Global Impact of the Antarctic Ozone Hole: Chemical Propagation

A model is presented for the chemical mixing of stratospheric air over spatial scales from tens of kilometers to meters. Photochemistry, molecular diffusion, and strain (the stretching of air parcels due to wind shear) are combined into a single one-dimensional model. The model is applied to the case in which chemically perturbed air parcels from the Antarctic stratosphere are transported to mid-latitudes and strained into thin ribbon-like filaments tmtil they are diffusively mixed with the ambient stratosphere. We find that the parcels may be treated as evolving in chemical isolation tmtil the final mixing. When parcels reach a transverse thickness of 50-100 m in the lower stratosphere, they are rapidly dispersed by the combination of molecular diffusion and strain. The rapidity of the final mixing implies a lower limit to the vertical scales of inhomogeneities observed in the lower stratosphere. For this sensitivity study we consider four types of Antarctic air: a control case representing unprocessed polar air; heterogeneous processing by polar stratospheric clouds (PSCs) that has repartitioned the CI,, and NOy families; processing that also includes denitrffication and dehydration; and all processing plus 90% oz6ne depletion. Large abtmdances of C10, resulting initially from heterogeneous processing of stratospheric air on PSCs, are sustained by extensive denitrification. (One exception is the case of Antarctic air with major ozone depletion in which C10 is convened rapidly to HC1 upon release of small arnotrots of NO,, as a result of the extremely nonlinear CI,,-NOy chemical system.) C10 concentrations in the mid-latitude stratosphere should be enhanced by as much-as a factor of 5 due to the mixing of air processed around the Antarctic vortex and will remain elevated for most of the following season. Chemical propagation of the Antarctic ozone hole occurs in two phases: rapid loss of ozone in the heterogeneously processed parcels as they evolve in isolation, and more slowly, a relative recovery of ozone over the following months. Another important effect is the transport of denitrffied Antarctic air reducing NO,, and hence the total catalytic destruction of ozone throughout the southern mid-latitudes. In Antarctic air that has already been depleted of ozone within the vortex, little additional loss occurs during transport, and the propagation of chemically perturbed air acts partially to offset the deficit at mid-latitudes caused by dynamical dilution of the ozone hole. In air which has not experienced substantial ozone loss, chemical propagation can generate a net ozone deficit of order 2-3% at mid-latitudes. that destroy ozone would be shut down; if, however, the parcel remains isolated chemically at mid-latitudes, ozone loss may continue. We present here a model for the chemical mixing of stratospheric air that combines photochemistry, molecular diffusion, and strain (i.e., the stretching of air parcels due to wind shear). These three processes can be represented by a high resolution, one-dimensional model with a grid scale of 10 ambient is shown to occur rapidly when the parcel reaches dimensions (cid:127)Now should be the smallest vertical structures of inhomogeneous composition observable in the lower stratosphere. The spatial resolution of studies using global models is insufficient to construct a one-dimensional model for the strain of air 2 and more slowly into HC1 residual perturbations to the chemistry of the mid-latitude by the reaction of C1 and CH 4. In our minimal case of stratosphere? Ozone loss is most rapid when C10 heterogeneous processing (case 1), when only the partitioning concentrations remain greater than 1 ppb for several days within families is perturbed, C10 levels fall rapidly from 2.5 following transport of parcels to mid-latitudes. C10-catalyzed ppb to 0.2 ppb in the first 8 days; C1ONO 2 increases to 1.9 loss of ozone may be truncated if the period of isolation of the ppb, becoming the dominant chlorine reservoir. Thereafter, the parcel is reduced by a more rapid rate of strain. A more concentrations of both C10 and C1ONO 2 decay slowly to the important factor governing C10 abundances in these steady state limit, with time constants of 10-20 days, as will are converted into HC1. depending on the amount of denitrification, enhancement of C10 and, of course, Antarctic ozone loss. In the case where denitrification occurs without ozone loss, C10 concentrations remain a factor of 5 above ambient levels after dilution.


