A quantitative analysis of the reactions involved in stratospheric polar ozone depletion

We present a quantitative analysis of the chemical reactions involved in polar ozone depletion in the stratosphere, and of the relevant reaction pathways and cycles. While the reaction pathways and cycles involved in polar ozone depletion are well known, quantitative estimates of the importance of single reactions or reaction cycles are rare. In particular, there is no comprehensive and quantitative study of the reaction rates and cycles averaged over the polar vortex under conditions of heterogeneous chemistry so far. We show time series of reaction rates averaged over the polar vortex in winter and spring for 5 all relevant reactions and indicate which reaction pathways and cycles are responsible for the vortex-averaged net change of the key species involved in ozone depletion, that is ozone, chlorine species (ClOx, HCl, ClONO2), bromine species, nitrogen species (HNO3, NOx) and hydrogen species (HOx). For clarity, we focus on one Arctic winter (2004/2005) and one Antarctic winter (2006) in a layer in the lower stratosphere around 54 hPa. Mixing ratios and reaction rates are obtained from runs of the ATLAS Chemistry and Transport Model driven by ECMWF ERA Interim reanalysis data. An emphasis is put on the 10 partitioning of the relevant chemical families (nitrogen, hydrogen, chlorine, bromine and odd oxygen) and activation and deactivation of chlorine.


Introduction
The chemistry of polar ozone depletion in the stratosphere has been the subject of ongoing research for the last 30 years (see e.g.review papers and text books by Wayne et al., 1995, Brasseur et al., 1999, Solomon, 1999, Brasseur and Solomon, 2005, Müller, 2011, and the reports of the World Meteorological Organization, WMO, 2011).In general, the chemistry of polar ozone depletion is understood very well (see e.g. the recent overview in Müller, 2011, or the special issue of the RECONCILE 1 project in this journal, von Hobe et al., 2013).Remaining issues, such as uncertainties in the formation pathways of Polar Stratospheric Clouds (PSCs) or uncertainties in the contribution of the different cloud types to chlorine activation (e.g.Lowe and MacKenzie, 2008;Peter and Grooß, 2012;Wohltmann et al., 2013), do not pose a serious challenge to the generally accepted basic theory.
While the reaction pathways and reaction cycles that are involved in ozone depletion are well known (e.g.Solomon, 1999;Müller, 2011), quantitative estimates of the importance of single reactions or reaction cycles are rare, and are limited to case studies or certain aspects of the chemical system (e.g.Grenfell et al., 2006) or apply mainly to conditions undisturbed by heterogeneous chemistry (e.g.Brasseur and Solomon, 2005).
2 Model and methods

Model overview
ATLAS is a global Chemistry and Transport Model (CTM) based on a Lagrangian (trajectory-based) approach.A detailed description of the model can be found in Wohltmann and Rex (2009) and Wohltmann et al. (2010).Updates to the chemistry module and polar stratospheric cloud module are described in Wohltmann et al. (2013).The model includes a gas-phase stratospheric chemistry module, heterogeneous chemistry on polar stratospheric clouds and a particle-based Lagrangian denitrification module.The chemistry module comprises 47 active species and more than 180 reactions.Absorption cross sections and rate coefficients are taken from recent JPL recommendations (Sander et al., 2011).

Model setup
Model runs are driven by meteorological data from the ECMWF ERA Interim reanalysis (Dee et al., 2011).The initial horizontal model resolution is 150 km.The runs use the hybrid pressure-potential temperature coordinate of the model, which is a pure potential temperature coordinate above 100 hPa.The vertical range of the model domain is 350 K to 1900 K. Vertical motion is driven by diabatic heating rates from ERA Interim.Two model runs are started, one for the northern hemispheric winter, and one for the southern hemispheric winter.The run for the northern hemisphere starts on 1 October 2004 and ends on 31 March 2005.The run for the southern hemisphere starts on 1 April 2006 and ends on 30 November 2006.Model data before 15 November 2004 or 1 May 2006 are not used for analysis to allow for a spin up of the mixing in the model and for a sufficiently stable vortex in the northern hemisphere.
In addition to the binary background aerosol, the model simulates three types of Polar Stratospheric Clouds, that is supercooled ternary HNO 3 /H 2 SO 4 /H 2 O solutions (STS), solid clouds composed of nitric acid trihydrate (NAT), and solid ice clouds.
The number density of NAT particles in the runs is set to 0.1 cm −3 , the number density of ice particles is set to 0.01 cm −3 and the number density of the ternary solution droplets to 10 cm −3 .A supersaturation of HNO 3 over NAT of 10 (corresponding to about 3 K supercooling) is assumed to be necessary for the formation of the NAT particles.A detailed discussion of the rationale behind these choices can be found in Wohltmann et al. (2013).For ice particles, a supersaturation of 0.35 is assumed based on Microwave Limb Sounder (MLS) satellite measurements of H 2 O (Waters et al., 2006) and ECMWF temperatures.
The treatment of conditions where both NAT and STS clouds are allowed to form has changed compared to Wohltmann et al. (2013).Since mixed NAT/STS clouds are commonly observed (e.g.Pitts et al., 2011), they can now form in the model to allow for a more realistic behaviour, see Nakajima et al. (2016) for details.
The settings for the polar stratospheric clouds largely favor the formation of liquid clouds (binary liquids and STS clouds) over the formation of NAT clouds and activation of chlorine predominantly occurs on liquid clouds in the model runs.
The Lagrangian particle model is used to simulate the nucleation, growth, sedimentation and evaporation of large NAT particles.These particles are formed with a nucleation rate of 7.8×10 −6 particles per h and cm 3 and an initial radius of 0.1 µm, wherever a supersaturation of 10 for HNO 3 is exceeded.Dehydration by falling ice particles is simulated by a simple new algorithm that irreversibly removes all ice above a given supersaturation, which is set to 0.7 here.
H 2 O, N 2 O, HCl, O 3 , CO and HNO 3 are initialized from all measurements of the MLS instrument performed during 1 November 2004 and 1 May 2006, respectively.CH 4 is initialized from a monthly mean HALOE (Halogen Occultation Experiment) climatology (mean of the years 1991-2002) as a function of equivalent latitude and pressure (Grooß and Russell III, 2005).NO x is initialized from the monthly mean HALOE data set by putting all NO x into NO 2 .ClONO 2 is calculated as the difference between Cl y and HCl.Cl y is taken from a Cl y -N 2 O tracer-tracer correlation from ER-2 aircraft and Triple balloon data (Grooß et al., 2002).As in Wohltmann et al. (2013), we increase the amount of ClONO 2 by 10 % at the expense of HCl, see the discussion there.BrONO 2 is assumed to contain all Br y , which is taken from a Br y -CH 4 relationship from ER-2 aircraft and Triple balloon data in Grooß et al. (2002).All values are scaled with a constant factor to give maximum values of 19.9 ppt.

