A parameterization of wave stress in the planetary boundary layer for use in mesoscale models

A parameterization of gravity wave stress generated by subgrid-scale topography is described and tested in a one-dimensional version of the Advanced Regional Prediction System (ARPS) model. It is argued that in the planetary boundary layer (PBL) where wave reflections occur, the so-called WKB method for evaluating wave stress may not be applicable. Gravity waves launched by a subgrid-scale Gaussian ridge are calculated on line using a linear wave model. The total flow is constrained to be convectively stable by using a terrain-height adjustment to decrease wave amplitudes and thereby prevent wave overturning. In this method when the waves grow large enough to overturn, the wave amplitudes are decreased by decreasing the maximum height of the terrain obstacle, H. At each time step, the ARPS model flow is modified by the divergence of the wave stress. The effects of wave-stress divergence on turbulence parameterization is examined using three turbulence closure schemes, K-theory with constant eddy diffusivity, the Smagorinsky closure, and the turbulence-kinetic energy closure. Also, the effects of vertical grid spacing are tested using spacings of 10, 20, 50 and 100 m. The model is initialized with a hyperbolic-tangent wind profile and constant Brunt–Väisälä frequency. It is shown that wave-stress divergence can lead to elevated layers of turbulence and diffusion where they would not occur in the absence of the wave-stress parameterization. It is also shown that if the vertical grid spacing is too great, then the effects of wave breaking are not fully realized.