The ECMWF medium-range prediction models development of the numerical formulations and the impact of increased resolution

Abstract

An outline is given of the numerical formulations that have been utilized for medium-range prediction at the European Centre for Medium-Range Weather Forecasts. The sigma-coordinate grid-point model adopted for the first phase of operational forecasting, and the hybrid-coordinate spectral model which replaced it, are described. Particular emphasis is placed on aspects of the time-stepping employed in the spectral model. It is shown how a semi-implicit treatment of the zonal advection of vorticity and specific humidity, and selective use of enhanced horizontal diffusion, enables time-steps to be used which are well over 50% longer than would otherwise be possible in a spectral model with a classical semi-implicit treatment of gravity-wave terms, with negligible computational cost and negligible impact on forecast accuracy, at T 106 resolution at least. Some discussion of the stability of the semi-implicit gravity-wave scheme is also included.