What is data assimilation?

Data assimilation is a general technique to combine measurements (which contain observation errors) with models that describe the time evolution of the system (which are generally incomplete, resulting in forecast errors). Assimilation improves the model state based on the information contained in the observations. It provides the most probable state of the system, given the uncertainties in the observations and model forecast.

For TM3-DAM the measurements are total columns of ozone as observed by the GOME satellite instrument [Burrows, 1999]. The model is a modification of the chemistry-transport model TM3 .

Figure 1: Top: a collection of 24 hours of GOME data, 30 Nov 1999. Bottom: the assimilated ozone field at 12 GMT, based on the GOME data. Apart from the ozone hole at the South pole (blue), very low ozone values are observed above the North Sea. Analysis based on the model shows that the low ozone values are mainly caused by an exceptional atmospheric flow and a transport of ozone-poor air from the subtropics to higher latitudes. The event lasted only a few days, and after that the ozone layer in the Northern Hemisphere returned to normal values. Ozone columns in Dobson units.

Why data assimilation?

There are several motivations for using data assimilation in the study of atmospheric chemisty in general and for GOME data in particular:
To extend the use of GOME data. Data assimilation converts a sequential list of satellite observations into global maps of ozone, filling the gaps in between the observations. See figure 1. These global maps are easy to use for intercomparisons with other observations and with modelled ozone distributions.
To generate a complete data base of three dimensional daily ozone distributions.
To improve the retrieval of ozone amounts (and other trace gases) from radiances measured by satellite instruments, by providing realistic first-guess vertical ozone profiles.
To obtain information about the accuracy of the observations, by confronting these observations with the model forecasts, and by comparing the assimilated products with other observations.
To obtain information about the performance of the various aspects in the model and possible problems, through the continuous confrontation of the model with new measurements.
To assist in validation campaigns for new satellite instruments.
To provide ozone forecasts. These provide a basis for UV forecasts and are useful, for instance, for the planning of measurement campaigns.
To perform case studies for special events, such as shown in figure 1. To identify the causes (e.g. chemistry versus transport) of the observed ozone distributions.

The model: introduction

The model provides an approximate description of the evolution of the three-dimensional distribution of ozone in the atmosphere. This evolution is determined by transport and chemistry. Ozone behaves as a tracer and is transported by the horizontal and vertical winds in the atmosphere. Ozone is also a reactive chemical, and the concentration of ozone is determined by the concentrations of other chemicals, emissions and deposition at the surface and the radiation intensity.

The model: transport

The tracer transport model (TM3) has been adapted from the global Tracer transport Model TM2 [Heimann, 1995], and calculates the horizontal and vertical transport of tracer masses. It is driven by the meteorological fields (wind, surface pressure, temperature) from the European Centre for Medium-Range Weather Forecasts (ECMWF). These fields are updated every 6 hours.

The model divides the atmosphere in 144 longitude by 72 latitude gridboxes and 44 vertical layers from the surface to 0.1 hPa (the mesosphere). The vertical layers are identical to the ECMWF layers in the stratosphere (where the ozone layer is situated). In the trosphere the amount of layers is reduced with respect to the ECMWF model. The numerical implementation of the transport is based on the second moments advection scheme [Prather, 1986]. The ozone distributions are plotted on a 1.25 degree longitude-latitude grid.

The model: chemistry

Stratospheric ozone chemistry is described by two parametrisations, one for gas-phase chemistry and one for heterogeneous ozone breakdown. These simplified schemes are fast: a more complete treatment of the chemistry would require the explicit modelling of in the oder of 50 chemical species, which is too computationally expensive for our purpose.

The gas-phase production and loss of ozone in the stratosphere is described by the chemistry parametrisation developed by [Cariolle, 1986]. The implementation in TM3 is discussed in [Jeuken, 1999], [Eskes, 2000]. Recently we have updated the Cariolle scheme with the ``Linoz'' linear ozone model coefficients as described in [McLinden, 2000].

Ozone breakdown as observed in the antarctic and arctic ozone holes are initiated by heterogeneous chemical processes that take place on liquid and solid cloud particles in the stratosphere, in the presence of polar stratospheric clouds (psc). The heterogeneous chemistry is modelled by a simple scheme that was developed by the Centre for Atmospheric Science, Cambridge University [Braesicke, 2000]. This scheme introduces an additional 3D tracer field which describes the degree of chlorine activation as a result of the psc formation. In the presence of activation ozone is depleted.

GOME observations

The GOME instrument measures the sunlight reflected from the Earth's atmosphere and surface in the spectral range 240-790 nm (UV-visible) [Burrows, 1999]. GOME is part of the ESA ERS-2 polar orbiting satellite. TM3-DAM assimilates vertical columns of ozone which are retrieved from the GOME spectra by the fast delivery service at the KNMI [Valks, 2000]. The pixel size of GOME is 40 by 320 km, and the swath width is 960 km, see figure 1. With this swath width GOME obtains global coverage in three days.

Assimilation scheme

The assimilation scheme in TM3-DAM is based on the Kalman filter equations, but the scheme avoids the extreme time and memory consuming aspects of the Kalman filter by fixing the correlations between the model forecast errors. This correlation is described by a time-independent function of the distance between the two points, and the shape and correlation length are determined from the forecast performance statistics. The variance (diagonal of the forecast error covariance matrix), however, depends on space and time and the evolution of the variance is described by the Kalman filter equations. As a result the scheme produces a detailed error estimate of the analysed ozone fields (see figure 2).

