Simulation and parameterization of vertically propagating convectively generated gravity waves

Abstract

In this work, we use a high-resolution, two-dimensional numerical model to simulate convection initiated with many different thermodynamic and wind profiles. The simulated convection produces gravity waves, some of which propagate vertically into the stratosphere. Several diagnoses are made of the convection. These include a gravity wave source diagnosis where source terms associated with heating and nonlinear advection are shown to be dominant. A diagnosis of the first and second moment equations is also performed, isolating the important terms in these equations in the troposphere and stratosphere. The empirical orthogonal functions of horizontal velocity, vertical velocity, and potential temperature are also calculated, yielding modes that represent convection and gravity waves. Moist updrafts and other convective phenomena are isolated using particle trajectory analysis and a conditional sampling analysis. Finally, the waves in the stratosphere were characterized using Fourier analysis. The waves generated by the simulated convection have characteristic wavelengths of 10-100 km, periods of 10-60 minutes, and phase speeds of -50 to 50 m s-1. Each of these ranges is consistent with waves that have been observed above convection in the stratosphere, and simulated in previous modeling studies. In simulations with stratospheric shear layers, the simulated waves are absorbed near their critical levels. A parameterization to represent the effects of convectively generated gravity waves in large-scale models is also proposed. The mechanism for the generation of the waves can be represented by transient topography. The effects of critical level absorption, wave breaking, and wave reflection are accounted for. The energy flux associated with the waves is shown to represent a sink to the perturbation kinetic energy of the convection, and a method to calculate this effect is proposed.