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On the assimilation of total-ozone satellite data

On the assimilation of total-ozone satellite data Citation for published version (APA): Levelt, P. F., Allaart, M. A. F., & Kelder, H. M. (1997). On the assimilation of total-ozone satellite data. Annales
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On the assimilation of total-ozone satellite data Citation for published version (APA): Levelt, P. F., Allaart, M. A. F., & Kelder, H. M. (1997). On the assimilation of total-ozone satellite data. Annales Geophysicae, 14(11), DOI: /s , /s DOI: /s /s Document status and date: Published: 01/01/1997 Document Version: Publisher s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. The final author version and the galley proof are versions of the publication after peer review. 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If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the Taverne license above, please follow below link for the End User Agreement: Take down policy If you believe that this document breaches copyright please contact us at: providing details and we will investigate your claim. Download date: 10. Sep. 2019 Ann. Geophysicae 14, (1996 EGS Springer-Verlag 1996 On the assimilation of total-ozone satellite data P. F. Levelt, M. A. F. Allaart, H. M. Kelder Royal Netherlands Meteorological Institute (KNMI), 3730 AE De Bilt, The Netherlands Received: 2 November 1995/Revised: April 1996/Accepted: 3 April 1996 Abstract. A two-dimensional model for advection and data assimilation of total-ozone data has been developed. The Assimilation Model KNMI (AMK) is a global model describing the transport of the column amounts of ozone, by a wind field at a single pressure level, assuming that total ozone behaves as a passive tracer. In this study, ozone column amounts measured by the TIROS Operational Vertical Sounder (TOVS) instrument on the National Oceanic and Atmospheric Administration (NOAA) polar satellites and wind fields from the Meteorological Archive and Retrieval System (MARS) archives at ECMWF have been used. By means of the AMK, the incomplete space-time distribution of the TOVS measurements is filled in and global total-ozone maps at any given time can be obtained. The choice of wind field to be used for transporting column amounts of ozone is extensively discussed. It is shown that the 200-hPa wind field is the optimal single-pressure-level wind field for advecting total ozone. Assimilated ozone fields are the basic information for research on atmospheric chemistry and dynamics, but are also important for the validation of ozone measurements. 1 Introduction Satellite measurements and ground-based measurements of ozone are essential for understanding the dynamical and chemical behaviour of ozone, for studying the ozonehole phenomena, for detecting trends in the ozone distribution and for determining the climatology of ozone. Global coverage of satellite measurements is important for most of these studies mentioned. Global total-ozone measurements are produced by satellite instruments like the Total Ozone Monitoring Spectrometer (TOMS) (Stolarski et al., 1991), the Solar Backscatter Ultraviolet Correspondence to: P. F. Levelt Radiometer (SBUV) (Heath et al., 1975), the TIROS Operational Vertical Sounder (TOVS) (Planet et al., 1984), the Global Ozone Monitoring Experiment (GOME) (Hahne et al., 1993) and, in the near future, the Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY) on board of ENVISAT (ESA s, European Space Agency, Environmental Satellite) and the Ozone Monitoring Instrument (OMI) (ESA document, in preparation, 1996) on board of METOP (EUMETSAT s, European Organization for the Exploration of Meteorological Satellites, Meteorological Operational Program). The GOME instrument on board of the ERS-2 satellite, ESA s Earth Resource Satellites, was launched in April GOME measures ozone and other trace gases and has a swath width of 960 km. This will result a global coverage in three days. For several of the mentioned studies, monitoring of the distribution of ozone is needed on a daily basis. However, the ozone maps are often hampered by missing data due to, for example, retrieval problems in the case of clouds (TOVS) or limited swath width (SBUV, GOME). In these cases only sparse data are obtained, and it is often difficult to characterise features in the ozone distribution. The atmospheric circulation and the total-ozone content of the atmosphere are strongly correlated. This has already been recognised for the northern hemisphere for almost seventy years (Dobson et al., 1928 and Dobson, 1968). In general, a high-pressure region will give rise to low ozone values, while an extratropical low will show up as a region with high