Multivariate data assimilation is achieved by introducing mass/wind balance relationships in the background term. Geostrophy is commonly used as such a relationship in mid-latitudes. For tropical latitudes, a new balance relationship on the basis of equatorial waves has been proposed. In order to combine the equatorial with the mid-latitudinal formulation, a new data assimilation scheme is developed. The balance relationships are formulated in terms of Hough modes. For the minimization of the cost function, a control variable is constructed, where the background error is projected onto an appropriate selection of Hough modes which are weighted with their respective background covariances. The covariance structures of the data assimilation scheme are examined with single observation experiments and the increments are discussed with respect to the balance relationships. Finally, the new proposed assimilation scheme is tested in a simple observing system simulation experiment. The application of an incomplete balance relationship based on geostrophy leads to a misinterpretation of observational data and thus to enhanced analysis errors. Only the combined balance relationship improves the tropical analysis. This improvement is expected to play an important role for the analysis quality, when future wind observations from the Earth Explorer Atmospheric Dynamics Mission are available.
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