A 29 year data set of stratospheric ozone from sequential assimilation of solar backscatter UV (SBUV) satellite ozone profile observations into a chemical transport model is introduced and validated against independent observations (satellite instruments and sondes). Our assimilated data set shows excellent agreement with ozone profile data from sonde measurements from high-latitude observation sites on both hemispheres and Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) satellite observations, including during polar night when no SBUV observations are available. Although we only assimilate ozone profiles, total column ozone in the assimilated data set is in good agreement with independent satellite observations from the Global Ozone Monitoring Experiment (GOME), the Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY), and the Total Ozone Mapping Spectrometer (TOMS). The data set can thus be viewed as a consistent long-term data set closing the gaps in satellite observations in order to investigate high-latitude ozone variability. We then use the assimilated data set to analyze the development and persistence of both high and low ozone anomalies in the Arctic stratosphere. Ozone anomalies typically develop in the 1000 K potential temperature (∼35 km) region and slowly descend from there, remaining visible for around 7 months. Anomalies in the stratospheric circulation, expressed by the Northern Hemisphere annular mode (NAM) index, show a large influence on ozone anomalies. Extreme phases of the NAM index (strong and weak vortex events) lead to the creation of distinctively shaped ozone anomalies, which first appear in the uppermost stratosphere and then rapidly cover the upper and middle stratosphere, from where they then slowly descend into the lowermost stratosphere within 5 months.
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 Polar ozone has shown large decreases on both hemispheres during the last decades, mainly attributable to anthropogenic emissions of ozone-depleting substances [World Meteorological Organization, 2007]. A large interannual variability of springtime total ozone can be observed, especially in the northern hemisphere during the 1990s and in the southern hemisphere during recent years. The principal mechanisms of ozone depletion have been studied extensively and are well understood [e.g., Solomon, 1999], especially concerning ozone depletion through heterogeneous chemistry during spring. The interannual variability of polar ozone during the rest of the year has received less attention, in particular the evolution of polar ozone anomalies in the middle stratosphere, their attribution to chemistry and dynamics and their persistence. A deeper understanding of the mechanisms which control polar ozone variability is desirable in order to predict the future evolution of the polar ozone layer in a changing climate. Some principal mechanisms of this variability are well established, e.g., that the amount of momentum deposition by planetary waves as described by the divergence of the upward directed component of the Eliassen-Palm (EP) flux during winter has a large influence on springtime polar ozone [e.g., Fusco and Salby, 1999; Randel et al., 2002; Weber et al., 2003; Kawa et al., 2005]. However, several aspects still remain unclear. For example, an unexpected correlation between midstratospheric Arctic ozone in autumn and total ozone in the subsequent spring was found by Kawa et al.  and Sinnhuber et al. . Moreover, Sinnhuber et al.  reported indications for a solar influence on the variability of stratospheric ozone through energetic particle precipitation.
 Parts of the uncertainties are due to the lack of reliable long-term data sets of stratospheric ozone at high latitudes. Sonde measurements are available year-round only at a few high-latitude stations, while long-term records from satellite instruments, which offer near-global coverage, usually rely on backscattered sunlight and are thus not available at high latitudes during winter. Passive infrared and microwave sounders, which measure emitted radiation rather than scattered light and are thus able to operate during polar night, have not yet produced long enough continuous time series of data.
 There have been several attempts to create consistent long-term data sets of stratospheric ozone outside high latitudes, e.g., Randel and Wu  performed a regression analysis of satellite observations of the SAGE (Stratospheric Aerosol and Gas Experiment) I and II solar occultation instruments; however, in their data set, information about ozone poleward of 60° is derived only from a single sonde station per hemisphere. A long-term assimilation of SBUV and other satellite ozone observations was also included in the ERA-40 reanalysis project conducted at the European Centre for Medium Range Weather Forecast (ECMWF) [Uppala et al., 2005], but this data set has some known difficulties related to the simultaneous assimilation of ozone profiles, total column ozone and other satellite data [Dethof and Hólm, 2004]. In this study, we will show that the ERA-40 data set is not suitable for our purpose due to a lack of adequate representation of high-latitude ozone variability. Our approach is to create a consistent long-term data set of stratospheric ozone by assimilating the whole available record (29 years) of SBUV satellite observations into a 3-D chemical transport model. We limit the assimilation to one data product (SBUV) and only assimilate one satellite at a time in order to avoid complications due to possible biases between different instruments.
 Originally developed for application in numerical weather prediction, data assimilation is a well-known tool in atmospheric science. During recent years, it has been increasingly used as a tool for enhancing the degree of realism achieved in modeling chemical species in the atmosphere [e.g., Chipperfield et al., 2002]. Ideally, it combines the advantages of global coverage by a 3-D model with the “realism” of external data, e.g., satellite observations. Through assimilation of measured data, the model is constantly “pulled” toward reality. Conversely, the model closes the gaps of measurements, such as lack of sunlight-dependent satellite observations at high latitudes during winter, and the assimilated data set may thus be viewed as a consistent extension of an observational data set.
 Two main types of assimilation schemes have been developed, sequential and variational. While the variational method produces smoother results, it is computationally more demanding and therefore not applicable for our project, which focuses on a long-term study of stratospheric ozone. We use the sequential assimilation scheme described by Khattatov et al.  and Chipperfield et al.  to generate a 29 year data set of stratospheric ozone.
 A key purpose of this study is the enhancement of our understanding of the variability of the polar ozone layer. In this study, we introduce and validate a long-term 3-D data set generated by the sequential assimilation of solar backscatter UV (SBUV) ozone observations into a chemical transport model (CTM). We characterize the evolution of ozone anomalies in the middle stratosphere by autocorrelation and composite plots of typical ozone anomalies. We find that much of the high-latitude ozone variability may be explained by variations in the Northern Hemisphere annular mode (NAM).
