which were partly immersed in an 12718 Introduction EGU ethanol sludge (∼160 K) made with liquid nitrogen. Purified formaldehyde was then collected in a U-tube dipped in liquid nitrogen (77 K). A given amount of pure CH 2 O was released to a 3-L glass bulb and three 0.1-L glass flasks, all of which were connected to the same manifold. Afterwards pressure inside the manifold was read by a capacitance manometer (MKS10, Baratron). We had once monitored the pressure 5 inside the 3-L glass bulb for 2 days and found no change, indicating no absorption or loss of CH 2 O. CH 2 O-free synthetic air was then introduced into the 3-L glass bulb to reach about ambient pressure and the final pressure was read by another capacitance manometer (MKS1000, Baratron) to determine the CH 2 O mixing ratio. EGU mass balance of CO if only photolysis of CH 2 O is considered. Because of such a non-conservation of CO in the reactor, we did not attempt to measure the ratio of the mixing ratios of H 2 to CO for each photolysis run to obtain the value of Φ(H 2 ). But, we tracked the actual fraction of H 2 produced by photolysis of CH 2 O, given as φ(H 2 ), which represents the ratio of the H 2 mixing ratio in the reactor to the initial CH 2 O mixing 5 ratio. Figure 1 shows the evolution of φ(H 2 ) throughout the periods of photolysis for experiments conducted with different reactor materials or light sources. The period of photolysis is given as number of daylight hours disregarding any parameters that might influence the actual photolysis rates of CH 2 O. For the short periods experiments (<12 h), φ(H 2 ) increases rapidly with the increase of photolysis time. With long periods of photolysis (>130 h), φ(H 2 ) converges toward an asymptote. By virtue of negligible production of H 2 through reactions other than the CH 2 O photolysis and little reactivity of H 2 in the reactor for the periods of the CH 2 O photolysis, φ(H 2 ) approaches an asymptotic value at a function of time. The asymptotic value of φ(H 2 ) is equivalent to Φ(H 2 ) when 15 CH 2 O is destroyed only by photolysis.
For the photolysis periods from 50 to 100 h, the measurements are scattered. We suspect that this is due mostly to photolytical effects rather than analytical errors. In particular, changes in radiation occurring over the course of the experiments on the roof (e.g., cloudiness, albedo, solar zenith angle (SZA), light scattering due to aerosol 20 content, etc.) may result in such different values. In addition, since the yield of the molecular channel peaks at longer wavelengths compared to the radical channel (Moortgat et al., 1983), φ(H 2 ) increases with the increase of SZA. As an indirect support for this speculation, photolysis of CH 2 O performed in the laboratory using Hg and Xe arc lamps shows that the uncertainty of replicate runs is merely about 2% for 25 the yield of H 2 and 3% for the δD values. Provided that the scatter is due to variations in parameters that influence photolysis rate of CH 2 O, we do not average the values for the same period of photolysis but use individual values for determining the isotopic fractionation occurring in the CH 2 O photolysis. Introduction

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The CH 2 O photolysis experiments conducted with a Xe arc lamp give an opportunity to examine a relation between Φ(H 2 ) and the range of wavelengths by which CH 2 O are photolyzed. As a Xe arc lamp emits photons within a broad range of wavelengths, the effective wavelength for the photolysis of CH 2 O depends on the cut-off wavelength for transmission through quartz which extends down to ∼200 nm. This is shorter than the 5 lower limit of solar wavelengths at the Earth's surface. Consequently, Φ(H 2 ) from the Xe arc lamp experiments should be smaller than that obtained with sunlight because of the dominance of the radical channel in CH 2 O photolysis at these short wavelengths (Moortgat et al., 1983). As shown in Fig. 1, φ(H 2 ) is almost the same for the two different irradiation periods, indicating that it has reached an asymptote. This asymptotic 10 value is smaller than that obtained in sunlight, which reflects a smaller value of Φ(H 2 ) using the Xe arc lamp.

