Interactive comment on “ Technical Note : SWIFT – a fast semi-empirical model for polar stratospheric ozone loss ”

Abstract. An extremely fast model to estimate the degree of stratospheric ozone depletion during polar winters is described. It is based on a set of coupled differential equations that simulate the seasonal evolution of vortex-averaged hydrogen chloride (HCl), nitric acid (HNO3), chlorine nitrate (ClONO2), active forms of chlorine (ClOx = Cl + ClO + 2 ClOOCl) and ozone (O3) on isentropic levels within the polar vortices. Terms in these equations account for the chemical and physical processes driving the time rate of change of these species. Eight empirical fit coefficients associated with these terms are derived by iteratively fitting the equations to vortex-averaged satellite-based measurements of HCl, HNO3 and ClONO2 and observationally derived ozone loss rates. The system of differential equations is not stiff and can be solved with a time step of one day, allowing many years to be processed per second on a standard PC. The inputs required are the daily fractions of the vortex area covered by polar stratospheric clouds and the fractions of the vortex area exposed to sunlight. The resultant model, SWIFT (Semi-empirical Weighted Iterative Fit Technique), provides a fast yet accurate method to simulate ozone loss rates in polar regions. SWIFT's capabilities are demonstrated by comparing measured and modeled total ozone loss outside of the training period.


Introduction
The importance of stratospheric ozone as a climate active gas has long been recognized (e.g.Forster and Shine, 1997;Gauss et al., 2006;Forster et al., 2007).Accounting for the interactions between climate change and ozone in climate models is usually accomplished by interactively coupling a stratospheric chemistry module to a global climate model (GCM): dynamical fields from the GCM provide input to the stratospheric chemistry module at a time step compatible with the GCM.The ozone fields generated by the chem-35 istry module are returned to the GCM, which uses them to calculate the radiative forcing.The radiative forcing induces changes in atmospheric temperatures which in turn influence dynamics, the distribution of trace gases and temperaturedependent chemistry.Such models, generally referred to 40 as chemistry-climate models (CCMs) in contrast to GCMs without a chemistry scheme (Austin, 2002;Eyring et al., 2006Eyring et al., , 2007)), are very computationally expensive.Thus, applying them to multiple greenhouse gas (GHG) or ozone depleting substance (ODS) emissions scenarios is prohibitive.