 The NAM [Thompson and Wallace, 2000; Baldwin and Dunkerton, 2001] constitutes the dominating pattern of climate variability in the Northern Hemisphere, on a seasonal as well as on a daily base [Thompson and Wallace, 2001]. The NAM represents the pressure difference between polar regions and lower latitudes and is closely related to other climate patterns such as the North Atlantic Oscillation (NAO) and the Arctic Oscillation (AO) [Thompson and Wallace, 2000]. Its phase can be expressed by a dimensionless index. A positive index corresponds to a strong meridional pressure gradient and a strong, more isolated polar vortex, while a negative index indicates a weak or even reversed meridional pressure gradient and hence a weaker vortex. Annular modes were shown to have a profound influence on total column ozone variability [Orsolini and Doblas-Reyes, 2003; Jiang et al., 2008a, 2008b].
 The layout of this paper is as follows. Model and satellite data used for assimilation are described in section 2, followed by a description of the assimilation algorithm in section 3. A validation of the assimilated data set against independent sonde and satellite observations is provided in section 4. Results concerning the evolution of Arctic ozone anomalies are presented and discussed in section 5.
2. Model and Data
 Our stratospheric CTM [Sinnhuber et al., 2003] (referred to as “CTMB” in Figures 1, 2, and 6) is run at a horizontal resolution of 3.75° × 2.5°. It uses 24 isentropic levels as vertical coordinates, ranging from 335 K to 2750 K (roughly 10–55 km) and thus covering the whole stratosphere. Horizontal transport is driven by analyzed wind fields and temperatures; in this study, we use ECMWF ERA-40 data 1979–1999 and ERA-INTERIM 2000–2007. Vertical transport is derived directly from interactively calculated diabatic heating rates using the MIDRAD scheme [Shine, 1987]. We use an updated version of the linearized ozone chemistry developed by McLinden et al. . Although this chemistry scheme is simple, using only one ozone tracer and net production rates parameterized according to ozone volume mixing ratio (VMR), temperature, and ozone column above the respective grid cell, it has been shown to generate realistic ozone fields [McLinden et al., 2000]. We choose not to employ the full chemistry including 50 tracers since we only assimilate ozone observations. In a full chemistry scheme, the internal balances between reactants have to be taken into account, which may be disrupted due to alteration of only one tracer, and would require additional correction [Chipperfield et al., 2002]. Since our interest is in studying the ozone field, we avoid this additional complication as the benefit is not clear.
 The effects of heterogenous ozone destruction are included in form of a simple parameterized polar chemistry which calculates the critical temperature TNAT for PSC formation in each grid box and destroys ozone at a defined rate as soon as the temperature T < TNAT when sufficient sunlight is available (solar zenith angle <85°). While critical parameters (ozone life time τ and solar zenith angle) have been fitted to reproduce ozone depletion in the Arctic winter of 1999–2000, this scheme has been shown to generate realistic results in other winters as well, e.g., the Antarctic winter of 2002 [Sinnhuber et al., 2003]; in order to account for the increasing concentrations of ozone depleting substances during the period of our long-term assimilation, we scale the ozone decay rate 1/τ linearly with the effective equivalent stratospheric chlorine (EESC).
 SBUV nadir viewing instruments have been flown on NOAA and NASA near-polar orbiting satellites and provide a continuous data set of stratospheric ozone since October 1978. We use version 8 retrievals (released 2004) [Bhartia et al., 2004] for the period 1979–2000 and version 8b retrievals (released 2008 as an update for v8) for 2001–2007. At several times, more than one satellite was operational; however, in order to eliminate effects of internal biases and maximize consistent time series, we assimilate only data from one satellite at each time. Selected satellites are listed in Table 1. Recently, McLinden et al.  presented a correction of the SBUV profiles which accounts for systematic drifts and biases of the several instruments obtained by using SAGE solar occultation observations. In this study, however, we use the SBUV data as provided on the version 8 DVD and the 2008 update; while such correction terms may be useful for establishing long-term trends, we instead choose to use observations from one consistent intercalibrated series of instruments.
Table 1. List of SBUV Satellites Used for Assimilation at Different Times
 Each model time step (30 min.), the CTM produces a forecast of the state of the atmosphere, denoted as a vector of ozone mixing ratios xf(t) ≡ xtf at time t of the dimension of nmod = nlon × nlat × nlev = 96 × 72 × 24 = 165888 = number of model grid cells (nlon, nlat, and nlev are numbers of longitudes, latitudes and vertical levels in the model). Along with the forecast of the ozone tracer itself, the variance of the tracer field as caused by errors in transport, chemistry and discretization is transported in the model and yields an error covariance forecast Btf. At the same time, observations of the “true” (unknown) state of the atmosphere xtt are made, denoted by the vector yt of dimension nobs = nobsloc × nobslev = total number of observation points (nobsloc is number of observation locations, nobslev is number of vertical observation levels. For SBUV observations nobs < 1000 in the 30 min assimilation window).
