Corresponding author: M. L. Salby, Faculty of Science, Macquarie University, Balaclava Road, Sydney, NSW 2109, Australia. (email@example.com)
 The ozone hole changes considerably from one year to the next. It varies between conditions in which springtime ozone is strongly depleted to others in which ozone is only weakly depleted. Those changes are shown to closely track anomalous planetary wave forcing of the residual circulation. The strong coherence with planetary wave forcing is consistent with similar coherence of springtime temperature, which modulates Polar Stratospheric Cloud (PSC). By controlling the lifetime of PSC, anomalous wave forcing determines the net activation of chlorine and bromine and, hence, springtime depletion of ozone during individual years. The strong coherence with planetary wave forcing affords long-range predictability. It supports a seasonal forecast of springtime depletion, which, through the ozone mass deficit, perturbs ozone across much of the Southern Hemisphere during subsequent months of summer. Conditioned upon wintertime wave structure, a hindcast of springtime depletion faithfully predicts the anomalous ozone observed. A reliable forecast of tropospheric planetary waves would thus enable springtime depletion to be predicted. The current evolution of Antarctic ozone is dominated by dynamically-induced changes. Representing its climate variability, those large changes obscure the more gradual evolution of springtime depletion, like that associated with the decline of chlorine. The strong dependence on planetary wave forcing, however, enables dynamically-induced changes of ozone to be identified accurately. Removing them unmasks the secular variation of Antarctic ozone, the part coherent over a decade and longer. Independent of dynamically-induced changes, that component discriminates to changes associated with stratospheric composition. It reveals a gradual but systematic rebound over the last decade. The upward trend is shown to be robust, significant at the 99.5% level. Uncertainty in this trend is thus small enough to make the probability of it arising through chance alignment of error less than 0.5%. The discriminated component mirrors the decline of effective stratospheric chlorine, representing a gradual return of springtime ozone toward its level in 1980 of 10–15%. It enables Antarctic ozone to be tracked relative to changes of chlorine, CO2, and other features of climate more reliably than is otherwise possible.
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 Each spring, ozone over the Southern Hemisphere is marked by the formation of the ozone hole. Total ozone over the Antarctic then decreases, achieving values over the south polar cap smaller than 220 Dobson Units (DU), as much as 120 DU smaller than historical (pre-1980) values.
 Ozone-depleted air is confined to high latitudes, inside the polar-night vortex. By summer, however, the vortex breaks down. Ozone-depleted air is then released to subpolar latitudes, where it is mixed and eventually homogenized [e.g., Atkinson et al., 1989; Ajtic et al., 2004]. By diluting subpolar ozone, this process perturbs ozone across much of the Southern Hemisphere during summer (when, contrary to springtime, its horizontal distribution is comparatively uniform). Through photochemical adjustment, the perturbation eventually disappears a couple of months later [Solomon, 1990]. Although the depression of summertime ozone is small compared to springtime depletion over the Antarctic, it is expansive, prevailing over major population centers and when UV exposure is great. The magnitude of the summertime anomaly is set by the “ozone mass deficit”, the net reduction of ozone over Antarctica during spring [Bodeker et al., 2005]. When ozone-depleted air is released to subpolar latitudes, the latter dictates by how much midlatitude ozone is diluted.
 About this average picture, the ozone hole changes considerably from one year to the next. As shown in Figure 1, springtime ozone ranges from values as small as 100 DU in some years, representative of strongly-depleted conditions, to values approaching 200 DU in others, representative of nearly-undepleted conditions (at least those representative of 1980, near the start of the satellite record). Varying likewise is the ozone mass deficit during spring, which later perturbs summertime ozone at midlatitudes [Huck et al., 2005].
 Attempts to understand these interannual changes focused initially upon the QBO, which modulates midlatitude ozone [Hasebe, 1984; Garcia and Solomon, 1987; Lait et al., 1989]. Antarctic ozone tracked the QBO during a handful of years in the 1980s. However, it diverged thereafter, when the large interannual changes evident in Figure 1 became manifest. Most of the interannual variance is then carried by other influences, developed below.
 Subsequent efforts to understand Antarctic ozone during individual years considered planetary wave activity, which accounts for much of the interannual variance of ozone over the Northern Hemisphere [Fusco and Salby, 1999; Newman et al., 2001; Hadjinicolaou et al., 1997; Salby and Callaghan, 2002]. The ratio of Sep/Mar ozone over the Antarctic is marginally correlated to wintertime-mean eddy heat flux [Weber et al., 2003]. However, when averaged over the entire winter season, eddy heat flux accounts for a small fraction of the interannual variance.