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The effects of ozone on climate are therefore usually incorporated into GCMs by prescribing ozone as an external boundary condition.In particular, in the majority of the CMIP5 simulations presented in the IPCC report, ozone is prescribed (IPCC, 2013, section 9.1.3.2.6).However, this approach re-50 sults in modeled ozone fields that are not internally consistent with the future evolution of the atmosphere in the GCM.Furthermore, prescribed ozone fields are unlikely to be aligned with the internal dynamics of the model, i.e. values typical of the polar vortex may be specified in regions outside of the 55 vortex as a result of vortex excursions within the model, or lower stratospheric air may be prescribed in the upper troposphere if the model has an anomalously high tropopause on that day.In such a model configuration atmospheric dynamics cannot interact with polar ozone chemistry.Incoher-60 ence between prescribed ozone and the GCM dynamics is likely to affect ozone radiative forcing and the resultant pattern of surface climate change.Thus, there is a need for fast stratospheric chemistry schemes that can be incorporated into GCMs.
A number of fast stratospheric chemistry schemes have been developed in the past.The Cariolle scheme (Cariolle and Déqué, 1986) expands the ozone continuity equation as a Taylor series up to first order around three variables, that is, the local value of the ozone mixing ratio, the temperature, and the overhead ozone column.The 8 coefficients for the resultant terms in the expansion are derived from a 2-D photochemical model, independently for each latitude and altitude.The scheme has been used in GCMs to model ozoneclimate interactions (Braesicke et al., 2006) and in chemical transport models to simulate ozone trends (Hadjinicolaou et al., 2005).An updated version of the Cariolle scheme, which includes a term for heterogeneous ozone chemistry, is used e.g. in the operational model of the European Centre for Medium Range Weather Forecasts (ECMWF) (Cariolle and Teyssèdre, 2007).
Linoz (McLinden et al., 2000;Hsu and Prather, 2009) is similar to the Cariolle scheme and calculates the net production of ozone as a function of the same three variables as the Cariolle scheme.Small perturbations about a chemical climatology are used to calculate coefficients of a Taylor series expansion of the net production in terms of these three variables.The system is highly constrained, with 7 tables each providing 216 profiles of parameters.Version 1 of Linoz excluded heterogeneous chemistry, and as a result there was no Antarctic ozone hole and no enhanced Arctic ozone loss during cold winters.Version 2 incorporates the polar stratospheric cloud (PSC) parameterization scheme of Cariolle et al. (1990).Both the Cariolle and Linoz schemes rely on a statistical representation of the sensitivity of the ozone ten-95 dency to the three controlling variables and are therefore unlikely to be applicable outside of the dataset on which they were trained.The FASTOC scheme (Bourqui et al., 2005) uses a large set of pre-computed transfer functions to mimic the response of a stratospheric chemical box model.It is not 100 tuned to present-day conditions and does not include any relaxation to a prescribed climatology in the region of active chemistry.
The SWIFT (Semi-empirical Weighted Iterative Fit Technique) model described in this paper is different in approach 105 from the Cariolle and Linoz schemes.It is a semi-empirical model as defined in the approach of Huck et al. (2013).The first version of SWIFT described in this paper includes heterogeneous polar ozone depletion only, which is by far the strongest anthropogenic perturbation of the state of the ozone 110 layer.The current version of SWIFT is conceived as a "proof of concept" and a version that is better suited for the operational use in a GCM is in development.This version will include a full treatment of extra-polar processes.
Rather than linearizing perturbations about some climato- To include the chemical mechanisms that are relevant for polar ozone loss the model describes the evolution of four 140 prognostic variables (ClONO 2 , HCl, total HNO 3 , and O 3 ) and two diagnostic variables (ClO x =Cl + ClO + 2 ClOOCl and HNO 3 in the gas phase) throughout winter, starting from prescribed initial conditions.All variables represent polar vortex averages of the respective species on a given verti-145 cal level, i.e. the model calculates only one value per time step and variable, which is representative for the whole polar vortex at this vertical level.A system of coupled differential equations describes the changes of the prognostic variables due to the relevant chemical mechanisms.The diag-150 nostic variables are derived from the prognostic variables at each time step.The model is driven by the daily values of the fractional vortex area that is cold enough to allow the existence of polar stratospheric clouds (Fractional Area of PSCs, FAP) and by the 24 h average of the fraction of the vortex 155 area that is exposed to sunlight (Fractional Area of Sunlight, FAS).Time series of FAP and FAS throughout the winter are derived from ECMWF ERA Interim meteorological reanalyses (Dee et al., 2011).
SWIFT is a model of chemical processes that influence po-160 lar ozone, which calculates chemically induced ozone change rates.In the training described in section 2.3 these rates are fitted to observations of chemical ozone loss rates from the Match program (Rex et al., 1998).Here we only show these chemically induced ozone losses as calculated by SWIFT, 165 not the ozone field itself.To construct an ozone field, ozone transport can be added externally by adding a climatological vortex average ozone source from the subsiding motion inside the polar vortex.When coupling SWIFT to a GCM, the transport of ozone should be carried out by the advection scheme of the GCM and the chemically induced changes as calculated by SWIFT should be added once a day.
For the other prognostic variables (vortex averages of ClONO 2 , HCl and total HNO 3 ) the chemically induced rates of change are much larger than the slow changes due to slow cross isentropic transport or mixing across the edge of the polar vortex.Hence their seasonal evolution is dominated by chemical processes.For these species the training (section 2.3) is done by fitting the seasonal evolution of their mixing ratios to satellite observations.That means that the small transport induced changes in these species are implicitly included in the fit parameters.The good performance of the model (see Section 3) justifies this approach.Hence, when coupling SWIFT to a GCM, these species do not need to be transported by the GCM.
In this initial version of SWIFT the model runs are performed on one fixed potential temperature surface close to the altitude where maximum ozone loss occurs.
In summary, in its current version SWIFT should be used to calculate ozone loss rates rather than the absolute abundance of ozone.The ozone loss rates from SWIFT can directly be used in a GCM environment that includes the transport of ozone and uses the chemically induced changes from SWIFT to approximate the ozone field.
The implementation of SWIFT into a GCM will basically proceed as follows: The rates of change of ozone in the polar vortex will be calculated for the small number of vertical levels of the GCM which are in the vertical range where heterogeneous ozone depletion is the dominant process.At every level, the vortex edge and the appropriate values of the vortex averages of ozone, FAP and FAS will be calculated at the beginning of a 24 h time step.The only species that is transported is ozone.The other species as HCl are represented by a single vortex average value per level, which is calculated internally and not communicated to the GCM.These values are initialized at the beginning of the model run and are only modified by the rates of chemical change produced by SWIFT.SWIFT will now be run with FAP, FAS and the mixing ratios as input at every level and will return a chemical rate of change for ozone and the other species at every level.The rate of change of ozone will be added to the mixing ratios of ozone of all grid points inside the polar vortex edge.Ozone needs to be transported either with the transport scheme of the GCM or with a future transport module of SWIFT.Outside of the polar vortex, values for the mixing ratios of ozone can either be prescribed from a climatology or will be calculated from a future extra polar module.

