180 Kikuro Miyakoda
(1)
In the atmosphere C = 100ms- 1 , so that forf= 10- 4 s-l, L=IOOOkm, whereas in
the ocean, C g = IOms-\ and L is of the order of 100 km. Because of the smaller
radius of deformation in the ocean, the horizontal grid size of an ocean model
needs to be much smaller than that for an atmospheric model. Near the equator the
ocean model requires even finer spatial resolution, i.e., 25km, in order to resolve
the oceanic Kelvin and Rossby waves.
The second issue is which type of model should be used, global or regional. A
brute force approach is simply to take a global model ofhomogeneously small grid
size, say 10 km. This approach is too expensive for typical research institutions and
universities, and perhaps can only be pursued by two or three major forecasting
centers. However, whether or not the major wor1d meteorologic al centers can keep
a constant and care fui watch on global weather is a good question. Of course, Europeans are more intimately monitoring the results over the European sector than
other parts of the wor1d.
10.2 Atmospheric and oceanic general circulation models
(GCMs)
10.2.1 Basic questions
The goveming equations for the atmosphere and the ocean are written below.
In general, atmospheric model computations are numerically more complicated
than the oceanic calcu1ations. This may be due to the far 1arger Reyno1ds number
for the atmosphere than for the ocean, and the large effect of condensation in the
atmosphere. The compressibility of the atmosphere is another complicating factor.
Since seawater is nearly incompressible, the equation of continuity for the ocean is
simplified and the Boussinesq approximation is used.
For simplicity, water vapor in the atmosphere and salinity in the ocean are omitted from the following equations.
Atmosphere
Ocean
Eqs. of motion
au">'
au
1 ap
- + V· Vu+w- -fv = - - -
at
az
pax
av">'
av
_ lap
at + v· Vv+w az +fu - -j)ay
Hydrostatic assumption
the same
the same
the same
(2)
(3)
(4)