The Use of Spline Interpolation in Semi-Lagrangian Transport Models

Abstract

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