We present the overview of the MOSE project (MOdeling ESO Sites) aiming at proving the feasibility of the forecast of the classical atmospherical parameters (wind speed intensity and direction, temperature, relative humidity) and the optical turbulence OT (CN2 profiles and the most relevant integrated astro-climatic parameters derived from the CN2: the seeing, the isoplanatic angle, the wavefront coherence time) above the two ESO ground-based sites of Cerro Paranal and Cerro Armazones. The final outcome of the study is to investigate the opportunity to implement an automatic system for the forecast of these parameters at these sites. In this paper we present results related to the Meso-Nh model ability in reconstructing the vertical stratification of the atmospherical parameters along the 20 km above the ground. The very satisfactory performances shown by the model in reconstructing most of these parameters (and in particular the wind speed) put this tool of investigation as the most suitable to be used in astronomical observatories to support AO facilities and to calculate the temporal evolution of the wind speed and the wavefront coherence time at whatever temporal sampling. The further great advantage of this solution is that such estimates can be available in advance (order of some hours) with respect to the time of interest
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