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 We compare tracer observations made during the northern winter of 1999/2000 with the results of simulations with a three-dimensional chemical transport model, driven by assimilated winds. During the course of the winter, very low concentrations of tracers of tropospheric origin (such as N2O) descend into the lower stratosphere within the polar vortex. The altitude of origin of this air has been a matter of debate in the literature; by midwinter, both observations and model results indicate a significant fraction of mesospheric air in the lower stratosphere. Observations from aircraft and balloon flights reveal markers of mesospheric air within the Arctic vortex in the lower and middle stratosphere. An artificial tracer introduced into the model mesosphere at the start of winter descends (being diluted as it does so) all the way down to the 450 K potential temperature surface by March. Modeled tracer-tracer relationships evolve through the winter in a way similar to observations, but the separation between vortex and extravortex curves is exaggerated, suggesting that the model exhibits excessive horizontal mixing within and into the vortex. The tracer-tracer relationships are used to identify partly mixed air as lying, in tracer-tracer space, in a region intermediate between the characteristic vortex and midlatitude relationships. Air lying in a collar region just inside the vortex edge is thus identified as being mixed, and this indicates excessive horizontal mixing in the model across the vortex edge.
 A three-dimensional chemical transport model, driven by assimilated winds, was used to simulate the evolution of a set of long-lived stratospheric tracers, chosen to reveal the model's transport characteristics. In this paper, we briefly describe the model calculations and illustrate the model tracer climatologies. The main emphasis, however, is on the tracer characteristics of the Arctic vortex (the descent of air inside the vortex and the effects of mixing into and within the vortex), and we compare critical indicators of model behavior with tracer measurements made during the Stratospheric Aerosol and Gas Experiment (SAGE)III Ozone Loss and Validation Experiment (SOLVE) in the winter of 1999/2000. As will be described in the following, the net descent of vortex air into the lower stratosphere is broadly in accord with observations: in particular, both the model and observations indicate significant penetration of mesospheric air all the way down to the 450 K isentropic surface. Tracer-tracer pairs develop distinct relationships within the vortex, but the observed difference between vortex and midlatitude relationships is exaggerated in the model. This discrepancy is ascribed to excessive mixing.
2. Model Details
 The chemical transport model used was the three-dimensional National Center for Atmospheric Research “MATCH” chemical transport model [Mahowald et al., 1997; Rasch et al., 1997], driven by assimilated meteorological data (from the NASA Goddard Space Flight Center) for the period 1 September 1998 to 31 March 2000. The input data, 6-hourly horizontal winds, temperature, and surface pressure, were interpolated from a 91 × 144 latitude-longitude grid, on 48 vertical “sigma” levels up to 0.0177 hPa, onto the model grid of 64 × 128 latitude-longitude points, with 52 levels up to a lid at 0.0062 hPa. The model vertical coordinate is hybrid sigma-pressure, becoming pressure above 72 hPa; the vertical resolution ranges from about 1.2 km in the lower stratosphere, to about 2 km near the stratopause, to about 4 km near the model top. The original data were first interpolated in the vertical, using cubic splines. At the three models levels lying above the top level of the assimilated data, horizontal velocities and temperatures were assumed uniform with height. (In the calculations described here, temperature was used solely for diagnostic purposes, to calculate diabatic heating rates and to locate isentropic surfaces.) In order to avoid spurious polar divergences that can be produced by a change in grid structure, the horizontal interpolation was performed by calculating vorticity and divergence, mapping them (together with temperature and surface pressure) onto spherical harmonics, performing a triangular truncation (at T21 resolution), and reconstituting the velocity, temperature, and surface pressure fields on the model grid. The choice of T21 eliminated small-scale features in the divergence, which are unconstrained by observations and therefore probably spurious, but without impacting on the large-scale flow. Vertical velocity was calculated from mass continuity on the model grid and set to zero at the top level of the model. Tracer advection in the model was effected through a flux form semi-Lagrangian advection scheme. (A description of the “SPITFIRE” advection scheme used here and of other aspects of the MATCH model can be found at http://www.cgd.ucar.edu/cms/match/.)
