The Barotropic Model
Three mathematicians named Courant, Friedrichs, and Lewy created a criterion
that, if violated, would lead to the "blowing up" of a
finite-difference weather prediction model. This CFL criterion is:
The speed of fastest winds in model must be less than or equal to
grid spacing divided by the time step.
Because of the CFL criterion, a modeler cannot arbitrarily choose a horizontal
grid spacing without also taking into account the time step of the model. If you
want fine horizontal resolution to see small-scale weather, you must have fine
time resolution too. Otherwise, the model "blows up"
What does it look like when a model "blows up"? Try it yourself using the below
applet. Troughs and ridges turn disintegrate when the horizontal grid spacing and
time step don't satisfy the CFL criterion. The forecast is ruined. (See
the detailed instructions, below.)
This applet is a barotropic model. You may change the time step, the spacing
between grid points, and the intensity of the initial field. Once you change one
of these, you must then click "Restart" for the change to take effect. The time
stepping will stop automatically every 48 hours; to continue past that point,
just click the "Run/Stop" button.
These applets were designed by Tom Whittaker and Steve Ackerman.