-coordinate model
The governing equations form a set of simultaneous partial differential
equations which cannot be solved using known analytic methods. Therefore
the equations have been discretized using finite difference methods.
The routines called to approximate the solution of the governing equations in each
time step of the model are described in this section.
The horizontal finite difference scheme is staggered, and the
Arakawa C-grid [34] has been used, see figures 1, 2 and 3.
Figure 1. Horizontal view of the location of 3-D variables in the staggered grid.
T, RHO and other scalar fields are defined in S-points. KM, KH, Q2 and Q2L are defined in
W-points.
Figure 2. Vertical view of the location of 3-D variables in the staggered grid.
T, RHO and other scalar fields are defined in S-points. KM, KH, Q2 and Q2L are defined in
W-points.
Figure 3. Horizontal view of the location of 2-D variables in the staggered
grid.
The model is written in FORTRAN 90 and the discrete versions of the state variables and parameters are gathered in a module, STATE, that may be addressed by all subroutines. Equations (36) - (41) are stepped forward in time using the same time step for all equations. The method of fractional steps is applied. That is a sequence of subroutines is called to perform specific subtasks and update the corresponding variables in MODULE STATE in each time step. After all subroutines are called the effects of all terms in the governing equations are included.
A description of the variables in MODULE STATE
is given in the appendix.