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 Coupled chemistry-climate model simulations are presented for the period 1951–2099 and 1951–2007. The model includes a tested parameterization for the production of active halogens from the source molecules. In run 1 the observed levels of chlorine and bromine are specified, as well as the sea surface temperatures (SSTs) from a coupled ocean-atmosphere model. Run 2 is identical to run 1 but observed SSTs are specified instead of model SSTs. In run 3 the bromine amount is reduced by 25% but otherwise the simulation is identical to run 2. The results show that the ozone hole is sensitive to SSTs and bromine amounts. For the period 1990–2007, when the ozone hole was fully developed, the area of the ozone hole was simulated to be largest in run 1 (11% smaller than observed), compared with underpredictions of 17% and 27% for runs 2 and 3, respectively. The effect of SSTs (difference between runs 1 and 2) is shown to arise from changes in the strength of the Brewer-Dobson circulation, which is weaker for the simulation with model SSTs. The sensitivity of the model results to bromine (difference between runs 2 and 3) indicates the need to include realistic bromine amounts as well as chlorine and may explain, in part, the substantial underpredictions of the ozone hole area in previous simulations. The results also suggest that a small residual ozone hole may still be present after 2070 and that the ozone hole may not disappear entirely this century.
 The accurate simulation of the Antarctic ozone hole remains an important challenge for climate models since, amongst other things, its development has contributed to the past poleward shift in the tropospheric westerly jet [Son et al., 2008], as well as contributing to the tropospheric southern annular mode signal via radiative processes [Thompson and Solomon, 2002, 2009; Gillett and Thompson, 2003; Chen and Held, 2007; Perlwitz et al., 2008]. Another reason for the need for accurate simulations of the ozone hole is that it is often used as a proxy for damage to the ozone layer, and the timing of its disappearance needs to be reasonably accurately predicted.
 For the chemistry-climate models (CCMs) which treat stratospheric processes to the best of our current abilities [e.g., Eyring et al., 2006], the simulated Antarctic ozone hole was typically found to be much smaller in area than observed. One reason for this is that most models underpredicted the amount of active chlorine in polar regions, partly due to inaccuracies in the simulation of the vortex edge region [e.g., Struthers et al., 2009] as well as differences in the photolysis of the source molecules. An additional reason is that for the simulations presented by Eyring et al., many of the participating models did not specify sufficient bromine. It now appears likely that there are additional unidentified sources of bromine from very short-lived substances which are estimated to be about one third of the known sources [e.g., Schofield et al., 2004, 2006; Sinnhuber et al., 2005; see also World Meteorological Organization (WMO), 2007, chap. 2]. CCMs are beset by additional problems in that the simulated Antarctic vortex is too leaky [Struthers et al., 2009] and lasts longer into summer than observed [Eyring et al., 2006, Figure 2]. These would tend to have opposite effects on the ozone hole, with the former leading to a less severe ozone hole but the latter maintaining the low ozone longer or even extending the period of actual destruction. The net effect is that the timing, development, and dissipation of the ozone hole during each spring season is not simulated accurately in detail and would be expected to vary from model to model. This suggests the need for caution in detailed comparisons between models and observations to ensure that such comparisons are truly representative of the model performance.
 Differences in the simulations of the ozone hole also arose in two sets of calculations of the Atmospheric Model with Transport and Chemistry (AMTRAC) which differed only in the sea surface temperature (SST) forcing dataset [Austin and Wilson, 2006], with model SSTs yielding a larger and deeper ozone hole than observed SSTs. It is possible that the reasons for this relate to the known impacts of the SSTs on tropopause characteristics and stratospheric circulation [Schnadt and Dameris, 2003; Fomichev et al., 2007; Austin and Reichler, 2008]. Polar processes are also affected by El Niño [e.g., Manzini et al., 2006; Garfinkel and Hartmann, 2007] which may not be well simulated by coupled ocean-atmosphere models, particularly those with a simplified stratosphere.
 Here, simulations from an improved version of our model, AMTRAC3, are investigated to try to establish reasons for the model underprediction in Antarctic ozone hole areas. Although we concentrate on the Antarctic ozone hole, diagnostics are also shown, when appropriate, for the Arctic. In particular, we explore the hypothesis that a systematic error in Antarctic ozone hole area arises from an incomplete specification of bromine sources. Also, the sensitivity of the Antarctic ozone hole to SSTs is investigated further to determine whether the results from the previous simulations of AMTRAC are confirmed. For those simulations, there are 45 years of directly comparable data [Austin and Wilson, 2006], three simulations of 15 years, but the interannual variability in the results was too large to form definite conclusions. It is certainly plausible that SSTs could have an influence on the ozone hole, since in addition to the influences shown by, e.g., Manzini et al.  and Garfinkel and Hartmann , tropical SSTs have been shown to affect the strength of the Brewer-Dobson circulation [Rosenlof and Reid, 2008]. Therefore the SSTs provide a way in which tropospheric climate change is communicated to the stratosphere in addition to the effect of greenhouse gas concentrations in causing stratospheric cooling. For CCMs (which are generally forced with the SST at the lower boundary) the SSTs are a climate related uncertainty in future ozone simulations which need to be considered in determining the dates of ozone recovery.
