Quantifying the Effect of Horizontal Propagation of Three-Dimensional Mountain Waves on the Wave Momentum Flux Using Gaussian Beam Approximation

Abstract

Abstract This work examines the influence of horizontal propagation of three-dimensional (3D) mountain waves on the wave momentum flux (WMF) within finite domains (e.g., the grid cell of general circulation models). Under the Wentzel–Kramers–Brillouin (WKB) approximation, analytical solutions are derived for hydrostatic nonrotating mountain waves using the Gaussian beam approximation (GBA), which incorporates both the wind vertical curvature effect and the height variation of stratification. The GBA solutions are validated against numerical simulations conducted using the Advanced Regional Prediction System (ARPS). In the situation of idealized terrain, wind, and stratification, the WMF obtained from the GBA shows a good agreement with the numerical simulation. The effect of wind curvature in enhancing the WMF is captured, although the WKB-based GBA solution tends to overestimate the WMF, especially at small Richardson numbers of order unity. For realistic terrain and/or atmospheric conditions, there are some biases between the WKB GBA and simulated WMFs, arising from, for example, the missing physics of wave reflection. Nonetheless, the decreasing trend of finite-domain WMF with height, because of the horizontal propagation of 3D mountain waves, can be represented fairly well. Using the GBA, a new scheme is proposed to parameterize the orographic gravity wave drag (OGWD) in numerical models. Comparison with the traditional OGWD parameterization scheme reveals that the GBA-based scheme tends to produce OGWD at higher altitudes, as the horizontal propagation of mountain waves can reduce the wave amplitude and thus inhibit wave breaking.