 The relation between the true state of the atmosphere xt and the observations y can be expressed by the observational operator H,
where ɛt is the overall error, composed of an observational error O and a representativeness error R,
 Essentially, the assimilation process performs an inversion of equation (1) to solve for xtt, which is not possible in the strict mathematical sense since equation (1) is, in general, both underdetermined and overdetermined. Inversion is thus performed by the process of optimal estimation [Rodgers, 2000] to provide the analyzed (or “optimal”) state xta (called “analysis” in the following), which is a best linear unbiased estimator to xtt. According to optimal estimation theory, the analysis is given by
K is called the Kalman gain. The analysis error covariance Bta is given by
 In practice, the essential part is the construction of a proper observation operator H which maps the model space to data space. In the case of direct assimilation of satellite observations, this is basically a horizontal and vertical interpolation operator. As nadir-viewing instruments, the vertical resolution of SBUV is rather coarse, amounting to roughly 7 km in the middle stratosphere [Bhartia et al., 1996]. Thus, we cannot consider different pressure levels as independent and treat a VMR measurement as a point-like observation at a certain pressure level (as may be done in the case of, e.g., solar occultation measurements which offer a much higher vertical resolution). In the retrieval process this limited resolution is expressed by averaging kernels, which are in principle specific to each observed profile and would also be needed for constructing the correct observational operator between SBUV O3 VMR and model O3 VMR. Here we employ an alternative method by assimilating not VMRs but partial columns, which have already been integrated vertically to a coarser resolution, and also by introducing a representativeness error expressed by the covariance R. In this case, the observational operator consists of a horizontal interpolation of model VMRs to the observation location, and a vertical integration to yield partial columns between the same margins as provided in the SBUV data. Since the lowest SBUV partial column includes the whole troposphere which is not included in our model, we assimilate only 12 out of the 13 partial columns provided (Each column is provided as total ozone in a layer between two pressure levels, approx. lower column boundaries: 64 hPa, 41 hPa, 25 hPa, 16 hPa, 10 hPa, 6.4 hPa, 4.1 hPa, 2.5 hPa, 1.6 hPa, 1.0 hPa, 0.6 hPa, 0.4 hPa. The last column extends to the top of the atmosphere.).
 As noted above, differences between the observations and the true state of the atmosphere are denoted by the overall error ɛ, which can be decomposed into an observational error O and the representativeness error R.
 The observational error O includes accuracy and precision of the instruments and is reported around 5% for SBUV in most of the stratosphere [Bhartia et al., 1996]. The representativeness error is more difficult to estimate, since it must include not only the effects of different vertical grids (profile structures smaller than the observational grid are smeared out and thus lost by the observation operator) but also the vertical oversampling of the satellite data since we do not convolute the model forecast profile with averaging kernels before comparing them to the satellite data. A rough estimate showed that R is in the order of 5% as well. Thus as the easiest option it was chosen to estimate the combined observational and representativeness error as 10%. A more detailed treatment was forgone as the quality of the overall assimilation result depends equally well on a reasonable treatment of model (“a priori”) errors, which is even more tricky.
 After calculation of advection and chemistry in each model time step (30 min), all SBUV observations available during this interval are read in and assimilated. The assimilation output xta (analysis) is passed back to the model along with the computed variance Bta, which serve as the initial state for the next model integration to yield xt+Δtf and Bt+Δtf at a later time t + Δt,
where M represents the (abstract) model integration operator. In a strict mathematical sense, the evolution of the error covariance matrix involves the tangent linear model
and is computed by
Q denoting some kind of error increase due to imperfections in the model.
 However, since the dimension of the covariance matrix B is nmod × nmod = 165888 × 165888, the evolution of the covariance cannot be calculated as in equation (8), but has to be simplified. Following the treatment of Khattatov et al. , we transport only the diagonal elements biia of Ba in the model integration (equation (8)) to obtain the diagonal elements bii of the forecast variance Bf. For the analysis step (equation (3)), the off-diagonal elements (covariances) are parameterized as
with Δrxy and Δrz distances in horizontal and vertical direction. Lxy and Lz are tunable coherence lengths, which we choose in accordance with Chipperfield et al.  to be Lxy = 1000 km and Lz = 2.8 km. During model integration, the analysis error variance bii,ta is first transported as a tracer,
and then increased by the error growth term qiit in order to account for the growing uncertainty in the modeled tracer in the absence of data,
 The numerical value for the error growth factor ε = 0.01 is an update from Chipperfield et al. , who used a very similar model (SLIMCAT) to assimilate ozone observations. Basically, ε is a tuneable parameter which is optimized to ensure a constant value of the χ2 diagnostic near its expectation value of 1. We find that as the long-term mean of the χ2 diagnostic is close to 1, the treatment of errors and error growth is reasonable in our assimilation scheme.
 The assimilation scheme described here was used to generate a 29 year three-dimensional ozone data set. In terms of computational requirements, the CTM with linearized ozone chemistry performs well (e.g., <1 min wall clock time per model day on a standard desktop PC). With assimilation, computation time is increased significantly due to the computational demands of the optimal interpolation algorithm (i.e. multiplication of the large covariance matrices, performed by multiple iterations here). Therefore the whole assimilation run was not performed in one piece, but as 29 separate threads, each covering 2 years, of which the first year was then discarded as overlap. A comparison of the first-year and second-year assimilation for each calendar year assimilated showed that in the middle and upper stratosphere, initial differences vanish after a month; differences below 470 K remain longer since SBUV is not sensitive in this region and thus the assimilation does not influence model O3 strongly, and O3 photochemical lifetime is long. After 10 months, differences have decreased to less than 5%, and after 12 months differences are less than 2% everywhere. Thus, we conclude that 1 year is well suited as overlap time. The method allows rerunning single years without the need to redo the whole assimilation, e.g., in order to study effects of a different choice of satellites (which we have not done so far).
 On a qualitative basis, the method seems to work well, as (1) in areas where SBUV observations are available, the model is pulled toward the observations, and (2) otherwise the CTM provides a consistent extension into areas without satellite coverage. However, in altitude regions where the photochemical lifetime of ozone is shorter than a day (Θ > 1200 K; z > 37 km), the value of the assimilated data set is limited since modeled ozone relaxes to its photochemical equilibrium state between satellite overpass times.
 A detailed validation of the data set is provided in the following section.
4. Validation of the Assimilated Data Set
 Here we present a first validation of our data set against independent observations. As mentioned in the introduction, ozone observations with polar coverage during winter are scarce (which is the reason for our assimilation project), and are either available only at single locations (sondes or other ground-based instruments) or for periods of only a few years (infrared/microwave emission sounders on satellites). We compare our assimilated profile ozone to sonde data from four high-latitude stations over long time periods. A first comparison with the MIPAS satellite instrument provides information how well spatial structures of ozone during Arctic winter are captured in the assimilated data set. Total (column) ozone (TO3) is not a central topic of our study; nevertheless it is interesting to establish how well it is reproduced in our assimilated data set. Here we compare TO3 in our assimilated data set to observations from the GOME instrument onboard the ERS 2 satellite [Coldewey-Egbers et al., 2005; Weber et al., 2005] and from the SCIAMACHY instrument on ENVISAT [Bovensmann et al., 1999; Bracher et al., 2005], as well as to the merged TOMS/SBUV data set [Stolarski and Frith, 2006].
