Investigating the yield of H2O and H2 from methane oxidation in the stratosphere

An important driver of climate change is stratospheric water vapour (SWV), which in turn is influenced by the oxidation of atmospheric methane (CH4). In order to parameterize the production of water vapour (H2O) from CH4 oxidation, it is often assumed that the oxidation of one CH4 molecule yields exactly two molecules of H2O. However, this assumption is based on an early study, which also gives evidence, that this is not true at all altitudes. In the current study we re-evaluate this assumption with a comprehensive systematic analysis using a state-of-the art Chemistry5 Climate model (CCM), namely the ECHAM/MESSy Atmospheric Chemistry (EMAC) model, and present three approaches to investigate the yield of H2O and hydrogen gas (H2) from CH4 oxidation. We thereby make use of Module Efficiently Calculating the Chemistry of the Atmosphere (MECCA) in a box model and global model configuration. Furthermore, we use the kinetic chemistry tagging technique (MECCA-TAG) to investigate the chemical pathways between CH4, H2O and H2, by being able to distinguish hydrogen atoms produced by CH4 from H2 from other sources. 10 We apply three approaches, which all agree that assuming a yield of 2 overestimates the production of H2O in the lower stratosphere (calculated as 1.5–1.7). Additionally, transport and subsequent photochemical processing of longer-lived intermediates (mostly H2) raise the local yield values in the upper stratosphere and lower mesosphere above 2 (maximum > 2.2). In the middle and upper mesosphere, the influence of loss and recycling of H2O increases, making it a crucial factor in the parameterization of the yield of H2O from CH4 oxidation. An additional sensitivity study with the Chemistry As A Boxmodel 15 Application (CAABA) shows a dependence of the yield on the hydroxyl radical (OH) abundance. No significant temperature dependence is found. We focus representatively on the tropical zone between 23◦ S–23◦ N. It is found in the global approach that presented results are mostly valid for mid latitudes as well. During the polar night the method is not applicable. Our conclusions question the use of a constant yield of H2O from CH4 oxidation in climate modeling and encourage to apply comprehensive parameterizations that follow the vertical profiles of the H2O yield derived here and take the chemical H2O 20

new figure 12b: Why does tagged H2O have already about 2.6 ppmv H2O in the troposphere? Does that mean, that already 1.3 ppmv of CH4 is already oxidized to H2O?
In the troposphere this type of calculation remains challenging, since H 2 O is part of the hydrological cycle. We would claim that even more than 2.6 ppmv is produced, but is to a large extent removed through condensation and sedimentation. Note, that over 90% of all CH 4 emitted at the surface is removed in the troposphere. What we indeed derive from Figure 12b is that in the troposphere all hydrogen from CH 4 is oxidized to H 2 O. The reason for this is the fast kinetic reaction chain under tropospheric conditions. Still, the chemically produced H 2 O in the troposphere is negligible compared to the overall tropospheric humidity, which is up to 3 magnitudes larger.

