THE USE OF SPLINE INTERPOLATION IN SEMI-LAGRANGIAN TRANSPORT MODELS

The accuracy of interpolating semi-Lagrangian (SL) discretization meth ods depends on the choice of the interpolating function. Results from barotropic transport simulations on the sphere are presented, using ei ther bicubic Lagrangian or bicubic spline SL discretization. The splin e-based scheme is shown to generate excessively noisy fields in these simulations. The two methods are then tested in a one-dimensional adve ction problem. The damping and dispersion relations for the schemes ar e examined. The analysis and numerical experiments suggest that the ex cessive noise found in the spline-based simulations is a consequence o f insufficient damping of the small scales for small and near-integer values of the Courant number. Inspection of the local Courant number f or the two-dimensional spline-based simulation confirms this hypothesi s. This noise can be controlled by adding a scale-selective diffusion term to the spline-based scheme, while retaining its excellent dispers ion characteristics.