Temporal Evolution of the Bromine Alpha Factor and Equivalent Effective Stratospheric Chlorine in Future Climate Scenarios

Future trajectories of the stratospheric trace gas background will alter the rates of bromineand chlorine-mediated catalytic ozone destruction via changes in the partitioning of inorganic halogen reservoirs and the underlying temperature structure of the stratosphere. The current formulation of the bromine alpha factor, the ozone-destroying power of stratospheric bromine atoms relative to stratospheric chlorine atoms, is invariant with climate state. Here, we refactor the bromine alpha factor, introducing climate normalization to a benchmark climate state, and reformulate Equivalent Effective Stratospheric 5 Chlorine (EESC) to reflect changes in the rates of both chlorineand bromine-mediated ozone loss catalysis with time. We show that the ozone-processing power of the extrapolar stratosphere is significantly perturbed by future climate assumptions. Furthermore, we show that our EESC-based estimate of the extrapolar ozone-recovery date is in closer agreement with extrapolar ozone recovery dates predicted using more sophisticated 3-D chemistry-climate models than prior formulations of EESC that employ climate-invariant values of the bromine alpha factor. 10

in reactions R1 -R3 below, in which inorganic chlorine is rapidly interconverted between the chlorine radical and the chlorine monoxide radical.
The gas-phase conversion of the dominant inorganic chlorine reservoirs to their active, ozone-destroying forms (reaction 30 R4) is too slow to be of atmospheric importance; however, heterogeneous reactions on the surfaces of stratospheric aerosols (Solomon et al., 1986;Brasseur et al., 1990), as indicated in reactions R5-R7, can be sufficiently fast to enable significant engagement of ClO x ozone-depletion cycling.
HCl Mechanisms of BrO x -mediated ozone depletion are much less dependent on the surrounding environment than mechanisms mediated by ClO x . This is because inorganic reservoirs of bromine are significantly less stable, enhancing the quantity of reactive halogen available for ozone processing. Bromine is up to two orders of magnitude more likely to be found in its active form than chlorine, depending on the physicochemical environment (Wofsy et al., 1975;Salawitch et al., 2005). Additionally, unlike the chlorine cycle presented in reactions R1-R3 which requires the presence of atomic oxygen and is accordingly slow 45 in the lower stratosphere or in regions of low actinic flux, catalytic processing of ozone facilitated by the addition of bromine is effective in these regions. Reactions R8-R11, the coupled odd bromine-chlorine cycle, and reactions R12-R16, the coupled odd bromine-hydrogen cycle, are examples of this chemistry in which atomic oxygen is not involved. The bromine interfamily cycles are responsible for a similarly-sized fraction of global lower stratospheric ozone loss as the chlorine cycle (reactions R1 -R3) (Salawitch et al., 2005;World Meteorological Organization, 2018;Koenig et al., 2020). This large fractional share of 50 ozone destruction chemistry occurs despite the fact that bromine is approximately two orders of magnitude less abundant than chlorine as a consequence of (a) the larger fraction of reactive bromine available at a given mixing ratio and (b) the catalytic reaction channels made accessible by the weaker bromine-oxygen molecular bond (Yung et al., 1980;McElroy et al., 1986;Brune and Anderson, 1986;World Meteorological Organization, 2018).
The bromine alpha factor, α Br , is a metric that quantifies the ozone-depleting efficiency of a bromine atom relative to chlorine.
This quantity is defined either as the ratio of ozone loss processing rates, as in Eq.
ozone abundance on a per-halogen-atom basis per Eq (2). In both formulations, α Br is computed as a function of calendar date, t, and location in the atmosphere, ρ. Daniel et al. (1999) demonstrate that both equations provide identical results when 75 changes in ozone are dominated by chemical rather than dynamical processes.
Values of α Br vary strongly as a function of pressure, latitude, and season. This variance is primarily a function of (a) 80 chemical environment, (b) prevailing actinic flux, (c) aerosol surface area, and (d) temperature (Solomon et al., 1992;Danilin et al., 1996;Ko et al., 1998;Daniel et al., 1999). Frequently, α Br is reported as an effective value for the stratospheric column, computed in a similar manner as in Eq.
(2), the key difference being that ρ represents the position of the stratospheric column. Likewise, it is common to provide a regional-annual average column α Br , which is computed as the average of column In vertical profiles, α Br tends to maximize in the lower stratosphere where reactive chlorine is less prevalent than in the middle stratosphere.