Production and loss rates
Reaction rates are calculated for every reaction separately in the ATLAS model.For this purpose, one artificial species per reaction is introduced to the model, which is produced at the same rate as the other products of the reaction.For instance, a reaction of the type where P is an artificial product species.The mixing ratio of the artificial product species is reset to zero every 24 hours.This way, P directly gives the 24 h averaged rates of production of the species C and D by this reaction and the 24 h averaged loss rates of the species A and B. The 24 h time period is used to capture the diurnal cycle of the photochemically active species.
For technical reasons, heterogeneous reaction rates with the same chemical equation, but on different surface types are added together in a single reaction rate.

Vortex averages
Production and loss rates are averaged over all air parcels of the model inside the polar vortex, which are situated in a layer between 61.3 hPa and 47.4 hPa.The logarithmic mean level of this layer is at 54 hPa.The vortex edge is assumed to be situated at the 36 PVU contour of modified potential vorticity (PV) in the northern hemisphere and at the −36 PVU contour in the southern hemisphere.Modified PV is calculated from the potential vorticity field of the ERA Interim reanalysis according to Lait (1994), with θ 0 = 475 K.
In order to obtain a more consistent picture of the ozone chemistry in the vortex, we exclude air parcels that experience a too high amount of mixing with extra-vortex air during the course of the model run.For that purpose, we initialize a "vortex Atmos.Chem. Phys. Discuss., doi:10.5194/acp-2017-66, 2017 Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 6 March 2017 c Author(s) 2017.CC-BY 3.0 License.tracer" as an artificial chemical species near the start of the model run (15 November in the northern hemisphere, 1 May in the southern hemisphere), which is set to 1 inside the vortex and to 0 outside the vortex.The vortex tracer is then transported and mixed like any other species in the model and can take any value between 0 and 1.We only include air parcels in the vortex mean, where the vortex tracer has a value greater than 0.7.
Without the vortex tracer, analysis would get much more complicated.An example may illustrate this: In the southern vortex, air masses rich in NO y are mixed into the edge region of the vortex during the course of the winter, while in the core of the vortex, air masses are depleted of nitrogen species due to denitrification.This does not only lead to differences in mixing ratios of the nitrogen species over the vortex, but also to different reactions being important in different parts of the vortex.For example, while very low ozone values are reached in the core of the vortex since deactivation into ClONO 2 is hindered, ozone values at the edge are higher and chlorine is also deactivated into ClONO 2 .

Different air masses
The 54 hPa level is not a material surface and we look at different air masses at different points of time, due to mixing, the movement of the isentropes relative to the pressure level and the additional sinking of the air masses relative to isentropes due to diabatic cooling.A similar caveat applies to the definition of the vortex edge.As a consequence of these transport effects, the temporal derivative of the vortex-averaged mixing ratio of a chemical species may deviate from the vortex-averaged chemical net production of this species.
Unfortunately, it is difficult to look at the same air mass over the course of several months, since an air mass with a well defined extent at the beginning of the winter will completely lose its identity due to mixing and transport during the course of the winter.

Equilibria
In many cases, two species X and Y with short lifetimes are in a fast equilibrium with each other, and will not change their mixing ratios if the external conditions do not change.For example, consider two fast reactions of the form Then, assuming that the change of the mixing ratios is zero where [X] is the concentration of X and k 1 and k 2 are the reaction constants, we obtain equilibrium conditions like Similar equations can be derived from more complex reaction systems.We use the equilibrium conditions in the following not only to show relationships between mixing ratios of different species, but also to determine the reactions involved in an equilibrium: For a given set of species, we start with a small set of reactions involved in the equilibrium derived from the vortexaveraged reaction rates, and calculate the mixing ratios of the species from the equilibrium conditions.Then, we compare these mixing ratios with the mixing ratios in the output of the model.If the mixing ratios determined by both methods do not agree with each other, we add reactions until we reach good agreement with a set of reactions as small as possible.