 Transporting a relatively large number of halogen source molecules (halons and chlorofluorocarbons) which have multidecadal timescales is a potentially large source of error in computing the halogen amounts. For example, in the Chemistry Climate Model Validation project (CCMVal) [Eyring et al., 2006] the concentrations of Cly varied amongst the models by a factor of more than two in the important polar lower stratosphere. We have made the decision that it is preferable to simulate ozone amounts accurately there than to risk the potential of incorrect halogen amounts. Many models have since improved their halogen simulation [e.g., Austin et al., 2010], although at the time of completion of our model simulations or the first submission of this paper we were not aware of these improvements. In AMTRAC the focus was on polar regions where the chlorine amount agreed well with observations, as designed by the parameterization, described in the appendix. Unfortunately, there was a chlorine high bias in low and middle latitudes [Eyring et al., 2006].
 AMTRAC3 is an improved version of AMTRAC, and is based on the recently improved model AM3. Changes have been made in both the climate core and in the stratospheric submodel.
 The major model differences in the core climate model are as follows:
 1. The first difference is the incorporation of the “cubed sphere” dynamical core [Putman and Lin, 2007]. The dynamical core has been implemented on a grid, based on the projections of the coordinates from the faces of a cube to the earth surface. This provides for a relatively uniform resolution over the entire globe, compared with the previous regular latitude-longitude grid. This model also has a more optimized performance on a massively parallel machine, since grid points are farmed out to the processors more uniformly in the horizontal, allowing more processors to be used with resulting lower wallclock time.
 2. The model convection scheme has undergone a complete overhaul since AM2, the previous core climate model for AMTRAC. The radiative properties of convective clouds, including shallow clouds predicted by the Bretherton et al.  scheme and the cell and mesoscale anvil clouds produced by the deep cumulus scheme [Donner, 1993; Donner et al., 2001; Wilcox and Donner, 2007] are also included.
 The major model differences in the stratospheric submodel, compared with AMTRAC, are as follows:
 1. The parameters of the chlorine and bromine scheme used in AMTRAC have been adjusted to agree better with observations. This has been achieved by reducing the effective photolysis rates (−dfi/dτ in Appendix A) of the CFCs in the lower stratosphere and increasing the rates in the tropical middle stratosphere to compensate. The high-latitude regions have not been significantly affected by these changes.
 2. Improvement in the scattering in the photolysis. The other major change in the photochemistry is that the scattering calculation in the photolysis lookup table has been corrected, following intercomparisons with the AM3 tropospheric chemistry scheme (L.W. Horrowitz, personal communication, 2008).
 4. The gravity wave forcing [Alexander and Dunkerton, 1999] has been adjusted in both hemispheres. In AMTRAC no PSCs were simulated in the Arctic because the polar vortex was too warm. When AMTRAC results were first obtained it was not clear whether the discrepancy was of dynamical or chemical origin. With the improved chemistry in AMTRAC3 the model polar temperatures needed to be adjusted. Following several experiments of 20 years' duration (results not shown) it became clear that in the nonorographic gravity wave forcing, the wave source terms, which are specified as a function of latitude, should be reduced. It will be shown later that this has resulted in realistic Arctic PSC amounts.
 5. The positions of the model vertical levels have been changed to be the same as the future Intergovernmental Panel on Climate Change (IPCC) version of the model (AM3). AMTRAC3 has 48 levels, as in AMTRAC, but there is increased stratospheric resolution, at the expense of mesospheric resolution. The model top layer is centered at 1.85 Pa, compared with AMTRAC, 0.33 Pa.
2.2. Model Simulations
 The simulations completed with AMTRAC3 are indicated in Table 1. Runs 1 and 2 were supplied in support of the Stratospheric Processes and their Role in Climate project CCMVal-2 [Eyring et al., 2008]. Run 1 corresponds to CCMVal-2 simulation REF-B2 and covers the period 1951–2099. It includes sea surface temperatures (SSTs) and sea ice taken from simulations of the coupled ocean-atmosphere model CM2.1 [Delworth et al., 2006; Knutson et al., 2006]. Greenhouse gas concentrations are taken from observations for the past and take future concentrations from SRES scenario A1b [IPCC, 2001]. Tropospheric CFC and Halon concentrations are specified from the A1 profile of WMO [2007, Table 8.5], but an additional one third Bry is included to allow for the additional unidentified sources that are likely to exist [WMO, 2007, chap. 2]. Throughout the simulation, a solar cycle is included in the radiative forcing and photolysis rates, using data from Lean et al. . For the future years, the solar cycles for the last five cycles are repeated sequentially. The initial conditions were taken from earlier simulations of the model which had undergone several stages of spin up during the model testing process. The initial state is therefore expected to be in approximate balance with the model simulation from the start, but nonetheless, the first few years of the simulation were generally ignored.
 Run 2 corresponds to CCMVal-2 simulation REF-B1. SSTs are taken from the Hadley Centre observed dataset [Rayner et al., 2006] (extended to the end of 2007), but otherwise the simulation and the initial conditions are identical to run 1. For run 3 the 1980 initial conditions were taken from run 2, with all the bromine values reduced by 25%. Otherwise, run 3 is identical to run 2. Run 3 therefore corresponds to just the currently known sources of bromine, ignoring the unidentified short-lived species.
3. Model Results: General Behavior
 It is now well established that polar ozone depletion is determined by a combination of low spring temperatures and high halogen concentrations [Solomon, 1999]. In this section we investigate these and related aspects of the model simulations.