Model equations
Polar ozone chemistry is well understood (e.g.review articles by Solomon, 1999, or von Hobe et al., 2013).Rather than encapsulating this chemistry in full detail, the SWIFT model is conceptual, i.e. instead of representing each individual chemical reaction by individual terms in the equations (as is done in full chemical transport models), the bulk effect of chemical mechanisms is considered.

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More than 90 % of the overall chemical loss of ozone during polar winter is due to the combined effect of the ClO + ClO, ClO + BrO and ClO + O catalytic ozone destruction cycles (Frieler et al., 2006).Figure 1a shows that the 24 h average ozone loss rate by these cycles at 50 hPa is a fairly 230 linear function of the concentration of ClO x (Cl + ClO + 2 ClOOCl).The reason is that non-linearities in the dominating ClO + ClO and ClO + BrO cycles mostly cancel (Fig. 1b  and c).
Since ozone loss can only occur in sunlight, it is also 235 a function of the time that the air mass is exposed to sunlight.Hence, the vortex-average ozone loss can be written as: with 240 where [. ..] denotes the mixing ratio of a species and d is an empirically determined fit parameter (as the parameters a-h and z in the following equations).The detailed approach to determine the values of the parameters is described in Sect.2.3.In principle d can also be derived from Fig. 1, which Prognostic equations would link d to the kinetic parameters in the model that has been used to produce Fig. 1.Equation ( 2) shows that estimating the vortex-average ozone loss rate requires good estimates of the evolution of ClO x through the winter.To estimate ClO x , the model needs to represent the key mechanisms that convert the reservoir species ClONO 2 and HCl into ClO x and vice versa.Once the concentrations of ClONO 2 and HCl have been determined, the concentration of ClO x is calculated from: where [Cl y ] is the overall amount of inorganic chlorine, which can be assumed to be constant in an individual air mass during any given polar winter.
The evolution of vortex-averaged ClONO 2 and HCl is estimated by: and where A, B, C, F , G and H represent the effects of chlorine activation and deactivation by the chemical mechanisms 265 described in Sects.2.1.1 and 2.1.2.The model equations are summarized in Table 1 and the terms used in the equations are given in Table 2.These terms are described in detail below.Cl 2 photolyses readily at wavelengths longer than those required for the ozone loss process.Hence, at sunrise most Cl 2 that may have formed during night will photolyse before the sun is high enough for efficient ozone loss to occur.During day Cl 2 cannot build up in significant quantities.Therefore, 280 the photolysis step can be ignored in a conceptual model of the ozone loss process.In terms of ozone loss the system of Reactions (R1) and ( R2) is equivalent to a system that directly produces ClO x in the initial heterogeneous Reaction (R1).Unless HCl is very low, the rate of Reaction (R1)

Chlorine activation mechanisms
285 depends only on the surface area density of the PSC particles and the concentration of ClONO 2 : The factor [HNO 3 ] • FAP represents the availability of reactive surfaces in a vortex-average bulk sense.

