Measurements of the Effects of Gravity Waves in the Middle Atmosphere Using Parametric Models of Density Fluctuations. Part I: Vertical Wavenumber and Temporal Spectra

Abstract

Parametric models of spectral analysis offer several distinct advantages over statistical methods such as the correlogram analysis. These advantages include higher spectral resolution and the ability, in principle, to separate correlated (i.e., wave) behavior from noise-driven (i.e., turbulent) behavior in the measurements. Here parametric models are used to highlight the spatial and temporal intermittency of the gravity wave spectrum. In Part II of this series the spatial and temporal spectrum are used to calculate energy dissipation and the eddy diffusion coefficient. The spectra are computed from measurements of density fluctuations obtained using a large power-aperture product lidar during a 6-h period on 30 August 1994. It is shown that parametric models provide an excellent representation of the temporal and spatial data series. One difficulty of parametric models is selecting the model order, an analogous situation to determining the proper lag in the correlogram procedure or the window length in the periodogram method. Extensive experimentation has shown that the ratio of the data matrix eigenvalues to the photon noise eigenvalues is an excellent indicator for the selection of the model order. The underlying spectral form found using the parametric models is similar to the standard correlogram method, that is, nominal underlying spatial and temporal spectral slopes between −2 and −4 and −1.25 and −2, respectively, with variability outside this range. The spatial–temporal behavior of the spectra is highly variable with numerous intermittent and intense features rising well above the photon noise floor. The vertical wavenumber spectra on this night may show a variation of spectral slope with height; however, the slope is both extremely sensitive to the noise level of the data, steepening as the signal-to-noise level increases, and highly variable in time. The temporal spectra also show considerable variation with height, both in magnitude and slope.