Meteorology: Understanding the Atmosphere Ackerman and Knox
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 the fastest winds in a model must be less than or equal to the 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 also have a fine time resolution; otherwise the model “blows up”
What does it look like when a model “blows up”? Try it yourself using the below applet (instructions). Troughs and ridges disintegrate when the horizontal grid spacing and time step don’t satisfy the CFL criterion. The forecast is ruined.
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. Each color represents a range in the height of the 500 mb surface, with green being relatively low heights, and yellow are higher heights.