### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Model and Data
- 3. Assimilation Method
- 4. Validation of the Assimilated Data Set
- 5. Results and Discussion
- 6. Conclusions
- Acknowledgments
- References
- Supporting Information

[1] 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.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Model and Data
- 3. Assimilation Method
- 4. Validation of the Assimilated Data Set
- 5. Results and Discussion
- 6. Conclusions
- Acknowledgments
- References
- Supporting Information

[2] 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.* [2005] and *Sinnhuber et al.* [2006]. Moreover, *Sinnhuber et al.* [2006] reported indications for a solar influence on the variability of stratospheric ozone through energetic particle precipitation.

[3] 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.

[4] There have been several attempts to create consistent long-term data sets of stratospheric ozone outside high latitudes, e.g., *Randel and Wu* [2007] 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.

[5] 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.

[6] 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.* [2000] and *Chipperfield et al.* [2002] to generate a 29 year data set of stratospheric ozone.

[7] 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).

[8] 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].

[9] 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

- Top of page
- Abstract
- 1. Introduction
- 2. Model and Data
- 3. Assimilation Method
- 4. Validation of the Assimilated Data Set
- 5. Results and Discussion
- 6. Conclusions
- Acknowledgments
- References
- Supporting Information

[10] 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.* [2000]. 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.

[11] The effects of heterogenous ozone destruction are included in form of a simple parameterized polar chemistry which calculates the critical temperature *T*_{NAT} for PSC formation in each grid box and destroys ozone at a defined rate as soon as the temperature *T* < *T*_{NAT} 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).

[12] 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.* [2009] 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 TimesTime | Satellite |
---|

10/1978–12/1988 | Nimbus 7 |

1/1989–12/1991 | NOAA 11 |

1/1992–7/1997 | NOAA 9 |

8/1997–12/2000 | NOAA 11 |

1/2001–12/2007 | NOAA 16 |

### 3. Assimilation Method

- Top of page
- Abstract
- 1. Introduction
- 2. Model and Data
- 3. Assimilation Method
- 4. Validation of the Assimilated Data Set
- 5. Results and Discussion
- 6. Conclusions
- Acknowledgments
- References
- Supporting Information

[14] 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 **x**^{f}(*t*) ≡ **x**_{t}^{f} at time *t* of the dimension of *n*_{mod} = *n*_{lon} × *n*_{lat} × *n*_{lev} = 96 × 72 × 24 = 165888 = number of model grid cells (*n*_{lon}, *n*_{lat}, and *n*_{lev} 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 **B**_{t}^{f}. At the same time, observations of the “true” (unknown) state of the atmosphere **x**_{t}^{t} are made, denoted by the vector **y**_{t} of dimension *n*_{obs} = *n*_{obsloc} × *n*_{obslev} = total number of observation points (*n*_{obsloc} is number of observation locations, *n*_{obslev} is number of vertical observation levels. For SBUV observations *n*_{obs} < 1000 in the 30 min assimilation window).

[15] The relation between the true state of the atmosphere **x**_{t} and the observations **y** can be expressed by the observational operator **H**,

where ɛ_{t} is the overall error, composed of an observational error **O** and a representativeness error **R**,

[16] Essentially, the assimilation process performs an inversion of equation (1) to solve for **x**_{t}^{t}, 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 **x**_{t}^{a} (called “analysis” in the following), which is a best linear unbiased estimator to **x**_{t}^{t}. According to optimal estimation theory, the analysis is given by

where

**K** is called the Kalman gain. The analysis error covariance **B**_{t}^{a} is given by

[17] 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 O_{3} VMR and model O_{3} 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.).

[18] 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**.

[19] 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.

[20] 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 **x**_{t}^{a} (analysis) is passed back to the model along with the computed variance **B**_{t}^{a}, which serve as the initial state for the next model integration to yield **x**_{t+Δt}^{f} and **B**_{t+Δt}^{f} at a later time *t* + Δ*t*,

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.

[21] However, since the dimension of the covariance matrix **B** is *n*_{mod} × *n*_{mod} = 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.* [2000], we transport only the diagonal elements *b*_{ii}^{a} of **B**^{a} in the model integration (equation (8)) to obtain the diagonal elements *b*_{ii} of the forecast variance **B**^{f}. For the analysis step (equation (3)), the off-diagonal elements (covariances) are parameterized as

with Δ*r*_{xy} and Δ*r*_{z} distances in horizontal and vertical direction. *L*_{xy} and *L*_{z} are tunable coherence lengths, which we choose in accordance with *Chipperfield et al.* [2002] to be *L*_{xy} = 1000 km and *L*_{z} = 2.8 km. During model integration, the analysis error variance *b*_{ii,t}^{a} is first transported as a tracer,

and then increased by the error growth term *q*_{ii}^{t} in order to account for the growing uncertainty in the modeled tracer in the absence of data,

[22] The numerical value for the error growth factor ε = 0.01 is an update from *Chipperfield et al.* [2002], 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 *χ*^{2} diagnostic near its expectation value of 1. We find that as the long-term mean of the *χ*^{2} diagnostic is close to 1, the treatment of errors and error growth is reasonable in our assimilation scheme.

[23] 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 O_{3} strongly, and O_{3} 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).

[24] 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.

[25] A detailed validation of the data set is provided in the following section.

### 6. Conclusions

- Top of page
- Abstract
- 1. Introduction
- 2. Model and Data
- 3. Assimilation Method
- 4. Validation of the Assimilated Data Set
- 5. Results and Discussion
- 6. Conclusions
- Acknowledgments
- References
- Supporting Information

[56] 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.

[57] 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.

[58] 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.

[59] 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.

[60] 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 NO_{y} 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.