 Much of that correlation, in fact, derives from just one year: 2002, when the Antarctic vortex behaved like the Arctic vortex, suffering an unprecedented mid-winter warming [Weber et al., 2003, Figure 5]. Exclusive of 2002, the ratio of Sep/Mar Antarctic ozone is uncorrelated to wintertime-mean eddy heat flux. Also depending on eddy heat flux is the areal extent of the ozone hole at spring equinox, chiefly through temperature changes in the surrounding collar [Newman et al., 2004]. With a correlation of ∼0.6, however, eddy heat flux accounts for less than 40% of the variance in springtime area. Further, the latter reflects changes of weakly-depleted ozone surrounding the ozone hole, not of strongly-depleted values in its core (Figure 1).
 Changes of the ozone mass deficit have been considered in relation to the eddy heat flux at 20 hPa and 60 S [Huck et al., 2005]. Along with changes of temperature over the South Pole, they follow interannual changes of eddy heat flux there - even during 2002, when the Antarctic vortex broke down prematurely [Hoppel et al., 2003]. Changes at 20 hPa, however, represent anomalous conditions in the middle stratosphere, which are largely determined by tropospheric behavior. Consequently, those changes are not the cause of anomalous ozone but, rather, are symptomatic of it: They derive from the same dynamical perturbations as anomalous ozone, originating in anomalous planetary wave activity in the troposphere.
 The current evolution of springtime ozone over the Antarctic is dominated by interannual changes. Reflected in Figure 1, those large changes represent the climate variability of Antarctic ozone, involving fluctuations that remain coherent over only a couple of years. They control anomalous summertime ozone, which affects midlatitudes during individual years. They also overshadow the more gradual evolution of Antarctic ozone, like that associated with the decline of stratospheric chlorine and bromine. In fact, owing to the prevalence of interannual changes, the recovery of Antarctic ozone is not expected to become manifest for several decades [World Meteorological Organization (WMO), 2006].
 Understanding interannual changes is essential for developing a seasonal forecast of springtime depletion and, hence, of anomalous summertime ozone over major population centers. Anomalous stratospheric behavior develops from anomalous tropospheric structure. It involves the residual mean circulation or Brewer-Dobson circulation, which is driven by Eliassen-Palm (EP) flux that measures the momentum transmitted upward by planetary waves. When integrated over latitude, upward EP flux at the tropopause is proportional to the gross (column-averaged) poleward drift of stratospheric air [Salby, 2008]. That motion converges over the winter pole to form downwelling and adiabatic warming, which controls Antarctic temperature during an individual winter. Wintertime temperature, in turn, controls PSC, through which chlorine and bromine are activated and ozone is ultimately destroyed. The nonlinear dependence of PSC makes chemical depletion inherently sensitive to temperature. PSC forms only at temperatures colder than ∼195 K, conditions that are achieved in the Antarctic stratosphere during polar night. What controls wintertime temperature, therefore, also controls PSC, activation of chlorine and bromine, and, thus, springtime depletion of Antarctic ozone.
 Here, we explore observed changes of ozone depletion over the Antarctic in relation to dynamical influences that control temperature. Following a description of the data, section 3 identifies changes of springtime ozone over the Antarctic that operate coherently with planetary wave forcing of the residual circulation. Anomalous springtime ozone, averaged over Sep–Nov and poleward of 70 S, is found to closely track upward EP flux at 70 hPa during the preceding months, averaged over Aug–Sep and poleward of 40 S. Section 4 then develops the relationship of wave forcing to anomalous temperature in the Antarctic stratosphere. The results are applied in sections 5 and 6 to perform a seasonal hindcast of springtime depletion. They are then used to isolate the secular variation of Antarctic ozone, the part that remains coherent over a decade and longer. Free of climate variability, that component discriminates to the systematic evolution of springtime ozone, including the climate signal associated with the decline of chlorine and bromine. The systematic evolution, like dynamically-induced changes that comprise the climate variability of Antarctic ozone, is validated against prospective changes: How springtime ozone in future years behaves in relation to the dependence on planetary wave forcing that was deduced from earlier years. The validation against future changes reveals that both components of the ozone evolution are robust.
