A Spline Collocation Scheme for the Spherical Shallow Water Equations

We present a spline collocation scheme for the numerical solution of the shallow water equations in spherical geometry. Space is discretized by bilinear spherical splines, adapted to a reduced longitude-latitude grid. The poles are not exceptional points in this approach. Time is discretized by standard centered diierences. We obtain a fully explicit and very eecient scheme that reduces to simple matrix-vector multiplications in every time step. No linear systems have to be inverted. The scheme is applied to a standard test set 13] and its accuracy is compared to recent results 1] that document the implementation of a preliminary version of the new global model of German Weather Service (DWD).