 As a first test of how well structures are captured during polar night, we compare our data set to observations from the MIPAS instrument on ENVISAT [von Clarmann et al., 2009]. Due to its observational technique as an infrared sounder relying on emitted rather than backscattered radiation, MIPAS can operate without sunlight and is thus one of the few sources for satellite ozone data covering the polar regions during winter (besides the Microwave Limb Sounders MLS/UARS, MLS/AURA, and the infrared spectrometers CLAES/UARS, ISAMS/UARS, and SAMS-LIMS/Nimbus7). Since ENVISAT was launched in 2002, MIPAS data are available only for a relatively short period, and not every day is fully sampled. Figure 1 shows maps of assimilated ozone together with MIPAS observations interpolated to several stratospheric pressures at 17 November 2007. As a reference, the corresponding SBUV ozone VMR at these pressures (as provided in the SBUV profiles data set and used for assimilation) are shown. Despite minor (expected) biases between the assimilated ozone and MIPAS observations, it is obvious that many structures of the ozone field are captured well in our data set, even though SBUV observations from NOAA 16 terminate around 58°N and no external information enters the assimilation beyond this latitude. As a quantitative measure of the good agreement even at high latitudes, Figure 2a shows the spatial correlation between MIPAS and our assimilated ozone poleward of 58°N, and Figure 2b shows their mean difference for the whole vertical range available. The correlation is higher than 0.6 for the whole stratosphere; values of 0.9 and more are attained throughout the middle stratosphere between 25 and 5 hPa (∼24–34 km). Absolute differences between assimilated ozone and MIPAS are generally negative (MIPAS observes higher ozone mixing ratios), differences amounting to 0.4 ppmv below 10 hPa and around −0.1 ppmv above 5 hPa.
 Ozone sondes provide highly accurate measurements which are, however, only available at single locations and are thus suitable for analyzing the time series and anomalies at single locations. We use ozone sonde data from four different stations: Ny-Ålesund (79°N, 12°E), Sodankylä (67°N, 27°E), Neumayer (71°S, 8°W), South Pole (90°S). We restrict ourselves to high latitudes since the central aim behind our project is to study high-latitude ozone variability, and thus especially the performance of the assimilation in the absence of data during polar night is interesting to us. At lower latitudes, assimilated ozone is strongly controlled by SBUV measurements which are available throughout the year, and thus a comparison there rather amounts to quantifying differences between SBUV and sonde observations, which is not the purpose of this study. Sonde data were available for the years 1992–2007 (Ny-Ålesund, Neumayer), 1991–2007 (South Pole) and 1989–2007 (Sodankylä). Altogether, more than 1600 sondes were used from Ny-Ålesund, more than 1400 from Sodankylä, more than 1250 from Neumayer and more than 1150 from South Pole.
 In the following, the assimilated data set is characterized by its mean offset from the sonde observations, and the correlation of anomalies.
 In Figure 3 the mean overall difference between monthly means of assimilated ozone and sonde ozone is shown. At all four stations, the picture is strikingly similar. In the middle and lower stratosphere, assimilated ozone is generally lower than sonde ozone; above 850 K, differences reverse. This picture is consistent with the differences to MIPAS observations for a single day (Figure 2), which shows differences of about −0.4 to −0.2 ppmv in the lower stratosphere that decrease to small (though negative) values above 7 hPa (∼900 K). Note the different vertical ranges of Figures 3 and 2 as sonde measurements terminate around 1000 K (32 km/5 hPa). In the middle stratosphere, differences are mainly attributable to differences between SBUV and sonde ozone. Below 450 K, however, SBUV is not sensitive and thus assimilation does not influence modeled ozone directly; differences there are an indirect effect presumably due to the downward transport of low-ozone air from higher altitudes. This will be subject of further investigation; however, the offsets are of an order of magnitude which is not detrimental to our purpose of studying ozone variability.
 As a measure of how well the variability of polar ozone is captured in the assimilated data set, Figure 4 shows the correlation of sonde ozone anomalies to anomalies in assimilated ozone. Anomalies are calculated in either case as monthly means of daily deviations from the annual cycle. Values of the correlation coefficient exceed 0.6 throughout the middle stratosphere at all stations, i.e. at altitudes where the sondes have their best accuracy, showing that our data set gives a realistic picture of ozone variability throughout most of the stratosphere. It is noteworthy that the realism of ozone anomalies, as depicted by this correlation, is independent of absolute offsets; even at altitudes where the relative VMR offset is large (up to −50% in the lowest stratosphere), ozone variability is still captured well. Only in the SH does the correlation and hence the realism of ozone variability in the assimilated data set decay rapidly below 450 K. This effect is at least partly attributable to the lower quality of the meteorological analyses used in driving the CTM in the SH.
