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### 3.3.1 Vertical Coordinate

The vertical coordinate is a hybrid sigma-pressure system. In this system,
the upper regions of the atmosphere are discretized by pressure only. Lower
vertical levels use the sigma (i.e. **p/p**_{s}) vertical
coordinate smoothly merged in, with the lowest levels being pure sigma.
A schematic representation of the hybrid vertical coordinate and vertical
indexing is presented below.
**Figure 3.1 Hybrid Vertical Coordinate.**

Pressure is defined as:

** p**_{(i,j,k) }= A_{k}P_{0}
+ B_{k}P_{s}(i,j)

where **p **is the pressure at a given level and latitude, longitude
grid point. The coefficients **A**, **B** and **P**_{0}
are constants. **P**_{s} is the model's current surface
pressure. **P**_{0} is set in the model code. The
input model initial conditions dataset sets **A** and **B** through
the variables **hyam,** **hyai,** **hybm**, and **hybi.**
The subscript "i" refers to interface levels, and "m" refers to the mid-point
levels. "**hyam**" then refers to Hybrid level "A" coefficient
on the interfaces. The above formula is also reported on the initial conditions
file.

More details on the theoretical nature of the vertical coordinate system
can be found in Hack *et al.* (1993).

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$Name: ccm3_6_6_latest2 $ $Revision: 1.38.2.1 $ $Date: 1999/03/25 21:38:22 $ $Author: erik $