This paper is the second of a series in which we aim to prove the feasibility of forecasting all the most relevant classical atmospheric parameters for astronomical applications (wind speed, wind direction, temperature, relative humidity) and the optical turbulence (C-N(2) and the derived astroclimatic parameters, such as seeing epsilon, isoplanatic angle theta(0), wavefront coherence time tau(0), etc.). This study is carried out in the framework of the MOSE (MOdelling ESO Sites) project, and is focused above the two European Southern Observatory ground-based sites of Cerro Paranal and Cerro Armazones. In this paper, we present the results related to the meso-nh model ability in reconstructing the surface layer atmospheric parameters (wind-speed intensity, wind direction and absolute temperature, 0-30 m above ground level). The model reconstruction of all the atmospheric parameters in the surface layer is very satisfactory. For the temperature, at all levels, the root mean square error (RMSE) is inferior to 1 degrees C. For the wind speed, it is similar to 2 m s(-1), and for the wind direction, it is in the range 38 degrees-46 degrees, at all levels, which corresponds to a RMSErelative in the range 21-26 per cent. If a filter is applied for the wind direction (winds inferior to 3 m s(-1) are discarded from the computations), the wind direction RMSE is in the range 30 degrees-41 degrees (i.e. RMSErelative in the range 17-23 per cent). The model operational forecast of the surface layer atmospheric parameters is suitable for different applications, as follows. It can be used for thermalization of the dome using the reconstructed temperature, hours in advance, of the beginning the night. It can provide knowledge in advance of the main direction from which strong winds will come during the night, which could allow an astronomer to anticipate the occurrence of a good/bad seeing night, and to plan observations accordingly. It can also prevent adaptive secondary mirror shake generated by the wind speed.