3.5 Model 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. Both input and output datafiles follow this format as well as internal model datastructures.

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.

More details on the theoretical nature of the vertical coordinate system can be found in Collins et al. [2004].