 A set of tracers was chosen to allow diagnosis of high-latitude transport characteristics in the model; the four tracers discussed in this paper are listed in Table 1. Each of them had a constant tropospheric mixing ratio specified everywhere below 400 hPa. For N2O, CFC-11, and NOy, sources and sink rates were prescribed from two-dimensional model output. Note that NOy was used solely as a diagnostic of model mixing: there is no attempt to include a polar sink through sedimentation, thus precluding any meaningful direct comparison with observations through the entire winter period. Age Γ was calculated according to the “ideal age” equation (Waugh and Hall, Age of stratospheric air: Theory, observations, and models, submitted to Reviews of Geophysics, 2002, and references therein):
Γ was set to zero below 400 hPa.
Table 1. Tracers and Their Characteristics in the Model Experiments
 First, a 10-year integration was run, with initial conditions as specified in Table 1, using 1 year of input fields (for 1 September 1998 to 31 August 1999) recycled for 10 years to produce adjusted tracer fields on 1 September 1999, which formed the initial conditions for the subsequent 7-month SOLVE run. Assimilated meteorological fields for the period 1 September 1999 to 30 March 2000 were used to drive the tracer model through the winter of 1999/2000.
3. Tracer Distributions
 Model distributions of age and N2O on 1 September 1999 are shown in Figure 1. The meridional distributions of the two tracers are similar, and in fact, the global scatter plot of age versus N2O (not shown here) is quite compact: there is little separation between tropics and high latitudes, consistent with previous stratospheric observations [Boering et al., 1996]. The model exhibits the pathology common to many models [cf. Hall et al., 1999] of producing ages younger than observed, the oldest stratospheric age in the model (on 1 September, as shown in Figure 1, or indeed at any time of year) being about 4.5 years in the high-latitude upper stratosphere and in the mesosphere, rather than about 6 years as deduced from CO2 observations in the polar vortices [Hall et al., 1999; A. Andrews et al., unpublished manuscript, 2001]. (In fact, in this same model driven by winds from a general circulation model, the age simulation improves dramatically when the pressure-based vertical coordinate is replaced by an entropy-based coordinate [Mahowald et al., 2002].)
4. Seasonal Variation in High Latitudes
Figure 2 shows the evolution in the model of N2O at the South Pole through a year. This should be compared with data from the South Pole in Figure 6 of Cheng et al. , showing similar behavior in South Pole observations of N2O during the winters of 1993 and 1995. The seasonal march of the isopleths follows a sawtooth pattern, with systematic isopleth descent from midsummer through late spring, at which time the vortex breaks down and the isopleths rapidly revert to their midsummer positions. The actual amount of descent of the tracer isopleths in the model through the year, decreasing from about 12 km in the middle and upper stratosphere to 2–3 km in the lower stratosphere, is comparable with that observed [Cheng et al., 1997]. However, there is a systematic upward displacement of the model isopleths relative to the observations (i.e., the modeled N2O concentrations are somewhat too high).
 Similar behavior is evident in the model Arctic. Figure 3 shows the evolution of zonal mean N2O at the North Pole: isopleth descent is sustained through the winter (except for a brief hiatus during a disturbed period in early December) until early March 2000, when the vortex weakens. The isopleth descent rate is relatively constant at fixed height through the fall/winter period but increases with altitude such that, between September and early March, the average rates of descent range from about 0.5 km per month in the lower stratosphere to about 1.5 km per month in the middle stratosphere. As a consequence, the typical isopleth descends rapidly in fall but slows as it reaches lower altitude. Because of the differential descent of the isopleths, the vertical gradient of N2O increases through the fall/winter period.