2. Data and Analysis
 Total ozone has been observed almost continuously since 1979 by the Total Ozone Mapping Spectrometer (TOMS) and its successor, the Ozone Monitoring Instrument (OMI), instruments that operated on several satellites. Studied here is the most recent retrieval, TOMS-V8, wherein the treatment over regions of snow and ice has been improved [Wellemeyer et al., 2004]. Coverage of the Antarctic during Austral winter and spring is provided by the following platforms: Nimbus-7 (1979–1993), Earth Probe (1996–2005) and OMI (2004-present). Except for a gap between 1993 and 1996 (when coverage by auxiliary platforms was limited and sporadic), these satellites provide a continuous record of springtime ozone over the Antarctic - one that now spans three decades.
 Contemporaneous with the ozone record is the record of 3D dynamical structure in National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalyses [Kalnay et al., 1996]. The NCEP record provides global fields, including dynamical structure in the tropics associated with the QBO. From it, wave structure is derived at tropospheric levels and upward, along with the distributions of Antarctic temperature and EP flux (Appendix A).
 From the full monthly record of each field variable, we remove the climatological-mean annual cycle. The result defines the interannual anomaly, as a function of month and year. Anomalous springtime ozone over the Antarctic is compared against anomalous EP flux from the troposphere. Integrating EP flux over the latitudes where it is upward and during preceding months collects anomalous momentum that has been delivered to the stratosphere during those months when planetary waves influence the Antarctic vortex. Where that momentum is absorbed (and, hence, where residual mean motion is forced) depends on the critical line of planetary waves (e.g., the zero wind line). The critical line swings between the summer and winter hemispheres according to the sign of equatorial wind and, hence, the phase of the QBO.
 Together, fluctuations of EP flux from the troposphere and of equatorial wind associated with the QBO represent anomalous wave forcing of the residual circulation. They drive an anomalous residual circulation, which influences polar temperature through anomalous downwelling and adiabatic warming. The latter favors wintertime temperature over the Antarctic that is anomalously warm during years of intensified EP flux and equatorial easterlies, but anomalously cold during years of weakened EP flux and equatorial westerlies.
3. Influences on Springtime Ozone
 For the moment, we consider an abbreviated record, extending only until 2006. The relationship of ozone to other properties can then be validated against behavior observed after 2006. Spanning two and a half decades, the abbreviated record still provides a large population of realizations of the ozone hole and contemporaneous realizations of dynamical structure. Plotted in Figure 2 is anomalous springtime ozone over the Antarctic (deviation from the post-1980 climatological mean), averaged poleward of 70 S and over Sep-Nov: . According to Figure 1, reflects the seasonal-mean depression of springtime ozone over the Antarctic. The anomaly therefore describes the mean state of the ozone hole during individual years. Springtime-mean ozone is characterized by a decline during the 1980s, up to the early 1990s when the Nimbus-7 record ends. By the start of the Earth Probe record, the decline has vanished. Replacing it is a nearly constant background level, wherein values are ∼120 DU lower than those around 1980. Superimposed on both segments are substantial fluctuations from one year to the next. Notice that, in 1988 and 2002, large positive excursions restore springtime ozone over the Antarctic almost back to levels of the early 1980s.
 These large interannual fluctuations represent the climate variability of Antarctic ozone. Involving changes that remain coherent over only a couple of years, they dominate its current evolution. Any systematic evolution of springtime ozone at present is overshadowed by such variability. For this reason, the current evolution of springtime ozone cannot be distinguished in the raw record from simply a constant background level, as is readily apparent and widely recognized [e.g., Hofmann et al., 1997; Yang et al., 2008].
 The decline of springtime ozone over the Nimbus-7 record does not have a counterpart in upward EP flux from the troposphere. Exhibiting little systematic trend, EP flux in the SH contrasts with that in the NH, where EP flux does exhibit a trend over the same period as does NH ozone [Fusco and Salby, 1999; Salby, 2008].