Introduction
It is beyond question that water vapour (H 2 O) is an important greenhouse gas (GHG). The current study focuses on stratospheric water vapour (SWV), which is by itself an influential driver of climate change. SWV, for example, induces a reduction of stratospheric ozone concentration (Stenke and Grewe, 2005;Revell et al., 2016), cools the stratosphere (Revell et al., 2012;Forster and Shine, 1999;Maycock et al., 2014) and produces a positive radiative forcing (Solomon et al., 2010). Changes in SWV are mainly driven by troposphere-stratosphere exchange (e. g. through deep convection in the tropics (Fueglistaler and Haynes, 2005)). However, there is also a chemical contribution to SWV, mostly by oxidation of methane (CH 4 ) and hydrogen gas (H 2 ). These gases are still abundant above the tropopause to act as significant in-situ photochemical sources 5 of H 2 O. Besides H 2 O, CH 4 is a powerful GHG as well, with a 34 times higher climate effect than an equivalent amount of carbon dioxide (CO 2 ) on a time horizon of 100 years (IPCC, 2013). It also introduces secondary climate effects through the additional SWV. The strong linkage of CH 4 and SWV represents a decisive factor of the net climate effect of CH 4 . Enhanced CH 4 concentrations are likely expected in the future Earth's atmosphere and can impact the otherwise rather dry stratosphere substantially (Rohs et al., 2006). 10 Nevertheless, to account for the contribution of CH 4 to SWV, in current climate modeling it is common either to use a Chemistry-Climate model (CCM) with a complex chemistry set up, which puts high demands on computational resources, or a General Circulation model (GCM) or Chemical Transport model (CTM) with -if at all -a parameterization of the chemical sources of SWV. A parameterization of the chemical feedback onto SWV requires to estimate the yield of H 2 O from CH 4 oxidation, which is defined as the production of H 2 O per oxidized CH 4 molecule. A common simple assumption of the yield 15 of H 2 O from CH 4 oxidation is that one oxidized CH 4 molecule produces two H 2 O molecules in the stratosphere. This simple parameterization is based on a first estimation of the H 2 O yield from CH 4 oxidation, using a simplified methane chemistry without chlorine in a two dimensional photochemistry model (le Texier et al., 1988). This is a widely accepted approximation (Myhre et al., 2007;Stowasser et al., 1999) and is also affirmed by aircraft observations, which state that 2· [CH 4 ]+[H 2 O] (also named as the total stratospheric hydrogen budget) is fairly constant in the 20 stratosphere being 6.8-7.6 ppmv (Hurst et al., 1999;Rahn et al., 2003;Dessler et al., 1994;Stowasser et al., 1999). Although this suggests that all atomic hydrogen (H) from CH 4 oxidation reaches H 2 O, it must be noted that the referenced observation studies do not distinguish, whether the H in H 2 O comes from CH 4 or from H 2 , which also originates from the troposphere.
Thus, calculations based on observed mixing ratios show a net production of H 2 O only, but not the yield of H 2 O specifically from CH 4 oxidation (Hurst et al., 1999). Furthermore, H 2 mixing ratios, when measured as well, show an almost absent vertical 25 gradient, which can be explained by the supposition that the H 2 sink is in photochemical equilibrium with its production from CH 4 oxidation. Hence, all additional H 2 by CH 4 is leveled by the oxidation of H 2 and balances the 2·[CH 4 ]+[H 2 O] and H 2 content in the stratosphere (Rahn et al., 2003). Nevertheless, Hurst et al. (1999) took the weak anti-correlation of H 2 and CH 4 into account and calculated a net production of H 2 O over loss of CH 4 of 1.973 ±0.003, differing from the assumed value of 2, which would be the case if all H goes into H 2 O. By analyzing satellite based measurements Wrotny et al. (2010) derived a 30 production of H 2 O over loss of CH 4 ratio of 2.0-3.7 in the upper stratosphere between 1.0-4.6 hPa, which is clearly ≥ 2.
Still, for reasons of simplification, several GCMs use the approximation that the yield of H 2 O from CH 4 oxidation is exactly two (Monge-Sanz et al., 2013;ECMWF, 2007;Austin et al., 2007;Oman et al., 2008;Boville et al., 2001;Mote, 1995;Eichinger et al., 2015). In the ECHAM/MESSy Atmospheric Chemistry (EMAC) model , for example, explicitly configured in a CTM-like set-up without interactive chemistry, the production of SWV from CH 4 oxidation is calcu-35 lated in a simplified way using a specifically introduced CH 4 tracer (by applying the CH4 submodel) according to: with γ H2O = 2 as the yield of H 2 O. Note, that if one wants to apply such a parameterization, one must specifically be aware not to mix yield of H 2 O from the oxidation of CH 4 (γ H2O ) with the yield from the oxidation of H 2 , originating from the troposphere. does also indicate that the yield from CH 4 oxidation itself must be even lower than suggested by the net production, which is 15 calculated based on observations. It is, therefore, questionable, if the assumption of γ H2O = 2 for the CH 4 oxidation is indeed applicable.
In this study we re-evaluate the findings of le Texier et al. (1988) with multiple approaches using a modern CCM with a complex state-of-the-art chemistry mechanism. Our goal is to assess the currently used assumption of the constant yield as in Eq. 1 with γ H2O = 2 and investigate, if a parameterization solely based on CH 4 is sufficient to reproduce the chemical yield 20 of H 2 O from CH 4 oxidation. As an additional remark, it should be noted that difficulties with yield estimates can be expected especially in the stratosphere, as it is vertically not as well mixed as the turbulent troposphere.
We show three approaches to determine the yield of H 2 O from CH 4 oxidation. The first two approaches use the kinetic chemistry tagging technique (MECCA-TAG, Gromov et al. (2010)), either (1) in a box model set-up with the Chemistry As A Boxmodel Application (CAABA, Sander et al. (2011a)) and (2)  We apply MECCA-TAG  in all approaches to run a comprehensive chemistry setup, while being able to track the production of H 2 O originating explicitly from CH 4 oxidation. A conceptionally different approach would be the 30 extended Crutzen's sequential method used by Johnston and Kinnison (1998) to estimate the gross ozone loss by CH 4 . The study of Johnston and Kinnison (1998) is an additional example for estimating a yield from CH 4 oxidation, although it focuses on CH 4 impacts on ozone (O 3 ) instead of H 2 O. By applying MECCA-TAG, however, it is not necessary to explicitly write down the chemical net reactions as this is done in the extended Crutzen's sequential method.
The paper is structured as follows: In section 2 we present the methods and theoretical background of our studies, followed by the results in section 3. Section 4 comprises a detailed discussion and section 5 summarizes the findings and gives an outlook for further studies. The applied global chemistry climate model is EMAC, which is a state-of-the art numerical chemistry and climate simulation system that includes sub-models describing tropospheric and middle atmosphere processes and their interaction with oceans, land and human influences . It uses the second version of the Modular Earth Submodel System (MESSy) to link multi-institutional computer codes. The core atmospheric model is the 5th generation European Centre Hamburg gen-10 eral circulation model (ECHAM5) (Roeckner et al., 2006 (Sander et al., 2005) and MECCA-TAG (kinetic chemistry tagging technique) .
The MECCA represents the chemical core of EMAC. The applied chemistry is based on a chemical mechanism, which, for example, was already used for the base simulations in the Earth System Chemistry integrated Modelling (ESCiMo) project (Jöckel et al., 2016). The mechanism is extended to resolve specific intermediates in the CH 4 → H 2 O reaction chain (e.g. methyl (CH 3 ) and methoxy radical (CH 3 O)), resulting in slightly more comprehensive chemical kinetics. The full chemical 20 mechanism is part of the supplement.