 A sequence of N2O profiles versus potential temperature θ at the model grid point nearest Kiruna is compared with observations for the same dates from the Lightweight Airborne Chromatograph Experiment (LACE) instrument (F. Moore et al., unpublished manuscript, 2001a) on the Observations of the Middle Stratosphere (OMS) balloon package and from the Airborne Chromatograph for Atmospheric Trace Species (ACATS) instrument [Elkins et al., 1996; Romashkin et al., 2001] on the ER-2 aircraft, in Figure 4. By November, a shelf of strong vertical tracer gradients has developed in the lower stratospheric profiles, similar to that evident in the LACE data on 19 November. The model shelf is located, however, about 70 K in potential temperature above that seen in the observations. This discrepancy implies either that (1) the initial field (on 1 September) had too much N2O at high levels (which would be consistent with the systematic discrepancy noted earlier in the Antarctic), (2) the isopleth descent rate in the lower stratosphere during fall is 15–20% too weak in the model, or (3) excessive mixing into the vortex is occurring in the model. Nevertheless, agreement improves later in the winter: see especially 5 March, where the model profile agrees very well with that obtained from the OMS flight. This improving agreement is at first sight surprising and may at least in part be coincidental: note the rapidly improved agreement between modeled and observed profiles in the course of a single week between 26 February and 5 March. However, over a longer period, improving agreement is also consistent with an error in the initial condition: the convergence of tracer isopleths has already been noted, and as will be seen below (Figure 5), the diabatic vertical velocity is convergent in high winter latitudes (greater cooling aloft), so that errors in vertical position actually decrease with time.
 Diabatic cooling rates were calculated from the heat budget and the model-determined vertical velocities. There is little systematic change in high-latitude cooling rates over the course of the winter. Zonal and monthly mean values of for December are shown in Figure 5. Mean diabatic cooling rates increase strongly with height in the Arctic, from around 1–2 K per day at 20-km altitude (about 500 K potential temperature), maximizing in the outer vortex, to 20 K per day in the vortex core at 40 km (about 1400 K), increasing further at higher altitudes. From Figure 4, the mean descent rate of the N2O isopleths through winter (19 November 1999 to 5 March 2000) is around 1 K per day in the vicinity of 500 K, which suggests that the isopleths within the vortex are descending at about the same rate as, or somewhat more slowly than, would be expected from mean diabatic cooling alone.
5. Descent of Mesospheric Air
 In the upper and middle stratosphere, the magnitudes of evident in Figure 5 are such that one might expect mesospheric air to descend all the way through the stratosphere by late winter. The N2O profiles in Figure 4 imply substantial isopleth descent, with mixing ratios of 20 ppbv reaching as low as 600 K (about 24 km) by March. It is not clear from the profiles that mesospheric air is involved at this level, as this mixing ratio isopleth had descended from around 38 km (about 1200 K) on 1 September (Figure 3). If the descending vortex air were unmixed, this would indicate that air located in the lower stratospheric vortex in late winter originates in the middle or upper stratosphere. However, direct evidence of a significant fraction of mesospheric air in the lower stratospheric vortex in March comes from two sets of observations. First, high-latitude observations of CO made from the Mark IV balloon flights of 3 December 1999 and 15 March 2000 show mixing ratios very much higher than typical stratospheric values. In December, elevated levels of CO were seen near the top of the profile at 32 km. The March data are illustrated in Figure 6. Mixing ratios of CO are elevated above 600 K, with values as high as 240 ppbv at 750 K. Elevated (though smaller) concentrations of CO at a similar altitude were also observed from ATMOS data in April 1993 [Rinsland et al., 1999]. The CO maximum in Figure 6 coincides with extremely low mixing ratios of N2O (less than 10 ppbv), ruling out the possibility of a tropospheric source for the CO. Rather, this air must have descended from the upper mesosphere, where CO is produced by the breakdown of CO2 [Allen et al., 1981]. An indication of the distribution of CO prior to the winter comes from measurements in November 1994 of CO in low and middle latitudes from the Atmospheric Trace Molecule Spectroscopy (ATMOS) Experiment instrument [Gunson et al., 1996]. These measurements show elevated values in the upper mesosphere (Figure 7); mixing ratios increase rapidly with height from a small fraction of 1 ppmv below 60 km to more than 10 ppmv near and above 80 km.