INTRODUCTION 1988; Polar Ozone Workshop, 1988]; in particular, much of
The appearance of a hole in the stratospheric ozone layer the chlorine has been convened to highly reactive forms such over Antarctica [Farman et al., 1985;Stolarski et al., 1986] as C10. Air parcels from the Antarctic lower stratosphere that has prompted a range of theoretical investigations on the origin are spun off from the vortex and reach mid-latitudes therefore of this phenomenon and its implications for ozone globally. contain not only an ozone deficit but also significant In particular, questions have been asked about the impact of perturbations to the chlorine and odd-nitrogen compounds. this ozone deficit throughout the southern hemisphere The persistence of this chemical signature in these parcels, and mixed on the smallest scale resolved by the model, typically In order to handle realistic wind fields, the concept of strain greater than 2 km vertically and 1000 km horizontally. must be introduced. We no longer must know the structure of Perturbations to stratospheric chemistry over Antarctica are the wind field relative to the orientation of the fluid parcel, but associated with reactions on polar stratospheric clouds (PSCs, instead require that the velocity field changes in a quasisee McCormick and Trepte [1986]): chlorine is converted to random manner over the space and time scales of interest (i.e., reactive forms, and sometimes water vapor and odd nitrogen the "white noise" field of Kraichnan [1974]). The theory of are both removed by precipitation [Toon et al., 1986; Molina random straining in a fluid states that the decay of the shortest et al., Wofsy et al., 1988]. Within the dynamically dimension of a parcel is approximately exponential with time isolated vortex, sunlight drives chemical reactions involving [Batchelor, 1959;Kraichnan, 1974]. C10 and BrO and can deplete local ozone abundances by as The atmospheric strain rate, S (s-•), which determines the much as 90% [Molina and Molina, 1986; Hofmann et al., stretching of an air parcel depends on details of the wind field 1987; McElroy and Salawitch, 1989]. In addition, these and air parcels, and cannot be derived simply from knowledge chemical perturbations are mixed into the mid-latitudes by air of the general circulation. One estimate of the value of S may "peeling off" the vortex [Juckes and Mclntyre, 1987] and may be made from the observed shear of the zonally averaged lead to later photochemical loss of ozone outside of the vortex. wind, typically 10 -3 s 4 (i.e., a change of 10 m/s over 10 km in The magnitude of ozone depletion within the vortex depends altitude). If such a large value were typical of random strain on details of the chemical perturbation, particularly on all scales, then chemically distinct air parcels would rapidly denitrification [Salawitch et al., 1988]. In our model the thin to sizes below any measurable threshold in less than a extent of denitrification controls the time scale for day; however, this large shear is most effective in stretching photochemical recovery in the air parcels spun out from the the planetary scale dimensions of a parcel. The vertical vortex. The catalytic destruction of ozone is driven by high gradient of the zonal wind does not produce a random strain concentrations of C10; the process is terminated either by this with exponential decay of parcel thickness, but rather leads to photochemical recovery or by diffusive mixing with thinning of parcels with a geometric limit: a parcel of unperturbed air. Additional photochemical loss of ozone at indefinite vertical extent and a horizontal scale of 1000 km mid-latitudes is greatest for those parcels that have been will be stretched rapidly to a thickness of 5 km in 2 days, but chemically processed by PSCs but transported to mid-latitudes will take 10 days to reach a thickness of 1 km. Therefore a before experiencing the large depletions associated with the uniform wind shear can rapidly reduce planetary-scale features, Antarctic ozone hole. This in situ loss of ozone complements but random strain in the wind field is necessary to reduce the depletion of ozone at southern mid-latitudes that occurs further parcel sizes. when ozone-poor air from within the Antarctic vortex is Random strain in the wind field is expected to occur on all dynamically diluted into the mid-latitude stratosphere. We scales due to the interaction of wind shears in the vertical and examine here this chemical propagation of the Antarctic ozone horizontal and other turbulent processes that lead to hole.
In section 2 we present the model for strain and diffusion, showing examples for an inert tracer. In section 3 we document the photochemical model, give examples of the evolution of perturbed chemistries within an isolated air parcel, and examine the chemical interface that develops between perturbed and ambient air. In section 4 we summarize our results and discuss the implications for widespread ozone loss due to the propagation of perturbed chemistry associated with the winter polar stratosphere.