The kinetic tagging technique MECCA-TAG
MECCA-TAG  enables the user to tag certain elements, without modifying the underlying standard chemical mechanism. It can either be applied for simulating isotopologues of selected trace gases or used to investigate elemental exchange between the species of interest. For example, a model study was carried out with focus on the carbon and oxygen 25 isotope composition of carbon monoxide (CO) ).
In the current study we use the tagging technique (in the so called fractional mode) to investigate the pathways of H atom transfer from the source CH 4 to H 2 O via all simulated intermediates. In order to do so, we create counterparts of the species of interest (e.g., those containing H) in an isolated doubled set of studied reactions (e.g., CH 4 oxidation chemistry) in the same chemical mechanism simulated. By doing so, we are able to quantify the fraction of molecules (hence their H content) 30 stemming from CH 4 oxidation only, as well as their production and loss rates, which are used for the yield calculations.
Furthermore, we improve the latter by quantifying the H, which is recycled in the given reactions.

CAABA
For the photochemical box model studies we use the Chemistry As A Boxmodel Application (CAABA) in model version 3.0 (Sander et al., 2011a). CAABA equipped with MECCA (CAABA/MECCA) provides an atmospheric chemistry box model,

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simulating single air parcels with the chemical mechanism identical to that used in EMAC. CAABA/MECCA is, moreover, using the MESSy interface to attach certain submodels to the box model system. The used submodels in the current study, in addition to MECCA, are SEMIDEP (applies deposition fluxes) and JVAL (calculates photolysis rates) (Sander et al., 2014).
CAABA simulates one box at one pressure and temperature specific for a given latitude and altitude in the atmosphere.
To derive a pseudo vertical profile of the yield, 35 independent boxes superimposed upon each other at the equator are 20 simulated with prescribed conditions following a standard atmosphere profile ((NOAA/NASA, 1976) accessed via https: //www.digitaldutch.com/atmoscalc/ (digital dutch, 1999)). The equatorial region is chosen for mainly two reasons: (1) the equatorial region is in terms of photochemistry most active and (2) we avoid the inactive photochemistry during the polar night. Since the boxes represent different temperature and pressure levels and therefore distinct chemical regimes throughout the middle atmosphere, it is possible to illustrate the vertical dependence of the yield.