3.1. Concentrations of Active Halogens
 For the simulations presented here chlorofluorocarbon (CFC) and halon amounts, observed and projected into the future, are specified in the troposphere. Rather than transport the individual chlorofluorocarbons, which would likely introduce large errors (see, e.g., Eyring et al. [2006, Figure 12] for the wide range of active chlorine amounts that may result), the chlorine and bromine rates of change are parameterized (see Appendix A). The most direct global comparison between observations and chlorine amounts is given by Figure 1a, which shows HCl from the model run 2 and from the Halogen Occultation Experiment [Russell et al., 1996]. The model generally underestimates the amount of HCl, which would imply, if the model chemistry is correct, that Cly is also underpredicted, especially in the tropics. Figure 1b shows the evolution of the 50 hPa inorganic chlorine and bromine amounts, Cly and Bry, for run 1 (model SSTs), averaged poleward of 60° latitude. Results for runs 2 and 3 (observed SSTs) are very similar for Cly and, for clarity, are not shown. Observations for the Southern Hemisphere Cly are estimates from Douglass et al.  and Santee et al.  for 1992 and Aura Microwave Limb Scanner for 2005. The bromine estimate is taken from WMO [2007, chap. 2] and assumes an estimated contribution of 5.5 ppt from very short-lived species. The parameterization reproduces observations for both Cly, and Bry, but there are large uncertainties in the atmospheric distribution of Bry, due to the uncertain concentrations of the short-lived species in particular.
3.2. Meridional Heat Fluxes
 The meridional heat flux, , where denotes the zonal average of x, and v′ and T′ are the perturbations from the zonal average for meridional wind and temperature respectively, is correlated with the stratospheric temperature [Newman et al., 2001; Austin et al., 2003]. Figure 2 shows the results obtained from the model results in which the daily heat flux at 100 hPa is averaged between latitudes 40° and 80° for the 2 month winter periods (July/August and January/February) and compared with the temperature at 50 hPa 1 month later, averaged over the latitudes 60°–90°. For convenience, the sign of v is reversed in the Southern Hemisphere to yield poleward heat flux values. The results are consistent with National Centers for Environmental Prediction (NCEP) observations, both in absolute amounts and in illustrating the correlation between heat flux and polar cap temperature. As indicated by Newman et al. , the heat flux is a measure of the resolved wave driving. When sustained over a period of time, the heat flux leads to increased adiabatic warming of the lower stratospheric polar regions.
 The details of the comparison are shown in Table 2. The correlations all exceed 0.6 and most of the correlations are above 0.75, which are statistically significant at the 99.9% level. Although the uncertainty in the gradient of the relationship is large, all the simulated values are consistent with observations. However, the simulations tend to have a larger gradient in the Southern Hemisphere than observed and a correspondingly lower temperature intercept, T0. Hence for typical heat flux values, the model agrees better with observations but is too cold for low heat flux values. This has important consequences for ice polar stratospheric clouds (PSCs) and indicates excessive model variability. In the Arctic no clear bias in the slopes exist, but the model tends to have lower wave activity and correspondingly lower stratospheric temperatures overall. Comparisons with previous AMTRAC simulations [Austin and Wilson, 2006] are also shown in Table 2 (TRANSA, TRANSB, TRANSC). These indicate major improvements in the Northern Hemisphere, with the newer model showing more sensitivity to heat flux. Since the heat flux is primarily determined by the resolved waves, while the gravity wave momentum deposition affects the polar temperature, the improvement in the relationship in Figure 2 is likely due primarily to the reduction in parameterized nonorographic gravity wave forcing. In the Southern Hemisphere, the previous AMTRAC simulations are in slightly better agreement with observations, in particular in showing slightly less sensitivity to heat flux. Again, this may be a result of the reduction in gravity wave forcing in AMTRAC3.
Table 2. Statistical Analysis of the Linear Regression Between the Area Averaged Temperature at 50 hPa Poleward of 60°N for February and March and the Meridional Heat Flux at 100 hPa Between 40° and 80°N for January and Februarya
Area averaged temperature is measured in K and meridional heat flux is measured in km s−1. Southern Hemisphere results are for the months August and September and July and August, respectively, and for convenience, the sign of the meridional velocity is reversed to give positive heat flux values. Here ρ is the correlation coefficient between the variables, T0 is the intercept of the line at zero heat flux, β is the gradient of the line, and σβ and σT0 are the standard errors of β and T0, respectively.
Run 1 1979–2005
Run 2 1979–2005
Run 3 1980–2005
 In a previous model intercomparison of this diagnostic [Austin et al., 2003], models showed a wide range in performance. The extended and revised NCEP analyses used here have resulted in substantial changes in the gradient of the heat flux versus temperature lines in both hemispheres (and corresponding changes in T0) so that the models presented by Austin et al.  are now generally in better agreement with revised observations than was apparent at the time of publication. More recent model intercomparisons [Eyring et al., 2006, Figure 3] have also shown the diagnostic, but a detailed statistical analysis comparable with Table 2 was not included. Nonetheless, there is no strong evidence that models have improved since Austin et al. .
3.3. SSTs and Stratospheric Forcing
Figure 3 shows the annual mean SST in the Equatorial Pacific (used to determine the Niño 3.4 index) for the experiments. Figure 3 also shows the meridional heat flux presented in section 3.2 and the tropical mass upwelling at 63 hPa, a slightly different level to that uss to reach the lower stratosphere, which is about 1 year in the tropics. After applying a 1-year phase lag to the SSTs, the correlation coefficient, ρ, between upwelling and SSTs is 0.44, 0.28, and 0.51 for runs 1, 2, and 3, respectively. The results for runs 1 and 3 are significant at the 95% confidence level using a two-tailed t-test. Model heat flux is poorly correlated with SSTs. However with model SSTs (run 1), the upwelling and heat flux values are smaller by 3% and 14%, respectively, than the values for runs 2 and 3 using observed SSTs, as indicated above.