 A second line of evidence comes from ages determined from in situ CO2 and SF6 balloon observations within the vortex on 5 March 2000, which show major differences all the way down to 450 K, with SF6 age being much the older (A. Andrews et al., unpublished manuscript, 2001; F. Moore et al., unpublished manuscript, 2001b). The two age profiles Γ(θ) are shown in Figure 8, together with the difference . The only reasonable explanation for this difference is that vortex air has been influenced by the mesospheric sink of SF6 [Hall and Waugh, 1998; F. Moore et al., unpublished manuscript, 2001b].
 To investigate the descent of mesospheric air into the vortex, we ran an experiment with a conserved “mesotracer,” initialized on 1 September 1999 with a nominal mixing ratio of 1 ppmv everywhere above 1 hPa (about 48 km) and zero everywhere below. The evolution of this tracer is shown in Figure 9. Mesospheric air in the model descends down to about 25 km (near 600 K) by 1 January 2000 and all the way down to 16 km (near 400 K) by the end of winter (31 March 2000). Qualitatively, this behavior is consistent with demonstrations of the descent of mesospheric air under advection by winds from general circulation models [Fisher et al., 1993; Eluszkiewicz et al., 1995] and from assimilated winds, with vertical motion derived from radiation codes [Manney et al., 1994; Sutton, 1994]. The correspondence in the model between low N2O and mesospheric air is illustrated in Figure 6; note how mesospheric air in the model extends all the way down to the shelf in the N2O profile, although correspondence between elevated CO and the N2O shelf is not so close in the observed profiles. In fact, the mesotracer reaches lower altitudes (peaking about 100 K lower in potential temperature) than the observed CO. (Recall also that the initial concentration of the mesotracer was chosen arbitrarily, and so only the shape of its profile is of any significance.) While this difference could simply be a manifestation of model error, note that the initial condition for the mesotracer (1 ppmv everywhere above 1 hPa in September) is not a good representation of early fall CO whose mixing ratio, as noted above, is much smaller than this below 60 km and grows strongly with height through the mesosphere. A more realistic initial condition might place most of the tracer mass near 80 km, but its proximity to the model lid would preclude a meaningful simulation. It is possible, therefore, that the altitude difference between the peaks of CO and the mesotracer on 16 March is simply a consequence of a similar altitude difference in the initial condition. It should be noted, however, that on the basis of other tracer experiments with more modest differences in initial altitude of the tracer center of mass, the final altitude profile of the tracer was found to be relatively insensitive to the initial altitude.
 Returning to Figure 9, note that by 31 March most of the tracer has been flushed out of the mesosphere. The tracer descends in the high latitudes of both hemispheres. (The Antarctic vortex is still present for almost 3 months following initialization on 1 September 1999, whence the descent of the tracer at high southern latitudes in the early stages of the simulation.) By 1 January 2000, most of the tracer in the Northern Hemisphere (about 70% of the tracer mass below 50 km) is within the vortex. The tracer mixing ratios have been moderately diluted by this stage. Subsequently, there is substantial and sustained dilution of the tracer mixing ratios within the vortex through the winter: maximum mixing ratios in the Arctic vortex decrease from the initial value of 1 ppmv to 0.6–0.7 ppmv by 1 January and to 0.25 ppmv by the end of March. Outside the vortex, tracer mass is expected to descend slowly, as the rapid stirring and mixing within the surf zone ensures that tracers are advected by the gross vertical velocity, averaged across the surf zone [Plumb, 1996; Sparling et al., 1997], the effects of diabatic cooling outside the vortex being masked by mixing with air subjected to weaker cooling in lower latitudes. Despite this caution, it seems clear that most of the mesospheric air (or that large fraction that ends up in the Northern Hemisphere) descends within the vortex. In fact, a simple mass budget calculation reveals that if the entire global mesosphere were to be transported, without dilution, into the vortex, that air would occupy the vortex down to a pressure of about 25 hPa. Allowing for the modeled dilution of about 75% nonmesospheric air by the end of March, this diluted air would extend to about 100 hPa (16 km), in accordance with model results.
