In the context of the MOSE project, in this contribution we present a detailed analysis of the Meso-NH mesoscale model performances and their dependency on the model and orography horizontal resolutions in proximity of the ground. The investigated sites are Cerro Paranal (site of the ESO Very Large Telescope - VLT) and Cerro Armazones (site of the ESO European Extremely Large Telescope - E-ELT), in Chile. At both sites, data from a rich statistical sample of different nights are available - from AWS (Automated Weather Stations) and masts - giving access to wind speed, wind direction and temperature at different levels near the ground (from 2 m to 30 m above the ground). In this study we discuss the use of a very high horizontal resolution (dX=0.1 km) numerical configuration that overcomes some specific limitations put in evidence with a standard configuration with dX=0.5 km. In both sites results are very promising. The study is co-funded by ESO and INAF.