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The quantity α Br is especially useful for the determination of parameterized estimates of the budget of reactive inorganic halogens given a mixture of halogen-containing halocarbons of an arbitrary mean age, as in the metric of Equivalent Effective Stratospheric Chlorine (EESC). This quantity expresses the ozone-depleting power of a parcel of well-mixed stratospheric trace gases as a function of mean stratospheric age of the parcel, Γ, and the trace gas background of the stratosphere at time t (Daniel et al., 1995;Newman et al., 2007). Equation 3 provides the most recently suggested formulation of EESC, in which f i (Γ) is 95 the time-independent fractional release factor for species i for a parcel of air with mean age Γ, which contains n i,Cl chlorine atoms and n i,Br bromine atoms, scaled by α Br (t, Γ), where it is assumed that Γ can serve as a proxy for ρ (Ostermöller et al., 2017;Engel et al., 2018). Inside the integral, the mixing ratio of species i is computed for each element comprising the age spectrum and normalized to the contribution of that element to the age spectrum. The tropospheric mixing ratio of species i, χ 0,i is adjusted to account for transit time within the stratosphere, t , and multiplied by the normalized release-weighted transit where Γ # i is the mean age of halogen-atom release.
EESC is frequently employed to approximate the date of stratospheric ozone recovery, often by using graph theory to determine when stratospheric chlorine levels will return to the levels observed in 1980 as a benchmark (Newman et al., 2006; World stratosphere (for which Γ is a proxy) and future date, following which a horizontal line is propagated in time at the value of EESC in 1980, and the intercept of the two traces is interpreted as the date of halogen recovery (and, it follows, the probable date of ozone recovery). The extrapolation is built on the assumptions that, as the climate evolves: (1) the alpha factor remains constant and (2) the amount of ozone destroyed by chlorine, on a per-chlorine-atom basis, also remains constant. However, projections of the future physicochemical state of the stratosphere do not necessarily provide for these two assumptions to 110 be true. Indeed, the envelope of future projections (e.g., RCP and SSP scenarios) of emissions of CH 4 , N 2 O, CO 2 , among other relevant species, indicate that it is nearly certain that these two assumptions will not be true, especially in the extrapolar stratosphere.
Significant variations between different climate models and possible states of the future atmosphere limit the skill level of model simulations in predicting ozone recovery dates (Charlton-Perez et al., 2010). These large uncertainties notwithstanding, 115 it is understood that there may be a super-recovery of global stratospheric ozone in the future as EESC declines and the stratosphere cools (Austin and Wilson, 2006;Li et al., 2009;Eyring et al., 2013;Banerjee et al., 2016;Chiodo et al., 2018).
The extent of super-recovery is primarily dependent on the degree by which rates of bimolecular ozone-loss processes are slowed and the rate of the termolecular formation of ozone is increased as a result of (a) local radiative cooling due to the enhancement of the stratospheric burden of anthropogenic greenhouse gases and (b) chemical suppression of ozone loss cycling 120 due to reactive anthropogenic greenhouse gas emission (Rosenfield et al., 2002;Waugh et al., 2009;Oman et al., 2010;Eyring et al., 2013). Future projections of ozone are also dependent on dynamical factors, such as the model response of the Brewer-Dobson circulation to greenhouse gas perturbation, which alters both the stratospheric lifetime of long-lived inorganic halogen precursors and the transport of ozone from the tropics where it is produced (Butchart et al., 2006;Plummer et al., 2010;Zubov et al., 2013).
125 Dhomse et al. (2018) provide constraints on the dates stratospheric ozone might recover to year 1980 benchmark thickness using a comprehensive multi-model framework (20 models, 155 simulations) spanning multiple greenhouse gas emissions scenarios, finding that while the date of Antarctic springtime recovery is most sensitive to Cl y inventories, extrapolar column recovery dates (and to a lesser extent, the Arctic springtime recovery date) are highly sensitive to the greenhouse gas forcing applied. In their analysis, Dhomse et al. (2018) indicate that mid-latitude ozone recovery will occur sooner in both hemispheres 130 for scenarios with greater radiative forcing. When greenhouse gases are fixed, the dates projected for midlatitude recovery (∼2060) are in close agreement with the EESC-based estimates provided in Engel et al. (2018) of 2059; however, greenhouse gas perturbations hasten projected midlatitude recovery dates in 3-D models by ∼10 years in the northern hemisphere and ∼20 years in the southern hemisphere (Eyring et al., 2010(Eyring et al., , 2013Dhomse et al., 2018).
Regardless, it is known that the decay of EESC is the strongest driver of ozone recovery (Meul et al., 2014;Banerjee et al., 135 2016). While EESC is expected to decrease in the future, it is increasingly evident that the inorganic halogen background might be significantly perturbed by natural geological processes under certain circumstances (Klobas et al., 2017). Volcanic eruptions are now known to frequently inject small quantities of inorganic chlorine into the lower stratosphere (Carn et al., 2016), and there exists evidence for the periodic and profound volcanic injection of inorganic chlorine in the ice core record  , 1980, 1990, 2000) c Informed by Fleming et al. (1999) d Informed by Meinshausen et al. (2011) and Watanabe et al. (2011) (Zdanowicz et al., 1999) following large, explosive eruptions. Additionally, it is now apparent that volcanic bromine and iodine 140 may partition more effectively to the stratosphere than volcanic chlorine (Theys et al., 2009(Theys et al., , 2014Schönhardt et al., 2017;Gutmann et al., 2018). The expected enhancement in ozone-loss processing rates due to additional volcanogenic inorganic halogens following a future, large, halogen-rich explosive eruption is not well constrained, partially because the temporal evolution of the ozone processing rates of bromine relative to chlorine is largely unknown.
In this work, we present the first assessment of column α Br in future climate change scenarios. Additionally, we evaluate 145 the sensitivity of column α Br to prescribed perturbations of reactive greenhouse gases while anthropogenic halocarbons slowly decay as the century progresses. We then refactor α Br , such that estimates of EESC can more accurately be related to the ozone-destroying power of the inorganic halogen background of the stratosphere given a particular benchmark date. Finally, we show that this method provides much better agreement between EESC-based estimates and 3-D CCM estimates of ozone recovery to the 1980 benchmark date.