 Global total column ozone data are available from a number of satellite instruments. A continuous data set of satellite-observed TO3 is provided by the TOMS/SBUV merged data set using TOMS (Total Ozone Mapping Spectrometer) and SBUV observations from 1979 to 2008. However, in order to validate our data set against completely independent observations, here we select data from GOME and SCIAMACHY instruments, which have been flying on ESA research satellites [Bracher et al., 2005; Weber et al., 2005]. GOME provided global ozone data from 1995 to mid-2003, while SCIAMACHY has been in continuous operation since mid-2002. Although GOME and SCIAMACHY are two independent instruments, their retrieval algorithms and observations are sufficiently similar to allow merging their data sets into one, covering 1995 to 2007. During the 1 year overlap period, offsets between GOME and SCIAMACHY are less than 1% for most latitudes and months, and maximize at 3.5%, which is far less than offsets to the assimilated data set. We use GOME for the period 7/1995–6/2003 and SCIAMACHY for the period 7/2003–12/2007. Monthly zonal mean TO3 in our assimilated data set is shown in Figure 5a. Interannual variations correlate very well with GOME/SCIAMACHY observations (Figure 5b), with correlation coefficient exceeding 0.8 for most latitudes and months. In Figure 5c, the difference of zonal monthly mean GOME/SCIAMACHY and assimilated TO3 is shown. Differences are significant (in relative terms, 5–20%) and reach up to 70 DU in northern hemispheric spring; however, a large part of this offset is due to the tropospheric column, which is not included in our model. The climatological ozone column below 330 K (the bottom level of our CTM) is shown in Figure 5d (taken from the climatology of Fortuin and Kelder ); if this column is taken into account, the remaining difference of the assimilated TO3 to GOME/SCIAMACHY reduces to around 5%. Taking into account that we do not assimilate total ozone, the agreement to independent observations is remarkable.
 A validation of TO3 from our assimilated data set to the TOMS/SBUV merged data set shows essentially the same features as revealed in the GOME/SCIAMACHY comparison. Correlation coefficients are always larger than 0.5 and exceed 0.9 for most latitudes and months, and the offset is very similar to the GOME/SCIAMACHY record. We do not show the corresponding figure here as the good agreement to our data set may be partly attributed to the consistency of the TOMS/SBUV merged TO3 data set with the assimilated SBUV profiles.
4.4. Comparison to ERA-40 Ozone
 The ERA-40 reanalysis [Dethof and Hólm, 2004; Uppala et al., 2005] provides a 3-D global long-term data set of stratospheric ozone obtained from a 3DVAR assimilation of SBUV profile ozone and TOMS column ozone. While ERA-40 total column ozone has been reported to agree well with independent observations [Dethof and Hólm, 2004; Jiang et al., 2008b], studies involving ERA-40 ozone profiles seem scarce. Comparing ERA-40 ozone to sonde observations at high latitude, we find that although the annual cycle is captured well, polar ozone variability is underestimated in this data set. Figure 6 displays correlations between ERA-40 ozone and Ny-Ålesund sonde observations for the years 1991–2001 (black line with symbols). Figure 6a compares the monthly mean ozone VMR time series including the annual cycle, while Figure 6b only shows correlations between monthly mean anomalies (mean annual cycle subtracted). At the Arctic site of Ny-Ålesund, the ERA-40 correlation to sondes is generally rather low and in particular much lower than the correlation of our assimilated data set to the sondes (black line without symbols). Thus the ERA-40 ozone data set seems not suited to address our research objectives.
5. Results and Discussion
5.1. Characterization of the Data Set: Ozone Anomalies
 A central focus of this study is the analysis of Arctic ozone variability. Throughout this chapter, we use zonal means over high geographical latitudes as well as zonal means over high equivalent latitudes, distinguishing high-latitude ozone and vortex ozone. Equivalent latitude values were calculated from the potential vorticity for every model grid point and ozone VMR then averaged in 5° bins. Averages over an equivalent latitude range denote area-weighted means of these bins. The three-dimensional nature of our data set allows to switch between these reference systems and to separate geographical effects due to displacement of the polar vortex, which are contained in the zonal picture, from processes within the polar vortex. Although a distinct polar vortex does not exist during summer months, equivalent latitude is a useful reference system for distinguishing polar air masses throughout the year.
 As a first step, we characterize polar ozone anomalies in our data set (by “anomalies” we refer to deviations from the annual cycle as obtained from the full 29 year data set). Figure 7 shows relative vortex ozone anomalies (i.e., divided by the multiyear average annual cycle) averaged over 75–90°N equivalent latitude for the whole assimilation period. Anomalies are calculated on a daily basis; a 3 day running mean has been applied in order to smooth the image. Alternating patterns of positive and negative anomalies (up to ±50%, exceeding the color scale) are visible, many of which seem to develop in the middle to upper stratosphere during winter months and then descend downward to the lower stratosphere, where they remain for a long time. Downward propagation of large positive anomalies is, for example, visible during the 1980s (1979/80,1980/81,1981/82). These structures develop in October to December at potential temperatures of ∼1000 K (∼34 km) and more, and then descend to ∼500 K (∼20 km) during the winter months, from where they slowly descend further and remain visible for up to a year. Similar, albeit somewhat weaker, anomalies are observed in 1987/88, 2005/06. During the 1990s, negative anomalies dominate. Note, e.g., the large negative anomalies in the winters 1995/96 and 1996/97. The negative anomaly developing end of 1995 remains in the lower stratosphere almost unchanged for more than a year. Other examples for descending negative anomalies may be found in 1989/90, 1994/95, 2002/03, 2004/05, 2003/04, some of which also show long residence times in the lower stratosphere.
 The descending behavior of high-latitude ozone anomalies is to be expected from the stratospheric circulation; in the absence of light during winter the anomalies subside undisturbedly. However, the lifetime of anomalies is remarkable as they seem to appear also during months when the lifetime of ozone is short (less than a month above 700 K, less than a week above 850 K, less than a day above 1200 K during summer).
 The picture for the Southern Hemisphere is very similar (Figure 8). Positive and negative anomalies typically develop at the beginning of winter in the middle to upper stratosphere and then descend to the lower stratosphere. In spring, the picture is disrupted by heterogeneous ozone depletion after 1982, which is by far more important in the SH. Throughout the first years of the assimilation, outstandingly large positive anomalies are visible in the lower stratosphere in spring. These are statistical artifacts due to the persistent formation of the Antarctic ozone hole in later years. Since the focus of our research is on Arctic ozone, we only consider the Northern Hemisphere from now on.
