A Three-Dimensional Nonhydrostatic Ray-Tracing Model for Gravity Waves: Formulation and Preliminary Results for the Middle Atmosphere

Abstract

The WKB ray-tracing formalism is extended to accommodate internal gravity waves of all frequencies in a rotating, stratified, and compressible three-dimensional atmosphere. This includes the derivation of equations governing the dispersion and refraction of the ray paths, a realistic wave amplitude equation that takes into account both radiative and turbulent damping effects, and extensions of previous wave saturation schemes to accommodate dynamical and convective instabilities along generally slanted axes. These equations have been numerically coded into a global ray-tracing model that the authors have applied to the three-dimensional CIRA 1986 reference atmosphere model in a series of preliminary experiments to investigate the impact of the newly incorporated features on synthesized wave fields in the middle atmosphere. Three main points emerge from these experiments. First, there is a striking reduction in the high-frequency cutoff with decreasing horizontal wavenumber due to a more complete dispersion relation. Second, adoption of a climatological, height-varying turbulent diffusivity profile based on measurements indicates that turbulent damping is more important than scale-dependent infrared radiative damping over a wide range of wavelengths and frequencies in all but the lower levels of the middle atmosphere. Last, the authors demonstrate that the presence of climatological planetary waves during the northern winter produces greatly varied ray paths for waves of fixed characteristics launched from different longitudes. The implications of these findings for future ray-tracing studies are discussed.