2 Model, Experiment, and Validation
The AER-2D chemical transport model was employed with 19 latitudes (90 • S-90 • N) and 51 levels (1000-0.2 hPa) for this work. The model includes 104 chemical species, accounting for F y , Cl y , Br y , I y , NO y , HO x , O x , SO x , and CHO x chemistry.
Chemical reactions (314 kinetic reactions and 108 photochemical reactions) were computed using rate constants and cross sections as recommended in the most recent (2015) JPL data evaluation (Burkholder et al., 2015). Additionally, the model features very-short lived bromocarbons (Wales et al., 2018). Experiments performed in the historical past were informed by historical climatologies obtained from Fleming et al. (1999).
Halogen perturbation scenarios were prepared in the manner of Daniel et al. (1999). Namely, CFC-11 proxy molecules (CFCl 3 A and CFBr 3 ) were constructed to provide identical transport and release of halogen atoms between model runs. For 165 bookkeeping purposes, this was done for both chlorine and bromine delivery (e.g., the molecule labeled as CFCl 3 A has the same chemical kinetics and photolysis rates as CFC-11, providing 3 chlorine atoms upon decomposition, but can be perturbed in the model separately from CFCl 3 ). Experiments were performed as outlined in Table 1. Experiments of a certain scenario (e.g., bkg2020RCP8.5, Cl2020RCP8.5, Br2020RCP8.5) were initialized from identical 20-year chemical-climatological spunup boundary conditions. Evaluations were conducted at constant chemical and climatological conditions corresponding to the 170 last year of each decade (e.g., 1980, 1990, ..., 2100). Perturbation and control experiments were evaluated over the course of 20 model years, a duration determined to be an appropriate period for the perturbation gas to reach chemical-dynamical steady-state. Data analysis was conducted on the final 12 months of each experiment and control run. Perturbation gas surface mixing ratios were selected to produce global and local ozone depletion of less than 1% in each climate state relative to the unperturbed condition to prevent instability in the chemical Jacobian. Prior evaluations of α Br were computed with static chemistry-climate states. Because the relative ozone-processing rate of bromine to chlorine is likely to change as time propagates within chemistry-climate scenarios, and also between chemistry- climate scenarios at the same point in time, we add a dependence on the chemical-climate state, ξ, to the defintion of α Br (Eq. (4)).
Furthermore, we recognize that the ozone-processing power of chlorine and bromine are independently sensitive to changes in the physicochemical background of the stratosphere. The two variables must be separated in order to understand the evolution 200 of the change in the processing power of bromine and chlorine as a function of climate state. To accomplish this, we define the eta factor, η Cl and η Br , in Eq. (6) and Eq. (7) as the ratio of the change in ozone following the addition of chlorine or bromine at time t, location ρ, and climate state ξ to the change in ozone following the same perturbation in a benchmark chemical-climate state, Ξ.

