11.2.1 Slicing through the 3-D prognostic data

Since there is a large separation in speed between internal and external gravity wave modes, the equations of motion are divided into a set of internal mode (3-D or baroclinic) and external mode (2-D or barotropic) equations for computational efficiency. The external mode equations represent the vertical integral of the full equations while the internal mode equations represent deviations from the vertical mean. In support of this division, prognostic data is divided into 3-D and 2-D data.

Two time levels of 3-D prognostic data at $\tau-1$ and $\tau$ are illustrated in Figure 11.1b. Two time levels are needed because it takes two time levels to integrate the equations forward in time. The dashed line marks a longitudinal slice at latitude index ``jrow'' through both time levels. Within each slice, data is arranged as follows: The zonal component of velocity (internal mode only) is first, followed by the meridional component of velocity (internal mode only) and then temperature (T) and salinity (S). In general, there may be n=1,nt tracers but typically nt=2 with n=1 referring to T and n=2 referring to S. Therefore, each latitude row indexed by ``jrow'' contains $imt\cdot km \cdot (2+nt)$ data points for two time levels.

Figure 11.1c is a schematic of all 3-D prognostic data arranged by two time levels of latitude slices on disk from south to north by increasing global index ``jrow''. The disk area may also be thought of as a ramdrive which is just an array in memory dimensioned as 3D(imt,km,variable,jmt,2). The ``2'' accounts for the two time levels. A third time level for $\tau+1$ is not needed on disk because updated data at $\tau+1$ can be written back over the $\tau-1$ area. However, in the memory window discussed below, space for the third time level $\tau+1$ is needed. This is the reason why it is best to arrange prognostic data on a ramdrive rather than opening the memory window up to contain all of the latitude rows.