Testing a radiative upper boundar condition in a nonlinear model with hybrid vertical coordinate

Abstract

The application of a radiative upper boundary condition (RUBC) in a mesoscale numerical weather prediction (NWP) model with hybrid vertical coordinate is presented. Results of two- and three-dimensional numerical simulations are discussed. Starting from earlier work by Klemp and Durran (1983) and Bougeault (1983) the radiative upper boundary condition is formally derived for a hybrid vertical coordinate. The basic assumptions include hydrostaticity, linearity, neglect of Coriolis effects and restriction to internal gravity waves. The resulting RUBC is global in space and local in time. In a second step. the RUBC is tested in a twodimensional vertical-plane version of the NWP model, in which essential properties of the full three-dimensional model have been preserved. Gravity wave experiments clearly show the superiority of the RUBC over the commonly used lid-type upper boundary condition. For the setting with an isolated bell-shaped mountain with resolution-independent steepness, the RUBC tends to work more effectively with increasing horizontal resolution. At the same time, the application of a radiative instead of a lid-type, and thus reflecting, upper boundary condition appears to become more important with decreasing mesh width. Finally, the RUBC is introduced into the full three-dimensional NWP model. This requires further approximations. In particular for a limited-area model, the geopotential field at the uppermost model level needs to be bi-periodic. Here, a linear detrending technique is applied. First results for a weather situation with strong northwesterly flow towards the Alps show that application of the RUBC drastically reduces the development of unrealistic standing, hydrostatic mountain waves, which become apprent as distinct mesoscale ridge-trough structures in the simulation with the lid-type upper boundary. Implications of the RUBC on the time-stepping procedure of the NWP model are also discussed. In the experiments whown, the additional RUBC-terms are treated explicitly.