A box model simulation of the CH 2 O photolysis
To examine the actual photochemistry in the reactor, we constructed a 1-box model composed of 33 photochemical reactions, including photolysis of CH 2 O and H 2 O 2 as 15 well as formation of HCOOH (see Appendix A.). The model was run under conditions of standard atmospheric temperature and pressure with the other boundary conditions from the results from the Tropospheric Ultraviolet and Visible (TUV) radiation model (http://cprm.acd.ucar.edu/Models/TUV). As shown in Fig. 2

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As shown in Fig. 3, whereas photochemical destruction of CH 2 O forms CO and HCOOH, both of which are further oxidized by reacting with the OH radical, the unique source of H 2 in the reactor is CH 2 O photolysis to the molecular channel (R2) and that H 2 destruction by the OH radical is negligible (<0.1% of H 2 has reacted at 99% of CH 2 O being oxidized). Hence, a substantial portion of the initial CH 2 O is converted to products other than CO, but the H 2 produced is accumulated in the reactor reaching an asymptote.
The time evolutions of φ(H 2 ) were predicted by applying the values of Φ(H 2 ), J CH 2 O , and J H 2 O 2 from the TUV radiation model described above to the 1-box model (see Fig. 1). The results appear comparable to the measurements for photolysis periods of 10 <12 h. However, there are substantial differences between the measurements and the model predictions at longer photolysis periods. In particular, it is difficult to reproduce the asymptote of measurements which substantially differs from the model predictions that are based on most likely values of parameters under photochemical conditions in Mainz, Germany (solid and dashed lines in Fig. 1). As shown in Fig. 3b, ∼10% of 15 CH 2 O is destroyed by the reactions with radicals. This leads to the lower asymptotes of φ(H 2 ) than the value of Φ(H 2 ) obtained from the TUV radiation model because φ(H 2 ) is smaller than Φ(H 2 ) by a factor corresponding to the fraction of CH 2 O photolyzed. In order to predict the asymptote of φ(H 2 ) from measurement, the value of Φ(H 2 ) would be ∼0.74, the value that the TUV radiation model predicts when SZA is near 85 • in the 20 location of Mainz.
3.3 Isotope effect of the CH 2 O photolysis to the molecular channel Figure 4 shows the variation of the δD value of H 2 (δD-H 2 ) as a function of φ(H 2 ). The isotopic ratios are normalized with respect to the δD value of the initial CH 2 O. Thus, a δD-H 2 value of zero means that the isotopic ratio of the H 2 in sample air is the same as 25 that for the initial CH 2 O. The air samples whose values of φ(H 2 ) approach the asymptotes at long photolysis times for both the sunlight and EGU of CH 2 O yields H 2 that has the same isotopic ratios as the initial CH 2 O. This observation and the evolution of δD-H 2 as a function of φ(H 2 ) give us crucial information to aid in determining the hydrogen isotopic fractionation processes occurring at (R1) and (R2) as follows.
According to the results from the 1-box model described in Sect. 3.2, most of the 5 CH 2 O in the reactor is broken down by photolysis (>90%) with the remainder destroyed mostly by reaction with OH (<8%) while HO 2 and H radicals play only a minor role (<2%) (see Fig. 3b). The rate of change of the CH 2 O mixing ratio in the reactor can thus be described as: where J is the sum of photolysis rates of (R1) (i.e., j r ) and (R2) (i.e., j m ) and K is the sum of the products of the relevant photochemical reaction rate coefficients (k i ) and radical concentrations (X i ) as follows.
In the same way, for the next abundant isotopologue, CHDO, one obtains: where J ′ and K ′ indicate the sums of the photolysis rates and the photochemical reaction rates for CHDO, respectively. In terms of non-equilibrium kinetics, the isotopic fractionation factor is represented as the kinetic isotope effect (or simply 20 isotope effect), which is expressed by the ratio of reaction rates for the different isotopologues, one of which has a rare isotope substituted for the common one (Melander and Saunders, 1980). We define here the isotopic fractionation factor as 12724 ACPD 7,2007 Hydrogen isotope fractionation in the photolysis of formaldehyde EGU the ratio of photochemical reaction rates or photolysis rates of an isotopologue which has a single deuterium to that for the most abundant isotopologue. For instance, the isotopic fractionation factor for the molecular channel, α m is: Hence, J ′ and K ′ in Eq. (4) have the following relationship with the corresponding 5 rates for CH 2 O by means of isotopic fractionation factor, α i .