Short overview of the chemical evolution
The evolution of the chemistry of polar ozone depletion can be divided into several phases (see also Solomon, 1999, for an overview).For orientation, Figure 1 shows the evolution of temperature and sunlight in both hemispheres.
After the polar vortex forms in late autumn and early winter in response to the cooling of the atmosphere in the beginning of polar night, air masses in the vortex are well isolated from mid latitudes.In the first phase in early winter, chlorine, the main player in the chemistry of ozone depletion, is present mainly in the form of species that do not contribute to ozone depletion.
These passive reservoir gases are mainly HCl and ClONO 2 .Chemical activity is low due to the lack of sunlight in the polar night.This period lasts from the forming of the vortex until the first polar stratospheric clouds form.
In the second phase, HCl and ClONO 2 are transformed from passive reservoir gases to Cl 2 through heterogeneous reactions on the surface of polar stratospheric clouds (Solomon et al., 1986), which condense when temperatures in the polar night get cold enough.A second effect of the clouds can be the removal of large quantities of HNO 3 and H 2 O by sedimentation (denitrification and dehydration), which can prolong ozone loss later in spring.In the model setup used here, activation predominantly occurs on liquid STS clouds and only to a lesser part on solid NAT clouds.Unfortunately, observations of PSCs are not detailed enough to sufficiently constrain the ratio of activation on STS versus NAT clouds, and there is also uncertainty in Atmos.Chem. Phys. Discuss., doi:10.5194/acp-2017-66, 2017 Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 6 March 2017 c Author(s) 2017.CC-BY 3.0 License.other parameters like size distribution, number densities and required supersaturation.However, chlorine activation and ozone loss are robust quantities with respect to changes in PSC parameterizations (Wohltmann et al., 2013).
The third phase starts when sunlight comes back, enabling catalytic cycles to destroy ozone in large quantities.Cl 2 is transformed to Cl and ClO by photolysis.Then ozone is removed mainly by the catalytic ClO dimer cycle and the catalytic ClO-BrO cycle.The second cycle makes ozone destruction sensitive to the amount of bromine and to bromine chemistry.At the same time, reactions that deactivate active chlorine and that are dependent on sunlight gain importance.Hence, there is a constant competition between activation and deactivation in this phase, as long as it is cold enough.
In the fourth phase, when temperatures rise in spring and PSCs dissolve, chlorine is deactivated into the reservoir gases again and ozone loss significantly decreases.
4 Budgets of the chemical families and chemical evolution arranged by families 4.1 Nitrogen species NO y is defined as the sum of all nitrogen containing species except for the long-lived source gas N 2 O, which is the source of all other nitrogen species in the stratosphere.N 2 O has both natural and anthropogenic sources in the troposphere (e.g.WMO, 2011;Montzka, 2012).The majority of NO y is in the form of HNO 3 in the considered altitude range.This is due to the fact that removal of HNO 3 by photolysis and OH is not very efficient at these altitudes.The initial level of HNO 3 is about 13 to 14 ppb in both hemispheres and the initial NO y is about 1 ppb higher.Figure 2 shows that the mixing ratio of HNO 3 (and NO y ) declines to about 3 ppb in February in the northern hemisphere and increases again in March due to transport.In contrast, HNO 3 decreases to about 0.5 ppb (with NO y at 1 ppb) in the southern hemisphere after June.The rate of change of HNO 3 is not dominated by chemical changes, but by changes by denitrification, i.e. the irreversible removal of HNO 3 by sedimenting cloud particles, as shown in Figure 3. Denitrification is much more severe in the southern hemisphere due to the lower temperatures, leaving almost no NO y (Figure 1).The amount of NO y present in the other important nitrogen reservoir ClONO 2 is limited by the mixing ratio of Cl y (less than 3.5 ppb).Thus, ClONO 2 never contributes more than about 25 % to NO y .
NO x is defined as the sum of the short-lived and reactive species NO, NO 2 , NO 3 and 2 N 2 O 5 , which only form under sunlit conditions from the longer lived HNO 3 .Only a small part of NO y is in the form of NO x under sunlit conditions, typically less than 2 ppb in the northern hemisphere and less than 0.75 ppb in the southern hemisphere.For the following discussion, it is reasonable to define an "extended" NO x , which also includes ClONO 2 (and, much less importantly, BrONO 2 and HO 2 NO 2 ), since these species are in very fast equilibria with the "classical" NO x species under sunlit conditions.
The extended NO x mixing ratios can be changed by a number of reactions.Vortex-averaged reaction rates of these reactions for the northern and southern hemisphere are shown in Species NO3, BrONO2, ClNO2 and N are not shown due to their small mixing ratios.
The OH reaction contributes about 60 %-80 % to the production.Extended NO x is lost to HNO 3 mainly by the heterogeneous reactions and by the gas-phase reaction The reaction N 2 O 5 + H 2 O proceeds on the background aerosol, not only when polar stratospheric clouds are present.When sunlight comes back to the vortex in spring, reactions R1-R2 are not in equilibrium with R3-R5 and produce extended NO x from HNO 3 .Due to the denitrified conditions in the southern hemisphere, much less NO x is produced there.
Note that the introduction of an extended NO x does not work very well under polar night conditions, since ClONO 2 is not in equilibrium with the classical NO x then, which can be seen in the fact that extended NO x is lost in polar night due to heterogeneous reaction of ClONO 2 , although no NO or NO 2 is present.Figure 5 shows the partitioning of extended NO x during daytime and at night.Daytime averages are defined over the parts of the vortex where the solar zenith angle is smaller than 80 • and nighttime averages are defined over parts of the vortex where the solar zenith angle is larger than 100 • .Except for early winter, NO x proper is only present in appreciable quantities after the start of March or October, respectively.During daytime, the partitioning between NO and NO 2 is so fast that steady state conditions can be assumed.The three reactions that determine the equilibrium are Figure 6 shows the formation and loss rates of NO to illustrate this (the corresponding plots for NO 2 look identical, but mirrored).The equilibrium condition derived from these reactions is In the southern hemisphere during daytime, the fraction of NO compared to NO 2 is much higher than in the northern hemisphere (80 %-90 % NO and 10 %-20% NO 2 in the southern hemisphere, and 20 %-40 % NO and 60 %-80 % NO 2 in the northern hemisphere).The higher NO levels are caused by the much lower ozone levels in the southern hemisphere (see Figure 19), which shifts the equilibrium by hindering the O 3 + NO reaction.At night, no NO is present, since the reaction NO 2 + hν does not take place.NO 3 only plays a negligible role for the budget of NO x due to the fast reaction into NO 2 by during daytime and into N 2 O 5 at night (see discussion of R13).
Despite the relatively low mixing ratios, NO x plays an important role in ozone chemistry.In addition to the equilibrium between NO and NO 2 , there is a fast equilibrium between NO 2 and ClONO 2 under sunlit conditions, so that all three species are coupled.ClONO 2 is to a good approximation in an equilibrium between and Reaction R10 is the dominating branch of the ClONO 2 photolysis.The equilibrium condition for ClONO 2 can be written as Alternatively, since NO and NO 2 are in equilibrium, this can also be expressed in terms of NO Production of NO x from HNO 3 in spring will increase NO 2 .In turn, ClONO 2 will increase almost instantly at the expense of NO 2 to match the equilibrium condition again.In this sense, ClONO 2 is produced from HNO 3 via NO x in spring.This is an important deactivation pathway for active chlorine in the northern hemisphere, since it consumes ClO.
There is a striking difference in ClONO 2 production in spring between the northern and southern hemisphere.While ClONO 2 increases to 2 ppb in the northern hemisphere, it stays below 0.1 ppb in the southern hemisphere due to the strongly denitrified conditions there.The hindrance of the deactivation path via ClONO 2 under denitrified conditions prolongs the period of ozone loss, since the other deactivation path via the reaction Cl + CH 4 is only effective under low ozone levels (see section 4.3.2).ClONO 2 stays relatively constant in March in the northern hemisphere after the initial increase, since the decrease in ClO is compensated by an increase in NO 2 .In the southern hemisphere, ClO drops to even lower values after October due to missing ozone.
The mixing ratio of N 2 O 5 is governed by At night N 2 O 5 is produced slowly by reaction R13, with NO 3 produced by During daytime, no N 2 O 5 is produced, since the NO 3 produced by reactions R10 and R15 is easily photolyzed.However, N 2 O 5 is only slowly depleted during daytime, so that N 2 O 5 levels during daytime and at night are comparable in the northern hemisphere (up to 30 % of classical NO x is in N 2 O 5 ).In the southern hemisphere, low ozone levels hinder the production of The produced N 2 O 5 can react back to the reservoir HNO 3 via reaction R3 (see Figure 4).

