I. NUMERICAL SCHEME FOR HYDRODYNAMIC EQUATIONS[J].Oceanologia Et Limnologia Sinica,1998,29(3):232-240.

The Arakawa C-grid is adopted in the present model. In the horizontal, the spheric coordinate is adopted to facilitate large area computations. In the vertical, the grid levels are consistent with the z-coordinate. The topography is represented by a stepwise bottom. The superiority of using the z-coordinate instead of the sigma-coordinate in the vertical discretization is that it can avoid the instability in the region of steep topography and the excessive artificial diffusivity across isopycnal surfaces induced by the layout of grid points in line with the sigma-coordinate.

The computations of the external and internal modes are coupled with each other. The external mode computations are performed with a time step generally shorter than 10 times the CFL condition for wave propagation and the internal mode computations are performed with a time step shorter than the CFL condition for advection. The latter is generally longer than the former. In the external mode computations, the advection and bottom friction terms are calculated based on the internal mode results and thus the errors existing in the corresponding terms of the 2-D equations can be removed. To retain the consistency between external mode and internal mode results, the computed depth-averaged velocities of the internal mode are adjusted to be equal to the velocities of the external mode. This implies that internal mode computations only specify the vertical variations of the velocity.