By definition, the isotopic fractionation factor for CH 2 O, α f , is In Eq. (8a), the ratio of j m to J represents the yield of H 2 from photolysis of CH 2 O (Φ(H 2 )), and the ratio J/(J + K ) is the fraction of CH 2 O that is photolyzed. Designating the latter as Γ, α f can be rewritten as: Or simply, where α hν represents the isotopic fractionation factor for photolysis of CH 2 O. Since the amount of radicals produced along the experiments is not constant, Γ is not a constant but a variable being a function of time. In addition, strictly speaking Φ(H 2 ) varied during the sunlight experiments as did SZA (Fig. 2b). Accordingly α f is changing along with 20 ACPD 7, 2007 Hydrogen isotope fractionation in the photolysis of formaldehyde EGU the CH 2 O photolysis and photochemical reactions. Nevertheless, assuming that α f is constant gives a convenient way to determine the isotopic fractionation factor for the production of H 2 , α m . Integrating Eqs. (1) and (4) where R o is the isotopic ratio of the initial CH 2 O,R Q is that for the remaining CH 2 O during the run of experiment, and f the fraction of the remaining CH 2 O. Thus, the isotopic ratio of the products (R p ) as a function of CH 2 O photochemical destruction can be obtained by mass balance: Actually R p is sum of the isotopic ratios of the products formed by CH 2 O photolysis and its photochemical reactions with radicals. The isotopic ratio of the H 2 , R m , which is produced from CH 2 O photolysis to the molecular channel, can be derived from the following derivatives: 15 and Solving Eq. (11) and Eq. (12) with inserting the solutions of Eq. (1) and Eq. (4), respectively, and the definition of α m in Eq. (5), R m has the following relation with R o . 2007 Hydrogen isotope fractionation in the photolysis of formaldehyde  (10), the ratio of the isotopic ratios of H 2 and all products from CH 2 O photochemistry is the same as the ratios of their isotopic fractionation factors: By the same way, the isotopic ratios of the products of the radical channel of CH 2 O 5 photolysis and of photochemical reactions results in a same relations: From the relations of Eqs. (14), (15), and (16), it is immediately recognized that R p is composed of the fractions of the isotopic ratios of the products from two channels of 10 CH 2 O photolysis and its photochemical reactions, which is represented by their reaction rates as the same as for isotopic fractionation factor of CH 2 O in Eq. (8b).
Since we measured the evolution of R m with φ(H 2 ), α m can be determined from the relation Eq. (13). As f approaches 1 (thus, φ(H 2 ) goes to zero), R m /R o in Eq. (13) 15 becomes the value of α m , which is in turn represented by the value of δD-H 2 as follows: Accordingly, the intercept in Fig. 4  EGU photolysis of CH 2 O for short periods were conducted with high CH 2 O mixing ratios of 50 ppm, a similar amount of initial CH 2 O, was applied in the 1-box model to determine the value of α m . Its uncertainty, 0.02, was determined such that all measurements for the short periods experiments are predicted by the 1-box model within the range of errors (see Fig. 4).
The assumption that α f is constant should be valid during the 5 initial stage of photolysis of CH 2 O because the amounts of radicals, in particular the OH radical, produced are too small to affect α f (see Fig. 3b). Even if α f were not constant, it would not interfere with the determination of α m because the α f 's in (13) cancel for f = 1.
