Abstract
The Crank-Nicholson method may not give useful results in detailed prediction of the thermal planetary boundary layer unless tune steps on the order of 10 s are used. In similar problems, lower order time differencing methods give reasonable results with time steps as large as 300 s. The reason for the superior behavior of the lower order schemes relative to straightforward application of the Crank-Nicholson technique is due to a better treatment of short waves which appear to be critically important in nonlinear terms.
