Terrain-following coordinates

Terrain-following coordinates A system of vertical levels parallel to the terrain surface. 

The above transformations result in changes of the components of the wind field from (ux, uy, uz) to (ux, uy, w), where for the terrain-following coordinate system (McRae et al. 1982a)... 

One should note that for the physical coordinate system boundary conditions must be applied at z = h(x,y), while for the terrain-following systems application is at C, = 0 and z = 0 (Figure 25.6). In the following discussion we will use the simple terrain-following coordinate transformation (25.31), which effectively flattens out the terrain, leading to the flat modeling domain shown in Figure 25.6d. 

The numerical model used in this study is a nonhydrostatic, primitive equation with terrain-following sigma(o) vertical coordinate MM5 version 3. The simulation performed for this study was run on two-way interactive nesting model. They consist of a 6-km grid (Doj, mesh size of 181 X 181), a 18-km grid (Doj, mesh size of 121 x 121) and a 54-km grid (Doj,... 

Mesoscale model equations have been solved in a Cartesian coordinate framework. Each coordinate in this system is perpendicular to the other two coordinates at every location. Most mesoscale models, however, transform to a generalized vertical coordinate. The most common coordinates are some form of terrain-following transformation, where the bottom coordinate surface is terrain height or terrain surface pressure. The result of these transformations is that the new coordinate system is not... 

A simple conception of the notion of exact differential can be obtained from the following down-to-earth example In a hilly terrain, two points (1) and (2) are delimited. A variable h[x,y) denoting the height level of the terrain as a function of the xy coordinate is analogous to what is designated a state variable in thermodynamics. The differential dh x, y) is an exact differential because it is evident that... 

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