3.4 Isotope effect of the CH 2 O photolysis to the radical channel 10 Given that complete photolysis of CH 2 O yields H 2 that has the same isotopic ratio as that of the initial CH 2 O (Fig. 4), we can also determine the isotopic fractionation factor, α r , which governs the isotopic fractionation occurring at (R1). However, in this case the Rayleigh model cannot be applied because the value of α f varies with time due to changes in the amounts of radicals (see below). We ran a photochemical 1-box model 15 instead, which consists of the 33 reactions mentioned in Sect. 3.2 as well as critical reactions of CHDO and HD to determine α r as follows: In Fig. 4 several model runs under different conditions are plotted. As an ideal case, we assume that CH 2 O is destroyed exclusively by photolysis. Since in this scenario α f is constant as the reaction proceeds, the Rayleigh model can be applied to determine α r . In Eq. (13), as f approaches 0, the ratio of R m to R o becomes the ratio of α m to α f , 5 which is represented by the value of δD-H 2 at the end of photolysis. As the values of δD-H 2 converge at zero, α f = α m and thus α m = α r according to the relation in Eq. (8b) since Γ=1. This scenario is however unlikely considering the substantial production of radicals via the radical channel (R1), which may in turn react with CH 2 O in the reactor as described above. Introduction of the reactions of H and/or HO 2 with both CH 2 O and 10 CHDO with and without kinetic isotope effect do not significantly change the evolution of δD-H 2 compared to the ideal scenario that only accounts for CH 2 O photolysis. However, it is apparent that the reaction of OH and CH 2 O is critical for determination of α r , as the δD-H 2 value for the final product of H 2 reaches only ∼ -170‰. Taking the kinetic isotope effect for the reaction of CH 2 O with OH radicals into account increases the δD- 15 H 2 value for the final product a little to ∼-130‰. Applying the kinetic isotope effect for the reaction of HD with OH does not improve the model to simulate the measurements because of too slow reaction rate of H 2 +OH. However, decreasing the value of α r from 0.50 to 0.22 (thus larger isotope effect) makes it possible to reach the δD-H 2 value of the final H 2 to zero and significantly improves the predicted evolution of δD-H 2 com-20 pared to the measurements. Therefore, providing that the TUV radiation model and the reaction rates applied in the 1-box model are correct, our best estimate of α r is 0.22 and the isotopic fractionation factor of CH 2 O due to photolysis (α hν ) results in 0.40 for Φ(H 2 ) = 0.647, the yield of H 2 which is the best estimate from the TUV radiation model for the average conditions of Mainz at the times of the experiments (see Fig. 2).
As the value of α r in the present study is not determined directly by measurement, but is based on model calculations, we conducted sensitivity runs to estimate the uncertainty of α r by varying the values of the various parameters used in the 1-box model. These parameters are the mixing ratio of CH 2 O in the reactor, Φ(H 2 ), photolysis rates 12729 Introduction EGU of CH 2 O and H 2 O 2 , kinetic isotope effects for the reaction of CHDO with the radicals, and the uncertainty of δD-H 2 for the final product (Table 2). Among them α r is most sensitive to the ratio of the photolysis rate of H 2 O 2 to that for CH 2 O because large production of OH by photolysis of H 2 O 2 leads to the increase of the fraction of CH 2 O that reacts with OH in the reactor, which in turn forces the value of α r to be smaller to compensate it (see Eq. 8b). The same effect can be introduced to the variation of α OH for CH 2 O + OH and of Φ(H 2 ). Sensitivity runs for the potential error in the δD-H 2 value of final product shows the largest impact to α r among the parameters because of its large potential error of 40‰, which includes the uncertainty of the δD value of the original CH 2 O(=4‰). Overall most of the uncertainty for α r originates from the uncer-10 tainties in Φ(H 2 ) and the δD-H 2 of final products. Quadratic sum of the errors incurred by these parameters are 0.08.

Comparison with previous research
To our knowledge three experiments have been done in sunlight (Table 3): One exper-15 iment investigated the isotopic fractionation of CH 2 O itself by measuring time evolution of the amount of isotopologues, CH 2 O and CD 2 O using an optical method (Feilberg et al., 2007a, Feilberg et al., 2005, another experiment examined the same isotopic fractionation but for CH 2 O and CHDO using the same technique (Feilberg et al., 2007b), and the other measured the D/H ratio of H 2 produced from the photolysis of CH 2 O 20 which is reported in a conference proceeding abstract (Crounse et al., 2003). In the latter study a similar procedure as in the present study was apparently applied. However, the lack of details of the experiment, in particular the fraction of H 2 (φ(H 2 )) and the δD value of the original CH 2 O used for the photolysis experiments, both of which are critical to determine α m , makes it difficult to infer α m from this single value of δD.  (Feilberg et al., 2007a) using an optical technique. This value is smaller than the value for J CHDO /J CH 2 O (= α hν ) of 0.40(±0.03) determined in the present study as expected from the convention that double-deuterated formaldehyde is more stable than the single-deuterated one in view of zero point energy.