3.1. Changes of EP Flux From the Troposphere
 To discriminate to ozone changes that depend on dynamical changes, the record of springtime ozone is high-pass filtered to fluctuations that operate on timescales shorter than decadal. As the timescales are widely separated, this can be readily achieved through regression onto a low order polynomial or spline, which is then subtracted from the full record (Appendix A). The resulting interannual anomaly of springtime ozone is plotted in Figure 3 (solid). Notice that, while it captures year-to-year swings in Figure 2, the interannual anomaly contains no systematic variation on timescales longer than a couple of years. Long-term evolution, including any systematic change (e.g., trend), must therefore be isolated to the component of springtime ozone independent of this one. Together with the accompanying structure of anomalous ozone (section 3.3), the fluctuations in Figure 3 describe interannual changes in the ozone mass deficit, which subsequently perturbs summertime ozone across the Southern Hemisphere. During individual years, springtime ozone deviates from its climatological mean by as much as 50–80 DU. The positive anomaly during 2002, which approaches 100 DU, is almost as great as the average depletion of springtime ozone (Figure 1).
 Superimposed in Figure 3 is anomalous upward EP flux at 70 hPa, averaged poleward of 40 S and over the preceding months of Aug-Sep, (dashed). EP flux has been scaled by its covariance with (see equation (1)), representing the component of springtime ozone that varies coherently with . Measuring anomalous wave transmission during late winter, closely tracks the record of anomalous springtime ozone. The two achieve a correlation of 0.94. Similar correspondence holds for averages over neighboring periods, latitudes, and levels. For example, ozone averaged poleward of 60 S and at 100 hPa averaged over Jul-Sep likewise achieves a correlation in excess of 0.90. Notice that the correspondence in Figure 3 holds even during large excursions in 1988 and 2002. The outstanding variance, the part that does not vary coherently with , is most apparent during the early 1980s.
3.2. The QBO
 Outstanding variance is considered in changes that are independent of fluctuations in . Represented by the component orthogonal to , they follow from the time series of springtime ozone and its correlation to :
where and are the respective std deviations. represents the component of anomalous ozone that varies independently of . (The procedure is tantamount to Gram-Schmidt Orthogonalization of unexplained variance, which is then projected onto a different predictor.)
 The component of independent of is explored in relation to the QBO. By controlling the critical line of planetary waves, the QBO modulates upward propagation. In particular, it determines where EP flux is absorbed strongly and, thereby, where residual mean motion is forced [e.g., Holton, 1992].
 Dependence on the QBO is evaluated by projecting onto the record of equatorial wind during the same months as anomalous (Aug-Sep). The projection of onto equatorial wind maximizes near 10 hPa, corresponding to a phase of the QBO with equatorial easterlies there. (It is noteworthy that the same QBO phase maximizes the relationship to NH ozone [Salby and Callaghan, 2002].) In that phase, the QBO positions equatorial westerlies in the lowermost stratosphere and equatorial easterlies in the middle stratosphere. This configuration of equatorial wind removes the critical line in the lowermost stratosphere into the summer hemisphere – away from the vortex. Simultaneously, it advances the critical line in the middle stratosphere into the winter hemisphere – toward the vortex. Planetary waves in the wintertime troposphere then propagate upward freely until reaching the middle and upper stratosphere, where they suffer strong absorption. The latter intensifies the poleward drift at those levels. Upon converging at high latitude, the anomalous poleward drift drives anomalous downwelling and adiabatic warming in the Antarctic lower stratosphere, where ozone is concentrated. In the opposite phase of the QBO, absorption in the middle and upper stratosphere is weakened. This leads to weakened downwelling and reduced adiabatic warming in the Antarctic lower stratosphere.
 Superimposed in Figure 3 is the component of springtime ozone that varies coherently with both and the QBO (dotted). Much of the outstanding variance that was uncorrelated with has been eliminated. Accordingly, the correlation to observed springtime ozone has increased – to 0.97. Its significance exceeds 99.99%. The probability that the correspondence arises through a chance alignment of error (via two-tailed t test with > 20 dof) is thus smaller than 0.01%.
 Jointly, and the QBO represent anomalous planetary wave forcing of the residual circulation during late winter. This dynamical forcing accounts for virtually all of the interannual variance of springtime depletion. Included are tropospheric influences like ENSO, which must enter through . Also entering through is a small indirect contribution from the QBO, to which is weakly correlated. With a correlation of ∼0.4, it accounts for ∼15% of the variance of . Notice that variance during the early 1980s which was not accounted for by alone has now been mostly captured. This finding is consistent with the identification of those early fluctuations with the QBO [Garcia and Solomon, 1987]. Over the longer record, however, the preponderance of variance in springtime depletion is accounted for by fluctuations of .
