The alternate 4D-Var assimilation of the same rawinsonde observations was found to produce measurable improvements in the cyclone intensity and position. It is hoped that further improvements can be attained through the 4D-Var assimilation of vertically integrated TOMS ozone observations. However, work carried out thus far suggests that TOMS ozone observations are likely to have an impact on the forecast only if combined with additional information that constrains the model fields in the medium and lower-troposphere. This is because most of the tropospheric ozone is located above the tropopause. The much needed information on the model tropospheric fields can be obtained through the inclusion of more types of observations in the assimilation experiments (e.g. satellite derived rainfall rates). It also anticipated that, through the vertical correlations, the background error covariance matrix will be instrumental in correctly constraining the analysis increments in the troposphere that result from the assimilation of TOMS ozone observations. A method of evaluating the background error covariance matrix on the basis of an ensemble of background error fields that are assumed to provide a good sample of the distribution of all possible error structures will be presented. Using the exact definition of the background error covariance matrix, the auto-correlations and multivariate cross-correlations are obtained through ensembles of vector products. Computational feasibility is achieved by restricting the number of error fields to ten and assuming that the subspace spanned by the five leading eigenvectors of the (ensemble) background error covariance matrix contains all the information on the statistics of the background errors. The performance of the 4D-Var assimilation system that uses such a background error covariance matrix will be compared with the previous system that only uses a diagonal matrix of error variances. A discussion of our ongoing research with an emphasis on the best strategies for assimilating TOMS ozone into atmospheric models will be offered.

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