| 10 | | ''Δy''). The grid can be stretched in the vertical direction well above the ABL to save computational time in the free atmosphere. The Arakawa staggered C-grid ([#harlow Harlow and Welch, 1965]; [#arakawa Arakawa and Lamb, 1977]) is used, where scalar quantities are defined at the center of each grid volume, whereas velocity components are shifted by half a grid width in their respective direction so that they are defined at the edges of the grid volumes (see Fig. 1). The bottom boundary is indicated by the first ''w''-component (''w(k=0)'') whereas the top boundary is indicated by ''w(k=nz)''. In case of no-slip (Dirichlet) condition at the ground, the first grid point for scalars and ''u'',''v'' is defined at the same height as ''w(k=0)'' (0m) to simulate a constant flux layer using Monin–Obukhov similarity theory. In case of free-slip (Neumann) condition, however, the first grid point for scalars and ''u'',''v'' lies at ''-dz/2'' within the ground and using a constant flux layer is not allowed anymore. At the top boundary, the last scalar grid point (''nzt+1'') is ''dz/2'' above ''w(k=nzt)'', similar to the bottom in case of free-slip (Neumann) condition. However, if the user wants to have exact symmetric vertical boundaries, he or she must shift the uppermost grid point for scalars and ''u'',''v'' to the height of ''w(k=nzt)''. '''Note''': Due to same array sizes of ''u'', ''v'', and ''w'' the uppermost grid point of the model domain is ''w(k=nz+1)''. |
| | 10 | ''Δy''). The grid can be stretched in the vertical direction well above the ABL to save computational time in the free atmosphere. The Arakawa staggered C-grid ([#harlow Harlow and Welch, 1965]; [#arakawa Arakawa and Lamb, 1977]) is used, where scalar quantities are defined at the center of each grid volume, whereas velocity components are shifted by half a grid width in their respective direction so that they are defined at the edges of the grid volumes (see Fig. 1). |
| | 11 | |
| | 12 | The bottom boundary of the model domain is indicated by the first ''w''-component (''w(k=0)'') whereas the top boundary is indicated by ''w(k=nz)''. In case of no-slip (Dirichlet) condition at the ground, the first grid point for scalars and ''u'',''v'' is defined at the same height as ''w(k=0)'' (0m) to simulate a constant flux layer using Monin–Obukhov similarity theory. In case of free-slip (Neumann) condition, however, the first grid point for scalars and ''u'',''v'' lies at ''-dz/2'' within the ground and using a constant flux layer is not allowed anymore. At the top boundary, the last scalar grid point (''nz+1'') is ''dz/2'' above ''w(k=nz)'', similar to the bottom in case of free-slip (Neumann) condition. However, if the user wants to have exact symmetric vertical boundaries, he or she must shift the uppermost grid point for scalars and ''u'',''v'' to the height of ''w(k=nzt)''. '''Note''': Due to same array sizes of ''u'', ''v'', and ''w'' the uppermost grid point of the model domain is ''w(k=nz+1)''. This point doesn't play a role for solving the mode equations. |