3.3. Structure of Anomalous Ozone
 Planetary wave forcing is represented by the dotted record in Figure 3, wherein contributions from and the QBO are scaled by their covariances with ozone. The structure of anomalous springtime ozone that operates coherently with that forcing follows in similar fashion, from the covariances with local ozone; details may be found in Salby and Callaghan . Figure 4 plots, as a function of latitude, the anomaly of springtime ozone that is introduced by a 1-std deviation increase of planetary wave forcing. From small values at midlatitudes, anomalous ozone increases sharply at latitudes poleward of 60 S. It mirrors the pattern of ozone depletion over the Antarctic that defines the ozone hole. The anomaly thus deepens the ozone hole in one phase of planetary wave forcing, but shallows it in the opposite phase. At low latitude, the anomaly is reversed. Accompanying positive anomalous ozone over the Antarctic is negative anomalous ozone over the tropics. In each region, the ozone anomaly is strongly coherent with anomalous wave forcing (Figure 3).
 Reciprocal changes over the Antarctic and tropics are a signature of the residual circulation. Intensified downwelling over the Antarctic is accompanied by intensified downward/poleward transport of ozone-rich air, along with warmer temperature and reduced PSC. Both influences favor increased springtime ozone. Compensating intensified downwelling over the Antarctic is intensified upwelling over the tropics. By importing additional ozone-lean air from the troposphere and accelerating its ascent at photochemically-active levels, intensified upwelling favors reduced springtime ozone [Avallone and Prather, 1996; Salby and Callaghan, 2002].
 The anomaly in springtime ozone maximizes over the South Pole, where it exceeds 30 DU. Changes between neighboring years of ±1–2 std deviations in planetary wave forcing can therefore introduce changes in springtime depletion as large as 50–100 DU. These changes are consistent with interannual changes of minimum ozone (Figure 1). Such changes are large enough to approach the average depletion of Antarctic ozone that defines the ozone hole (Figure 2). An analogous conclusion for Arctic ozone was reached by Rex et al. . They observed that springtime ozone over the Arctic varies from strongly-depleted conditions following cold winters, analogous to the Antarctic vortex being perturbed through halogen chemistry, to nearly undepleted conditions following warm winters, more typical of the Arctic vortex.
4. Relationship to Anomalous Temperature
 A parallel analysis has been performed on column-averaged temperature above 100 hPa. Involving integration over pressure, the latter is an analogue of total ozone. Plotted in Figure 5 is the record of anomalous temperature, averaged poleward of 65 S and over Sep-Oct (solid). Like ozone, Antarctic temperature experiences large changes between years. During 1988 and 2002, the excursions are particularly large, driving Antarctic temperature 5–10 K above its climatological mean.
 Superimposed in Figure 5 is the component of anomalous temperature that varies coherently with anomalous and the QBO (dashed), averaged over the same latitudes and months as in the analysis of anomalous ozone (section 3). Like anomalous ozone, anomalous temperature closely tracks anomalous wave forcing of the residual circulation during late winter. The records achieve a correlation of 0.93. As before, they track one another even during large excursions, like those in 1988 and 2002.
Figure 6 presents the structure of anomalous temperature that operates coherently with planetary wave forcing, which is represented by the dashed record in Figure 5. It has been calculated in the same manner as Figure 4 for ozone. Displayed is the anomalous temperature that is introduced by a 1-std deviation increase of planetary wave forcing. From small values at midlatitudes, anomalous temperature increases poleward of 60 S. Positive values there reflect anomalous downwelling and adiabatic warming, which are introduced during years when planetary wave forcing is intensified. The anomaly maximizes over the South Pole, where it approaches 3 K. Changes of wave forcing between neighboring winters of ±1–2 std deviations can thus introduce changes of Antarctic temperature as large as 5–10 K. At low latitude, anomalous temperature is reversed. It reflects anomalous upwelling and adiabatic cooling, which compensate changes over the Antarctic. Those dynamical influences on temperature at low latitude may be augmented by diminished radiative warming, which would accompany reduced ozone in the tropics (Figure 4). Like the structure of anomalous ozone, opposite changes at high and low latitudes are both strongly coherent with anomalous wave forcing (Figure 5).