MODEL FOR STRAIN AND DIFFUSION
Within a fluid an arbitrarily defined volume, such as a parcel of air molecules in the atmosphere, is subjected to the effects of at least two dynamical processes on vastly differing scales: the almost random straining or stretching of the fluid voltune due to bulk motions, and true mixing with the neighboring fluid due to diffusive processes such as molecular diffusion [Batchelor, 1959;Kraichnan, 1974]. We have created a one-dimensional model that combines these two processes and is easily integrable into our photochemical model.

Random Strain
Wind shear is an elementary notion from fluid dynamics. If there is a velocity gradient in the wind field, then any initial structure in the atmosphere will be stretched out in a direction perpendicular to the gradient. The shorter dimensions of the structure will decay inversely with time. However, wind fields in the atmosphere are not static; the direction and amplitude of winds are constantly changing on all spatial scales. irreversible deformation and thinning of air parcels (e.g., twodimensional turbulence on isentropic surfaces [Mclntyre, 1988;Juckes and Mclntyre, 1987]). From numerical models [Juckes and Mcintyre, 1987], the e-folding time for decay of the smallest dimension of air parcels (i.e., l/S) is found to be less than a few days in the lower stratosphere; however, this model is two dimensional and does not resolve the vertical.
In this paper we adopt the value, S = 10 -5 s -•, for most calculations.
A compact parcel of air, defined, for example, by high concentrations of a passive tracer, will be stretched out into a convoluted ribbon-like structure [Batchelor, 1952;Welander, 1955;Kraichnan, 1974;Juckes and Mclntyre, 1987] whose minimum dimension decays as exp(-St). The derailed shape of the final structure is irrelevant. The strain-induced transformation conserves mass, and hence the distorted parcel may be treated as a large surface area with a thickness equal to the minimum dimension, e.g., a ribbon. It is across the surface of this ribbon that irreversible diffusive mixing occurs, resulting in the loss of the identity of the original air parcel.
We construct a one-dimensional model for the strain of air parcels by choosing the axis along the minimum dimension of the parcel and assuming that volume is conserved by expanding the surface area of the ribbon in the other (unresolved) dimensions. Diffusion (discussed in the next section) is effective only across this surface, that is, along the one dimension we are modeling. We choose a uniform grid with spacing Az (in centimeters) denoted by 2 i = i Az for i = 1 to N Concentrations of a tracer, Ci, are defined at each point 2 i. A perturbed parcel is defined by a set of points having values of molecules through air as a function of altitude in the midc i different from the ambient air, represented by the latitude stratosphere. Data for most atmospheric species, surrounding grid points. During the calculation the length of especially for the chemically reactive radicals, are lacking. For the grid contracts with time as this study we focus on altitudes centering on the Antarctic

Az(t) = Az(0) exp(-St) (2)
The mass of air associated with a given grid point, however, remains constant since the area perpendicular to the grid must increase proportionally. The integrated effects of chemistry or diffusion over the entire volume (parcel plus ambient) can be calculated using equal weighting for the grid points over all times.

Molecular Diffusion
The strain model presented above is dimensionless and becomes interesting only when physical processes of a given scale, such as molecular diffusion, cause interaction between adjacent grid points in the thinning parcel. The diffusion equation relating the concentrations is

•)c/i•t = D •2C/•Z2 (3)
where D is the diffusion coefficient (in square centimeters per second). We couple the strain and diffusion processes by solving the implicit diffusion relation

ci(t ) = ci(t-At ) + [ci_](t)-2ci(t)+ci+l(t)] D At / Az(t) 2 (4)
noting that Az changes with time (equation (2)). For boundary conditions we assume that the tracer gradient is zero at the endpoints (i=1, i=h0. Under atmospheric conditions, molecular diffusion is likely to be the most important final process contributing to the irreversible mixing of chemically distinct air parcels. Values for the diffusion coefficients of common gases are available and range from 1 to 100cm 2 s -1 under stratospheric temperatures and densities [Mason and Marrero, 1970]. Figure 1 shows examples of D for the diffusion of several ozone hole, about 20 km or 50 mbar, where most values of D cluster around 3.5 cm 2 s -]. In most of the following calculations we assume a uniform value of D for all species but also present cases with slower diffusion rates for larger molecules.