gradients in total-ozone values and high total-ozone values behind the centre of the low (Heijboer et al., 1996). This relation can be quantified using the correlation between vertically integrated potential vorticity and total ozone, as found by Allaart et al. (1993). In Fig. 1a, a map of retrieved TOVS satellite data measured on 23 April 1992 is shown. The data have been gathered over a period of 24 h. Due to missing data (normally only one-third of the globe is covered with TOVS data), it is difficult to recognise specific features or coherent structures in the global ozone field. Another fundamental problem with the use of data from polar orbiting satellites is that the observations 1112 P. F. Levelt et al.: Assimilation of total-ozone satellite data Fig. 1. a Raw NOAA TOVS total-ozone data (in DU) for 23 April 1992; b assimilated NOAA TOVS total-ozone data (in DU) for 23 April 1992 at 1200 UTC are not made simultaneously. Global maps can be constructed by overlaying subsequent tracks observed at different times. However, spurious gradients due to changes in the ozone distribution in time can occur between adjacent tracks measured at different times. An example of this is shown in Fig. 2, where the global ozone map of 23 April 1992 produced from Nimbus-7 TOMS-data constructed by overlaying subsequent tracks is presented. Spurious gradients on the dateline at 180 E, at the top of the picture, are clearly visible. Data-assimilation techniques can be used to perform a more sophisticated interpolation. By taking into account the transport of ozone, maps of the total-ozone distribution at any given time can be produced. For this purpose a two-dimensional (latitude/longitude) advection and data-assimilation model has been developed [the Assimilation Model KNMI (AMK)] in which total ozone is advected by a wind field at a single pressure level. The data assimilation is performed by taking weighted averages of advected ozone and ozone-satellite measurements. To our knowledge this is one of the first times in which a data-assimilation technique has been used for total ozone. The model uses wind fields from the European Centre for Medium Range Weather Forecasts (ECMWF) model and total-ozone data measured by the TOVS instruments; i.e. AMK is an off-line model which does not calculate its own wind field. The three-dimensionality of the atmosphere versus the two-dimensionality of total ozone poses however a problem. Total-ozone data do not determine in a unique way the ozone profile. If a threedimensional model is used for the advection, an approach is to assume a vertical ozone distribution, and normalise this with total-ozone observations. As there is a wellestablished relation between the ozone mixing ratio and potential vorticity (Danielsen, 1985), an obvious choice is to take the potential-vorticity profile as an approximation Fig. 2. NASA TOMS total-ozone map (in DU) for 23 April Spurious gradients are visible at the date line 180 E (top of the picture) for the ozone profile; this was done by Lary et al. (1995). However, in the AMK the problem is solved differently; in this paper it is shown that the changes in the total-ozone field can be described accurately (i.e. within the uncertainty of TOVS) by advecting total ozone using only wind fields at a single pressure level. Moreover, a procedure to determine which level should be used is presented. In Fig. 1b, the ozone field at 23 April 1992 at 1200 UTC resulting from the AMK is shown. Different meteorological features are clearly distinguishable in the ozone distribution, for example an extended tongue of high ozone values between Alaska and Russia (top of the picture), which is not clearly distinguishable in Fig. 1a and displaced in Fig. 2. In this paper it will be shown that the AMK is able to cope with the incomplete space-time distribution of satellite data, by virtue of data-assimilation techniques. Maps P. F. Levelt et al.: Assimilation of total-ozone satellite data 1113 without spurious gradients, as shown in Fig. 2 (constructed by plotting adjacent tracks of TOMS data), can then be obtained. A third method of representing satellite data is the use of weighted time- and space-averaging of satellite data. Global maps without gaps in the data-field (see Fig. 1a) and without strong spurious gradients due to different times of observation as shown in Fig. 2, can then also be obtained. However, this kind of interpolated map will not be able to capture the dynamics in the ozone field, and gradients in this field are therefore not described properly. Moreover, the AMK is also suitable for predicting the ozone field a few days ahead. The data-assimilation technique used in the AMK is chosen for its relative simplicity in order to limit the computation time of the model. Moreover, for the purpose of assimilating only column amounts of ozone from TOVS, a more elaborate data-assimilation technique is not needed, given the relatively high data rate of the TOVS instruments. 