 Some insight into why springtime depletion closely tracks anomalous wave forcing during late winter (Figure 3) comes from the annual march of temperature. Figure 7 plots 50-hPa temperature over the Antarctic, composited separately in years when wave forcing during Aug-Sep is intensified (positive ) and in years when it is weakened (negative ). For each, the coldest temperature is achieved around August. Antarctic temperature then approaches 185 K. This is cold enough to support widespread PSC I, involving small particles of Nitric Acid Trihydrate (NAT), as well as larger particles of water ice that comprise PSC II [Hamill et al., 1988; WMO, 1987]. The minimum temperature is about the same for both groups of years. However, the subsequent return to warmer temperature differs conspicuously. During years of weakened wave forcing (solid), the wintertime depression of temperature is prolonged: The coldest temperatures, those which support PSC, then persist through September. This is significantly longer than those temperatures persist during years of intensified wave forcing (dashed), when PSC conditions conclude in August.
 Prolonged PSC conditions during years of weakened wave forcing favor increased activation of chlorine and bromine during winter. The latter, in turn, favors increased springtime depletion of ozone – inside the vortex, which forms the core of the ozone hole (Figure 1). Just the reverse is favored during years of intensified wave forcing, when PSC conditions are abbreviated. The influence on ozone through halogen activation may be augmented by other factors that are also modified by changes of planetary wave forcing. Among them is the collar of weakly-depleted ozone surrounding the core of the ozone hole, the extent of which is sensitive to temperature as well as mixing [Bodeker et al., 2002; Newman et al., 2006]. The collar, however, is found equatorward of 70 S and, hence, outside the core of the ozone hole, upon which Figure 1 and this analysis focuses. More relevant to strongly-depleted values is transport of ozone-rich air from above and from subpolar latitudes. Isentropic mixing into the polar cap accounts for much of the observed difference in polar ozone between warm and cold winters over the Arctic [Salby, 2011]. However, its involvement over the Antarctic is comparatively minor.
5. Predictability of Springtime Depletion
 The strong dependence of springtime depletion on planetary wave forcing is established by coherent changes in a large population of years, one that contains many degrees of freedom (dof). The inferred dependence should therefore be statistically stable and, hence, robust. Indeed, the probability that the correspondence in Figure 3 arises from a chance alignment of error is less than 0.01% (section 3). The dependence of springtime depletion on planetary wave forcing should therefore be obeyed not only during years from which their relationship was deduced, but afterwards as well.
 If EP flux is known during late winter, from observations or from a forecast of the tropospheric circulation, then the observed dependence determines the subsequent depletion of ozone during spring. For a seasonal prediction (e.g., from the preceding months of winter), this requires only planetary wave structure at tropospheric levels, which determines EP flux into the stratosphere. Secondary support from the QBO is determined by observations of equatorial wind, which, over a couple of months, varies only gradually and predictably.
 Superimposed in Figure 3 is a hindcast of anomalous springtime ozone during 2007 (open circle), predicted from wave forcing during the preceding months of winter but via the dependence observed only until 2006. Anomalous ozone that was actually observed during 2007 (solid) is well predicted. Indeed, the observed anomaly is captured as accurately as are anomalies during preceding years (ie, those from which the dependence was deduced). Similar accuracy is recovered for seasonal predictions in subsequent years. Also displayed in Figure 3 are hindcasts of anomalous springtime ozone during 2008 and 2009. Like the one for 2007, they have been determined from planetary wave forcing during the preceding months of late winter (Aug-Sep), but via the dependence that was observed only until 2006. The dependence on wave forcing is robust: Even two and three years beyond those from which it was deduced, observed anomalies in springtime depletion are accurately predicted. Augmenting the records of anomalous springtime ozone and planetary wave forcing with these years increases their correlation further – to 0.98.
6. Systematic Evolution of Springtime Ozone
 As discussed in Salby et al. , accurate identification of dynamically-induced changes enables one to isolate the evolution of springtime ozone that is associated with changes of composition, including the systematic decline of stratospheric chlorine. Here, we explore the stability of the inferred evolution, as we did in section 5 for interannual changes of springtime depletion and their dependence on planetary wave forcing.
 The current evolution of springtime depletion is dominated by interannual changes, which comprise the climate variability of Antarctic ozone. According to the development in section 4, those changes are chemical, involving the same processes responsible for the ozone hole. However, through temperature, they are induced by dynamics. The interannual changes overshadow more gradual changes of Antarctic ozone, like those associated with the decline of chlorine and bromine. Owing to the magnitude of interannual changes, this will remain the situation for some time.