Hydrogen species
The sources for HO x = OH+HO 2 are mainly H 2 O, CH 4 and HNO 3 .The source for stratospheric water is humid tropospheric air "freeze-dried" at the tropopause and sources for CH 4 are both natural (wetlands) and anthropogenic (e.g.WMO, 2011;Montzka, 2012).CH 4 is slowly oxidized to H 2 O in the stratosphere (see also below).Figure 7 shows that the mixing ratio for H 2 O is between 2 ppm and 6 ppm and that CH 4 has a mixing ratio of about 1 ppm.The decrease of H 2 O in July in the southern hemisphere is caused by dehydration by sedimenting cloud particles, similar to the situation for HNO 3 .The northern hemisphere is not cold enough for the formation of a significant amount of ice clouds.
Production and loss processes of HO x are fairly complicated (Hanisco, 2003).Figure 8 shows the production and loss rates of an extended HO x , where we have included some species that are not a net source or sink of HO x over a diurnal cycle (extended HO x = OH + HO 2 + H + HOCl + HOBr + HO 2 NO 2 ).Particularly in the southern hemisphere, production from CH 4 oxidation, which can be initiated by with X = Cl, O( 1 D), OH and then continues with a complicated chain of reactions involving CH 2 O (see Hanisco, 2003, for more details), plays an important role.The maximum yield of this reaction chain is 4 HO x per CH 4 , but the yield is normally 5 lower (Hanisco, 2003).For example, the HCl formed by R16 with X = Cl lowers the yield of the reaction chain starting with this reaction because of the reaction Reaction of water with O( 1 D) HO x is in equilibrium with HOCl under sunlit conditions and when chlorine is activated Hence, the heterogeneous reaction is also a sink for HO x .
HO x levels are about 1 to 4 ppt under sunlit conditions in both hemispheres (Figure 9).At night, no HO x is present, since there is no production and HO x recombines into water and HNO 3 (Figure 8).HOCl can reach mixing ratios of up to 0.15 ppb in both hemispheres, as long as chlorine is activated.Figure 9 shows that HO x does not simply scale with the amount of sunlight, HNO 3 , H 2 O and CH 4 : In the southern hemisphere, HO x shows a peak under conditions of both chlorine activation and sunlight, related to the fact that reactions like Cl + CH 4 and HOCl + HCl play a role in HO x production.
Figure 9 also shows the partitioning of HO x .Similar to NO x , there is a fast equilibrium between OH and HO 2 .The partitioning inside HO x is determined mainly by Figure 10 shows the rates of HO 2 production and loss to illustrate that (the corresponding plots for OH look similar, but mirrored, and ClO + HO 2 is replaced by HOCl + hν).The production and loss rates of HO x proper are dominated by the reactions R21 and R22 which form the equilibrium with HOCl (not shown).
The equilibrium is mainly on the side of HO 2 in both hemispheres.The fraction of OH is somewhat higher in the southern hemisphere (about 20 %-40 %) than in the northern hemisphere (about 10 %-20 %).Absolute OH levels are of relatively similar magnitude (up to 1 ppt in the southern hemisphere and up to 0.5 ppt in the northern hemisphere).
Equations for the equilibrium values of OH, HO 2 and HOCl can be derived from reactions R21 to R27.The ratio of OH and HO 2 under sunlit conditions in the northern hemisphere and in the southern hemisphere before mid-September is in good approximation given by That is, the ratio depends only on O 3 , ClO and NO.The equation can be simplified to under conditions when chlorine is activated and no NO is present (before March and mid-September, respectively) and to in spring (end of March) in the northern hemisphere.In the southern hemisphere, the change between conditions rich in ClO x and rich in NO x can be seen in a change in the relative partitoning (Figure 9).A similar discussion and expressions for mid-latitudes can be found in Cohen et al. (1994).
Under sunlit conditions and when chlorine is activated, the equilibrium of HOCl is given by At night, HOCl remains constant (except for heterogeneous processing), since neither the photolysis reaction nor the ClO + HO 2 reaction can proceed.
HO x is relevant for ozone depletion, since the reactions HCl + OH → H 2 O + Cl and ClO + OH → HCl + O 2 play a role in chlorine activation and deactivation (note that the second reaction differs from reaction R24 in the products).In addition, chlorine can be activated by the heterogeneous HOCl + HCl reaction.