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Note that the purpose of the box model simulation is to demonstrate the steady state conditions expected at different altitudes.
In order to do so, we mimic the effect of vertical transport between the boxes by prescribing the vertical distribution of the relevant species concentrations for: Other species, particularly the OH and HO 2 , are unconstrained in the simulations unless otherwise noted. All initial mixing ratios of the chemical species are taken from a climatology over the years 2000-2010 of the RC1SD-base-10 EMAC simulation of the ESCiMo project (Jöckel et al., 2016). This simulation is carried out at T42L90MA resolution with specified dynamics, hence a Newtonian relaxation is performed with respect to meteorological reference data (ERA-Interim reanalysis data from ECMWF (Dee et al., 2011) to be more precise) concerning the prognostic variables divergence, vorticity, temperature and 10 (logarithm of) surface pressure.
Because a priori fractions of H from CH 4 (or tagged H) in the species of the chemical mechanism are not known, all tagged species are initialized with zero. and is displayed dimensionless throughout this work. 20 The loss of CH 4 (L CH4 ) in MECCA includes the reactions with OH, O( 1 D) and Cl, as well as photolysis (see Reactions (R1) -(R6)).
with reaction rates of a, from Sander et al. (2011b) and photolysis rate of b, calculated by JVAL (Sander et al., 2014).
In consecutive reactions H is again recycled into H 2 O. The direct yield calculated by Eq.
(2) represents the H 2 O, which is produced in the chemical mechanism and directly emerges from CH 4 oxidation. However, this is not the additional H 2 O of the whole chemical process. It also cannot be used in a simplified set-up for the methane chemistry and the production of SWV parameterized as by Eq. (1), because no chemical depletion of water is considered. Hence, we suggest to define the 10 effective yield of H 2 O, which takes into account that water is recycled in consecutive reactions and that recycled water is again destroyed. The process is sketched in Fig. 1. During this recycling process, some H is converted to species other than H 2 O, filling up to a steady state or leaving the HOx-cycle once and for all. The effective yield is therefore always equal to or smaller than the direct yield in a closed system.
We define the effective yield of H 2 O in this study as in Eq.
(3), with µ accounting for the lost H 2 O, due to subsequent loss 15 and recycling of H 2 O molecules: Variables are listed in Table 1.  of H 2 O in the stratosphere is slightly shifted vertically. Above the stratopause, the recycling of H 2 O becomes more important. This is indicated by increased secondary loss and production of H 2 O and is further reflected by the reduced effective yield in the mesosphere.
Due to the implementation of the tagging technique, counting of recycled H (as described in section 2.1.2) can only be applied with respect to one species at a time. Hence, the effective yield can only be calculated either for H 2 O or H 2 in the same 5 simulation. Similar to that for H 2 O, recycling of H 2 is calculated in the chemical mechanism, that is, the recycled H is counted as soon as it is leaving H 2 . The corresponding formula for H 2 is derived similarly to Eq. (3) and reads as follows: Direct and effective yield are equal, as long as the loss of H 2 O is negligible or the recycling is lossless. concentrations. This reduces CH 4 loss and H 2 O production to a nighttime-low. A diurnal average smoothes the difference between day and night to a representative value. This is based on the assumption that the system is in a quasi-steady-state. A quasi-steady-state implies that equal integral production and loss are simulated throughout a given time interval, e.g. a day, 15 a month or a year. Monthly γ H2O averages, as presented in this study, which average over the simulated diurnal cycle, are sufficient for the application of a simplified CH 4 loss/H 2 O production rates calculation with prescribed monthly varying OH distributions.
For these reasons, we apply in our analysis Eq.
(3) to annual averages of the production and sink terms simulated in the boxes representing conditions typical for the tropics, where in addition seasonal variations are negligible. In the global simulations 20 with EMAC we calculate an average over zonally averaged tropical bands.
In the following we compare the direct and effective yields of H 2 O and H 2 from CH 4 oxidation obtained in simulations with the box model and EMAC.
3 Results The direct and the effective yields do not differ significantly for water vapor throughout the stratosphere and most of the mesosphere. This suggests, that the H 2 O recycling at these pressure levels and chemical regimes is predominant and all broken down water is regenerated. Nevertheless, in the mesosphere at approx. 0.1 hPa, the effective yield decreases more strongly than the direct yield, reaching the minimum of 0.17 at 0.02 hPa, with a slight increase to 0.39 at the topmost layer at 0.01 hPa.

Box model approach
The value of 2 between 4 and 0.2 hPa reflects that all H from CH 4 reaches H 2 O eventually at these altitudes, supporting the 10 assumption as accepted in the literature. In the lower stratosphere and upper mesosphere, however, the box model results show that assuming a yield of 2 will lead to an overestimated H 2 O production.
The yield of H 2 (see Fig. 3 (right)) shows a mostly anti-correlated behavior with respect to the yield of H 2 O. Throughout most of the stratosphere the effective and direct yields of H 2 differ by about 0.2, while the effective yield drops down to A good indicator for the rate of general chemical reactivity in the atmosphere is the CH 4 lifetime, which is mostly influenced by both, temperature, and the concentration of the reaction partners. The lifetime of CH 4 (τ CH4 ) with respect to its sinks OH, 5 chlorine (Cl), O( 1 D) and photolysis is defined as:

Sensitivity with respect to OH
The results of the previous section reveal that the effective yield of water vapor from CH 4 oxidation depends on the box location, hence the chemical regime at a certain pressure level. Particularly, OH is one of the major oxidants shaping the chemical regime and largely controls the conversion of CH 4 to H 2 and H 2 O , respectively. In the simulations shown above (Exp1) the OH is unconstrained, however, its final (equilibrated) OH concentration does not deviate much from the initial values (see Fig. 5).

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The following sensitivity study aims towards understanding the relationship between the OH and the vertical profile of the yield. It is investigated whether the variations of the yield are directly related to OH variations or to other parameters.
In further sensitivity simulations with CAABA, OH is initialized with the reference from EMAC multiplied with constants and kept constant throughout the simulation. This introduces an additional prescribed hydrogen carrying species, which introduces or withdraws hydrogen to or from the system. However, contribution of OH to the total H abundance in the system was 10 found negligible. The first four simulations reduce the OH concentration by the factors of 0.5 (SS1), 0.1 (SS2), 0.05 (SS3) and 0.01 (SS4) respectively, while the fifth one is performed with a doubled OH concentration (SS5). One additional simulation represents the reference simulation (Ref), which started with an OH concentration identical to the analysis above, except that OH is kept constant. The simulations are listed in Table 2. The simulation set-up uses extreme perturbations of the OH concentration to provide a qualitative estimate of the impact of OH onto the H 2 O yield from CH 4 oxidation.

