4 Meso-Nh model initialization

4.1 Orographic model

The results presented in this paper have been obtained using a high resolution orographic model (500 m $\times$ 500 m) centered on Paranal mountain (70.40 W, 24.61 S). In Fig. 1 we display the 2D map of the orographic model related to the total available surface domain. It corresponds to a domain of 60 km $\times$ 60 km, that is a 120 $\times$ 120 grid point matrix. Two horizontal dashed lines mark the extension of a second orographic model related to a reduced portion, still preserving the general geographic structure of the region: a sea shore to the west, a sharp mountain chain along the Chilean coast, a broad mountainous region which includes the peak of Paranal and a few higher mountains to the east of Paranal. It corresponds to a domain of 60 km $\times$ 20 km sampled on 120 $\times$ 40 grid points, which was used for all the simulations presented in this paper.

  

Figure 1: Orographic model - 120 $\times$ 120 grid points equivalent to 60 km $\times$ 60 km - Horizontal resolution: 500 m $\times$ 500 m. The position of the Paranal mountain is marked by a black square. Dashed lines mark the domain used for the simulations presented in this article: 60 km $\times$ 20 km. Colour figure on Web A&AS site

4.2 Input data for the model initialization

The model initialization is critical for the numerical technics. After a simulation, the quality of the output and the input data are strictly correlated. We used, as input data, the ECMWF analysis taken at the (70.31 W, 23.62 S) grid point and the radiosounding from Antofagasta station (70.43 W, 23.43 S). The analysis are 3D fields at low spatial resolution produced by the meteorological centers for forecast needs. A more detailed analysis of the data that we used will be given in a further article. The numerical model is initialized with a vertical profile of P, q, T, U, V (pressure, humidity, temperature and wind) describing the meteorological situation of a given night, upstream with respect to the wind direction, from the geographical region analyzed. The forecast values of the hydrodynamic variables of the prognostic equations provided by the model are produced following a deterministic computation. One can expect that the higher the spatial vertical resolution of the different parameters (P, T, $\vec{V}$) the better the precision and sensitivity of the simulations will be. In general, the meteorological radiosoundings have a better vertical resolution than the analysis but they have a poorer temporal sampling (at the best, only two measurements are available each day). Moreover the station density is not uniformly distributed over the world.

4.3 Spatio-temporal x, y, z, t initialization

For all simulations presented in this paper, a computational time step $t_{\rm s}= 2.5$ s was found to be necessary to achieve stable simulations (Masciadri et al. 1997). We analyzed 60 $\times$ 20 km around the Paranal mountain with an horizontal resolution of 500 m. We used the following vertical resolution: 50 m for the first vertical mesh $\Delta{z(1)}$, a vertical stretching of $30\%$ over the first 3 km that is

 

$$\frac{\Delta{z(k+1)}}{\Delta{z(k)}}=1+30/100$$ (29)

and a constant resolution of 600 m from 3 km to 20 km. The choice of the stretching for the lowest grid points was made to save computing time, preserving maximum resolution where the effects of orography are the most important and the development of turbulent eddies is the most efficient. The atmosphere is thus sampled on 40 levels with a vertical resolution ranging from 50 near the ground to 600 m at high altitude.