Overview and partitioning
When the polar vortex forms, the majority of chlorine is present in the form of HCl and the remainder is present in the other important reservoir gas ClONO 2 .Figure 11 shows the partitioning between the various inorganic chlorine species (Cl y ).The Nighttime averages (parts of the vortex where the solar zenith angle is larger than 100 • ).Days without sufficient data for averaging are not shown (grey bars).Species ClNO2 and BrCl are not shown due to their small mixing ratios.available amount of Cl y is about 2.7 to 3.3 ppb in the considered altitude range (the increase is due to transport from above).In both hemispheres, the initial mixing ratio of HCl is about 2 ppb (75 % of Cl y ) and the initial mixing ratio of ClONO 2 is about 0.7 ppb.Cl y is produced by photolysis and reaction with O( 1 D) from chlorofluorocarbons (CFCs), hydrochlorofluorocarbons (HCFCs) and similar species of mainly anthropogenic origin (e.g.WMO, 2011;Montzka, 2012).
In early winter, passive reservoir gases HCl and ClONO 2 are transformed to Cl 2 through heterogeneous reactions on the surface of polar stratospheric clouds (starting in December in the northern hemisphere and May in the southern hemisphere).
Since the major reaction that transforms the reservoir gases to Cl 2 is HCl + ClONO 2 (e.g.Solomon et al., 1986, see also section 4.3.2), the amount of chlorine that can be activated is limited by the mixing ratio of the less abundant ClONO 2 .While Under polar conditions, the dimer of ClO plays an important role.Reactions that determine the ratio of ClO and its dimer Reactions R30 and R31 are also part of the ClO dimer ozone loss cycle (see section 4.5).Note that reaction R31 includes an intermediate step over ClOO not shown here.Figure 12 shows the partitioning of ClO x = ClO + 2 Cl 2 O 2 .Active chlorine is mainly present in the form of Cl 2 O 2 at night and in the form of ClO during daytime.At night, only small levels of ClO are maintained by the interplay between the forward and backward reaction R32 and R30 (see also Wayne et al., 1995Wayne et al., , p. 2836)).
During daytime, most Cl 2 O 2 is photolyzed into Cl which reacts to ClO and there is an equilibrium between ClO and Cl 2 O 2 .
About 70 % of ClO x is present as ClO during daytime.
When chlorine is activated from December to the beginning of March in the northern hemisphere and from May to September in the southern hemisphere, ozone is removed by the ClO dimer cycle and the ClO-BrO cycle (see section 4.5).ClO x peaks at about 2.4 ppb in the northern hemisphere and at about 2.0 ppb in the southern hemisphere.

Reservoir HCl
Figure 13 shows the time evolution of the vortex-averaged reaction rates of all relevant reactions that change HCl.In early winter (up to the end of December in the northern hemisphere and up to the end of July in the southern hemisphere), HCl is removed by heterogeneous reactions on polar stratospheric clouds and active chlorine is produced.When sunlight returns, this is followed by a phase of competition between HCl removal by heterogeneous reactions and deactivation of ClO x into HCl by gas-phase reactions (most pronounced in August in the southern hemisphere).In the southern hemisphere, this is followed by a phase of deactivation of active chlorine into HCl by the Cl + CH 4 reaction in September to October.Finally, when sunlight comes back, the gas-phase loss reaction HCl + OH becomes important and competes with the production by Cl + CH 4 .In the southern hemisphere, HCl is near equilibrium during this time, while in the northern hemisphere, chlorine that was initially deactivated into ClONO 2 is slowly transformed into HCl.

HCl loss (chlorine activation)
The most important heterogeneous loss reaction for HCl is Another heterogeneous activation channel for HCl is While this reaction plays a smaller role in the northern hemisphere, the reaction is important in the southern hemisphere in the months August and September.In the southern hemisphere, the HOCl + HCl reaction accounts for about 70 % of the HCl activation by heterogeneous reactions and in the northern hemisphere it accounts for about 30 %. HOCl only exists in significant amounts when chlorine is activated.In the southern hemisphere, this causes a shift from activation by ClONO 2 + HCl in early winter to activation dominated by HOCl + HCl later.
The only other reaction that removes HCl in relevant quantities is the gas-phase reaction with OH, which is only important under sunlit conditions: In the northern hemisphere, the reaction is relevant in late winter (March).For the southern hemisphere, the reaction is relevant in October and later.

HCl production (chlorine deactivation)
HCl is only produced by reactions that are indirectly dependent on sunlight.Deactivation of active chlorine occurs mainly into HCl in the southern hemisphere but predominantly into ClONO 2 in the northern hemisphere.The reason for this is that deactivation into ClONO 2 is hindered in the southern hemisphere by strong denitrification (absence of NO 2 ), while normally it would be the preferred pathway of deactivation.
In the long term, the partitioning of HCl and ClONO 2 in spring and summer favors HCl.This can be seen in the fact that in the northern hemisphere, HCl is produced from ClONO 2 in spring after ClO x has been deactivated into ClONO 2 some time earlier (see also section 4.3.3 and Figure 17), while in the southern hemisphere, active chlorine is deactivated mainly into HCl.
The chemical change rates of both HCl and ClONO 2 decrease to zero in November in the southern hemisphere.The reaction is the main production reaction for HCl in both hemispheres.In addition, it is responsible for deactivation under ozone hole conditions in the southern hemisphere.The reaction becomes similar in importance to Cl + CH 4 as a production process for HCl around late February in the northern hemisphere, and plays a smaller role earlier and later in winter.In the southern hemisphere, the reaction is not negligible around September and October.The reaction is responsible for a part of the chlorine deactivation in both hemispheres.The reaction ClO + OH has two product channels.The channel into HCl yields about ≈ 8 % of the products (the other channel is into ClO).