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The results of the sensitivity simulations are shown in Fig. 6. First of all, the initial experiment Exp1 (see Fig. 3) and the reference experiment of the sensitivity study Ref (see Fig. 6 red line), show mostly consistent results compared to each other concerning the effective and direct yield, which confirms that prescribing OH is adequate. However, in the upper mesosphere, where the OH concentration has the largest difference (cf. Fig. 5 Considering the sensitivity simulations SS2-SS4, the effect of OH reduction on γ H2O becomes more apparent. The effective yield drops to zero already above 60 hPa. The direct yield shows strongly reduced values in the stratosphere, with a local minimum at 20 hPa for SS2 and SS3 and a bit above for SS4, being 1.08, 0.92 and 0.78 respectively. Above 20 hPa the direct 10 yield increases towards a local maximum at 2 hPa, following the profile of the CH 4 lifetime. Above 2 hPa the direct yield decreases nearly monotonically.
In the experiment SS5, with doubled OH, γ H2O is about 0.07 higher compared to experiment Ref and nearly replicates the results of experiment Exp1 in the mesosphere, where the OH equilibrated at a value of about twice that of the reference OH concentration from EMAC.    The γ H2 shows an anti-correlated behavior to that of the H 2 O yield, however, as an exception, doubling of OH shows a lower yield than the reference in the mesosphere.

Dependencies on pressure and temperature
The results shown in the previous subsection indicate that there is an OH dependence in both the effective and direct yield. To investigate whether this dependency is systematic, simulated H 2 O yields are plotted as γ H2O versus OH mixing ratio in Fig. 7.

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Generally, there is no linear correlation between these two parameters. However, a systematic dependence is evident for each box, i.e. at each pressure level. The slope of the correlation is thereby dependent on the pressure level. For higher pressure the gradient is low and becomes steeper for lower pressure levels.
The slope of the correlation of OH and the direct yield (see Fig. 7 (right)) is smaller for pressure levels at 2-80 hPa than the slope of the effective yield (see Fig. 7 (left)) at corresponding pressure levels. Moreover, the effective yield has a sharp 10 transition from low to high OH values, while the direct yield increases more gradually.
The scatter plots give evidence that in a certain range of pressure levels the yields exhibit a saturation-like behavior with respect to OH concentrations. Furthermore, there is no indication of a connection between the yield-OH-dependence and the temperature (see Fig. 8 and the non-ordered colors indicating the temperature), despite the fact, that reaction rates in the CH 4 → H 2 /H 2 O-cycle are usually stronger impacted by temperature than by pressure.
We carried out additional sensitivity studies in order to investigate the temperature dependence of the yield on a given pressure level. Results are displayed in Fig. 9. The simulation set-ups are identical to that of experiment Ref, except that temperature in every box was varied within -15 K to +15 K with 5 K steps. This temperature range is chosen as it represents 5 a range exceeding day-night differences (less than ±5 K) and the annual cycle (less than ±10 K) in the tropics. In the lower stratosphere there is no indication of a significant temperature sensitivity of the effective and direct yields. The latter also does not show any significant sensitivity at higher altitudes. The effective yield in the upper stratosphere and mesosphere shows a small dependence in a way that lower temperatures increase the yield and vice versa.
Consideration of the obvious vertical dependence and the very low temperature dependence gives evidence that not the 10 physical parameters (temperature and pressure) themselves are crucial for the H 2 O yield, but rather the chemical composition of the box (i.e., among others, abundances of OH, HO 2 , O( 1 D) and Cl). This chemical composition, however, changes with altitude (hence with pressure) and depends additionally on transport.

Global model approach
As stated before, the box model approach does not take into account vertical transport and requires certain assumptions. Consequently, the boxes do not fully represent atmospheric conditions. To investigate the production of SWV in a comprehensive set-up, MECCA-TAG is applied in a global simulation with EMAC. The full chemistry of MECCA plus MECCA-TAG, which more than triples the amount of simulated tracers, increases the computational demands substantially. The additional tracers 5 in the model defined by MECCA-TAG are basically counterparts of the tracers of the regular chemical mechanism and are marked (tagged) to be distinguishable from each other. In the following, these tracers are indicated by the label tagged. A spin-up simulation of 6 years with a reduced vertical resolution is carried out to pre-adjust tagged tracers. The results shown here originate from a subsequent simulation, which is executed for another two years model time.