 As the dynamically-induced changes in Figure 3 contain no long-term variation, any systematic evolution is isolated to the component of springtime ozone that is independent of those changes. Further, the strong dependence of springtime depletion on planetary wave forcing during late winter enables the dynamically-induced component to be identified accurately. Removing the latter leaves the component of springtime ozone that is independent of dynamically-induced changes. Largely free of climate variability, it describes the other contribution to ozone variability: The secular variation, which represents the long-term evolution of springtime ozone.
 The secular variation of springtime ozone is plotted in Figure 8 (solid). Independent of dynamically-induced changes, it is discriminated to ozone changes that follow from changes of photochemical environment. Included are sporadic enhancements of aerosol following volcanic eruptions and gradual variations of chlorine and bromine. This component still exhibits year to year fluctuations - because the dependence on planetary wave forcing is not perfect. Nonetheless, the climate variability remaining has been reduced to only ∼10% of that present in the full record of springtime ozone, which is superimposed (dotted).
 The systematic component exhibits a gradual but sustained increase over the last decade. The upward trend is, upon close inspection, visible even in the full record of springtime ozone - especially with the exclusion of the unrepresentative excursion during 2002. However, in the full record, it is overshadowed by large interannual changes that dominate the current evolution of Antarctic ozone. The rebound visible in the component independent of dynamically-induced changes contrasts with earlier studies, which accounted for only part of the interannual variance (section 3). The corresponding evolution therefore remained dominated by climate variability, statistically indistinguishable from a constant background level. The component in Figure 8, on the other hand, is nearly free of climate variability – because it is discriminated to the evolution of springtime ozone that is independent of dynamically-induced changes. Consequently, the upward trend over the last decade is highly significant – at the 99% level. Visible back to the late 1990s, it represents a gradual return of springtime ozone toward its level in 1980 of 10–15%.
 As for the treatment of interannual changes (section 5), applying the dependence on planetary wave forcing that was observed until 2006 to subsequent years reveals the stability of the inferred evolution. Removing from the full ozone record dynamically-induced changes during 2007, 2008, and 2009 yields the extrapolated evolution superimposed in Figure 8 (open circles). Those values continue the gradual but systematic rebound that is apparent during the preceding decade. The sustained rebound is thus robust. In the extended record, it is then manifest almost as long as was the decline during the 1980s and early 1990s. As a result, the associated trend increases in significance, especially with the exclusion of the unrepresentative year 2002. Even for a conservative estimate of only 5 dof (accounting for interdependence of years), it exceeds the 99.5% level. (As it represents the sum of three independent time series, viz of , , and the QBO, the component independent of dynamically-induced changes should actually contain well more than 10 dof.) Uncertainty in the upward trend is determined by the significance level. It is thus small enough to make the probability that the trend arises from a chance alignment of error less than 0.5%.
 The gradual rebound apparent in the component of springtime ozone that is independent of dynamically-induced changes should not be altogether surprising. Although estimates vary in detail, stratospheric chlorine is known to be on the decline [e.g., Jones et al., 2011]. Once the interannual variance has been accurately accounted for (Figure 3), all that can remain is the long-term evolution of springtime ozone. Were the latter not to evolve systematically with the evolution of chlorine, it would imply that the fundamental understanding of the ozone hole is incorrect.
 Superimposed in Figure 8 is the evolution of Equivalent Effective Antarctic Stratospheric Chlorine (dashed). EEASC measures the loading of halogens that are available for activation, principally chlorine and bromine [Newman et al., 2006]. The evolution plotted corresponds to a mean age of air of 5 years and a bromine scale factor of 60, as suggested by chemical transport calculations [Chipperfield and Pyle, 1998].
 For these values, the calculated evolution of effective chlorine matches the observed evolution of springtime ozone – once dynamically-induced changes have been accounted for.
 The satellite record is now long enough to have collected a large population of observed states of the ozone hole and contemporaneous states of dynamical structure. In that population, springtime depletion of Antarctic ozone is strongly dependent on planetary wave forcing of the residual circulation during late winter. Dynamically-induced changes of ozone account for virtually all of the interannual variance of springtime depletion. The observed dependence is obeyed even during extreme years like 2002, when the polar-night vortex unravelled prematurely (albeit temporarily), limiting ozone loss. Validation against independent data, springtime depletion in future years, reveals that the dependence on wave forcing is robust.