The role of Cl in HCl production
The rate of the Cl + CH 4 reaction is proportional to the mixing ratio of Cl. Figure 14 shows the mixing ratio of Cl for both hemispheres.Figure 15 shows that Cl is determined by the two source reactions and a reaction that removes Cl Reaction R31 is coupled to the catalytic ClO dimer cycle.Cl levels are considerably higher in the southern hemisphere due to a lack of ozone, which hinders the recombination to ClO.This favors the deactivation of active chlorine over the Cl + CH 4 reaction.Cl shows a very distinct behaviour in the southern hemisphere.It does not just increase with the amount of sunlight, but shows a peak in September, followed by a near constant plateau.This curve shape is approximately repeated in the curves of the reaction rate of the Cl+CH 4 reaction, since CH 4 is relatively constant.Figure 15 shows that the peak in Cl mixing ratios in the southern hemisphere is related to reaction R31, i.e. the catalytic ozone destruction.In contrast, the plateau is related to the NO x reaction R7 (see also Wayne et al., 1995Wayne et al., , p. 2836)).

Reservoir ClONO 2
Figure 16 shows the reaction rates of the most important reactions changing ClONO 2 .As discussed in section 4.1, the gross change rates of ClONO 2 are dominated by a near equilibrium between the reactions and under sunlit conditions.Net changes of ClONO 2 are induced by changes in NO x which shift the equilibrium.The net change of ClONO 2 is one order of magnitude smaller than the gross rates.Figure 17 shows the net effect of R10-R12 (yellow area) and all other reactions that play a role in changing ClONO 2 .These reactions, which are all loss reactions, remove ClONO 2 either by heterogeneous reactions or gas-phase reactions of ClONO 2 with a radical.The most important heterogeneous reaction is the same as for HCl The reactions of ClONO 2 with a radical are of the type where X is X = O, Cl, OH.The reaction with Cl is the dominating reaction.
In early winter in the polar night (December in the northern hemisphere, May and June in the southern hemisphere), the loss of ClONO 2 by heterogeneous reactions is dominating, leading to the activation of chlorine.After the complete depletion of ClONO 2 , this is followed by a phase with only small production and loss, due to near-zero levels of both NO x and ClONO 2 .
The peak in production in early spring in the northern hemisphere (end of February and beginning of March) is caused by the net production of extended NO x from HNO 3 and is the main deactivation pathway for active chlorine in the northern hemisphere.Then, ClONO 2 is out of equilibrium and more ClONO 2 is produced by ClO + NO 2 than is lost by photolysis.In the southern hemisphere, the rates are much lower due to the strongly denitrified conditions.In late March, ClONO 2 is lost in the northern hemisphere and finally converted to HCl, which is the favored reservoir under summer conditions.In the southern hemisphere, rates are low in late October and November, since the deactivation already occured into HCl.

Bromine species
Sources of inorganic bromine, which has both natural and anthropogenic sources, are mainly halons and methyl bromide, but also some short-lived species (e.g.WMO, 2011;Montzka, 2012).Inorganic bromine (Br y ) levels in the stratosphere are about 20 ppt at maximum (e.g.WMO, 2011), with marginally lower levels in the altitude range considered here.Bromine chemistry is still somewhat uncertain due to uncertainties in the reaction constants (Sander et al., 2011;von Hobe and Stroh, 2012).
Atomic bromine is released from the source gases mainly by photolysis.Under sunlit conditions, it is in equilibrium with Reactions with rates which cannot be distinguished from the zero line at plot resolution are not shown.
Figure 18 shows the partitioning between the various inorganic bromine species.Bromine is mostly present in the form of HOBr and BrONO 2 at night before chlorine activation starts.In contrast to the less reactive chlorine, these are not real reservoir gases, since they easily photolyze into Br and react further to BrO during daytime, which gives bromine a great potential to destroy ozone despite the low mixing ratios (e.g.Lary, 1996).BrO is a dominant species during daytime (e.g.Lary, 1996), except in October and November in the southern hemisphere, when the reaction Br + O 3 is hindered by the low ozone levels and Br mixing ratios are significant.Heterogeneous reactions play only a minor role and are not needed for activation (e.g.Lary et al., 1996;Wayne et al., 1995).As long as chlorine is activated, almost all bromine is in the form of BrCl at night (e.g.Lary et al., 1996;von Hobe and Stroh, 2012).BrCl is produced by the reaction