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The three topmost model layers in the upper mesosphere (0.06-0.01 hPa) are possibly subject to artifacts due to the nearby top of the global model and are therefore not considered in this analysis. It is assumed that the trend, which is evident below 0.1 hPa, showing decreasing γ H2O values also applies to the upper mesosphere, which would be similar to the box model results in the section above.
In Fig. 11   They also show a local maximum in loss of CH 4 and primary production of H 2 O below the stratopause and the strongly pronounced secondary loss and production of H 2 O in the middle and towards the upper mesosphere.

Ratio of H:H 2 :H 2 O
A different approach than the first two presented ones to determine γ H2O in the stratosphere is to use the fact that the vertical 5 profile of the H content in terms of atoms is fairly constant above the tropopause (see Fig. 12 Figure 12 (right) shows the tagged H content in the same manner. In this panel the difference between the total H 2 including the transported H 2 from the troposphere, which is observed in atmospheric 10 measurements, and the H 2 solely produced by CH 4 becomes distinguishable. The contribution of H 2 produced from methane increases with altitude (corresponding to γ H2O <2), whereas the H 2 originally injected from the troposphere decreases (by 18 Figure 11. Separate loss of CH4 and primary and secondary loss and production of H2O from the global simulation (23 • S-23 • N). In Fig. 13   This minimum is not equally plain in the tagged H 2 O. Note that tagged H 2 O in the troposphere is already lower than the total H 2 O, since it is solely produced by CH 4 oxidation. When CH 4 ascends from the troposphere through the cold point into the stratosphere it continuously produces H 2 O, although at low rates (due to low temperatures). Therefore, tagged H 2 O is still 10 produced by CH 4 and even though it partly freezes out, the proportion to H and H 2 is not much impacted. However, in the lower stratosphere the mixing ratio of tagged H 2 increases, while H 2 O is still restrained by the cold point. This behavior becomes more apparent in case of the tagged species, since their absolute amounts are fairly low compared to the total ones.
Nevertheless, the H portion of tagged H 2 O and total H 2 O behave similar above the minimum at the tropopause, as seen in the maximum around the stratopause and in the lower mesosphere and the strong decrease in the middle mesosphere and 15 above. The general behavior of the vertical profile also agrees well with the above findings of the yield calculations using box model and global model results.

