We present and validate a set of equations for representing the atmosphere's large-scale general circulation in an Earth system model of intermediate complexity (EMIC). These dynamical equations have been implemented in Aeolus, which is a Statistical Dynamical Atmosphere Model (SDAM) and includes radiative transfer and cloud modules (Coumou, 2011; Eliseev, 2013). The statistical dynamical approach is computationally efficient, and thus enables us to do climate simulations at multi-millennia timescales, which is a prime aim of our model development. Further, this computational efficiency enables us to scan large and high-dimensional parameter space to tune the model parameters. <br><br> We optimize the dynamical core parameter values by tuning all relevant dynamical variables to ERA-Interim reanalysis data (1983–2009) using monthly mean data of climatology data as well as the data for the El Niño and La Niña composites. We use a Simulated Annealing optimization algorithm, which approximates the global minimum of a high-dimensional function. <br><br> With non-tuned parameter values, the model performs reasonably in terms of its representation of zonal-mean circulation, planetary waves and storm tracks. The Simulated Annealing optimization improves in particular the model's representation of the northern hemisphere jet stream and storm tracks as well as the Hadley circulation. <br><br> The regions of high azonal wind velocities (planetary waves) are accurately captured for all validation experiments. The zonal-mean zonal wind and the integrated lower troposphere mass flux show good results in particular in the Northern Hemisphere. In the Southern Hemisphere, the model tends to produce too weak zonal-mean zonal winds and a too narrow Hadley circulation. We discuss possible reasons for these model biases as well as planned future model applications.