Oxygen species
Figure 19 shows the vortex-averaged mixing ratios of ozone for the northern and southern hemisphere.Ozone stays relatively constant at values between 1.5 ppm and 2.5 ppm in the northern hemisphere, since the change by ozone depletion is nearly cancelled by transport of air rich in ozone from above and over the vortex edge.In contrast, ozone values decrease from 2.5 ppm to less than 0.5 ppm in the southern hemisphere, both due to weaker transport and larger ozone depletion.
O 3 is in a very fast equilibrium with O.The dominant cycle is part of the well-known Chapman chemistry (Chapman, 1930) We follow the usual convention here to treat O 3 and O together as odd oxygen O x (e.g.Brasseur and Solomon, 2005;Solomon, 1999).Since O mixing ratios are low, the chemical rate of change of O x is nearly the same as the rate of change of ozone.
Odd oxygen is destroyed by several catalytic cycles.It is well known (e.g.Solomon, 1999) that the two dominating cycles in anthropogenic polar ozone depletion by halogens are the ClO dimer cycle (first proposed by Molina and Molina, 1987) The ClO dimer cycle is able to work, because the Cl 2 O 2 photolysis, which produces Cl and not ClO, is fast compared to the competing Cl 2 O 2 loss reaction Cl 2 O 2 + M (Wayne et al., 1995(Wayne et al., , p. 2836)).The uncertainty of the rate constant of the Cl 2 O 2 photolysis R31 and the rate constant of the BrO + ClO reaction R38 are two of the parameters which produce the largest uncertainties with respect to ozone loss in models, although much of the uncertainty in the photolysis has been resolved recently (Kawa et al., 2009;von Hobe and Stroh, 2012).
Figure 20 shows the contribution of the different catalytic cycles to the net chemical rate of change of ozone.For this purpose, the reaction rates of the rate limiting step of the reaction cycles have been used.This is possible here without ambiguities, since all rate limiting reactions are only involved in one cycle.
As long as appreciable amounts of ClO exist (January to February in the northern hemisphere, June to September in the southern hemisphere), the ClO-ClO cycle contributes about 50 % to the net ozone loss and the ClO-BrO cycle contributes The most important null cycle acting on odd oxygen apart from reactions R41 and R42 is the nitrogen cycle

Conclusions
We have given a quantitative analysis of the reactions involved in polar ozone depletion in the stratosphere.For clarity, this study focuses on vortex averages in a layer around 54 hPa.The reactions and reaction cycles involved in polar ozone depletion are well known, but quantitative estimates of the partitioning of the chemical families or the importance of single reactions and reaction cycles are rare.To our knowledge, this is the first comprehensive study providing quantitative results averaged over the polar vortex under conditions perturbed by heterogeneous chemistry.The main aim of this study is to quantify numbers for the partitioning of HO x , NO x and ClO x , the relative importance of production and loss reactions and the timing of the reactions.Some selected findings are: -The ClO dimer cycle contributes about 50% to the vortex-averaged ozone loss at 54 hPa in both hemispheres, while the ClO-BrO cycle contributes about 40%.
-In the southern hemisphere, there is a clear shift from chlorine activation by the ClONO 2 + HCl reaction in early winter to activation by the HOCl + HCl reaction later in winter.HOCl + HCl accounts for about 70% of the activation of HCl in the southern hemisphere, while it accounts for 30% of the activation in the northern hemisphere.
-ClO x peaks at 2.0-2.5 ppb.About 70% of ClO x is present as ClO during daytime at 54 hPa.
-HO x levels peak at 4 ppt.HO x is mainly produced from CH 4 oxidation in the southern hemisphere, while in the northern hemisphere, production by HNO 3 , CH 4 and H 2 O play comparable roles.The partitioning between OH and HO 2 results in 20%-40% OH in the southern hemisphere and in 10%-20% OH in the northern hemisphere.
-NO x levels are smaller than 2 ppb in the northern hemisphere and smaller than 0.75 ppb in the southern hemisphere due to the denitrified conditions there.The partitioning between NO and NO 2 during daytime results in 80 %-90 % NO in -The solubility of HCl in STS droplets is underestimated.This is a promising possibility, but it requires changes to the solubility that are above the stated uncertainties of the solubility parameterization by Luo et al. (1995) that is used in the model.
Since there is not enough evidence to narrow down this list to a likely candidate, we decided on an empirical approach: We introduced a temperature offset for the calculation of the Henry constant of HCl and changed the offset until we obtained a good agreement of measured and modeled HCl, which was the case for an offset of −5 K.The effect of the changed Henry constant is twofold: First, it increases the amount of HCl dissolved in STS droplets.Second, it increases the rates of the heterogeneous reactions (even if only small amounts of HCl are dissolved) by changing the γ values.The HCl mixing ratios of the model runs with the changed Henry constant agree well with the satellite measurements for the southern hemisphere and the northern hemisphere after beginning of January, but a discrepany remains in December.

FractionFigure 1 .
Figure 1.Vortex-averaged temperature (blue), vortex minimum temperature (dashed blue) and fraction of the vortex in sunlight (yellow) for the Arctic winter 2004/2005 (left) and the Antarctic winter 2006 (right) at 54 hPa.The thin blue line shows the threshold temperature for the formation of NAT clouds used in the model.The vortex tracer criterion described in the text was not applied (in contrast to all other figures).

Figure 3 .
Figure 3. Vortex-averaged net chemical reaction rate of HNO3 (red) for the Arctic winter 2004/2005 (left) and the Antarctic winter 2006 (right) at 54 hPa and sum of the vortex-averaged change by sedimentation and the net chemical reaction rate (blue).

Figure 4 .
Figure 4. Vortex-averaged chemical reaction rates of reactions changing extended NOx (NO + NO2 + NO3 + 2 N2O5 + ClONO2 + BrONO2 + HO2NO2) for the Arctic winter 2004/2005 (left) and the Antarctic winter 2006 (right) at 54 hPa.Production reactions are shown positive and are separated by a line in the legend from the loss reactions, which are shown negative.The net change of extended NOx is shown as a green line.Reactions with rates which cannot be distinguished from the zero line at plot resolution are not shown.

Figure 5 .
Figure 5. Vortex-averaged partitioning of extended NOx species for the Arctic winter 2004/2005 (left) and the Antarctic winter 2006 (right) at 54 hPa.Top row: Daytime averages (parts of the vortex where the solar zenith angle is smaller than 80 • ).Bottom row: Nighttime averages (parts of the vortex where the solar zenith angle is larger than 100 • ).Days without sufficient data for averaging are not shown (grey bars).