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Only when HCl concentrations become very low is the reaction also limited by the uptake rate of HCl on the PSC particles.The rate of Reaction (R1) then also depends on HCl concentrations.For HCl concentrations below 1 % of Cl y , A is defined as: Term G represents the effect of The efficiency of this process depends on the concentration of ClONO 2 and the availability of sunlight: During winter this is a minor loss channel for ClONO 2 , but in spring it controls the repartitioning between ClONO 2 and HCl in the Arctic.With the exception of the last few weeks in Arctic winters, the model would do well without this term, 305 and it is not very important for the calculated ozone loss.Term H accounts for the effect of the heterogeneous reaction followed by photolysis of HOCl Reaction (R5) is rapid during daytime.For the purpose of the conceptual model it can be included in Reaction (R4) based on the same arguments that have been discussed for the Cl 2 photolysis in term A. Reaction (R4) is efficient only at tem-315 peratures well below the PSC formation temperature threshold (Wohltmann et al., 2013).If FAP is large, temperatures in the core part of the cold region will typically be well below the PSC formation temperature threshold so that term H starts to become relevant.Hence this mechanism is assumed

Term Expression Remark
to start being efficient only if FAP exceeds a certain threshold, which is represented by the parameter y: Equation ( 9) uses only the fraction of FAP that exceeds the threshold of y, assuming that only in the central region of large PSC areas temperatures will be sufficiently low to make Reaction (R4) efficient.

Chlorine deactivation mechanisms
Term B describes the chlorine deactivation by formation of ClONO 2 , which results from the photolysis of HNO 3 followed by the fast reaction of NO 2 with ClO: Unless ClO concentrations are very low, Reaction (R7) is fast and can be ignored in the conceptual model: i.e.ClONO 2 is assumed to directly form from Reaction (R6).
[HNO 3 ] g denotes the mixing ratio of HNO 3 in the gas phase.
If ClO x , and hence ClO, are very low, Reaction (R7) also limits the production of ClONO 2 .For ClO x less than 5 % of Since significant dehydration occurs in the Antarctic, the late winter abundance of total water is reduced to about 25 % of 360 the levels commonly found in the Arctic, also reducing the concentrations of OH by the same factor.Therefore an additional scaling factor of 0.25 is used in the term F for the Antarctic: 2.1.3Sequestration and irreversible removal of HNO 3 The processes described above regulate the balance between ClO x and the reservoir gases HCl + ClONO 2 .Other than FAP and FAS, the only remaining inputs required to solve the model equations are total and gas-phase HNO 3 (c.f.Terms A 370 and B in Sects.2.1.1 and 2.1.2).Because of strong denoxification during polar winter (heterogeneous conversion of NO x into HNO 3 on cold background aerosol, where NO x denotes the sum of all shortlived nitrogen oxides), N 2 O, HNO 3 and ClONO 2 are the 6 M. Rex et al.: SWIFT -a fast model for polar stratospheric ozone loss only nitrogen oxide species that exist at significant abundances at that time.Under polar winter conditions N 2 O is inert, and the abundance of ClONO 2 is about an order of magnitude smaller than that of HNO 3 .Hence, the total abundance of HNO 3 is not altered much by chemistry during polar winter.
The only process that significantly changes total HNO 3 in the model is denitrification, i.e. the irreversible removal of HNO 3 due to sedimentation of HNO 3 -containing particles.Denitrification only occurs if either individual PSC particles persist sufficiently long (many days) to grow to sizes of a few micrometers, or if temperatures fall so low that water ice can accumulate on the PSC particles, which lets them grow rapidly.Both processes require large values of FAP: the slow growth of particles can only occur if air mass trajectories exist that stay within the potential PSC region for many days, requiring large PSC areas.Furthermore, when ice temperatures are reached, conditions are very cold and PSC areas are typically very large.Hence, in the model, the denitrification process is only triggered if the threshold value y for FAP 395 is exceeded: The fraction of HNO 3 in the gas phase is calculated from the total HNO 3 abundance at each time step by: The first term represents the gas-phase HNO 3 outside of the area where temperatures are below the PSC formation threshold (here gas phase equals total), and the second term includes the average fraction z of HNO 3 still in the gas phase in areas where temperatures are below the PSC threshold.The latter includes the fact that PSCs will only form in parts of the region where they are thermodynamically stable, due to the nucleation barrier (Pitts et al., 2007).410