6. Tracer-Tracer Relationships
 The relationships between CFC-11 and N2O in the extratropical stratosphere from the model and observations are shown in Figures 10 and 11 for 19 November 1999 and 5 March 2000. On 1 September (not shown) the model relationship is fairly compact, though with some spread in the curved region, with the high-latitude points on the inner part of the curve. By 19 November (Figure 10) the scatter has increased considerably. The LACE data from the 19 November OMS balloon flight lie along the inner part of the curve, and in fact the colocated model profile is quite close to the observations. Between November and March (Figure 11), the envelope of the modeled relationship changes little outside the vortex; rather, the evolution of the modeled relationship is dominated by concentration into two dominant curves representing vortex and extravortex air and by the separation and straightening of the vortex curve. The development in the model during fall of increasing spread on the concave side of the preexisting curve is indicative of mixing into the vortex, as described by Plumb et al. . This mixing is consistent with the dilution of the mesotracer during the same period, but the latter is occurring at higher altitude. The subsequent evolution, especially the reducing curvature, during winter is indicative of mixing within the vortex. In fact, the development of a compact vortex relationship implies that interior mixing is stronger than any mixing across the vortex edge since the latter, by injecting midlatitude air with different tracer-tracer characteristics, will tend to produce scatter into the relationship.
 Most of the observations during this period were made within the vortex, with the exception of measurements made on the ER-2 transit flight of 15 March. These extravortex data show reasonably good agreement with the modeled extravortex relationship. Within the vortex, however, the substantial change in the modeled CFC-11:N2O relationship is not evident in the observations. While the data do show a clear vortex/extravortex separation in March, the shift in the relationship observed within the vortex during this time, though real [Ray et al., 2002], is much smaller than that in the model, and the separation between vortex and extravortex relationships in March is not as great as that in the model. This implies either that the model mixing within the vortex is excessive or that mixing across the vortex edge is too weak [Plumb et al., 2000]. In order to determine whether this mixing is occurring horizontally or vertically, we used tracer-tracer relationships to identify the location of the mixed air.
 The characteristics of mixing within the model are best revealed through the NOy:N2O relationship, which exhibits the strongest curvature of the model tracer pairs and for which the curvature extends over a wide range of N2O space; thus the relationship is sensitive to mixing over the same wide range. (Because of the absence of any sedimentary loss of NOy in the model, we make no attempt here to use the relationship to compare model with observations, but we use it purely as a model diagnostic.) The relationship in the model (north of 40°N and above 100 hPa) on 1 February 2000 is shown in Figure 12. There is clear vortex/extravortex separation at this time, with most points lying very close to one of the two curves characterizing vortex and extravortex air. In addition, there is a smaller population of points lying between the two curves. This population, which for convenience we label as “intermediate,” comprises air that either is in transition (i.e., recent midlatitude air that has been subjected to mixing but has not yet been mixed enough to acquire “vortex” characteristics) or is the product of mixing between air masses with both vortex and extravortex characteristics. We first define certain regions in the NOy:N2O relationship. The lines in the figure mark two regions, the lower box encompassing “vortex” data points and the upper region (enclosed by the polygonal box lying between the highly populated vortex and extravortex curves) containing “intermediate” points. This identification is not all-inclusive: not all such points are contained within the given regions. Figure 13 shows the location of “vortex” points in the lower bin at 480 ± 20K, confirming that this air fills the vortex. There is no intermediate air at this altitude. In the potential temperature range 725 ± 25 K, there are intermediate points around the inner edge of the vortex (Figure 14), and vortex points deeper within (Figure 15). At the core of the vortex is air too low in N2O to appear in either bin; this is high-altitude air, originating in early winter in the mesosphere and upper stratosphere. Note that tracer-tracer relationships are sensitive only to mixing in regions of curvature in the relationship and that different indicators may exhibit different consequences of mixing. In particular, this finding of apparently “unmixed” air in the NOy:N2O relationship in the core of the vortex at 725 K is not inconsistent with the dilution of the mesotracer at the same altitudes: the mixing is (by implication) occurring between air masses located on the near-linear section (at low N2O) of the relationship where there is no sensitivity to the effects of that mixing.
