Mountain Wave Analysis Using Fourier Methods; Final rept

摘要

Eigenanalysis of temperature and wind profiles can reveal distinct resonances at mesoscale wavelengths. Fourier transform methods are well suited to analyze resonant modes such as mountain waves due, in part, to (1) their fast computation speed for large wave number domains compared to numerical forecast models and (2) their requirements for only a coarse horizontal background state. Common traits of Fourier mountain wave models include use of the Boussinesq approximation and neglect of moisture and Coriolis terms. Solutions are provided to linearized elliptic partial differential equations expressed in terms of height or velocity perturbation using complex phase functions. Lower boundary conditions are defined using the Fourier transform of the terrain height field which is typically modified to ensure linear assumptions are satisfied and to avoid effects associated with periodic horizontal boundary conditions. Two mountain wave models, Smith Three-Layer and Broutman MWFM-3, are examined. Both models have a strong theoretical basis and are well documented in the refereed literature. These models can allow for both hydrostatic and non-hydrostatic wavfe modes but do not permit more than one wind turning point in their representation of the phase functions. The two models have undergone limited verification for real-world environments using aircraft and satellite data and have been compared with non-linear numerical model integrations. The Broutman MWFM-3 model, having been developed to include tropospheric and stratospheric wave propagation and having no theoretical limit on top height, is favored for testing in an operational forecast environment.