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Data and spectral decomposition

We have used the 50, 30 and 10 hPa level of stratospheric geopotential and temperature data of the 21-year period 1976 to 1996 from the Free University Berlin. As daily values were not available regularly every day during whole year, we finally used the monthly means of spectral coefficients. We analyzed all the midnight data in the northern hemisphere at 64 gridpoints on each of 32 Gaussian latitudes. Using the standard algorithm of the spectral method, we applied Fourier decomposition along the Gaussian latitudes and transformation in terms of associated Legendre's polynomials in meridional direction obtaining the spectral coefficients which are generally complex (for detailes see, e.g., Bourke et al., 1977, Haltiner and Williams, 1980, Machenhauer, 1979). It should be pointed out that the decomposition is good enough to provide substantial information about the circulation patterns. For the rhomboidal truncation by wavenumber 7 the comparison of the original field and the field reconstructed from the truncated spectral domain is under 1% of difference for the geopotential and slightly worse for the temperature. Even for truncation by wave number 5 only a very limited area displays a higher error, the difference generally remaining very low.

Most of results presented here is based on this data analysis. Moreover, we used for the analysis a huge database of reanalyses from NCEP as well , where just appropriate spectral coefficients are available for period 1948-now four times per day in 28 levels for vorticity, divergence, temperature, etc. in triangular truncation by wavenumber 64.