Initialization
The prognostic variables are initialized at the beginning of the winter (1 December in the Arctic and 20 May in the Antarctic).Since the model is conceptual at this stage, the abundances of the chemical species are normalized, and the initial concentrations for the three different families are set to unity: The partitioning of Cl y between HCl and ClONO 2 at 460 K is taken from Fig. 1 of Harris et al. (2010), which is based on an analysis by Santee et al. (2008) of data from the Microwave Limb Sounder (MLS, Livesey et al., 2011) on the 425 Aura satellite and data from the Fourier Transform Spectrometer, which is part of the Atmospheric Chemistry Experiment (ACE-FTS, Bernath et al., 2005): For long-term studies, the secular variation of [Cl y ] can also be set to represent the long-term evolution of Equivalent Effective Stratospheric Chlorine (EESC; e.g.Newman et al., 2007), an estimate of the total effective amount of halogens 435 in the stratosphere.To compare the normalized model abundances with observations of vortex-averaged mixing ratios, the following scaling factors have been used for 460 K: ).Match is an approach to derive chemical ozone loss rates from coordinated ozonesonde observations (e.g.Rex et al., 1998).[Cl y ] has been determined from the sum of [HCl] and [ClONO 2 ] at the beginning of the winter.

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A model with initial concentrations based on the scaling factors would give identical results to the normalized formulation described here.It would then calculate absolute values for the vortex-average mixing ratios and ozone loss rates rather than the normalized values shown here.The normal-455 ization moves the degrees of freedom, which usually are in the model initialization, to the scaling factors, an approach that is convenient for such a conceptual model.

Training of the model
The fit coefficients a-h, y and z of SWIFT (Table 3) are 460 chosen such that the model best represents measurements of HCl, ClONO 2 , gas-phase HNO 3 and ozone loss rates as derived from observations.For this procedure, HCl and HNO 3 measurements from MLS, ClONO 2 from ACE-FTS and ozone loss rates from Match are used.For HCl, ClONO 2 465 and HNO 3 , vortex averages have been calculated from the individual data points, and the vortex averages on the retrieval surfaces have been interpolated to the potential temperature surface of 460 K that is used in the model.Ozone loss rates from Match represent vortex averages and have 470 been retrieved on the model level.
FAP and FAS are calculated by assuming the vortex edge at the 31.2PVU potential vorticity contour.The area where the formation of nitric acid trihydrate (NAT) polar stratospheric clouds is possible is calculated from the equations given in Hanson and Mauersberger (1988) and divided by the vortex area to give FAP.For FAS, the area above a solar zenith angle of 95 To train SWIFT, the model parameters are fitted to minimize a cost function, which is defined as the sum of the absolute values of the differences between all observations (divided by the scale factors) and the corresponding model values.For the ozone loss rates, the individual differences were weighted by the reciprocal of the uncertainty of the respective observation.For HCl and ClONO 2 , the individual uncertainties of the vortex-averaged observations are assumed to be equal for all dates.
Calculating the differences from the normalized data ensures that the same weights are used for all chemical species, independent of their absolute abundance.But since ozone loss rates are two orders of magnitude smaller than the normalized abundances of the chemical species (ozone loss rates are on the order of % per day), their differences were multiplied by 50 to give them a weight in the cost function that is comparable to that of the chemical species.In addition, the ozone loss rates of the model have been averaged over 14 days to match the time resolution of the Match ozone loss rate observations.The average differences are calculated individually for all species, and these averages are summed to give the cost func-tion, weighted by the reciprocal of the average uncertainty of the measurements of that species.This results in identical weights for all species even if the number of available measurements is different.
The numerical algorithm described in Huck et al. (2013) 520 has been used to solve the optimization problem.The set of parameters determined by the optimization procedure is listed in Table 3.To limit the degrees of freedom in the fitting procedure, the "PSC threshold" parameter y has not been fitted but is estimated from Fig. 2.13 of WMO (2011).