 In recognition of the qualitative view of ozone anomalies obtained in Figures 7 and 8, we now seek to investigate their behavior in a systematic way. In order to quantify the residence time of anomalies, we calculate the autocorrelation of ozone anomalies in vertical and temporal dimensions with respect to ozone anomalies at a fixed midstratospheric model level (631 K, ∼25 km). This level is chosen as a representative of the connection range between the higher stratosphere, where many ozone anomalies originate, and the lower stratosphere, where they then subside and remain. Varying the decisive potential temperature level between 600 and 700 K does not change results significantly. Figure 9 shows the correlation coefficient 1 year backward and forward in time. As expected from the qualitative picture described so far, the autocorrelation structure displays a consistent pattern descending from the upper (>1000 K) to the lower stratosphere. The correlation coefficient itself declines relatively fast both in the past and future, attaining values of 0.5 or less 2 months before and after day zero. Nonetheless, the whole picture seems consistent, and due to the long time series, even low correlation coefficients are significant.
 In addition, we show the descent curve obtained by integrating the heating rates forward and backward in time from 631 K. This gives a feeling for the approximate path the descending air follows on average due to the negative heating rates in polar regions. For comparison, the potential temperature curves obtained from heating rates averaged over all year (solid line) and only over the winter months December to February (dashed line) are shown. We show both lines since large anomalies typically evolve during winter and may thus be expected to propagate downward faster that expected from the annual average heating rates. In fact, the autocorrelation pattern seems to descend even faster on first sight; however, one should be careful when interpreting Figure 9. A more detailed analysis on each model level shows a somewhat bimodal distribution of the correlation coefficient for about 150 days in the past. Two branches are visible, one which roughly follows the winter heating rates, and one which descends much faster, covering the range from 1500 K to 630 K within ∼30 days. We interpret this fast-descending branch as due to the fact that anomalies often appear almost instantaneously throughout a large vertical range in the upper stratosphere (see Figure 7) and thus do not exactly follow the heating rates, a finding that will be discussed further in section 5.2.
 In order to obtain a quantitative view of the development and lifetime of typical midstratospheric ozone anomalies, we now analyze composites of high and low ozone anomalies, which are identified here by the date when the ozone anomaly at 631 K exceeds 1.5 standard deviations (of the whole record). As before, the level is selected as a transition between upper and lower stratosphere, and the threshold values are selected so that the number of events provides for a reasonable statistics while ensuring that effects do not get blurred due to a weak threshold. In order to assure that anomalies are not counted more than once, we require that the ozone anomaly stays below the threshold value for 60 days before the onset date. With these parameters, 22 positive and 14 negative ozone anomaly events are detected. Figure 10 shows the composite plots of positive (Figure 10a) and negative (Figure 10b) ozone anomalies, and their difference (Figure 10c), as equivalent latitude means northward of 65°N. 65° is chosen as southern boundary since this area contains the polar vortex; moving the boundary to 70° or 75° does not change the picture significantly. The time axis is drawn with respect to the onset day of the ozone anomaly at 631 K and extends from 160 days before to 160 days after the event. In addition to the anomalies as fractions of annual cycle values (colors), the levels of significance are shown as black contour lines. These values are obtained from a Student's t test, in a very similar fashion as that by Kodera . In Figures 10a and 10b, the levels of significance indicate the significance of a departure from the multiyear annual cycle values at the respective days, while in Figure 10c the contours indicate the statistical significance of the difference between ozone VMRs under positive and negative anomaly conditions, as obtained from a Student's t test for significantly different means.
 Both positive anomalies Figure 10a and negative anomalies Figure 10b seem to originate at ∼1000 K about 2 months before day 0, which then descends slowly to the lower stratosphere while intensifying to ∼10% for a month or so. The anomaly stays significant for around 4 months and is visible for 5 months after day 0, resulting in an average overall lifetime of 7 months from appearance at 1000 K to decay at 450 K. This is confirmed by the difference plot (Figure 10c), which shows a compact and highly significant anomaly signature propagating from 1000 to 450 K in 7 months.
 The long persistence of ozone anomalies which can be observed in our assimilated data set is remarkable and raises the question how anomalies evolving in ∼1000 K may persist on timescales of several months when the photochemical lifetime of ozone at these altitudes is below 10 days for most of the year. Although large anomalies, especially negative ones, occur more frequently during winter months (when the photochemical lifetime of ozone is long), the onset dates are not restricted to winter and also include events during summer (8 out of 22 positive and 2 out of 14 negative events occur from April to September). In a recent paper, Tegtmeier et al.  have reported an unexpectedly long persistence of ozone anomalies in the middle stratosphere at midlatitudes, and hypothesized that this persistence is connected to transport-induced anomalies in odd nitrogen (NOy). Since NOy, which has a lifetime exceeding 1 year at 30–40 km, acts as an ozone destructing agent through the NOx cycle, NOy anomalies perturb the chemical ozone balance on timescales far beyond the photochemical lifetime of ozone itself. Thus we hypothesize that transport-induced NOy anomalies may play a role for the long persistence of polar ozone anomalies observed here, but this assumption is speculative at the moment and requires further testing.
 Around day 0 in Figure 10, a vertical “branch” of the anomaly is visible both in the positive as in the negative case, reaching into the upper stratosphere. This is at least partly a contribution from NAM events, which are described further in the next section.
5.2. Relation to NAM Phase
 Parts of the variability of polar ozone are attributable to dynamic effects. A good indicator of the dynamic state of the NH atmospheric circulation is given by the Northern Hemisphere annular mode (NAM), which constitutes the dominating pattern of climate variability in the Northern Hemisphere [Thompson and Wallace, 2000; Baldwin and Dunkerton, 2001], on a seasonal as well as on a daily base [Thompson and Wallace, 2001]. The NAM represents the pressure difference between polar regions and lower latitudes and can be expressed as a dimensionless index, which is usually calculated on pressure surfaces. A positive index corresponds to a strong meridional pressure gradient and a strong, more isolated polar vortex, while a negative index indicates a weak or even reversed meridional pressure gradient and hence a weaker vortex. The NAM data set we use is an update from the data set introduced and analyzed by Baldwin and Dunkerton  and was obtained from M. Baldwin's Annular Modes Web page (http://www.nwra.com/resumes/baldwin/nam.php).
