Recently ECMWF has implemented in its operational semi-Lagrangian model a finite element discretization for the vertical based on cubic B-splines. This provided the infrastructure also for the use of cubic splines for the vertical interpolations in the semi-Lagrangian advection scheme.

Semi-Lagrangian schemes using cubic splines are known to be less diffusive and less dispersive then schemes using cubic Lagarange interpolation but can suffer from noise due to large over- and undershooting near sharp gradients. We will present results from our investigations into the benefit or otherwise of using cubic spline interpolation for the vertical advection of the dynamical variables (winds, temperature and humidity) and for tracers in the ECMWF model and discuss ways of alleviating the noise problem associated with spline interpolation.