3 Results
Figures To assess the interannual variation of the calculated ozone loss, the time integrated normalized mixing ratio loss at 540 460 K (i.e. a value ranging from zero for no loss to one for complete loss of ozone) is used as a proxy for the column ozone loss, by multiplying it with a factor of 260 DU.This factor has been determined by fitting the normalized mixing ratios to column loss observations.Figure 5 shows the inter-545 annual variation of the proxy total ozone loss compared with total ozone loss observations (updated from Rex et al., 2006).The agreement of the absolute values is caused by fitting the scaling factor to observations, but the correlation between the time series is striking.full chemical models.In principle, most of these parameters can be linked to the underlying reaction kinetic parameters that are usually determined from laboratory measurements.However, in SWIFT these parameters are trained on observations of the atmosphere, rather than on observations in the laboratory.It is important to note that these empirical parameters are intrinsic physical properties of the involved molecules and mechanisms, and do not change with changing climate conditions.Hence SWIFT will still give a good representation of the chemical conditions inside the polar vortices in a changing climate, unless the meteorological conditions become so drastically different from the range of present-day conditions that currently unimportant mechanisms become relevant.However, climate models do not suggest that such dramatic climate change will occur during the next century or so.SWIFT includes all major feedbacks between climate change and polar ozone loss.However, in its current version SWIFT does not include all potential feedbacks, e.g., changes in stratospheric age of air or changes of NO y or to-585 tal sulfate are currently not accounted for, but many of these can be included in future versions of the model.
The semi-empirical model described here can also be used for the ozone loss in individual air masses as a semiempirical box model.The parameters FAP and FAS would 590 then be defined to give the fractional time the individual air mass spends in PSC conditions or in sunlight, respectively, and a different set of fitting parameters has to be determined, e.g., by using a box model with full chemistry for the training of the semi-empirical model.(black;Rex et al., 2006).

Fig. 1 .
Fig. 1. 24 h ozone loss as a function of ClOx mixing ratios at 50 hPa.(a) Total, (b) by the ClO + ClO catalytic cycle, and (c) by the ClO + BrO catalytic cycle.

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Term A describes the loss of ClONO 2 and HCl and the production of ClO x due to the heterogeneous reactionHCl + ClONO 2 → Cl 2 + HNO 3 (R1)followed by the photolysis of Cl 2Cl 2 + hν → 2 Cl (R2) 275

5504Fig. 2 .
Fig. 2. Overview of SWIFT results and observations for the Arctic winter 2004/2005.All data are shown in normalized units (more details see text).(a) FAP (cyan) and FAS (magenta).Lines in (b)-(d) represent SWIFT results, dots represent vortex-averaged observations.(b) HNO3 (gas phase, gray, observations from Aura MLS).(c)HCl (green, observations from Aura MLS), ClONO2 (blue, observations from ACE-FTS), and ClOx (red, "observed" ClOx is derived by using a constant Cly minus the HCl and ClONO2 observations).(c) Ozone loss rates (observations from Match).The loss rates of normalized ozone have been multiplied by 50 to facilitate plotting on the same scale.Error bars represent 1σ statistical uncertainties.

Fig. 5 .
Fig.5.Year-to-year variability in total chemical ozone loss in the Arctic estimated from SWIFT (red) compared with observations (black;Rex et al., 2006).
chemical and physical processes known to affect the time evolution of these species.The model is not 120 required to be linear and can cope well with the significant non-linearities occurring in polar ozone chemistry.Since our model is based on an approach that tries to mimic the physical and chemical processes as close as possible it is expected to behave more realistically, especially in conditions that 115 logical state, SWIFT describes the seasonal evolution of the key trace gases driving ozone destruction in a set of coupled first order differential equations.The equations have terms based on the

Table 1 .
List of equations used in SWIFT.

Table 2 .
List of the terms used in the differential equations.

Table 3 .
List of parameters.
• in the vortex is calculated and divided by the vortex area.The model is trained on the seasonal evolution of these quantities during one Arctic winter (2004/2005) and one Antarctic winter (2006).In the Antarctic, Match ozone loss rates are only available for winter 2003, but MLS and ACE-FTS data is not available for 2003.Since the meteorology during the 2003 Antarctic winter was reasonably similar to that in 2006, and FAP and FAS for these two Antarctic winters are not significantly different, we have used the ozone loss rates from the Match campaign in 2003 for the 2006 2 and 3 show the evolution of the model species throughout the Arctic winter 2004/05 and the Antarctic winter 2006, respectively.Overall, the model reproduces the seasonal evolution of the key species and of the observed 530 ozone loss rates throughout these winters well.Figure4shows results for some additional Arctic winters, for which either satellite data or Match data is available for comparison.These winters cover a range of different meteorological conditions, including one with very late ozone loss (1996/1997), 535a warm winter with little ozone loss (1997/1998) and one with complicated dynamics, which is a challenge for this simple chemical model(2007/2008).