Mountain wave parametrization in a transient gravity wave model

Orography induced gravity waves are investigated in a Multi Scale Gravity Wave Model (MS-GWaM) over idealized topography. MS-GWaM is a prognostic gravity-wave model, which parametrizes both the propagation and dissipation of subgrid-scale GWs. It is a Lagrangian ray-tracer model, which applies WKB-theory and calculates the propagation of ray volumes in spectral space. Its novelty is that not only the dissipative effect, but also the non-dissipative effects due to direct wave-mean flow interaction are captured. In our conceptual studies we investigate mountain wave generation, which is induced via a time-dependent large-scale wind encountering a prescribed topography. The framework used in our experiments is the PincFloit model, which integrates the pseudo-incompressible equations. We use it both in low resolution with MS-GWaM and in high resolution LES mode as a wave resolving reference. In the reference LES simulations the idealized topography, a mountain chain, is represented with an immersed boundary method. In the MS-GWaM experiments there is no resolved topography, but its effect is modelled as a lower boundary condition. The lower boundary condition is represented by initializing ray volumes with wave number and wave action density depending on the mountain characteristics and the large scale wind speed, based on the assumption that the flow follows the terrain. In the wave resolving reference experiments the flow does not strictly follow the terrain, but other instabilities (rotor formation, boundary layer separation) arise around the mountains. These processes decrease the available momentum transported by GWs, which was initially not accounted for in MS-GWaM. Thus an overestimation of wind deceleration was found in the MS-GWaM parametrization compared to the wave resolving simulation. To correct for this overestimation, an effective mountain height is introduced into Ms-GWaM, which is calculated by a scaling function between mountain height and flow properties using the Froude number.