Numerical Weather Simulations with Different Formulations for the Advection of Humidity and Cloud Water

Abstract

This study investigates the effect on short-range weather prediction of using different numerical advection schemes for humidity and cloud water. Comparisons are made between predictions using the basic centered and upstream schemes and the more sophisticated Smolarkiewicz and Bott schemes. The main purpose of these alternative schemes is to reduce numerical diffusion and dispersion errors encountered in the basic schemes and thereby preserve the shape of features such as fronts. At the same time those schemes are efficient enough to be a realistic choice for operational models. The simulations are made with a numerical weather prediction model with 150-km horizontal resolution and ten levels. Frontal movements over large distances have been investigated in a domain that extends from eastern North America through Europe. The simulations yield little sensitivity to the choice of advection scheme for cloud water. On the other hand, a large sensitivity to the treatment of the humidity advection is found. This is connected to a substantial feedback with the model dynamics through release of latent heat. Larger numerical errors are identified with the basic schemes than with the alternative schemes, which yield a better shape preservation of the frontal zones. The centered scheme tends to give the heaviest precipitation and the deepest cyclones, while the upstream scheme gives least precipitation. Exaggerated low-level cloudiness is found with the Bott scheme and, to some extent, the Smolarkiewicz scheme. This appears to be caused by insufficient adjustment of other parts of the model to the new, more accurate, transport formulation. The Bott scheme has less numerical diffusion than the Smolarkiewicz scheme, but is somewhat more expensive computationally.