Recent work reported by the same group (Feilberg et al., 2007b) has a particular interest as the goal of the experiment is the same as the present study, but approaches it in a different way. In this experiment, the authors determined the values of α m and α hν as 0.55(±0.02) and 0.63(±0.01), respectively. The value of α m is similar to, while that for α hν is far larger than, the values determined in the present study. Actually the large discrepancy of α hν points to a much larger difference in the value of α r between Feil-  Feilberg et al. (2007b) is that the degree of the isotopic fractionation in CH 2 O photolysis to the molecular channel is larger than that for the radical channel, being opposite to the results from the present study and from early results by McQuigg and Calvert (1969

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given quantum yield for CH 2 O photolysis. The direct inference of α hν , however, had to be corrected to account for the losses of CH 2 O and CHDO by the reaction with OH radical and large leakage of air in the chamber as well as production of CH 2 O from the wall. In addition, their values of α r and α m depend on which value of the quantum yield for CH 2 O photolysis are applied. In our study, performed at the level of natural 5 deuterium abundance, α m is the "directly" inferred quantity, and α hν follows from the fact that the isotopic compositions of the initial CH 2 O and of the H 2 that are formed from complete photolysis are identical. At present we are not able to pinpoint why there is such a large discrepancy in the isotopic fractionation factors of CH 2 O between the two studies. More experiments can resolve this issue.

Atmospheric implication
The determination of α m and α r may provide an important insight to comprehend what causes the enrichment in deuterium throughout the photochemical oxidation pathway from CH 4 to H 2 . The overall composite of isotopic fractionation factors from CH 4 to H 2 , α CH 4 −H 2 , may be defined as: where R 0 H 2 represents the hydrogen isotopic ratio of H 2 produced by photochemical oxidation of CH 4 and R CH 4 is that for CH 4 . Strictly speaking, α CH 4 −H 2 differs from the general definition of isotopic fractionation factor in that it is a function of not only thermodynamic conditions but also environmental parameters such as radiation, radical 20 species and their concentrations in the atmosphere. Nonetheless, given a system with these parameters, α CH 4 −H 2 can be considered as an isotopic fractionation factor. Rhee et al. (2006a)  EGU as the initial CH 4 . Gerst and Quay (2001) and Price et al. (2007) also expected D in the H 2 from photochemical oxidation of CH 4 to be enriched by a factor of 1.2-1.3. As Gerst and Quay (2001) described in detail, α CH 4 −H 2 represents the results from the combination of several factors that are associated with photochemical chain reactions from CH 4 to H 2 . These factors include: (1) isotopic fractionation occurring during the reaction of CH 4 with OH (α CH 4 ), the rate-determining step of the photochemical chain reactions of CH 4 , as well as the subsequent isotopic fractionation processes occurring along the way to CH 2 O (α Σ ), (2) the branching ratios of deuterated species, e.g., CH 3 D, CH 2 DOOH, and CH 2 DO, (3) the factor of 2 brought up by the reduction of the number of hydrogen atoms from CH 4 to CH 2 O, and finally (4) isotopic fractionation occurring during the photolytical production of H 2 from CH 2 O. Assuming that CH 2 O is in a photochemical steady state, as it has a far shorter chemical lifetime than CH 4 and H 2 , point (4) is represented by the ratio of the isotopic fractionation factor of the H 2 produced (α m ) to that for CH 2 O (α f ) (Rhee et al., 2006a). Note that α f differs from α hν by the effect of isotopic fractionation arising from reaction with OH radical (α OH ) in the 15 troposphere. Combining all these factors yields: 20) where β CH 4 is the branching ratio for the deuterated product, CH 2 D, in the reaction of CH 3 D and OH, and β p is a combined branching ratio for other short-lived intermediates, CH 2 DOOH, and CH 2 DO. 20 Regarding the right-hand side of Eq. (20), the value of α CH 4 is 0.78(±0.07) at 298 K (Gierczak et al., 1997) and decreases with the decrease of temperature, that for β CH 4 is at most unity but most likely is less than unity as Gerst and Quay (2001) speculated, and the same is expected for β p . In the subsequent reactions, there is no