 The mean Equatorial Pacific SSTs are 1.3 K lower in run 1 compared with runs 2 and 3, whereas for the tropical mean as a whole, the model SSTs are only 0.07 K lower than observed. Previous work from both observations and modeling [e.g., Garfinkel and Hartmann, 2007; Sassi et al., 2004; Manzini et al., 2006] has shown that El Niños influence the stratosphere by changing the planetary wave forcing. The possible implication of these studies therefore is that the higher observed SSTs in the Equatorial Pacific have led to increased tropical upwelling and increased meridional heat flux in our runs 2 and 3, compared with run 1 (model specified SSTs). The mechanism whereby tropical upwelling affects meridional heat flux has not been identified in these runs and would need further examination with further simulations, which is beyond the scope of the current work. Instead, in the next subsection we consider the possible effects on polar processes of the increased heat flux for observed SSTs.
3.4. Polar Stratospheric Clouds
 From the previous subsections it can be seen that the SSTs influence tropical upwelling and likely meridional heat flux. In turn, the heat flux affects the polar cap temperature in the lower stratosphere which influences PSCs and or meridional transport of ozone and trace species. An estimate of the extent of PSCs and their impact on ozone may be derived by considering the areas where the 50 hPa temperature is lower than 188 K (approximate ice PSCs) and 195 K (approximate NAT PSCs) integrated over time for the winter and spring seasons (Figure 4, solid lines). Henceforth, we denote instantaneous 50 hPa areas as ANAT or AICE when referring to PSCs and A195 or A188 when referring to temperature. A195 and A188, integrated over the year was shown in the work of Austin et al.  for a range of different models and observations. Figure 4 (broken lines) also shows ANAT and AICE for run 1, taking into account the local water vapor and nitric acid amounts. The differences between the curves are dominated by the differences in water vapor. These have particularly large effects on AICE or A188, especially prior to the year 1985. Also, for the Arctic, very few points below 188 K were encountered, and for much of the period the water vapor concentration was below 4.6 ppmv, needed to trigger ice PSCs at 188 K. Consequently AICE was negligible. For a period during the mid 21st century AICE increased and was higher than A188 due to an increase in water vapor to 4.8 ppmv. In general, in the model used here, the ice PSCs are not as important as NAT PSCs in contributing to ozone loss. Also, although ANAT has a larger overall trend than A195, this has a small impact on the details discussed in the remainder of the paper, for which the PSC effects are considered for the period 1990–2010. Therefore henceforth we concentrate on the cold areas, A188, and especially A195.
3.4.1. PSCs in the Recent Past
Figure 5 shows the results obtained for the cold areas for all three simulations, together with values derived from NCEP analyses. For 1977 and 1978, the Antarctic A195 values were found to be about 50% lower than all other years, with a larger fractional change in the A188. Since there appears to be no reason for these outlying data points, the values there have been replaced by those from the ECMWF Reanalysis (ERA-40) data. Generally, after about 1975, ERA-40 and NCEP analyses produced similar low temperature areas, although the values are larger in ERA-40, especially for the Arctic. Prior to about 1975, the ERA-40 values are much larger than NCEP and so the statistics in Table 3 cover only the period 1980–2000 for ERA-40.
Table 3. Comparisons Between Simulations and Observations for Selected Quantitiesa
NCEP or NIWA
Cold areas A188 and A195 are the areas colder than 188 K and 195 K on the 50 hPa surface, accumulated for the whole winter and spring period. The temperatures correspond approximately to the thermodynamic equilibrium temperature for ice and nitric acid trihydrate, respectively. The anomalous NCEP values for Antarctica in 1977 and 1978 have been replaced in the figures and in the statistics by the values computed from ERA-40 data. The ERA-40 data quoted are for the period 1980–2000 (see text). The values indicate mean quantities with 2σ uncertainty limits for the mean, where σ is estimated as s/ where s is the standard deviation of the values and n is the number of years included in the analysis. The units of A188 and A195 are hemisphere% × days. The Antarctic minimum, area, and mass deficit are in units of DU, 1012 m2, and Mt, respectively.
 Over Antarctica, the cold areas from all three simulations are in reasonable agreement with observations, except that A188 is larger than observed (see Table 3). This is related to the cold bias and the oversensitivity of the model to the heat flux, indicated in Table 2 and Figure 3: for situations when the meridional heat flux is lower than normal, the model temperature is lower than would have been observed. During the integrations A195 generally increased, although there is no similar indication in the NCEP data. However, trends in the data are not considered reliable due to the mix of data sources included and that they are not corrected for long term drift [Randel et al., 2009].