 Anomalous planetary wave forcing also introduces changes of Antarctic temperature. A signature of anomalous downwelling, those changes are not limited to the stratosphere. Coherent changes of temperature are visible as low as 500 hPa [Salby and Callaghan, 2004]. In concert with the strong temperature dependence of PSC, these changes of dynamical structure introduce changes of springtime depletion as large as 50–100 DU.
 The strong dependence on planetary wave forcing makes possible a seasonal forecast of springtime depletion. Conditioned on EP flux during late winter, it faithfully predicts the ozone depletion which is later observed during spring. The latter, in turn, determines anomalous summertime ozone across the Southern Hemisphere, which is perturbed when ozone-depleted air inside the polar-night vortex is released to subpolar latitudes.
 Their strong dependence on planetary wave forcing, enables dynamically-induced changes of springtime ozone to be identified accurately. Removing them unmasks the secular variation of ozone, the part that remains coherent over a decade and longer. Independent of dynamically-induced changes, which comprise the climate variability of Antarctic ozone, this component describes the climate signal of springtime ozone. Included are systematic changes associated with the gradual variation of composition, like chlorine, bromine, and greenhouse gases. The secular variation exhibits a gradual but systematic increase since the late 1990s, one that mirrors the decline of stratospheric chlorine and bromine. The sustained increase, even in years after those from which dynamically-induced changes were defined, indicates that the trend is robust. It is consistent with the high statistical confidence of the observed rebound. Free of dynamically-induced changes, which dominate behavior on timescales shorter than a decade, this component enables the evolution of springtime ozone to be tracked more reliably than is otherwise possible. Ozone can then be compared against the evolutions of chlorine and CO2, as well as the tropospheric circulation and ice cover, changes of which have likewise been suggested in relation to Antarctic ozone [WMO, 2006; Intergovernmental Panel on Climate Change, 2007; Turner et al., 2009].
 The record of NCEP reanalyses provides 3D dynamical structure. In terms of mean and wave fields, the meridional and vertical components of EP flux follow as [see, e.g., Dunkerton et al., 1981]
provides the time series of wave activity flux, contemporaneous with time series of other dynamical properties and total ozone from TOMS/OMI.
 The interannual anomaly of each field variable is constructed, as a function of month and year, by removing the climatological mean (post-1980). Averaging anomalous total ozone poleward of 70 S and over Sep-Nov then yields the record of anomalous springtime ozone over the Antarctic plotted in Figure 2.
 To discriminate to dynamically-induced changes, anomalous springtime ozone is high-pass filtered to fluctuations that operate on timescales shorter than decadal. (The procedure is analogous to “prewhitening” behavior, focusing upon short-term fluctuations. Coherent over limited intervals, they provide a large population of independent events.) Following Båth , the high-pass-filtered behavior is obtained by removal of low-pass-filtered variation from the full record. The timescales apparent in Figure 2 are widely separated: One operates on intervals of a couple of years, whereas the other operates on intervals longer than a decade. Consequently, the low-frequency variation can be captured by regression of anomalous ozone onto a low order polynomial or spline, with sufficient degrees of freedom to represent the long-term evolution [Båth, 1976]. (While isolating low-frequency variance, this procedure averts the need for window mechanics to treat boundary effects that are introduced by spectral transform.) In light of the long-term evolution in Figure 2, the low-frequency variation is well represented by regression onto a piecewise linear variation. Analogous to a first-order spline, one linear segment spans the continuous interval observed by Nimbus 7 and another spans the continuous interval observed by subsequent satellites. Removing that low-frequency variation leaves the high-pass-filtered component, which is plotted in Figure 3 (solid). Comparison against Figure 2 confirms that it faithfully represents the large interannual changes that punctuate the full record of springtime ozone. Dominated by interannual variability, the high-pass-filtered component is seen to be free of long-term variation. Any trend must therefore be isolated to the remaining component of the full record.
 Subjected to similar analysis are dynamical properties, like temperature and EP flux, which are likewise discriminated to fluctuations shorter than decadal. Interannual changes in one record (e.g., in ozone) can then be related to coherent changes in another (Figures 3 and 5). Such coherence establishes the component of anomalous ozone that operates dependently with anomalous dynamical structure. The latter follows by scaling anomalous dynamical structure by its covariance with anomalous ozone; see equation (1). Once identified, that component is removed - from the full record of anomalous ozone. Left is the component of anomalous ozone that is independent of anomalous dynamical structure.
 The authors are grateful for values of EEASC that were provided by NASA GSFC and for constructive comments that were provided during review.