Combined Strain-Diffusion Model
Strain is the most important process acting on a chemically perturbed air parcel until the smallest dimension thins sufficiently so that molecular diffusion becomes dominant. In our calculations the process of mixing passes from a straindominated regime to a diffusion-dominated regime. While diffusion occurs continuously across the interface between two air parcels, the random strain sharpens the gradients that have been smoothed by molecular diffusion, nullifying its effects. We present here results from the combined strain-diffusion model for the mixing of an air parcel containing elevated concentrations of a passive tracer.  Figure 2 highlights the final days, beginning with day number 6, in which the parcel may still be identified as distinct from the background. The final dispersion of the parcel into the surrounding air is a rapid process, taking about 4 days for the peak concentration within the parcel to drop from greater than 95% to less than 10% above background. This time interval is independent of D in these calculations but occurs at different spatial scales depending on the value: about 20 m for D = 3.5 cm 2 s -•, and 60 m for D = 35 cm 2 s -1.
We define as a diagnostic the full width of the pulse at c = 0.9 (FW90; note that after FW90 drops to zero, the pulse   Figure 3b. The random strain acting alone produces a 2 days this percentile drops to zero. straight line equivalent to exponential decay with rate S In the stratosphere a parcel of chemically perturbed air that (equation (2)). When diffusion becomes significant, the curve is "peeled off" from the polar vortex is expected to have begins to depart from a straight line, and the value of FW90 dimensions on the scale of planetary waves or synoptic-scale decays more rapidly than an exponential. This point is clearly weather systems: a few kilometers in the vertical and several visible for each curve in Figure 3 and occurs at specific values hundred kilometers horizontally. Horizontal scales are of the parcel width for different values of D (Figure 3a) but is typically about 100 times greater than the corresponding almost independent of S ( Figure 3b). Diffusion alone cannot vertical ones [Holton, 1979;Juckes and Mclntyre, 1987]. As rapidly disperse the air parcels during this final stage without the parcel is stretched into a ribbon, the ratio of horizontal to the simultaneous and continuing action of random strain. vertical dimensions is expected to remain constant at first. On For most of the lifetime of the parcel, very little mixing smaller scales, strain associated with gravity waves and occurs with the ambient air, and chemical perturbations turbulence is not expected to maintain this 100:1 aspect ratio, initially associated with the parcel remain intact. Calculations and thus air parcels reduced to vertical thicknesses of 50 m show that diffusive mixing with the background air is may have coherent horizontal extents of less than 1 km. unimportant until the limiting diffusion length is reached, However, the final diffusive mixing of the parcel will occur by molecular diffusion acting most probably in the vertical day. The chemical integration of an air parcel can be direction [Juckes and Mclntyre, 1987]. computed over consecutive diurnal cycles, or a parallel series An obvious consequence of the random strain model is that of diurnal calculations can be used to force a photochemical one might expect to observe air parcels of different sizes at a steady state such that the diurnal cycle of each species repeats frequency inversely proportional to their minimum dimension, from day to day. The model for strain and diffusion presented in section 2 demonstrates that a chemically distinct air parcel may be treated in isolation until its final, diffusive mixing with ambient air. The duration of this isolation depends on the rate of random strain, which for values discussed here yields mixdown times of 5 to 20 days. In this section we follow the chemical evolution of heterogeneously processed stratospheric air, assuming that the parcel originated from within the Antarctic vortex and was dispersed rapidly to mid-latitudes by large-scale atmospheric motions. We define arbitrarily a sequence for the chemical perturbations to Antarctic air: ( [Prather, 1974], and (4) twilight photolysis for solar zenith angles up to 96 ø .

Photochemical Evolution
A parcel of Antarctic air is relocated to 45øS on November 1 and allowed to evolve in isolation for 20 days. This  HO2NO2 a, C1ONO2 a, BrONO2 a  HC1, C1, C12, C10, HOC1 Thus air that has already experienced large photochemical depletion of 0 3 over Antarctica (case 3) does not undergo much further loss when transported to mid-latitudes. On the other hand, air that has been chemically primed, but not exposed to sufficient sunlight to deplete the ozone over Antarctica, will experience significant ozone loss at midlatitudes.