 Over the Arctic, the model results are a considerable improvement on previous simulations of AMTRAC [Austin and Wilson, 2006], which did not simulate any Arctic PSCs [Butchart et al., 2010]. In the new model simulations presented here, adjustments in the gravity wave forcing have considerably improved the agreement with NCEP data, and there are also ice PSCs present occasionally. However, in the Arctic the absence of PSCs in the previous model results may have been less critical, arguably for the wrong reason; ozone loss still occurred in the Arctic spring, but due to heterogeneous processes on cold aerosol, rather than on PSCs. The NCEP observations suggest that A195 has increased substantially since the middle 1960s, as noted in other works using similar diagnostics [e.g., Rex et al., 2006], from both radiosonde and data assimilation fields. Figure 5 does not show this clearly, but in the 11-year smoothed results (Figure 4) our results also simulate an increasing trend in Arctic A195. Recent analyses of results of the Canadian Middle Atmosphere Model [Hitchcock et al., 2009] also show an increase in simulated PSCs. Table 3 indicates that although the uncertainty is very large, the Arctic A188 values are simulated to be similar to that observed. The simulated Arctic A195 values are apparently too high, but for the period 1960 to 1979, the NCEP values are much smaller than for the subsequent period and therefore a climatology from NCEP data may be unreliable. Moreover, because of the large interannual variability during the period 1980 onward, the difference from NCEP data is only just significant at the 95% confidence level. For the full results shown in Table 3, the run 1 (model SST forcing) cold areas are about 20% smaller than in either runs 2 or 3 (observed SST forcing). The consistency between runs 2 and 3 in this respect is supporting evidence that the Arctic NAT PSCs have been affected by the model SSTs, although the difference between run 1 and run 2 is only significant at the 90% confidence level. Over the Antarctic, the model PSCs are only slightly larger in area for run 1 than for run 2, and this is also significant only at the 90% level. Note that there is a difference between runs 2 and 3 in Table 3 for Antarctic PSCs when identical periods are not considered. The suggestion is that the ozone hole has induced an increase in NAT PSCs by about 5%, although this is not confirmed in the NCEP data.
3.4.2. Future PSCs
 Over the full time frame of the run 1 simulation, three separate regimes can be identified in Antarctic cold areas (Figures 4 and 6). The cold areas generally increased from the start of the simulation until about 2010, decreased until about 2050 and then remained about constant until the end of the simulation. It is suggested that the initial increase is due to the combined radiative effect of ozone loss and CO2 increase. During the middle period, ozone recovery led to increased solar heating which reduced PSC amounts and counteracted the CO2 cooling. In the final stage as the rate of ozone recovery reduced, the CO2 cooling was likely balanced by the effects of the increase in the Brewer-Dobson circulation. Such secular variability is absent from the Arctic PSCs, although the envelope of peak values tends to increase during the simulations.
 With the Canadian Middle Atmosphere Model, Hitchcock et al.  simulate increases in June Antarctic PSCs in the 21st century, but a decrease in late October, similar to that found here. Their Arctic calculations also showed no clear overall trend in the 21st century.
4. Polar Ozone and the Factors Controlling It
 In the previous section, the model results have been investigated, focusing on differences in polar temperatures and cold areas and how they differ between the experiments. We now fit a linear regression model to the results to investigate the likely factors controlling polar ozone in the chemistry climate model. Here, we look at parameters which are easily derivable from routine model and observational data. It is their simplicity which has to some extent enabled them to pass the test of time. We do not address more complex parameters which could be explored and for a given model may address certain model weaknesses.
4.1. Linear Regression Model
 The following linear regression model is used:
where A(t) is the model polar ozone quantity and t is time in years. Cly and Bry are the inorganic chlorine and bromine amount at 50 hPa averaged over the latitude range 60–90° and SST (K) is the annual mean sea surface temperature in the Equatorial Pacific. HF is the heat flux at 100 hPa, , as described in section 3.2, and for convenience the sign of HF is reversed in the Southern Hemisphere so that HF is positive. F10.7 is the solar flux at 10.7 cm, commonly used to explore the sensitivity of processes to solar effects, and ε is the residual. The above equation was fitted using data from all three runs for the period 1980–2089 (166 points), and 1980–2059 for the ozone mass deficit, although only one simulation (run 1) extends beyond 2007. All three runs were used together in order to separate the Bry contribution from the Cly contribution. Using additional results prior to 1980 and after the stated end dates led to a poorer statistical fit, as the ozone hole was not well developed in the model. Use of other independent variables, such as the tropical mass flux did not yield statistically significant coefficients for the fits.
Equation (1) was solved for the coefficients ai using the least squares algorithm developed for the Numerical Algorithms Group (NAG) library (www.nag.com). Statistical uncertainties and the variance explained by the different terms were obtained from the NAG routine output and are standard statistical measures. Table 4 shows the regression coefficients calculated for the minimum Antarctic ozone and the maximum area of the ozone hole in each spring season simulated by the model.
Table 4. Linear Regression Fit for Polar Ozone Quantities Together With the One Standard Error for the Fita
Antarctic Hole Area
Antarctic Ozone Mass Deficit
Solar coefficients a5 were all small and insignificant and have not been shown. Here σ is the uncertainty for the fit given by the square root of the residual sum of squares divided by the square root of the number of points used in the regression. Units are Antarctic ozone hole area, 1012 m2; Antarctic ozone mass deficit, Mt; Antarctic and Arctic minima, Dobson Units (DU). The units of the independent variables of the regression are Cly, ppbv; Bry, pptv; SST, K; HF, K ms−1; and the regression equation itself is A(t) = a0 + a1Cly + a2Bry + a3 (SST − 300.0) + a4HF + a5F10.7 + ε(t).
