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Summary Report No. 51

Struktur der Amplitudengleichung des Klimas

A. Hauschild (April 1999)

The structure of the "amplitude equation", a new dynamic equation on the seasonal time scale is derived, in which the weather scales may be treated statistically. The elsewhere-introduced climate-specific seasonally smoothed amplitudes and phases of the Fourier spectral representation are used as new prognostic variables. For the vorticity it is shown, that the still unsolved problem of the parameterisation of subscale transports may be solved in the "amplitude equation".

The approach could be successful because of the empirically derived statistical properties of the amplitudes (Poisson distribution and ergodicity) and of the phases (equipartition) of sub-planetary waves could be used. They allow a scale separation of weather and climate and lead to a tremendous reduction of the number of the horizontal degrees of freedom of the amplitude equation to be between 103 and 104.

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