2 Data description The wind data are acquired from the Meteorological Archive and Retrieval System (MARS) archives at ECMWF. The 6-h forecast ( first guess ) horizontal windfield components at single pressure levels with a resolution of 1 1 are used. First-guess wind fields are used instead of analysed wind fields; experiments showed that firstguess wind fields and analysed wind fields resulted in practically the same global ozone field. Wind fields are available every 6 h (at 0000, 0600, 1200 and 1800 UTC) and the wind field is assumed to be frozen during each 6-h interval. The TOVS total-ozone data are from the National Oceanic and Atmospheric Administration (NOAA) (Smith et al., 1979). The TOVS instrument on board the NOAA s operational meteorological polar satellites measures the thermal infrared emission of the atmosphere in several channels. One channel coincides with an absorption band of ozone near 9.7 μm. NOAA National Environmental Satellite, Data, and Information Service (NESDIS) computes the total-ozone content from the measured infrared radiances (Planet et al., 1984). These total-ozone data with a resolution of 80 to 120 km are also stored in, and available from, the MARS archives. The ozone data of both NOAA-11 and NOAA-12 satellites are used. 3 Model description The AMK is a two-dimensional (latitude/longitude) global model with a uniform horizontal resolution of approximately km (Levelt and Allaart, 1994). The grid boxes are equally spaced in latitude, but their number at each latitude circle decreases, going from the equator towards the poles, in order to maintain the uniform resolution. It is an off-line model which advects total column ozone with a pre-calculated wind field. Total ozone is assumed to behave as a passive tracer. This approximation applies only if the dynamical timescale (typically 6 h) is much smaller than the chemical timescale of ozone. This condition is valid for the upper troposphere and the lower stratosphere, where the chemical lifetime of ozone varies from weeks to months, except under ozone-hole conditions. The AMK advects and assimilates column amounts of ozone and uses no ozone-profile information. The crucial assumption made is that transport of ozone column amount can to a good approximation be described by the wind field at a well-chosen pressure level. In the upper troposphere and the stratosphere, air, and hence ozone, flows approximately along surfaces of constant potential temperature and constant potential vorticity. In the extratropics, potential-temperature surfaces approximately coincide with isobaric surfaces. Therefore column amount of ozone can be advected along isobaric surfaces. A wind field at a single pressure level is used; which pressure level is optimal is discussed in Sect. 5. The core of the AMK is the solution of the linear advection equation, assuming ozone column amount (φ) to behave as a passive tracer, and v to be the wind field: φ t #v φ 0. (1) A huge body of literature exists on the solution of the advection diffusion equation [e.g. Rood (1987) for an extensive review, and references therein]. Here, the firstorder forward-in-time upwind technique is implemented to solve the advection equation, resulting in the following formula for the two-dimensional case: φ φ!δt min (u,0)φ!φ x!x!max (u,0) φ!φ x!x!min (v,0) φ!φ y!y!max (v,0) φ!φ y!y, (2) where x and y are respectively the longitudinal and latitudinal direction, u and v are respectively the wind field in the x and the y direction, φ and φ is the tracer field before and after the advection step with timestep Δt t!t, i is the index of the gridbox in longitudinal direction and j is the index for the gridbox in latitudinal direction and max (u, 0) or min (u, 0) means that the maximal or minimal value of u and 0 should be taken, respectively. The timestep Δt for the advection is limited by the Courant-Friedrichs-Lewy (CFL) criterion. Due to the uniform resolution of the grid towards the poles, the timestep can be chosen 50- to 100-times larger than on a1 1 grid. Δt is taken to be 6 min. 4 Data assimilation The data-assimilation technique used in the model is the so-called single-correction method, introduced by 1114 P. F. Levelt et al.: Assimilation of total-ozone satellite data Bergthórsson and Döös (1955), which is the forerunner of the method of successive corrections (Daley, 1991). In the implementation of the method used here, an analysed ozone field at time t#δt is obtained by taking a weighted average between the background field at t#δt and observed ozone data obtained between t and t#δt. For practical reasons the assimilation timestep is the same as the advection timestep in the AMK (Δt 6 min). Starting from an ozone field at t, a first-guess ozone field at t#δt is calculated with the advection procedure already mentioned. This first-guess field is used as a background field in the data-assimilation procedure. The background ozone field at t#δt (φ) is weighted with observed ozone data (φ) obtained between t and t#δt, using only a single correction step. An analysed ozone map at t#δt is then obtained. The analysed ozone value φ is defined by: φ φ #¼ (φ!