210.4 ± 9.7
328.5 ± 13.9
−3.5 ± 1.2
−20.0 ± 2.6
−58.9 ± 3.5
−32.2 ± 5.0
8.75 ± 0.44
14.2 ± 0.9
0.1 ± 0.9
1.4 ± 1.3
0.40 ± 0.11
0.82 ± 0.21
3.3 ± 1.3
−1.5 ± 1.9
−0.45 ± 0.17
−0.64 ± 0.33
4.5 ± 0.6
−1.6 ± 0.9
−0.78 ± 0.08
−1.2 ± 0.2
4.2. Polar Ozone Minima
 The minimum ozone results are shown in Figure 7 in comparison with National Institute for Water and the Atmosphere (NIWA) ozone data [Bodeker et al., 2005]. The solid curves represent the reconstructions of the ozone minima from the regression equation. Qualitatively the simulations agree with NIWA analyses, although in the Antarctic, neither model simulation captures fully the secular evolution of minimum ozone. During the period 1995–2005 when the ozone hole is fully formed, all three model simulations overpredict the loss. This is due to the model cold bias, suggested in Figure 2, which leads to an increase in the vertical extent of severe ozone depletion. This leads to further cooling and the generation of more PSCs above and below the normal ozone hole region. During the early stages of the ozone hole, in about 1980, when differences in chemical depletion rates were not substantial, both runs 2 and 3 (observed SSTs) agree better with the ozone observations than run 1 (model SSTs). This suggests that the SSTs played a role in the respective simulations. A statistical comparison between observations and model results is given in Table 3. As noted above, each of the model simulations gives rise to excessive local ozone depletion of typically 20 DU in the column. Because of this, the low bromine specification appears to yield the best simulation, although for the wrong reason. The linear regression explains 88% of the variance, and all of the coefficients included in the regression fit are statistically significant at the 95% confidence level, except the bromine term.
 For the Arctic (Figure 7, bottom), the results have considerable scatter and again agree qualitatively with observations. Although the ozone amounts generally declined with increasing halogen amounts, other factors apparently have a more prominent role. The regression line fit reveals only that chlorine was playing a significant role in determining the minimum ozone. Other factors led to the high variance in the ozone minimum, and the regression line fit explains only about 40% of the variance. Neither the Arctic nor the Antarctic results show any significant sensitivity to the solar cycle.
4.3. Area of the Antarctic Ozone Hole
Figure 8 shows for the three simulations the maximum area of the ozone hole in each spring season, indicated by the 220 DU total ozone contour. The model results are similar to each other, although the low bromine simulation gave rise to significantly smaller areas. Early in the runs, the simulation with observed SSTs was closer to observations, but as the ozone hole developed fully, the simulation with model SSTs showed better agreement. It is possible that the observations underestimate the size of the early ozone hole because the relevant region may have been in twilight or darkness and therefore unobserved by satellite instruments. For example, a smaller ozone hole tends to be confined closer to the pole, and hence measurements need to be made within a few degrees of the pole, requiring more demanding measurements than if the ozone hole is very large. In contrast, no such bias would exist in the model.
 A detailed statistical comparison between NIWA ozone analyses and the model results is given in Table 3. All three simulations underpredict the observed ozone hole area, by 11%, 17%, and 27% for runs 1, 2, and 3, respectively. Eyring et al.  show comparisons between the previous Run A simulation of AMTRAC [Austin and Wilson, 2006] and Total Ozone Mapping Spectrometer data for the period 1990–1999. The mean results obtained for run 3 (82.3 DU and 19.0 × 106 km2) for the minimum and mean area are very similar to the results obtained with the previous model, 80.5 and 19.9, respectively. However, the previous simulations had too much interannual variability compared with observations whereas in the new results interannual variability is similar to that observed. It is therefore likely that if the previous simulations had been completed with more realistic bromine amounts, the results would have been closer to those of Run 2 (observed SSTs), although many changes have been included since the early simulations were completed. Hence a direct comparison is not completely rigorous.
 The regression coefficients in Table 4 suggest that both Cly and Bry have a significant impact on the simulated ozone hole area. The effectiveness of Bry compared with Cly is 1000a2/a1 = 46 ± 13(1σ) for the ozone hole area. This compares with a global average value of 52–71 calculated by a number of two dimensional models [WMO, 2007, chap. 8]. The regression analysis also indicates no significant sensitivity to solar processes.
Figures 7 and 8 suggest that the Antarctic ozone hole may not disappear this century. The model results obtained here are consistent with our previous results [Austin and Wilson, 2006] in simulating a small residual ozone hole of about 3 × 106 km2. Examination of the regression terms (equation (1)) indicates that this is primarily due to the amount of halogen projected for 2099 which is similar to the amount for 1975. The fact that an ozone hole of this size was not observed in 1975 may be due to the limited spatial coverage of observations then available. Again, whether the ozone hole will persist this long depends on whether the projected halogen concentrations are realized.
4.4. Antarctic Ozone Mass Deficit
 The “ozone mass deficit” is taken to be the total mass of ozone reduced below the 220 DU threshold [Bodeker et al., 2005]. In practice this is likely to be a lower limit to the true chemical ozone mass depletion, since ozone depletion from a climatological value above the 220 DU threshold is not considered. In principle, dynamical changes could also contribute to ozone reduction. Several authors [e.g., Huck et al., 2007] have suggested alternative diagnostics for the chemical depletion related to the ozone mass deficit, but these are not applied here and will likely be the subject of further investigations. The results obtained for the current simulations, averaged over the period 1 September to 31 October, are shown in Figure 9. The results are very similar to the maximum ozone hole area but show much more interannual variability. A statistical comparison of the results is given in Table 3 for the period 1990–1999, corresponding to observations given by Eyring et al. . The ozone mass deficit for the simulation with observed SSTs is in good agreement with the observed ozone mass deficit and has not changed materially since Eyring et al. . For the simulation with low Bry, the results were considerably smaller than observed. The large interannual variability in the ozone mass deficit likely arises from excessive variability in the model polar temperature (not shown). By contrast, although variability in the temperature has an impact (primarily in the observations in 2002), the maximum ozone hole area is more dependent on the chemistry.