Discussion
The presented results show three different approaches in estimating γ H2O . Taking the results of the separate approaches together gives the opportunity to discuss certain processes, which are differently parameterized and decisive for the yield estimation.
We first want to discuss the general benefits and limitations of the approaches.
In the box model we have the opportunity to study a chemical regime without transport. It enables us to solely assess the 5 involved chemical kinetics. Clearly, the box model chemistry does not fully represent the intended atmospheric conditions.
Setting certain species to a constant value does change the chemical regime. However, without constraints on the chemical species the model would run into a new equilibrium, which changes the regime as well. It therefore needs careful weighing to specify, which species should be kept constant and which species should be allowed to re-adjust, to be able to simulate a representative chemical regime. 10 In the global model, we are not restricted to one vertical profile, but can evaluate the yield in three dimensions. Nevertheless, the effects of transport and chemical regime onto the yield cannot be separated, since transport influences the chemical regime. The vertical profile of γ H2O is for this reason susceptible to changes in dynamical processes as for example the Brewer-Dobson circulation.
The third approach, which used the total H budgets and portions, helps to quantitatively evaluate the methods, which are calculating the effective yield. It shows the actual portion of hydrogen from CH 4 in the total hydrogen without a production and loss term, which is sensitive to variations in the chemical regime. Yet, this approach is not directly linked to the loss of 5 CH 4 and it is not possible to explicitly resolve the influence of chemistry, since, for example, it is not clear if the decreasing values of γ H2O in the mesosphere are due to the increasing loss of H 2 O or due to the reduced oxidation of CH 4 . Figure 14 shows the vertical profiles of the H 2 O yields and H portions calculated by the approaches described in the previous sections combined in one plot.
Comparing the results of the box model and the global model in the lower stratosphere, γ H2O in the global model is lower 10 than in the box model. This suggests that CH 4 -produced H 2 O is transported into the stratosphere, where it is destroyed, adding to the loss of H 2 O. This reduces γ H2O while the oxidation of CH 4 is low, due to the exceptionally long lifetime of CH 4 due to low temperatures and low OH concentrations. In the upper stratosphere, global model γ H2O is larger than box model γ H2O and, more importantly, larger than 2, which is attributed to transport. This time, CH 4 -derived intermediates :::::::::: intermediate H 2 :::::::: molecules : are elevated and produce H 2 O independent of the CH 4 oxidized in this region. This contradicts the assumption that two H 2 O molecules are immediately produced from CH 4 oxidation, since intermediates, :::::::::: specifically ::::::::::: intermediate H 2 ::::::::: molecules, do play an important role. This is furthermore consistent with the findings of Wrotny et al. (2010), who calculated 5 a yield larger than 2 in this area as well. However, our results are lower than from Wrotny et al. (2010). As they stated in their conclusions "the net loss of H 2 [...] drives additional H 2 O production, thus producing positive vertical gradients in H 2 O+2*CH 4 " (Wrotny et al., 2010). In other words, they attribute the values above 2 to the production from H 2 . Our method distinguishes H 2 produced by CH 4 oxidation from H 2 from other sources (e.g. transport from the troposphere) and our yield is only defined for the CH 4 originating part. Therefore it is lower than reported by Wrotny et al. (2010). 10 In the  from other sources. The minimum of the H portion of H 2 O in the lower stratosphere and its maximum close to the stratopause and in the lower mesosphere therefore shows that the production of H 2 O from CH 4 oxidation relative to the production of H 2 from CH 4 oxidation is smaller in the lower stratosphere and becomes larger towards the upper stratosphere. Accordingly, we conclude that our estimation that γ H2O differs significantly from 2 in the lower stratosphere is reliable.
Altogether, the different approaches yield consistent results. All suggest a yield of less than 2 in the lower stratosphere, 30 varying between 1.5 and 1.7. The smallest value is estimated in the global simulation Exp2, where the yield is larger than the one of le Texier et al. (1988), which is γ H2O =1.3 at corresponding altitudes. The results of le Texier et al. (1988) also showed a maximum around 1 hPa, which is consistent with our results, albeit being a bit above 1.8 and with that lower than our estimate of 2 (or more in case of the global simulation) in that region.
Overall, the estimated yield of H 2 from le Texier et al. (1988)  These values differ from our findings in the box model approach. Our estimated γ H2O is smaller and our γ H2 is larger than estimated by Hurst et al. (1999). As noted before, by using observational data it is not possible to distinguish between H 2 from the troposphere and H 2 produced by H from CH 4 , which results in this rather low net production of H 2 . Assume, for example, that H 2 is not produced in the stratosphere. The mixing ratio of H 2 will then decrease with respect to altitude. However, the 15 contribution from CH 4 oxidation onto H 2 fills up the oxidized molecules, and only if γ H2 ·[CH 4 ] is larger than the total loss of H 2 , observed H 2 and CH 4 are anti-correlated. Using the kinetic tagging gives us the opportunity to distinguish between the total loss of H 2 and the loss of those H 2 molecules carrying H from CH 4 . Our findings provide therefore an additional insight into processes, which determine the observed vertical profiles and provide estimates for the contribution of CH 4 separated from the background H 2 and H 2 O. 20 The study of Wrotny et al. (2010), based on a correlation analysis of satellite measurements, derived a yield of 2.6-2.7 at 1.0 hPa (depending on the satellite product and error assumptions). These are larger than our estimate, which is less than 2.3.
Nevertheless, we agree that the yield can be larger than 2, but a direct comparison of our model results with the measurement based derivation of Wrotny et al. (2010) is not possible for the arguments given above.
Summarizing, our results suggest that applying γ H2O =2 as the contribution to H 2 O by the oxidation of CH 4 in climate 25 models likely overestimates the kinetic yield of H 2 O in the lower stratosphere and in the mesosphere above 0.2 hPa.
Based on our simulations, in the lower stratosphere between 100 and 10 hPa, the portion of H 2 O from CH 4 is in the range of 25% to 44% (calculated by Fig. 12  parameterizations, which target this issue in their 2D atmospheric models. Based on our results, we recommend to apply a parameterization, which is not solely based on the loss of CH 4 , but accounts for the reduced yield in the lower stratosphere and 10 also includes the loss of H 2 O.
It must be noted that atmospheric transport is not constant in time. The Brewer-Dobson circulation, for example, changes in future climate projections (Butchart et al., 2010). A simple parameterization of γ H2O cannot take these changes in transport into account, since they depend on various factors. This raises indeed the question, whether a simplified parameterization of 15 γ H2O is at all applicable for future climate projections, or if it is necessary to simulate the full-chemistry for an accurate representation of SWV. The need of on-line chemistry for meaningful climate projections has anyway already been shown e.g.
by Chiodo and Polvani (2017) for a realistic response of Southern Hemisphere (SH) circulation to CO 2 changes.
Keeping these challenges in mind we are interested in deriving a parameterization as an intermediate stage between the very simple constant yield and the on-line chemistry. This is beyond the scope of the current study. Nevertheless, in the paragraph 20 below we provide a sketch of such a parameterization together with its limitations and requirements.
One could start with a parameterization as introduced by Eq. (1), however, with a pressure p (and latitude φ) dependent γ H2O (p, φ) derived from our vertical yield profiles. This adds a vertical dependency to the chemical production of H 2 O per CH 4 oxidized. As long as no large variations or trends in the stratospheric transport are expected within the simulation period, our profile is a good approximation. The limitation is, however, that the pressure (and latitude) dependence is likely to change 25 with changing climate.
At higher altitudes (above 0.2 hPa) the yield in Eq.
(1) could be replaced or supplemented by an explicit parameterization of the chemical loss of H 2 O, mostly via photolysis and the reaction with O( 1 D), see MacKenzie and Harwood (2004) and McCormack et al. (2008). In the simplified methane chemistry of EMAC, for example, a predefined O( 1 D) is also used for the reaction with CH 4 and could be reused for the reaction with H 2 O. Again, the same limitation holds: under climate change, 30 water vapor, and photolysis rates are likely to change.
Furthermore, for the sake of completeness concerning the chemical source of SWV, the contribution of H 2 transported from the troposphere into the stratosphere needs to be included as well. This requires at least one additional tracer for H 2 and a parameterization of the vertical profile of γ H2O from troposphere originated H 2 oxidation.
Last but not least, we doubt that a simple three-tracer (H 2 , H 2 O, CH 4 ) parameterization will be possible without a nearly full chemical mechanism, because the oxidation rates largely dependent on ozone. Such an approach will hardly be meaningful for climate simulations.

