Implementation of the Semi-Lagrangian Method in a High-Resolution Version of the ECMWF Forecast Model

Abstract

In this article the implementation of the semi-Lagrangian method in a high-resolution version of the ECMWF forecast model is examined. Novel aspects include the application of the semi-Lagrangian scheme to a global model using the ECMWF hybrid coordinate in the vertical and its use in a baroclinic spectral model in conjunction with a reduced Gaussian grid in the horizontal. The former Eulerian vorticity-divergence formulation is first converted into a momentum-equation formulation that is considerably more economical, thanks in part to the incorporation of Legendre transform efficiencies that were previously demonstrated for the shallow-water equations. The semi-Lagrangian formulation is presented in detail, together with a discussion of computational aspects that are relevant for executing the high-resolution model efficiently on a modestly parallel supercomputer. The impact of formulation changes is assessed via numerical experiments on a set of 12 independent cases. In particular it is shown that, by virtue of using a larger time step, the semi-Lagrangian version is several times more efficient than the Eulerian scheme, that the hybrid-coordinate configuration maintains its design advantage over the sigma-coordinate version in the stratosphere, that the ?vertically noninterpolating? scheme performs better than the ?fully interpolating? method, and that the increase in horizontal resolution from T106 to T213 (enabled in part by the gains in model efficiency) has a significant positive impact.