Figure 6 .
Figure 6.Vortex-averaged chemical reaction rates of reactions changing NO for the Arctic winter 2004/2005 (left) and the Antarctic winter 2006 (right) at 54 hPa to illustrate NOx partitioning.Production reactions are shown positive and are separated by a line in the legend from the loss reactions, which are shown negative.The net change of NO is shown as a green line.

Figure 7 .
Figure 7. Vortex-averaged mixing ratios of H2O and CH4 for the Arctic winter 2004/2005 and the Antarctic winter 2006 at 54 hPa.

Figure 8 .
Figure 8. Vortex-averaged chemical reaction rates of reactions changing extended HOx (OH + HO2 + H + HOCl + HOBr + HO2NO2) for the Arctic winter 2004/2005 (left) and the Antarctic winter 2006 (right) at 54 hPa.Production reactions are shown positive and are separated by a line in the legend from the loss reactions, which are shown negative.The net change of extended HOx is shown as a green line.Methane oxidation is modelled by simplified net reactions in ATLAS, the reactions denoted as methane oxidation in the legend are Cl + CH4 → HCl + CH2O + HO2 and Cl + CH2O → HCl + CO + HO2.

Figure 9 .
Figure 9. Vortex-averaged partitioning of HOx species for the Arctic winter 2004/2005 (left) and the Antarctic winter 2006 (right) at 54 hPa.Daytime averages (parts of the vortex where the solar zenith angle is smaller than 80 • ).Nighttime averages are near zero and not shown.Days without sufficient data for averaging are not shown (grey bars).

Figure 10 .
Figure 10.Vortex-averaged chemical reaction rates of reactions changing HO2 for the Arctic winter 2004/2005 (left) and the Antarctic winter 2006 (right) at 54 hPa to illustrate HOx partitioning.Production reactions are shown positive and are separated by a line in the legend from the loss reactions, which are shown negative.The net change of HO2 is shown as a green line.

Figure 11 .
Figure 11.Vortex-averaged partitioning of inorganic chlorine species (Cly) for the Arctic winter 2004/2005 (left) and the Antarctic winter 2006 (right) at 54 hPa.Top row: Daytime averages (parts of the vortex where the solar zenith angle is smaller than 80 • ).Bottom row: photolysis of Cl 2 Cl 2 + hν → Cl + Cl (R28)immediately followed by the reactionCl + O 3 → ClO + O 2 (R29)to produce ClO.The time between first activation and the first sunlight becomes apparent in a Cl 2 peak in December and May in Figure11.

Figure 12 .
Figure 12.Vortex-averaged partitioning of ClOx for the Arctic winter 2004/2005 (left) and the Antarctic winter (right) at 54 hPa.Top row: Daytime averages (parts of the vortex where the solar zenith angle is smaller than 80 • ).Bottom row: Nighttime averages (parts of the vortex where the solar zenith angle is larger than 100 • ).Days without sufficient data for averaging are not shown (grey bars).

Figure 13 .
Figure 13.Vortex-averaged chemical reaction rates of reactions involving HCl for the Arctic winter 2004/2005 (left) and the Antarctic winter 2006 (right) at 54 hPa.Production reactions are shown positive and are separated by a line in the legend from the loss reactions, which are shown negative.The net change of HCl is shown as a green line.Reactions with rates which cannot be distinguished from the zero line at plot resolution are not shown.

Figure 14 .
Figure 14.Vortex-averaged Cl mixing ratios for the Arctic winter 2004/2005 and the Antarctic winter 2006 at 54 hPa.

Figure 15 .Figure 16 .
Figure 15.Vortex-averaged chemical reaction rates of reactions involving Cl for the Arctic winter 2004/2005 (left) and the Antarctic winter 2006 (right) at 54 hPa.Production reactions are shown positive and are separated by a line in the legend from the loss reactions, which are shown negative.

BrO.Figure 17 .
Figure 17.Vortex-averaged chemical reaction rates involving ClONO2 for the Arctic winter 2004/2005 and the Antarctic winter 2006 at 54 hPa.In contrast to Figure 16, the net production rate of the fast cycle ClONO2 +hν → Products / ClO+NO2 +M → ClONO2 +M is shown.This cycle is separated by a line in the legend from the loss reactions.The green line shows the net change of ClONO2 by chemistry.

)Figure 18 .Figure 19 .
Figure 18.Vortex-averaged partitioning of inorganic bromine species for the Arctic winter 2004/2005 (left) and the Antarctic winter 2006 (right) at 54 hPa.Top row: Daytime averages (parts of the vortex where the solar zenith angle is smaller than 80 • ).Bottom row: Nighttime averages (parts of the vortex where the solar zenith angle is larger than 100 • ).Days without sufficient data for averaging are not shown (grey bars).

Figure 20 .
Figure 20.Vortex-averaged net chemical loss of odd oxygen by different catalytic cycles.The red line shows the net chemical change rate of ozone.The contribution of the different cycles is shown by the reaction rates of their rate limiting step.Only the three most important cycles are shown, the contribution of other cycles is negligible.The ozone increase in the right panel is caused by the O2 + hν reaction.
Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2017-66,2017   Manuscript under review for journal Atmos.Chem.Phys.Discussion started: 6 March 2017 c Author(s) 2017.CC-BY 3.0 License.about 40 % (see alsoGrenfell et al., 2006, for case studies of the partitioning).Loss cycles of the formX + O 3 → XO + O 2 XO + O → X + O 2 O + O 3 → O 2 + O 2where X = OH, H, NO, Cl, Br, which dominate in most latitudes and seasons, only play a minor role in the polar lower stratosphere due to the relatively low production of atomic oxygen by photolysis (e.g.von Hobe and Stroh, 2012).