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By substituting this refactored definition of α Br into Eq. (5) for the computation of EESC, we can now quantify the ozonedepleting power of an air parcel in the stratosphere, propagated in time without bias to changes in the rates of bromine and chlorine ozone-loss catalysis (Eq. (9)) relative to the benchmark chemoclimatic state. Note again that ρ has been substituted with Γ per Engel et al. (2018). (9) Equation 9 provides a more appropriate basis for a graph-theory approximation of future inorganic halogen ozone-loss processing than prior approaches because the ordinate now represents Equivalent Effective Stratospheric Chlorine normalized to a benchmark atmospheric state rather than an instantaneous equivalent EESC with a time-varying ozone-processing power 220 per chlorine atom. Eq.

Calculation of
(2), because the non-local factors at time t in some evolved climate state are not likely to be the same as they were during the benchmark time period.  Table 2 for the historical period and for future scenarios. These results are also visualized in Figure 3 for (  Historical temperature fields obtained from Fleming et al. (1999).
Historical and future greenhouse gas emissions specified per Meinshausen et al. (2011).
Future temperature fields derived from Watanabe et al. (2011).

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A sensitivity analysis was conducted on α Br , η Cl , and η Br in order to clarify the differences presented in Figure 3. In this analysis, α Br , η Cl , and η Br were calculated in the manner previously described, but with the chemistry-climate perturbation, ξ, identical to the chemoclimatic benchmark, Ξ, except for a single perturbed parameter. Four variables were perturbed separately: Panel (a) of Figure 4 demonstrates that α Br is only slightly sensitive to changes in the mixing ratio of N 2 O between preindustrial and 2x RCP 8.5 year 2100 levels. Unlike α Br , both η Cl and η Br , as shown in panels (e) and (i), decline monotonically and with nearly identical gradients, as both the bromine and chlorine cycles are suppressed through reactions with NO x . This suppression arises primarily via the direct formation of the halogen nitrate, as in reaction R17, but also due to a reduction in the availability of HO x reaction partners as a result of reaction R18.
Variation in the model output as a function of the mixing ratio of CH 4 is presented in Figure 4 panels ( The effect of changing Br y /Cl y ratios was investigated over the range of 0.0054 -0.0088. This range encapsulates the 285 minimum and maximum ratios expected between the years 1980 -2100 according to WMO 2018 Table 6-4. These values were computed according to Eq. (11) using halocarbon mixing ratios prescribed by WMO 2018 Table 6-4, the fractional release factors of Newman et al. (2006), and an age spectrum of the form of Hall and Plumb (1994). The values of α Br , η Cl , and η Br are presented in Figure 4 panels (c), (g), and (k), respectively. Values of α Br generally decrease as the ratio of Br y /Cl y increases.
290 Danilin et al. (1996) demonstrated that α Br in the polar vortex is highly dependent on the relative mixing ratios of available bromine and chlorine, maximizing at low Br y /Cl y because of the enhanced abundance of ClO reaction partners for each BrO radical in those conditions. Within the polar vortex the fraction of ozone loss due to the slower chlorine peroxide cycle declines as Br y /Cl y increases; however, the extent of ozone depletion following the addition of bromine does not increase proportionately  14 https://doi.org/10.5194/acp-2020-276 Preprint. Discussion started: 8 April 2020 c Author(s) 2020. CC BY 4.0 License.
stratosphere render the chlorine peroxide cycle ineffective for the loss of ozone. We find that the extent of ozone loss following the addition of bromine increases significantly due to BrO x -ClO x and BrO x -HO x cycles rather than staying essentially constant as in the polar vortex conditions of Danilin et al. (1996).

