Computation of the Finite Difference Quotient in Longitude on a Uniform Longitude-latitude Grid in High-latitudes

In consideration of small time step or Fourier filtering having to be taken in the integration of thee grid model in high-latitudes due to the convergence of the grid points near the poles, a difference scheme has been presented, which can avoid such difficulties mentioned above. The scheme can be constructed on the basis of any given finite difference scheme. It is the same as the latter in form, but requires that the grid-length used should be adjusted so as to let the time step to be as large as the one used in midlatitudes and the computational stability criterion to be satisfied. In computation it is convenient and there is nearly no extra operational amount. Furthermore, if the original scheme is mass-or-energy-conserving, the new scheme also has such a property.