 In fact, this last point illustrates the important fact that the classifications just made on the basis of the NOy:N2O relationship are specific to that relationship: they do not allow us to locate all mixed air. For example, while Figure 13 shows the vortex at 480 K to be filled with air that falls on the vortex relationship in NOy:N2O space, much of the same air in fact lies in the “intermediate” region in CFC-11:N2O space. Air that we have classified as intermediate in NOy:N2O space has been subjected to mixing, but the converse is not necessarily true.
 This extent of the downward penetration of mesospheric air in the model vortex, consistent with the observations of CO and of SF6-CO2 age differences, has important lessons both for the modeling of stratospheric composition and for our conceptual picture of the mesospheric circulation. The picture suggested by the model is that, to a first approximation, the mesosphere is completely flushed during a single winter. This is, in fact, consistent with conventional estimates of the meridional residual mean velocities, ranging from about 1 m s−1 near the stratopause to more than 10 m s−1 in the upper mesosphere, both systematically toward the winter pole: a velocity of 1.3 m s−1 is sufficient to move from pole to pole in 6 months. Moreover, the fact that much of this air (in the model) descends within the winter vortex has implications for our understanding of mesospheric dynamics. It is understood that the pole-to-pole mesospheric branch of the middle atmospheric circulation is driven by the mesospheric “gravity wave pump” [ e.g., Haynes et al., 1991], as depicted in Figure 16, which is analogous to the “Rossby wave pump” of the winter stratosphere [Holton et al., 1995]. The spectrum of upwelling gravity waves is clipped by selective breaking in the stratospheric jets, leaving the spectrum dominated by waves with easterly phase speeds above the winter westerlies and with westerly phase speeds above the summer easterlies. As a consequence, the wave-induced force produced when these waves break in the mesosphere is westward in winter, eastward in summer, both of which pump the circulation toward the winter pole. Now, if the mesospheric pumping were spatially homogeneous, mass continuity would dictate broad, relatively uniform descent throughout the winter hemisphere, a pattern that is difficult to reconcile with the picture we deduced above, which (together with the diagnosed distribution of ) appears to require more concentrated descent in high latitudes. If correct, this picture requires concentrated gravity wave pumping above the vortex edge (and thus above the polar night jet), which is consistent with the expectation that selective breaking of the westerly component of the wave spectrum should there be the most complete.
 Of course, high-latitude descent is also driven by processes other than gravity wave drag. Rossby wave drag is widely presumed to be the dominant driving mechanism in the stratosphere, although Rossby-wave-driven mean descent may maximize at the edge of, rather than within, the vortex [e.g., Schoeberl et al., 1992; Bühler and Haynes, 1999; Sobel and Plumb, 1999]. As the winter jet is established in fall and early winter, a transient meridional circulation is produced with high-latitude descent. However, the amount of descent is modest, compared with what has been described here. On quasi-geostrophic assumptions, the residual mean velocity is
where ∇ · F is the divergence of the Eliassen-Palm flux and is the mean zonal wind. Since the quasi-geostrophic problem is linear, the components of the circulation driven by the two terms on the right are simply additive. The component driven by the wave drag ρ−1∇ · F is the “wave-pumped” circulation described by Haynes et al.  and noted in the previous paragraph. (In fact, it is the circulation in steady balance with the instantaneous wave drag, not quite the same thing as the response to the evolving drag.) The second component is that associated with the evolution of the mean wind. During the summer-to-winter transition, a poleward circulation must accompany the development of the westerly polar night jet such that the Coriolis term generates the jet: the net poleward displacement δy associated with this circulation is simply , where is the change in wind speed over the summer-to-winter transition. The maximum is about 100 m s−1 at 60°N, giving δy ≃ 800 km. Now, mass continuity poleward of 60°N implies an average downward displacement δz = γ(aρ)−1∫z∞ρ δ ydz, where γ is the geometric factor cos (π/3)/[1 − sin (π/3)] = 3.73. Given that ρ = ρ0 exp (−z/H) and that our estimate for δy is the maximum value (it is smaller at most altitudes), it follows that δz ≲ 3.25 km. While not insignificant, this is so much smaller than the actual descent that we conclude that the actual descent is dominated by wave drag, rather than by transience.
