A global numerical weather prediction model with variable resolution: Application to the shallow‐water equations

We follow the approach suggested by F. Schmidt to implement a spectral global shallow‐water model with variable resolution. A conformal mapping is built between the earth and a computational sphere and the equations are discretized on the latter using the standard spectral technique associated with a collocation (Gaussian) grid. We prove that the only non‐trivial conformal mapping which exists between the two spheres is based on the transformation introduced by Schmidt, but the pole of the collocation grid has no longer to coincide with the pole of dilatation. We implement the technique in an explicit model, where only minor modifications to a uniform resolution model are needed. The semi‐implicit scheme and the nonlinear normal mode initialization are proved to work satisfactorily. 24‐hour forecasts show that the method is successful in dealing with the shallow‐water equations and allow us to discuss the potential of the approach.