 The regression fit for the ozone mass deficit is given in Table 4. This shows very similar results as the ozone hole area with negative contributions from the SSTs and heat flux and positive contributions from Cly and Bry. The ratio of the effectiveness of Bry to the effectiveness of Cly is given by 1000a2/a1 = 58 ± 15. This is slightly larger than the value obtained from the ozone hole area results and is close to the value obtained (52–71) for global ozone from two-dimensional models [WMO, 2007, chap. 8]. No significant sensitivity to the solar term was found in the results.
4.5. Antarctic Ozone and PSCs
 In the presence of high chlorine amounts, the rate of change of ozone during the spring period depends on the presence of PSCs, and hence over a period of time, the low ozone region will be determined by the region of PSCs. In practice the PSC edges will tend to be transported over a period of months, and this will tend to expand the region of low ozone. It might be expected, therefore, that the ratio, Γ between the area of the ozone hole and the seasonal mean area of the PSCs is an invariant of the atmospheric system. Because of the absence of extensive water vapor measurements, the presence of PSCs is taken to be indicated by a temperature of 195 K, which is also applied to the model results for consistency. Using the observations of NCEP temperature data and NIWA ozone data, the value of Γ was explored for A195 averaged over different months. The choice of period was not in practice very critical, but it was found that the ratio was most nearly constant when A195 for the winter and early spring were chosen (July to September) and compared with the maximum size of the ozone hole, as measured by the 220 DU contour. The results are shown in Figure 10 for the observations and for the model simulations of AMTRAC and AMTRAC3.
 In all cases Γ starts small in 1980 due to limited ozone loss and tends toward a near constant value from about 1992 onward, by which time chlorine was close to its peak value. The values of Γ are given in Table 5. For the AMTRAC simulations, Γ is slightly but significantly smaller for the simulations with observed SSTs (TRANS) than for the simulations with model SSTs (FUTUR), but both values of Γ are much larger than observed. For the AMTRAC3 simulations, a similar relationship is noted between the observed (run 2) and model SST (run 1) simulations, but the model SST results are much closer to the observed value of Γ.
Table 5. Ratio, Γ, Between the Maximum Area of the Ozone Hole and the Area of the Temperature Less Than 195 K at 50 hPa Averaged Over the Period July to Septembera
Values indicate mean quantities over the period 1992–2007 with 2σ uncertainty limits for the mean (excluding systematic errors). Here σ is estimated as s/ where s is the standard deviation of the values and n is the number of years included in the analysis. Results are presented for the mean of the three AMTRAC simulations with observed SST forcing (TRANS) and for the three simulations with model SST forcing (FUTUR). The observed value of Γ was calculated using NCEP temperature data and NIWA ozone [Bodeker et al., 2005].
1.35 ± 0.07
1.49 ± 0.04
1.15 ± 0.04
1.07 ± 0.05
1.00 ± 0.05
1.21 ± 0.03
 Note that the stratospheric warming year 2002 appears as only slightly unusual in the observed value of Γ, 1.31, compared to the 1992–2007 mean of 1.21, emphasizing the usefulness of the diagnostic in correcting for the influence of interannual variability in the dynamics. Over the 1992–2007 period, the observed Γ had a variance of 4.3%, indicating that Γ is a good approximation to an “atmospheric invariant” while chlorine remains high.
 In simulations of a coupled chemistry climate model, we have found that the ozone hole size and depth are sensitive to atmospheric bromine levels and to the specified sea surface temperatures. The model includes a previously tested parameterization for the production of active halogens from the source molecules. The chemistry climate model was run with SSTs specified from a coupled ocean-atmosphere model but which had a simplified stratosphere. The SSTs were different from observations in the Equatorial Pacific and it was suggested that this gave rise to the 6% difference in the size of the ozone hole. The ozone hole was also simulated to be sensitive to bromine amounts, with a 25% reduction in bromine giving rise to a 10% reduction in the size of the ozone hole.
 The simulation with observed SSTs had an ozone hole about 17% smaller than observed, possibly because the simulated Antarctic vortex edge may not be as sharp as observed [Struthers et al., 2009]. The discrepancy for the simulation with model SSTs was smaller (11%) but the precise mechanism whereby these differences occurred could not be pinpointed with the limited number of simulations completed. The SSTs had a small but notable influence on PSCs in the Arctic, and a similar sized but opposite effect in the Antarctic, although the results were only significant at the 90% level. Nonetheless, the model results are consistent with previous work which suggested that SSTs in the Equatorial Pacific have an influence on the stratosphere [e.g., Garfinkel and Hartmann, 2007]. This influence likely occurred via changes in ozone transport and meridional heat flux with the low bias in the Equatorial Pacific SSTs giving rise to less ozone transport in the southern hemisphere and a deeper and larger ozone hole. It follows that future simulations of the ozone hole are dependent on the accurate simulation of tropical SSTs and El Niños. Since the ozone hole in turn affects tropospheric processes [Chen and Held, 2007; Perlwitz et al., 2008; Son et al., 2008], the ozone hole is an important process coupling the stratosphere and the troposphere.