compelling rationale that the more deuterated isotopologues react faster than the lighter 25 ones considering the theoretical view of lower zero point energy for the isotopically heavier isotopologues. Thus, the value of α Σ may not be larger than unity. The last two parameters in Eq. (20) EGU α f is a combined isotopic fractionation factor due to photolysis and photochemical reactions of CH 2 O by the fraction of the reaction routes as shown in Eq. (8), the value is the weighted mean of the isotopic fractionation factors involved in the reactions. As listed in Table 3 under the radiation conditions of Mainz, the best values of α m and α r were estimated as 0.50(±0.02) and 0.22(±0.08), respectively, from the present study. 5 Feilberg et al. (2004) determined the value of α OH as 0.781(±0.006). The optimal values of Φ(H 2 ) and Γ in Mainz were calculated as 0.647(±0.039) and 0.69(±0.28), respectively, for the periods of experiments using the TUV radiation model at a weighted mean SZA of 62.7 • (see Fig. 2). In order to determine Γ, we calculated OH radical concentrations and their uncertainties from the relationship between the photolysis rate  (8b) the resulting value for α f is 0.51(±0.11). Most of its uncertainty is carried over from the uncertainty of OH. The ratio of α m /α f (=0.97(±0.21)) results slightly smaller than unity, but because of its large uncertainty, coming from the uncertainty of OH concentration, 15 it is not possible to judge whether the CH 2 O photolysis could lead to a depletion or enrichment of D in the H 2 produced with respect to the parent CH 2 O. When using the values of isotopic fractionation factors determined by Feilberg et al. (2007b), the CH 2 O photolysis leads to the depletion of D in the H 2 , however, even taking into account the uncertainty of α m /α f (see Table 3). 20 We extend the calculation of the ratio of α m /α f to a range of values of Φ(H 2 ) and Γ, assuming that the values of α m , α r , and α OH determined from the present study and Feilberg et al. (2004) are applicable to the entire troposphere. The potential ranges of Φ(H 2 ) for the troposphere were estimated using the TUV radiation model with varying SZA at the altitudes of the US standard air. In order to estimate Γ for the tropo-25 sphere, it is necessary to know the reaction rate of CH 2 O + OH at a given time and place. The reaction rate coefficient varies ∼15% in the troposphere due to change in temperature, while the OH concentration varies in the order of magnitude with its peak occurring at local noon. The peak values are well above 10 7 molecules cm EGU (e.g., Berresheim et al., 2003), leading to Γ ∼0.45. Thus, the range of Γ is likely to be between 0.4 and 1 in the troposphere. As shown in Fig. 5, the ratios of α m /α f vary from ∼0.8 to ∼1.2, which suggests that, depending on the values of Γ and Φ(H 2 ) in the troposphere, the H 2 produced from the CH 2 O photolysis would be either enriched or depleted in D. For instance, at the Earth's surface the values of α m /α f along the track of 5 the sun are likely to be lower than unity, thus yielding the depleted H 2 in D with respect to the parent CH 2 O. Finally, we examine the range of α m /α f that can be reconciled with the values of α CH 4 −H 2 inferred for the tropospheric conditions. In the literature it is reported that α CH 4 −H 2 would be between 1.2 and 1.3 in the troposphere (Gerst and Quay, 2001;Price et al., 2007;Rhee et al., 2006a). According to Gierczak et al. (1997), the value of α CH 4 at the tropospheric mean temperature of 272 K is 0.77(±0.08). Inserting these values into Eq. (20), the lowermost value for α m /α f will be ∼0.8 when the branching ratio for deuterated compounds (β CH 4 and β p ) and α Σ unity. When these three values follow Gerst and Quay (2001)'s speculation (β CH 4 ×α Σ ×β p = 0.96×0.77×0.96), α m /α f 15 is 1.15. These two values of α m /α f bound the range which was estimated for the typical values of Γ and Φ(H 2 ) in the troposphere (Fig. 5). This suggests that even if α m /α f is smaller than unity it is still possible that H 2 formed from the photochemical oxidation of CH 4 is enriched in D with respect to the original CH 4 due to the factor of 2 that arises from the reduction of the number of hydrogen atom. Recent laboratory 20 experiment (Nilsson et al., 2007) reports the branching ratio for CH 2 DO reacting with O 2 to be 0.88(±0.01), suggesting β p to be lower than unity and that α m /α f is likely to be larger than unity.

