Computational mesoscale models such as RAMS, MM5, ARPS and HOTMAC, use conformal map projections to define the topography with respect to a tangent-plane XYZ coordinate system where Z is replaced by a terrain-following coordinate. The procedure consists in computing a point (X,Y) on the XY-plane via the map-projection of a point on the terrestrial sphere with geographic coordinates (l,f), and if H is the terrain elevation on (l,f), then it is assumed that the terrain elevation on (X,Y) is also H because the map projection takes into account the earth curvature. In this work it is shown that (i) the correct terrain elevation Z on (X,Y) cannot be computed because map projections do not consider the datum H to compute X and Y. (ii) The datum H is only an approximation of the correct elevation Z, and the approximation is valid on a horizontal domain D(L)=2LX2L with L bounded by 60 km when the terrain elevation data have an uncertainty of 30m. Applications of mesoscale models have used a domain D(L) with L=650, 882, 1665 km. In these cases the error of the terrain elevation reaches up 67, 120 and 450 km, respectively. A coordinate transformation to compute the correct terrain elevation from a Digital Elevation Model, is given. Analytic solutions of the governing equations show that the use of a map-projection topography in the definition of a terrain-following vertical coordinate generates a wrong atmospheric flow when L is large.