 We find that the variability of polar ozone is connected to the NAM phase. Figure 11 shows ozone anomalies in the midstratosphere (600 K, ∼24 km), here for the years 2000–2001. For comparison, zonal means (solid black line) and equivalent latitude means (dashed black line) north of 75°N are shown, both referring to the left axis. The NAM index at 30 hPa, corresponding to roughly the same altitude, is superimposed (gray line, right axis). It is obvious that zonal anomalies follow the inverted NAM index closely and instantaneously. This is understandable, as a weakening of the vortex during low NAM phases usually coincides with a geographical displacement of the vortex, leading to higher than average ozone mixing ratios at high latitudes, while a strengthening of the vortex also induces a stricter confinement to high latitudes, thus lowering average mixing ratios there. However, even though the correlation coefficient itself shows a weaker anticorrelation, also equivalent latitude ozone anomalies appear well related to the NAM phase, especially to strong NAM excursions, albeit with a time lag. This time lag is quantified more precisely in Figure 12, where the correlation between the whole ozone anomaly time series to the NAM index is plotted as a function of offset time between the curves (same model and NAM levels as before). While the anticorrelation to zonal anomalies shows a distinctive peak at day zero (no offset), the peak of the equivalent latitude anticorrelation is broader and shifted by 10 days (indicated by an arrow). Hence we conclude that dynamical variations of the stratosphere as expressed by the NAM phase affect zonal high-latitude ozone anomalies immediately and strongly (for the 29 year time series, the correlation coefficient reaches values of <−0.7), which is in part due to geographical effects. If such geographical effects are eliminated by the transition to equivalent latitude coordinates, the anticorrelation is weaker but still present (maximum anticorrelation −0.4), and the effects are shifted in time by about 10 days. We explain this result as a distinct sign of the mixing in of ozone rich air during a disturbed vortex (negative NAM) and the stronger relaxation toward lower photochemical equilibrium ozone mixing ratios during a stronger, more secluded vortex (positive NAM), when transport of ozone rich air into the vortex is largely inhibited.
Figure 11 suggests that especially large NAM anomalies have a profound influence on polar ozone variability. In order to study this aspect further, we now investigate the evolution of ozone anomalies especially in connection with such large NAM anomalies, or “strong” and “weak” vortex events. In order to distinguish such events, we follow the definition of Baldwin and Dunkerton , who classified “strong” and “weak” vortex events by the date when the NAM index at 10 hPa first exceeded certain threshold values of +1.5 in positive and −3.0 in negative direction, after 60 days of not exceeding these limits. The event indicates the onset of an anomaly in stratospheric circulation.
 With the above definition applied, 20 strong and 12 weak vortex events are found in the time span covered by our assimilation. NAM events occur from December to February; in order to make the ozone changes due to NAM events comparable in spite of the different background values of ozone at the respective onset times, we normalize the anomalies by the annual cycle.
 In Figure 13, the evolution of vortex ozone anomalies is shown as composites of anomalies during weak and strong vortex events, and their difference, in the same way as in Figure 10. In Figures 13a and 13b, colors represent relative ozone anomalies averaged poleward of 65° equivalent latitude during weak and strong vortex events, respectively; black contour lines indicate the significance of deviations from the mean annual cycle. For better viewing, a 5 day running mean has been applied to smooth Figure 13. As already mentioned, we choose the 10 hPa surface to distinguish NAM events, which corresponds to a midstratospheric potential temperature of around 840 K.
 Before the weak vortex event (Figure 13a), only little changes in ozone are visible, which are hardly significant. About 10 days before the NAM event, a downward propagating positive anomaly appears in the uppermost stratosphere, which intensifies to ∼10% almost instantaneously after the threshold day and rapidly descends to the middle stratosphere. Simultaneously, a large positive anomaly (∼10%) appears at around 600 K, which merges with the downward propagating anomaly from the upper stratosphere, resulting in a more than 10% anomaly in the midstratosphere. Since the descent of the upper stratospheric anomaly is by far too fast to be attributable to actual physical transport of air, we conclude that the dynamical information propagates downward and induces the ozone anomaly. At ∼500 K the meridional ozone gradient reverses, and a weakening of the vortex structure leads to mixing in of ozone deprived air, which leads to the negative ozone anomaly observed below 500 K. NAM events decay on a timescale of ∼60 days [Baldwin and Dunkerton, 2001]. Nonetheless the ozone anomaly in the middle stratosphere continues to exist long after the NAM index has returned to standard values, slowly descending to the lower stratosphere. Although only significant on a level of 1.65 standard deviations (90%), the anomaly is well visible as ∼5% enhancement up to 120–150 days after the event, when it reaches the lower boundary of our CTM.
 In the case of strong vortex events (Figure 13b), the observed anomalies are smaller, but the general picture is strikingly similar with inverse signs (note the reversed color scale). A negative anomaly arises first in the upper stratosphere. The propagation of the anomaly to the middle stratosphere is less compact than in the weak vortex case, and part of the negative anomaly appears to remain in the upper stratosphere for more than a month, intensifying to ∼−10% and slowly descending to ∼1500 K, where it vanishes after 50 days. Inverse to the weak vortex composite picture, a negative anomaly develops in the middle stratosphere at 500–700 K, accompanied by a positive anomaly below 500 K (which is, as mentioned above, attributable to the reversal of the meridional ozone gradient at this potential temperature level). The negative anomaly reaches values of ∼5% and slowly propagates downward on the same timescale as the positive anomaly in the weak vortex case. Also in this case, the ozone anomaly remains visible for months after the NAM phase has relaxed to “normal” values, and reaches the lower boundary of our model 120–160 days after the NAM event onset.