Conclusions
The CH 2 O photolysis experiments conducted in sunlight under ambient conditions 25 allowed us to determine the isotopic fractionation factors for both the radical (R1) and molecular (R2) channels. The H 2 produced is depleted in D by 500(±20)‰ ACPD 7,2007 Hydrogen isotope fractionation in the photolysis of formaldehyde EGU with respect to the initial CH 2 O. The radical channel (R1) appears to have a much stronger isotopic fractionation than the molecular channel (R2), resulting in D enrichment of the remaining CH 2 O by 780(±80)‰. This isotope effect is significantly larger than the result obtained from the experiments in the EUPHORE reaction chamber by Feilberg et al. (2007b), a difference we do not understand at present.

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Applying the isotopic fractionation factors obtained from the present study to the conditions of Mainz, CH 2 O photolysis may produce the H 2 that is slightly depleted in D. However, the large uncertainty in the combined isotopic effects of photochemical reactions of CH 2 O, which primarily originates from the uncertainty of OH concentration, makes it impossible to precisely define the role of CH 2 O photolysis in the D enrichment 10 of H 2 . In the troposphere, CH 2 O photolysis may produce the H 2 either enriched or depleted in D with respect to the parent CH 2 O depending on the fraction of CH 2 O that reacts with OH or that is photolyzed to H 2 . Nonetheless, our estimated range of α m /α f (∼0.8 to ∼1.2) in the troposphere, the ratio of isotopic fractionation factors which determines the degree of D enrichment of H 2 at steady state of CH 2 O mixing ratio, can 15 meet the production of the H 2 enriched in D with respect to the original CH 4 by the factor reported in the literature. 20 The 1-box model is composed of 33 reactions (Table A1) Rohrer, F. and Berresheim, H.: Strong correlation between levels of tropospheric hydroxyl radicals and solar ultraviolet radiation, Nature, 442, 184-187, 2006. Spence, R. and Wild, W.: The preparation of liquid monomeric formaldehyde, J. Chem. Soc., 338-340, 1935. Stoeckel, F., Schuh, M. D., Goldstein, N., and Atkinson, G. H.: Time-resolved intracavity laser 5 spectroscopy: 266 nm photodissociation of acetaldehyde vapor to form HCO, Chem. Phys., 95, 135-144, 1985. Su, F., Calvert, J. G., and Shaw, J. H 7,2007 Hydrogen isotope fractionation in the photolysis of formaldehyde   doi:10.1029/2006GL026310, 2006.: Evaluation of the rate constant for the reaction OH + H 2 CO: Application of modeling and sensitivity analysis techniques for determination of the product branching ratio, J. Chem. Phys., 91 (7), 4088-4097, 1989. ACPD 7,2007 Hydrogen isotope fractionation in the photolysis of formaldehyde  Symbol keys are the same as in Fig. 1. Several model sensitivity runs are shown with solid lines. Yellow shading indicates potential isotopic fractionation evolutions for various ranges of Φ(H 2 ) for the location of Mainz, and cyan shading represents the isotopic fractionation evolutions using the daily-mean value of Φ(H 2 ) during the experiments according to the TUV radiation model described in Fig. 2. For the short duration experiments, we assumed that the initial mixing ratio of CH 2 O in the 1-box model was 50 ppm, represented by magenta shading. When calculating the evolution of δD-H 2 using the 1-box model, we constrain the model such that the values of α m and α K (see text) are always 0.50 and 0.78, respectively, and that the complete photolysis of CH 2 O yields H 2 with a δD value that is the same as that of the initial CH 2 O. For comparison, the evolutions of δD-H 2 using the isotopic fractionation factors determined by Feilberg et al. (2007b) is shown as red solid line on the premise that the values of other parameters are the same as those in the present study (see Appendix A). 7,2007 Hydrogen isotope fractionation in the photolysis of formaldehyde