φ ). (3) Here φ and φ are background ozone at the gridpoint i and the observation point k, respectively, and φ is the observed ozone at observation point k, ¼ is a weighting coefficient and (φ!φ ) is the observation increment. If K observations are available, then Eq. 3 becomes: φ φ# ¼ (φ!φ), (4) wherein ¼ are the weighting coefficients which are a priori specified: ¼ σ ω(r )ρ σ# σω(r )ρ, (5) where σ is the observation-error variance, σ is the background-error variance, r is the distance between analysis point i and observation point k and ρ is a correction function. ω(r ) contains information about the influence of an observation at point k on the ozone value of the gridbox at point i that is being analysed. ω(r ) is assumed to be dependent only on the distance between i and k and has the following properties: ω(r ) 1 when r 0 and ω(r )P0 if r PR. The weight ω(r ) has been determined by several methods. Cressman (1959) and Sasaki (1960) adopted an r-dependent function for ω(r ), whereas Bergthórsson and Döös (1955) derived the weight ω(r ) statistically from data. In this paper the weights are estimated from the calculation of an error covariance matrix with elements (φ (φ, which corresponds to the mean of the product of the differences (φ ). It is assumed that the observation error is spatially uncorrelated as well as uncorrelated with the background error. This results in: and σ #σ for r 0, (6) where φ is the true ozone value, δ and δ are the error in the observation and the model, respectively, and μ(r )is the correlation between background ozone error at the observation points k and l. For the calculation of the elements (φ ) in the error covariance matrix the advected value at the gridpoint closest to the observation is taken. Furthermore, the covariance is assumed to be only dependent on the distance between the observations, and is thus not a function of their absolute positions or their relative orientation, which means that the correlation μ is only r-dependent. Thus, calculating the error covariance matrix gives information about the correlation between the error in advected ozone at point k and the error in advected ozone at point l, and as such provides a weight ω(r ) for the difference (φ at observation point k to be applied at gridpoint i (see Eq. 4). In this paper the correlation μ(r) is used as the weight ω(r ). The error covariance matrix is calculated by summing over contributions per distance interval r, where r is the distance between observation points k and l. In the absence of systematic differences between φ and φ, the error covariance should decrease to zero at large distance (r PR). This reflects the fact that observations which lie far apart from the gridbox being analysed have little influence. In Fig. 3 the error covariance matrix calculated per distance interval of 100 km is shown. At k l the error variance σ #σ is 250 and 350 DU for NOAA-11 and NOAA-12 TOVS data, respectively. For determining the coefficients ω(r ) from the covariance matrix we assume that the observation-error variance is equal to the background-error variance (i.e. σ σ ), which is a reasonable zero-order approximation. The observation-error variance, as well as the background-error variance, is then DU, resulting in an observation error of DU. The error in TOVS observations on the TIROS-N series of satellites is in the order of DU φ (φ (φ )!(φ ) (φ )!(φ ) δ δ!δ δ!δ δ #δ δ σ μ(r ) for r O0 Fig. 3. The error covariance (φ (φ averaged for 6 to 30 April 1992 P. F. Levelt et al.: Assimilation of total-ozone satellite data 1115 (Planet et al., 1984). The error correlation μ(r), and thus the weighting coefficients ω(r ), was then obtained after dividing the error covariance σμ(r) (for ro0) by the error variance σ. Equation 4 can then be written as: φ φ# μ(r r )ρ 1# μ(r r )ρ (φ!φ ). (7) The calculation of the error covariance was performed for the entire month April 1992 and the error covariance in Fig. 3 was obtained by averaging over the results from 6 April to 30 April 1992, allowing for a spin-up time of the model of 5 days. The 50-km point in the covariance plot is the average of th
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