Figure 13c shows the difference of Figures 13a and 13b, demonstrating the high significance of ozone changes induced by strong versus weak vortex events. As in Figure 10, the difference is normalized by the mean ozone VMR during strong and weak vortex events. The significance of the ozone difference between strong-vortex and weak-vortex phases was established by a Student's t test. Since the shape of positive and negative ozone anomalies during weak and strong vortex events is similar, but with inverted sign, also their difference closely resembles the weak vortex (or inverted strong vortex) pattern, with differences reaching 20% of mean ozone in the midstratosphere. We find that the significance of the anomaly exceeds 95% from the onset of the NAM event to the passage of the anomaly through the lower model boundary 5 months later. In the middle stratosphere, significance levels exceed 99% for more than 3 months.
 The fact that the ozone anomalies produced by strong and weak vortex events follow a very similar pattern is not trivial, since to our understanding the mechanisms are different. While the positive ozone anomaly following a weak vortex event is primarily caused by mixing in of ozone rich air from outside the vortex, the negative ozone anomaly following a strong vortex event is caused by photochemical ozone relaxation.
 The behavior of such purely dynamics-induced anomalies is distinctly different from that of “average” anomalies shown in Figure 10, as they transit most of the stratosphere almost instantaneously and then descend to the lower boundary of our model in 5 months. However, it should be emphasized that 7 out of 22 positive ozone anomalies shown in Figure 10 occur within 30 days of weak vortex events, and 7 out of 14 negative events occur within 30 days of strong vortex events. We find only one converse case: in January/February 1995, a negative ozone anomaly occurs almost a month before a weak vortex event. This is most probably a statistical artifact since the coincidence window of 30 days is taken in both directions, but usually the vortex event precedes the anomaly or occurs no later than 10 days afterwards.
 Our analysis shows that (1) ozone anomalies in the middle stratosphere display a long lifetime of 7 months on average while descending slowly to the lower stratosphere, that (2) NAM events play an important role for ozone variability, and that (3) NAM-induced ozone anomalies exhibit a behavior which is inversely similar in the case of strong and weak vortex events, but distinctly different from average ozone anomalies. NAM events trigger large ozone anomalies which first appear in the uppermost stratosphere, traverse most of the stratosphere within a few days, and then descend to the lowermost stratosphere within 5 months.
 We have introduced a consistent 29 year 3-D data set of daily stratospheric ozone created by the assimilation of SBUV satellite observations into our stratospheric CTM. The data set is in excellent agreement with independent sonde and satellite observations. Correlations of ozone anomalies between the assimilated data set and high-latitude ozone sonde measurements are high in both hemispheres. A comparison with the passive infrared sounder MIPAS on ENVISAT shows that also the spatial structure of high-latitude ozone during polar night is represented well. Thus we conclude that through the assimilation process, the available information from SBUV satellite observations is extended into areas which are not covered during polar night, and thus allows for an in-depth analysis of polar ozone during winter. As a first step into an enhanced understanding of the variability of the Arctic ozone layer, we investigate the development and persistence of ozone anomalies.
 Polar ozone exhibits large anomalies which predominantly appear in the middle to upper stratosphere, often during fall and winter, and subsequently propagate to lower levels, where they remain for up to a year. On average, ozone anomalies develop around 1000 K/35 km and then descend slowly, displaying a remarkably long lifetime of around 7 months. Positive and negative anomalies follow a very similar pattern.
 The variability in polar ozone is found to be closely related to anomalies in the stratospheric circulation, as expressed by the NAM index. Zonal high-latitude ozone anomalies in the midstratosphere show a strong and instantaneous anticorrelation to the NAM index, which is partly due to spatial displacement of polar air masses due to circulation anomalies. In the case of equivalent latitude anomalies the anticorrelation is weaker and exhibits a time lag of ∼10 days. In particular, large excursions of the NAM result in large ozone anomalies with the opposite sign as the NAM index anomaly. These dynamics-induced ozone anomalies follow a characteristic pattern, which is again strikingly similar in the case of positive anomalies (weak vortex events) and negative anomalies (strong vortex events), albeit with opposing signs. However, this pattern is distinctly different from the evolution pattern of average midstratospheric ozone anomalies, as NAM-induced anomalies cover most of the middle and upper stratosphere within days and then descend to the lowermost stratosphere within 5 months.
 The mechanisms linking NAM anomalies to anomalies in polar stratospheric ozone are well understandable, as a weakening of the vortex (corresponding to a negative NAM anomaly) leads to more mixing in of ozone rich air from midlatitudes, while a stronger vortex (corresponding to a positive NAM anomaly) inhibits this mixing and thus induces a relaxation toward the lower-ozone photochemical equilibrium state.
 The long lifetime of polar ozone anomalies observed here is remarkable. Further investigations will be needed in order to separate the roles of dynamics and chemistry for this persistence, e.g., the possible role of NOy anomalies. While the assimilated data set has already yielded insights into the evolution and persistence of high latitude ozone anomalies during winter, not available from previous observations, we expect that the assimilated data set will be useful for further in-depth investigation of the interaction of ozone chemistry and dynamics in the stratosphere. The assimilated data set may be obtained from the authors upon request.
 This research work has been funded by the German Research Foundation under the Priority Programme “Climate and Weather of the Sun Earth System.” We thank Martyn Chipperfield for sharing his assimilation code and expertise with us. SBUV data were taken from the V8 DVD released 2003 and the V8b update released 2008. ECMWF ERA-40 data used in this study have been obtained from the ECMWF data server through the special project DECDIO. We thank Peter von der Gathen for providing the Ny-Ålesund sonde data and Rigel Kivi for providing the Sodankylä sonde data and information on sonde observational errors. South Pole and Neumayer sonde data were obtained from the NDACC data server. We thank Gabi Stiller (FZ Karlsruhe) for providing the MIPAS data.