C10 formed by the heterogeneous processing. Recovery of When ozone concentrations are reduced by a factor of 10 NO x takes longer when denitrification has occurred (case 2 (case 3), the chemical evolution is unusual, as above noted for versus case 1). With large ozone loss (case 3) the evolution of NO x is quite unusual: it is partitioned predominantly in the form of NO because 03 levels are so low; NO x concentrations grow rapidly after day 4 and approach steady state values; the sudden rise corresponds to the rapid drop in C10
concentrations (see below). After 20 days the ratio NOJNOy for case 3 reaches 0.42, more than twice that for the other cases; 85% of the NO x is in the form of NO for case 3 as compared with 33% under more typical conditions. The partitioning of the C1 x family is shown in Figures 4c  (C10) and 4d (C1ONO2). The initial perturbations to C10 are large, resulting in mixing ratios as much as a factor of 50 greater than steady state (55 ppt). Abundances decline as C10 Figures 4a and 4b look similar to cases 1 and 2. Thereafter, when NO x levels reach a critical threshold, the chemical system becomes highly nonlinear and the C1-C10-C1ONO 2 partitioning shifts dramatically in favor of C1 [see Prather et al., 1979]. As a consequence, formation of HC1 proceeds rapidly and a new steady state is reached in which the abundances of C10 (10 ppt) and C1ONO 2 (38 ppt) are a factor of 30 less than the equivalent case 2. Thus with substantial ozone loss the chlorine cycle is effectively shut down at mid-latitudes, and the impact of chemical perturbations disappears rapidly.

N¸ x. For the first 4 days the decay of C10 and the rise of C1ONO 2 in
What are the critical factors controlling ozone loss and is converted rapidly into C1ONO 2 and more slowly into HC1 residual perturbations to the chemistry of the mid-latitude by the reaction of C1 and CH 4. In our minimal case of stratosphere? Ozone loss is most rapid when C10 heterogeneous processing (case 1), when only the partitioning concentrations remain greater than 1 ppb for several days within families is perturbed, C10 levels fall rapidly from 2.5 following transport of parcels to mid-latitudes. C10-catalyzed ppb to 0.2 ppb in the first 8 days; C1ONO 2 increases to 1.9 loss of ozone may be truncated if the period of isolation of the ppb, becoming the dominant chlorine reservoir. Thereafter, the parcel is reduced by a more rapid rate of strain. A more concentrations of both C10 and C1ONO 2 decay slowly to the important factor governing C10 abundances in these steady state limit, with time constants of 10-20 days, as both calculations is the amount of NOy: denitrified air will sustain are converted into HC1. substantially greater concentrations of C10 within the parcel. Ozone depletion associated with the transport of chemically perturbed air from the Antarctic to mid-latitudes will not be strongly influenced by the parcel's path (i.e., its history of latitudes and altitudes). When a parcel remains at 65øS (instead of 45øS as shown above), the perturbations to C10 take longer to decay, the colder temperatures increase loss from the dimer cycle, and thus ozone loss relative to the control at this latitude is about 10% greater after 10 days. Similarly, when the parcel evolves at lower altitudes, chemical recovery is slower and ozone loss is once again slightly greater. At higher altitudes, such as 24 km, photochemical recovery of NO x is more rapid, C10 concentrations decrease correspondingly, and the relative ozone depletion is about 2/3 of that at 20 km. Dynamical considerations may overshadow side by the erosion of C10 within the parcel. These effects occur, as discussed below, but are greatly suppressed by the action of atmospheric strain that continuously compresses the diffusion boundary.