 The low bromine case simulated here represented only the long-lived bromine sources. Consequently, many of the previous simulations in the work of Eyring et al.  will have had ozone holes which are too small because of the underestimate of bromine and because the vortex may not be as sharp as observed Struthers et al. , in addition to any other weaknesses. Because of the close relationship between ozone mass deficit and ozone hole area, models biased low in bromine will also likely show a low bias in simulated ozone mass deficit.
 The model results were also investigated using linear regression which confirmed that the results were sensitive to the chlorine, bromine and SSTs. This analysis suggested that for the ozone hole area and mass deficit, the ratio of the effectiveness of bromine to chlorine is approximately 46 ± 13 and 58 ± 15 (1 σ), respectively. This is consistent with the range previously estimated for the impacts of bromine on the global ozone loss rate [WMO, 2007, chap. 8] but would not necessarily be expected to apply to the area of the ozone hole.
 The new model results presented here show improved representation of polar processes in comparison with the previous version of the model. Reductions in the gravity wave forcing has considerably improved the agreement with NCEP polar temperature data, especially for the Arctic. Unlike the previous model version, the current model simulates Arctic NAT PSCs with about the frequency estimated from temperature observations, and there are also ice PSCs present occasionally. Since the meridional heat flux is primarily determined by the resolved waves, while the gravity wave momentum deposition affects the polar temperature, the heat flux versus temperature relationship [Newman et al., 2001; Austin et al., 2003] has been considerably improved in comparison with observations. Together, these dynamical improvements have led to a better physical relationship between the area of the ozone hole and the PSC area than present in previous simulations of the model. In particular, we support a new quantity, Γ, the maximum ozone hole area divided by the mean area T < 195 K at 50 hPa for July to September, as a new diagnostic for testing the ozone hole performance of CCMs in comparison with observations. For high chlorine levels the value of Γ from observations has low variance (4%), even after including the stratospheric warming year 2002. Moreover, the simulation with model SST forcing differs from observations by only about 5%, which is likely within the systematic error of Γ.
 With the improvements in the model performance since the previous model version (e.g., Γ, see Figure 10), some confidence can be attributed to our model predictions concerning the recovery of stratospheric ozone. On the basis of these results, the disappearance of the Antarctic ozone hole by the end of the 21st century is not assured. Depending on whether current projections of halogens are realized, it is possible that a small, residual ozone hole of about 3 million km2 will continue to occur most spring periods until the end of the century. Such a conclusion is also dependent on climate model performance and in particular whether model uncertainties are significant at the end of century length integrations, including possible ozone low biases. Nonetheless, several chemistry climate models have now simulated residual ozone holes for the halogen projections used here [Austin et al., 2010]. This would therefore seem to confirm that the halogen parameterization is not a significant limitation on the model results, which are more influenced by climate model performance and scenario uncertainties.
Appendix A:: Computation of Inorganic Chlorine and Bromine
 Transporting the model species more than doubles the computational burden of the model and to reduce this burden, special code is included to derive the amounts of inorganic chlorine and bromine. For each of the source terms
where t is time and Ji is the photolysis rate of the ith CFC. From this, summing over each CFC, we obtain
where ni is the number of chlorine atoms in the ith CFC. Terms are included to represent CFC11, CFC12, CH3Cl, CCl4, CH3CCl3, and HCFC22.
 Integrating equation (A1) between time t and t + the stratospheric lifetime of the parcel, we have
where the integration is along the path of the air parcel trajectory. Writing
Subtracting the age of air from the time, we obtain the equation that is used in the model
 For the bromine species (CH3Br, Halon1211 and Halon1301), the equivalent equation to equation (A8) is
where the fractional loss is gi for each bromine species Bi included. In the model itself, because of the large uncertainties in the coefficients, the values of dgi/dτ are replaced by a single term, dg/dτ where
The coefficients −dfi/dτ and −dg/dτ have been estimated from measurements of the source molecules as a function of latitude and pressure using data from the Cryogenic Limb Array Etalon Spectrometer on the Upper Atmosphere Research satellite [Nightingale et al., 1996; Roche et al., 1998], together with values from the Cambridge 2-D model [Bekki and Pyle, 1994] for the unobserved species.
 Thus the rates of change of Cly and Bry are determined from the tropospheric concentrations (Ci(t − τ)trop and Bi(t − τ)trop) attained earlier, according to the age of air at the stratospheric location. This age evolves in the model due to climate change [Austin et al., 2007]. This procedure is similar to specifying the photolysis rates as a fraction of the delayed (by τ) tropospheric value, rather than as a fraction of the local CFC amount.
 Many approximations are built into this parameterization, including the assumption of a single age of air for all the air parcels reaching a given location at a specific time and the assumption that the coefficients are independent of time. It is also assumed that photolysis is the dominant process breaking down the CFCs, although reaction with OH and O(1D) play a role in practice. Nonetheless these additional processes are themselves photolysis driven. To resolve these problems the coefficients have been adjusted to agree with observations where these exist. However, finding suitable extensive measurements of Cly and Bry has been difficult and comparisons with measurements made after the simulations were completed have revealed some remaining discrepancies in the tropics in particular.
 J.A.'s research was administered by the University Corporation for Atmospheric Research at the NOAA Geophysical Fluid Dynamics Laboratory.