Menagerie of vertical coordinates

1
Menagerie of vertical coordinates
Z coordinate (FV)
? coordinate
FV ? coordinate
? coordinate
Stacey 95
2
General vertical coordinate r

• Transformation
• Pressure gradient
• Hydrostatic balance
• Continuity

3
Terrain following coordinate

• Scale factor
• Hydrostatic balance
• Momentum eqns
• Continuity

• Fixed/square domain
• Pressure gradient error
• over steep topography
• Topography smoothed

4
Staceys coastal coordinate

• Scale factor
• Hydrostatic balance
• Momentum eqns
• Continuity

• Fixed domain
• No (very small) pressure gradient error
• Use finite volume method for accurate topography

5
Atmospheric eta coordinate

• Scale factor
• Hydrostatic balance
• Momentum eqns
• Continuity

• Fixed domain
• No (very small) pressure gradient error
• Use finite volume method for accurate topography

6
Interpreting scaled coordinates

• Physical space (x,z)
• grid changes with time
• non-zero w at surface

• Computational space (x,z)
• Grid fixed in time
• w0 at surface

w
w
z
z
x
x