Future EESC
Propagation of EESC using climate-invariant α Br per Eq.
(3) or climate-varying α Br per Eq. (5) produces significantly different dates of extrapolar halogen recovery than propagation of EESC using η-factor normalization as in Eq. (9). EESC values are 310 presented in Table 3 for historical and future chemistry-climate scenarios. In all cases, EESC compuations were informed by the time-independent fractional release factors provided in Table 1 of Engel et al. (2018). These EESC calculations are visualized in Figure 5.

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Taking chemistry-climate changes into account (when Eq. (9) is used for EESC computation) results in significant variations in future EESC between the RCP scenarios, as shown in panel (b) of Figure 5. For comparison purposes, as in panel (a)  c EESC using climate-variant αBr calculated per Eq. (5), EESC using η calculated per Eq. (9) and benchmarked to Ξ=1980. The divergences of expected EESC values between the calculation techniques are even more pronounced as the century unfolds. Panel (c) of Figure 5 provides the differences between EESC calculated using climate-dependent α Br with Eq. (5) and climate-normalized EESC calculated using Eq. (9). As the century ends, our eta factor method shows that there is a deficit exceeding 300 pptv EESC in the RCP 8.5 scenario relative to a calculation of EESC using the alpha factor method. These differences are negligible in the RCP 2.6 scenario because the greenhouse gas inventory of the RCP 2.6 year 2100 scenario 335 is very similar to the greenhouse gas inventory of the contemporary stratosphere. Intermediate GHG scenarios lie in between these two extremes.

Conclusions
The future stratosphere will be very different than the stratosphere of today in terms of trace gas loading, temperature structure, and radiative-dynamical transport. In this work, we used a 2-D chemical-transport/aerosol model to evaluate how differences 340 in the trace gas loading and the temperature structure of the future atmosphere might influence the relative rates at which inorganic halogen species destroy ozone. These differences can be quite large and are very sensitive to the chemistry-climate boundary conditions imposed.
The most significant perturbations of the stratospheric halogen background in the future are likely to arise from geological impulses. In this work, we provide the framework for adjusting EESC to accommodate changes in the processing rates of 345 both chlorine and bromine driven by climate and chemistry, such that EESC may be employed to predict ozone loss following such an event. Current formulations of the bromine alpha factor obfuscate the fact that rates of ozone destruction by bromine are changing alongside rates of ozone destruction by chlorine. In some cases, as in RCP 8.5, these rates change in concert, producing a time-invariant α Br ; however, the actual rates of ozone destruction would have changed significantly, producing an expected return to 1980 values 14 years earlier than predicted using prior formulations of EESC. For this reason, we have 350 refactored the bromine alpha factor in terms of a climate normalization using new eta factors, which provide an indication of the ozone-processing power of the atmosphere relative to a benchmark date.
Inserting η Cl and η Br into the formulation for the time-propagation of EESC, as in Eq. (9), teases out differences in the capability of the inorganic halogen background of the stratosphere to destroy ozone as a function of future climate scenario.
Using this treatment, we find that the emission of large quantities of CH 4 and N 2 O, as in the RCP 8.5 emission scenario,