When alenitrification occurs (case 2), C1ONO 2 becomes a Let us assume that over Antarctica the NOy levels including less significant reservoir for chlorine during the first 20 days, any alenitrification have not changed during the past two and the recovery of C10 is limited by formation of HC1. decades, while total chlorine (C1 x plus halocarbons)has more
The observable signatures of this chemical interface are shown in Figures 6-8 for cases 1-3. The abundance of NOy, a conservative tracer here, maintains a sharp gradient (cases 2 and 3) until day 6 when diffusive mixing across the interface is first apparent; spatial sumcmre disappears by day 12. Chemically active species evolve in isolation (as per Figure 4) until day 6; observable changes in the parcel during the early period are driven predominantly by chemistry. Thereafter the chemical front becomes identifiable. Diffusive mixing dominates after day 8, and the concentrations evolve rapidly as the parcel is finally dispersed into the ambient air. Certain species exhibit unique, nonlinear behavior at the these small differences in chemical evolution since, for diffusive interface in cases 2 and 3. Both C1ONO 2 (case 2) example, parcels remaining near the edge of the polar vortex and BrO (cases 2 and 3) show a sharp peak in concentration (65øS) will experience much greater wind shear and possibly at the boundary, visible only about days 6-8, when both be mixed more rapidly. diffusion and chemistry are active at the interface. For

Chemical Fronts
The chemistry-strain-diffusion model combines strain and diffusion (equations (2) and (4)) with photochemistry (equation (5)) by splitting their respective operations. The time step is governed by the chemical package, and the strain-diffusion calculation is applied after each chemical time step, separately to each species across the entire grid. For most of the calculations shown below, the diffusion coefficient D is set to 3.5 cm 2 s -•, independent of species. We recognize that molecular diffusion results in larger species diffusing more slowly and, in one case, set D = 1.0 cm 2 s -1 for HNO 3, C1ONO 2, BrONO 2 and other species denoted by an asterisk in Table 1.
The calculations are set up in one dimension across the minimum thickness of the parcel, presumably the vertical dimension at the start. The one-dimensional grid is initialized with a parcel of heterogeneously processed polar air occupying 5 boxes at one end of the grid (effectively "doubled" to 9 boxes by the mirroring of the zero-flux boundary conditions) and with ambient mid-latitude air in the remaining 45 boxes.

The parcel is followed from the initial size (10 3 m per grid box) until the mixing is complete (<1 m per grid box).
Through the choice of boundary conditions and initial partitioning, the modeled domain maintains an average composition that is equivalent to an 89-to-9 mix of ambient-toperturbed air. The initial, kilometer-thick layer would have significant gradients from top to bottom in photolysis rates and chemical composition; however, we focus here on the evolution and mixing of that air originating and remaining near 20 km (i.e., no substantial diabatic heating) and calculate the entire chemical evolution of the parcel for conditions at that altitude.
One expects to see a complex chemistry develop at the boundary between the ambient air and the polar air. High levels of C10 diffusing outward from the chemically perturbed polar air parcel should encounter ambient levels of NO 2 and C1ONO 2, this peak can be a factor of 2 greater than the abundances on either side. The buildup of C1ONO 2 and BrO at the interface is temporary; the excess is returned to other reservoir species when the parcel finally disperses.  Figure 9 (for case 2). If a predominant reservoir of the chemical family on one side of the interface is a large, slowly diffusing molecule and a small, rapidly diffusing species on the other side, then the family abundance will accumulate on the side of the more slowly diffusing reservoir. For example, the C1 x that builds up in certain regions, particularly those with initially high C1ONO 2, will be chemically repartitioned thus further enhancing the 03 diffusing inward. At this interface therefore production of abundance of C1ONO 2 in this region relative to the case with C1ONO 2 should rapidly rise. Furthermore, ozone destruction uniform diffusion (compare Figures 7 and 9). The effects of would be enhanced on one side of the interface by the outward differential diffusion in these calculations are small, and the The budgets for odd oxygen, during the 12 days of mixdown and for the following 3 months, are summarized in   Tables 2 and 3. For the control case 0, Table 2 Table 3 summarizes the evolution of 0 3 and the O,` budget for the four test cases in the season following the final mixing.
In cases 1 and 2 the largest loss of 0 3 relative to the control occurs during the isolation period (the first 12 days), thereafter 0 3 increases relative to the control. (All cases, including the control, show continued ozone loss throughout this period.) In case 3 the originally assumed ozone depletion (90% in the Antarctic parcel, resulting in a 12% decrease after complete mixing) shows enhanced recovery relative to the control, with only a 9% depletion at the end of the following season. The largest factor in this photochemical recovery is the reduced NO,`-cycle loss.
Polar denitrification and beterogenous processing play an important role in the ozone budget of the lower stratosphere at mid-latitudes, beyond that associated with the creation of the ozone hole itself and its subsequent transport to mid-latitudes. In the cases studied here, after complete mixing the perturbed chemistry acts to increase ozone, predominantly through At 20 km altitude 45øS November. Ozone mixing ratios averaged reductions in NO,`-catalyzed loss. In the decades before the 2.51 ppm over the 90 day integration. Evolution of air consisting of recent buildup of stratospheric chlorine, this processing of the Therefore following the breakup of the polar vortex, chemical propagation of the Antarctic ozone hole occurs in two phases: rapid loss of ozone in the heterogeneously processed parcels as they evolve in isolation; and slower relative recovery of ozone over the following months. In the case of Antarctic air which has not experienced substantial ozone loss, chemical propagation generates an ozone deficit at mid-latitudes. In air that has already been depleted of ozone within the Antarctic vortex, chemical propagation acts in the opposite sense and can partially offset the deficit at midlatitudes caused by dynamical dilution of the ozone hole.

