A numerical advection scheme with small phase speed errors

It is demonstrated that, for linear advection in one space dimension, a simple modification to the well-known Lax-Wendroff integration scheme leads to a substantial reduction in phase speed errors. The modification is designed in such a way that no additional restriction is placed on the timestep used in an integration. The improved performance is comparable or superior to that of previously proposed advection schemes, yet it is achieved without recourse to expensive or cumbersome computations. The new scheme is readily extended to two space dimensions and has been used in numerical weather prediction and sea wave modelling in the Meteorological Office. An example is given of an improved numerical forecast of the 500 mb height field which was obtained by applying the new scheme in the operational 10-level numerical weather prediction model.