Consistent Scale Interaction of Gravity Waves in the Doppler Spread Parameterization

The standard Doppler spread parameterization of gravity waves, which was proposed by C.-O. Hines and has been applied in a number of middle atmosphere general circulation models, is extended by the inclusion of all effects associated with vertical diffusion. Here the Wentzel–Kramers–Brillouin (WKB) approximation is employed to calculate the vertical propagation of the wave spectrum in the presence of wave damping. According to the scale interaction between quasi-stationary turbulence and the larger nonturbulent flow, all vertical diffusion applied to the resolved flow should damp the parameterized gravity waves as well. Hence, the unobliterated part of the gravity wave spectrum is subject to diffusive damping by the following processes: 1) the background diffusion derived from the model’s boundary layer vertical diffusion scheme, which may extend into the middle atmosphere, 2) molecular diffusion, and 3) the turbulent diffusion resulting from the truncation of the gravity wave spectrum by Doppler spreading, which thus feeds back on the unobliterated gravity waves. The extended Doppler spread parameterization is examined using perpetual July simulations performed with a mechanistic general circulation model. For reasonable parameter settings, the convergence of the potential temperature flux cannot be neglected in the sensible heat budget, especially in the thermosphere. Less gravity wave flux enters the model thermosphere when vertical diffusion is included, thus avoiding the need for artificial means to control the parameterized gravity waves in the upper atmosphere. The zonal wind in the tropical middle and upper atmosphere is found to be especially sensitive to gravity wave damping by diffusion.