Several aspects of the assimilation approach and the error modelling have been discussed in [Eskes, 1999], [Eskes, 2000], and [Jeuken, 1999]. For more details we refer to these papers.

Figure 2: Estimated forecast error distribution at 18 GMT, 21 June 2000. Scale in Dobson units. Three aspects of the Kalman filter are demonstrated by the figure: 1) new GOME observations lead to a reduction of the uncertainty at the swaths. 2) The forecast error increases with time, from left to right in the figure. 3) The forecast error is transported by the wind field, leading to irregular shapes of the swaths. The uncertainty is high at the South pole due to the lack of GOME observations in June.

Forecast skill

The figure below shows the difference between the GOME total ozone observation and the corresponding model forecast for the ozone column at the same position and time (o-f). The figure shows both the bias and the root-mean-square (rms) difference of (o-f) as a function of the latitude, averaged over all observations in March 2000. The rms difference is the sum of three contributions, namely the model forecast error, the observation error (noise) and the representativeness error (mismatch due to the difference between the model grid cells and the field of view of the satellite). The bias between the observations and forecast is smaller than 1 % for all latitudes. Note that the rms is largest for northern midlatitudes. This is related to the large variability of ozone in the Northern hemisphere in winter.

Figure 3: GOME observation minus model forecast statistics for March 2000. Solid curve: root-mean-square difference between the GOME ozone column and the model forecast. Dashed curve: average difference or bias between GOME and the forecast. The bias is smaller than 3 DU for all latitudes. Vertical scale in Dobson units.

A remark about biases

In general all observations have biases, or systematic offsets from the truth. Typical differences between the fast-delivery GOME total ozone product and ground-based stations are of the order of 3-5 percent, depending on latitude, season and solar zenith angle. In numerical weather prediction models it is common practice to apply a bias correction to observations before the assimilation. In TM3-DAM no such bias correction is applied. Through the assimilation the model adopts the ozone level as given by the observations, and in this sense the assimilated fields are higher-order GOME products. This is demonstrated in figure 3 (and figure 1) which shows that the bias between the model and GOME is very small. Given the small bias, the assimilated fields can be compared with independent observations to study the differences with either other satellite instruments or ground-based observations. An example of this is shown in figure 4.

Figure 4: A comparison between a GOME assimilated ozone field (left) and independent TOMS observations for the same day (right, taken from the TOMS home page of NASA). To minimise the mismatch in time, the assimilated field is shown at 12 o'clock local time. Note that the small scale structures in both plots are very similar. The large-scale differences in ozone values reflect the differences in the instruments, instrument calibration and the retrieval algorithms of total ozone. Date: 31 March 2000. Scale in Dobson units.

References:

P. Braesicke, private communications; Hadjinicolaou P., J.A. Pyle, M.P. Chipperfield, and J. Kettleborough, "Effect of interannual meteorological variability on middle latitude O3", Geophys. Res. Lett., 24, 2993-2996, 1997.

Burrows, J.P., M. Weber, M. Buchwitz, V. Rozanov, A. Ladstätter-Weibenmayer, A. Richter, R. Debeek, R. Hoogen, K. Bramstedt, K.-U. Eichmann, M. Eisinger, D. Perner, "The Global Ozone Monitoring Experiment (GOME): Mission concept and first results", J. Atmos. Sciences, 56, no. 2, pp. 151-175, 1999.

Cariolle, D. and M. Deque, "Southern Hemisphere medium-scale waves and total ozone disturbances in a spectral general circulation model", J.Geophys.Res., 91, 10825, 1986

Eskes, H. J., A. J. M. Piters, P. F. Levelt, M. A. F. Allaart, and H. M. Kelder, "Variational assimilation of total-column ozone satellite data in a 2D lat-lon tracer-transport model", J. Atmos. Sci., 56, 3560, 1999.

Eskes, Henk, Peter van Velthoven, Ghada El Serafy, and Hennie Kelder, "GOME ozone data assimilation and the ozone mini-hole of 30 november 1999", Proceedings of the ESA ERS - ENVISAT SYMPOSIUM, 16-20 October 2000, Gothenburg. (Article)

GOME fast delivery service, KNMI.

Heimann, M., "The global atmospheric tracer model TM2", Technical report no. 10, Deutsches Klimarechenzentrum (DKRZ), Hamburg, Germany,1995.

Jeuken, A.B.M., H.J. Eskes, P.F.J. van Velthoven, H. M. Kelder, and E.V. Holm. "Assimilation of total ozone satellite measurements in a three-dimensional tracer transport model", J. Geophys. Res., 104, 5551, 1999.

McLinden, C.A., S.C. Olsen, B. Hannegan, O. Wild, M.J. Prather and J. Sundet, "Stratospheric ozone in 3-D models: A simple chemistry and the cross-tropopause flux", J.Geophys.Res., 105, 14653, 2000.

Prather, M.J., "Numerical advection by conservation of second-order moments", J. Geophys. Res., 91, 6671, 1986.

P.J.M. Valks, A.J.M. Piters, J.C. Lambert, and C. Zehner "Improved near-real time GOME ozone column retrieval", Proceedings of the ESA ERS - ENVISAT SYMPOSIUM, 16-20 October 2000, Gothenburg.