TESTING A RADIATIVE UPPER BOUNDARY-CONDITION IN A NONLINEAR MODEL WITH HYBRID VERTICAL COORDINATE

The application of a radiative upper boundary condition (RUBC) in a me soscale numerical weather prediction (NWP) model with hybrid vertical coordinate is presented. Results of two- and three-dimensional numeric al simulations are discussed. Starting from earlier work by Klemp and Durran (1983) and Bougeault (1983) the radiative upper boundary condit ion is formally derived for a hybrid vertical coordinate. The basic as sumptions include hydrostaticity, linearity, neglect of Coriolis effec ts and restriction to internal gravity waves. The resulting RUBC is gl obal in space and local in time. In a second step, the RUBC is tested in a two-dimensional vertical-plane version of the NWP model, in which essential properties of the full three-dimensional model have been pr eserved. 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-indepen dent steepness, the RUBC tends to work more effectively with increasin g horizontal resolution. At the same time, the application of a radiat ive instead of a lid-type, and thus reflecting, upper boundary conditi on appears to become more important with decreasing mesh width. Finall y, the RUBC is introduced into the full three-dimensional NWP model. T his 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 re sults for a weather situation with strong northwesterly flow towards t he Alps show that application of the RUBC drastically reduces the deve lopment of unrealistic standing, hydrostatic mountain waves, which bec ome apparent as distinct mesoscale ridge-trough structures in the simu lation with the lid-type upper boundary. Implications of the RUBC on t he time-stepping procedure of the NWP model are also discussed. In the experiments shown, the additional RUBC-terms are treated explicitly.