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We present a new set of statistical-dynamical equations (SDEs) which can accurately reproduce the three-dimensional atmospheric fields of synoptic scale kinetic energy and momentum flux. The set of equations is closed by finding proper parameterizations for the vertical macro-turbulent diffusion coefficient and ageostrophic terms. The equations have been implemented in a new SD atmosphere model, named <i>Aeolus</i>. We show that the synoptic scale kinetic energy and momentum fluxes generated by the model are in good agreement with empirical data, which were derived from bandpass-filtered ERA-40 data. In addition to present-day climate, the model is tested for substantially colder (last glacial maximum) and warmer (2×CO<sub>2</sub>) climates, and shown to be in agreement with general circulation model (GCM) results. With the derived equations, one can efficiently study the position and strength of storm tracks under different climate scenarios with calculation time a fraction of those of GCMs. This work prepares ground for the development of a new generation of fast Earth System Models of Intermediate Complexity which are able to perform multi-millennia simulations in a reasonable time frame while appropriately accounting for the climatic effect of storm tracks

Three-dimensional parameterizations of the synoptic scale kinetic energy and momentum flux in the Earth's atmosphere