Conclusions
In this study, we present a comprehensive evaluation of current assumptions and estimates of the chemical yield of H 2 O from 5 CH 4 oxidation in the middle atmosphere. We show results of three different approaches to estimate γ H2O and discuss certain advantages and challenges.
We conclude that the widely used assumption that one CH 4 molecule produces two water molecules overestimates the kinetic H 2 O production in the stratosphere up to 4 hPa and in the mesosphere above 0.2 hPa. Our results show that a local yield larger than 2 in certain areas is possible through ascended intermediates :::::::::: intermediate : H 2 :::::::: molecules. In addition to that, transport is 10 generally an issue when dealing with kinetic yields, since it influences the chemical regimes at all altitudes. It also makes the interpretation of the presented approaches challenging, when these are investigated separately.
Nevertheless, the separate approaches presented in this study, show consistently that γ H2O is substantially lower than 2 in the lower stratosphere, has a local maximum between 0.2 and 0.4 hPa and is exceedingly low in the upper mesosphere. We find a low γ H2O in the middle and upper mesosphere, since the loss of H 2 O at higher altitudes increases, shifting the equilibrium 15 between H 2 O and H 2 towards H 2 . The chemical loss is therefore a crucial factor for the correct parameterization of SWV production from CH 4 oxidation. At some point, the loss of H 2 O is so strong that H 2 O is effectively destroyed per oxidized CH 4 .
An additional result from the box model simulation is that the chemical yield of H 2 O depends on the OH concentration and more general on the chemical kinetics. A strong temperature dependence, however, could not be detected. 20 Furthermore, the presented results agree with earlier kinetic estimates of γ H2O from le Texier et al. (1988), who state that not exactly two molecules are produced from CH 4 oxidation. Furthermore, our results give an additional insight into observations (e.g. Hurst et al. (1999); Rahn et al. (2003)), which are limited in detecting the chemical origin of H 2 O.
Overall, the results of the separate approaches give evidence that calculating the yield of H 2 O from CH 4 oxidation requires the loss of H 2 O to be taken into account, making the task of creating a simple parameterization challenging. The latter also 25 requires to admit a critical amount of assumptions about uncertain factors for an adequate atmospheric simulation. We therefore recommend, in order to maintain as much certainty as possible concerning the chemical yield of H 2 O, to implement a simplified H 2 O chemistry including the most important reactions determining the H 2 O yield. The extent of the resulting subset of the chemical mechanism is determinative for the correct representation of the H 2 O content in the middle atmosphere. However, it must be noted that a set of reactions required for the comprehensive simulation of H 2 O kinetics is not substantially different 30 from the one incorporated in the full chemistry setup and is therefore less beneficial in terms of computational resources than a parameterized model. Nevertheless, as stated before, a too simple parameterization introduces uncertainties, which makes it challenging to preserve the required accuracy for applications in the simulation of climate projections, where atmospheric dynamics (e.g. the Brewer-Dobson circulation) and chemistry potentially differ from the present-day atmosphere.
The investigations presented in this study should serve as a basis for future studies concerning the chemical yield of H 2 O in the stratosphere and mesosphere. The gained knowledge can be used to derive new parameterizations of the chemical yield of H 2 O for a potential application in GCMs. We furthermore thank all contributors of the project ESCiMo (Earth System Chemistry integrated Modelling), which provides the reference profiles and initial conditions as well as Christoph Kiemle for his internal review and valuable comments on the manuscript.

20
meccanism.pdf : The applied chemical mechanism of the box model and EMAC simulations.
supplement.pdf : Including 2D Profiles of the EMAC simulations in terms of γ H2O and the ratio of H:H 2 :H 2 O, as well as the data of the box model simulations.