 Thus the evidence for mesospheric air in the lower stratosphere implies that the gravity-wave-pumped mesospheric branch of the circulation comprises a significant fraction of the descent through the Arctic vortex all the way down to the lower stratosphere. This conclusion in turn implies that, just as we have come to recognize that general circulation models of the stratosphere must include a mesosphere, together with its gravity wave drag, in order to simulate stratospheric dynamics correctly, so chemical transport models of the stratosphere must allow high-latitude descent of air all the way from the mesosphere in order to simulate stratospheric composition correctly, even in the important region of the polar lower stratosphere, where most ozone loss occurs.
 The CFC-11:N2O relationship in the model developed an exaggerated vortex-midlatitude separation during the course of the winter. By using the modeled NOy:N2O relationship, we were able to identify the physical location of that component of the mixed air that is visible in this relationship; the tracer structure within the model vortex and its probable interpretation in the terms discussed by Plumb et al.  are as depicted schematically in Figure 17. High-altitude air descends within the vortex; at some stage, the tracer gradients across the vortex edge become sufficiently strong for even weak mixing to produce anomalous mixing lines on tracer-tracer plots (such as those discussed above) for which the canonical relationship is curved, thus producing what we have here called intermediate air. Subsequently (in time and in decreasing altitude), sustained mixing within the vortex transforms this noncompact, intermediate, tracer-tracer relationship into a distinct, curved, vortex relationship whose curvature steadily decreases. In time, the lower stratospheric vortex, containing air that has experienced this full sequence of events, is filled with vortex air, as we saw at 480 K in Figure 13. At higher altitudes, the transformation is incomplete: hence, at 725 K, the model vortex has undiluted air at its center, surrounded by a ring of fully mixed vortex air, which in turn, in the outer vortex, is surrounded by incompletely mixed intermediate air. As we noted earlier, these classifications of vortex and intermediate air masses are functions of the chosen tracer-tracer pair (in this case, NOy:N2O) on which the analysis is based, and the boundaries deduced from other tracer pairs (such as CFC-11:N2O) will in general be located differently.
 From a comparison of the observed evolution of the tracer-tracer relationships with those in the model, it appears that there is excessive internal mixing within the vortex: the continued evolution through the winter of 1999–2000 of the modeled CFC-11:N2O relationship is exaggerated in comparison with the observed behavior. From the spatial distribution of the mixed air, as defined on the basis of the modeled NOy:N2O relationship and summarized in Figure 17, it seems that the mixing processes responsible are occurring primarily in the horizontal. Spurious vertical mixing could conceivably be occurring in the model near the vortex edge, where the vertical gradient becomes locally large whenever the vortex edge has substantial slope, and in the lower part of the vortex where strong vertical gradients are formed by early winter. Indeed, the modeled CFC-11:N2O relationship does show intermediate air in the lower part of the vortex. However, it is difficult to explain the structure of mixed air revealed by the NOy:N2O relationship at higher altitudes, especially near 725 K, where vortex air is surrounded by a collar of intermediate air, without invoking horizontal mixing. On the face of it, excessive horizontal mixing could be a simple consequence of insufficient horizontal resolution: spurious numerical mixing resulting from the interpolations inherent in the semi-Lagrangian advection scheme should be reduced with higher spatial resolution. However, repetition of the final 7 months of the model run at doubled horizontal resolution led to almost no perceptible difference in the characteristics that have been described here. The mixing may therefore simply be characteristic of the input winds.
 We thank Susan Strahan and Steven Steenrod (NASA/GSFC) for providing the meteorological assimilation data, without which this work would not have been possible, and for advice on their implementation in the CTM. Darryn Waugh and Malcolm Ko provided the tracer sources and sink rates from two-dimensional model output. The modeling work at MIT and UCSB was supported by the National Science Foundation. Participation of the MIT group in the SOLVE experiment was supported by NASA.