IMPLICATIONS FOR GLOBAL OZONE
The model for strain and diffusion presented here makes predictions about the size distribution of chemically coherent air parcels in the stratosphere that can be tested by observation. The primary uncertainty in this model is the strain rate. Fundamental information on strain and mixing in the stratosphere may be obtained, ideally, by an observational analogue to the numerical experiments of Juckes and Mcintyre [1987]. Analysis of potential vorticity maps on isentropic surfaces might provide a measure of the initial strain rate for large parcels but would be limited by the accurate spatial resolution of potential vorticity in the assimilated wind fields. The Airborne Antarctic Ozone Experiment has made extensive chemical and meteorological measurements in the Antarctic stratosphere with high spatial resolution [for example: Anderson et al., 1989;Fahey et al., 1989;Tuck et al., 1989]. Analysis of the AAOE data set [Winkler and Gaines, 1989], especially in the chemically heterogeneous region just outside the vortex, should provide information about the sizes of distinct air parcels and their rates of mixing.
How large a chemical perturbation occurs at mid-latitudes when heterogeneously processed air from over Antarctica is finally mixed into the background stratosphere? Based on these calculations we expect the Antarctic air to remain isolated for 7-20 days following its separation from the vortex and to mix rapidly and completely within 30 days. The volume of Antarctic air is small (<10% of the southern hemisphere), but the impact on the mid-latitude stratosphere could still be large, depending on the amount of denitrification, enhancement of C10 and, of course, Antarctic ozone loss. In the case where denitrification occurs without ozone loss, C10 concentrations remain a factor of 5 above ambient levels after dilution. Return of C10 to ambient levels is determined by the time to reform HC1, 20 to 60 days depending on latitude. This mechanism may explain the high C10 values observed by Brune et al. [1988]  will not contribute any additional ozone loss at mid-latitudes A simple extension of these results to the northern hemisphere would take into account that substantial Arctic ozone loss has not yet been observed. The occurrence of major heterogeneous processing by polar stratospheric clouds has not yet been demonstrated for the Arctic stratosphere, although there are preliminary indications of such [Brune et al., 1988;Solomon et al., 1988;Mount et al., 1988]. Under these conditions, the propagation of chemically perturbed air may lead to spatially extensive loss of ozone of order few percent over northern mid-latitudes at the end of winter. This additional depletion may explain the discrepancy between the observed changes in column ozone (approximately-5% at 45øN winter from 1969 to 1986) and the predictions of global models (-2%), as discussed by the International Ozone Trends Panel [see Watson et al., 1988]. Further analysis awaits publication of results from t•e Airborne Arctic Stratospheric Expedition of 1989 and incorporation of these effects into global models.
Fundamentally, the heterogeneous chemistry in the winter stratosphere is necessary to initialize perturbations to stratospheric chemistry, but denitrification or corresponding increases in atmospheric chlorine that result in greater abundances of chlorine than odd nitrogen are necessary for extensive and sustained global effects outside of the Antarctic ozone hole.