SOME OCEAN MODEL FUNDAMENTALS
Sigma s u r f a c e s
Figure 12. Constant sigma surfaces as diagnosed in a z-model. Shown here is a
section along 150° W, as in Figure 11. Note the strong variations in the contours, as
determined by changes in the bottom topography.
Summary of the depth based vertical coordinates.
Depth
based vertical coordinates are naturally used for Boussinesq equations.
These coordinates and their specific thicknesses x,, are summarized in
Table 2.1. Notably, both the sigma and zstar coordinates have time independent ranges, but time dependent specific thicknesses. In contrast,
the depth and depth deviation coordinates have time dependent depth
ranges and time independent specific thicknesses. If plotted with the
same range as those given in Figure 11, surfaces of constant depth deviation and constant zstar are indistinguishable from surfaces of constant
depth. This result follows since the surface height undulations are so
much smaller than undulations in the bottom topography, thus making
the depth deviation and zstar coordinates very close to horizontal in
most parts of the ocean.