T. E. VanZandt

Evidence for a saturated spectrum of atmospheric gravity waves

Abstract The slope and power spectral density of atmospheric velocity fluctuations versus vertical wavenumber at large wavenumber are observed to be nearly independent of altitude. We suggest that such a universality is due to saturation of short vertical-scale fluctuations. A brief review of linear gravity wave saturation theory indicates a physical basis for such spectra. It is demonstrated that observed saturation spectra are not solely due to individually saturated waves but most likely result from amplitude limiting instabilities arising from wave superposition. We also show that while the spectrum is saturated at large wavenumbers, the total kinetic energy per unit mass and the characteristic vertical wavelength increase with altitude. Both of these predictions are consistent with observations.

Spectral Estimates of Gravity Wave Energy and Momentum Fluxes. Part I: Energy Dissipation, Acceleration, and Constraints

Abstract The spectral characteristics of atmospheric gravity wave motions are remarkably uniform in frequency and wavenumber despite widely disparate sources, filtering environments, and altitudes of observation. This permits a convenient and useful means of describing mean spectral parameters, including energy density, anisotropy, energy and momentum fluxes, and wave influences on their environment. The purpose here is to provide a general formulation of the mean energy spectrum as well as estimates of the wave energy and momentum fluxes and the flux divergences expressed as the energy dissipation rate and the induced accelerations in the lower and middle atmosphere. These results show spectral observations to be consistent with independent estimates of energy dissipation rates and to suggest a high degree of anisotropy of the gravity wave field under conditions of strong wave filtering by large-scale, low-frequency motions. In two companion papers, these results are employed to construct a parameterizat...

MST Radar Observations of a Saturated Gravity Wave Spectrum

Abstract We present vertical wavenumber spectra of mesoscale wind fluctuations using data observed in the troposphere, lower stratosphere and mesosphere by the MU radar at 35°N in Japan in October 1986 and June 1987, as well as lower stratospheric spectra obtained by the Arecibo UHF radar at 18°N in Puerto Rico in June 1983. These spectra are much more homogeneous than previously available spectra since all of the data were observed by the same radar technique, the data in the different atmospheric regions were taken essentially simultaneously, and all of the spectra were analyzed using very similar methods. In the large-wavenumber ranges of the observed spectra, the asymptomatic slopes and amplitudes agree well with the saturated gravity wave spectral model developed by Dewan and Good (1986) and Smith et al. (1987), which has a slope of −3 and a spectral amplitude proportional to the buoyancy frequency squared. The good agreement between the model spectrum and the observed spectra from different altitude...

A theory of enhanced saturation of the gravity wave spectrum due to increases in atmospheric stability

In this paper we consider a vertical wavenumber spectrum of vertically propagating gravity waves impinging on a rapid increase in atmospheric stability. If the high-wavenumber range is saturated below the increase, as is usually observed, then the compression of vertical scales as the waves enter a region of higher stability results in that range becoming supersaturated, that is, the spectral amplitude becomes larger than the saturation limit. The supersaturated wave energy must then dissipate in a vertical distance of the order of a wavelength, resulting in an enhanced turbulent energy dissipation rate. If the wave spectrum is azimuthally anisotropic, the dissipation also results in an enhanced vertical divergence of the vertical flux of horizontal momentum and enhanced wave drag in the same region. Estimates of the enhanced dissipation rates and radar reflectivities appear to be consistent with the enhancements observed near the high-latitude summer mesopause. Estimates of the enhanced mean flow acceleration appear to be consistent with the wave drag that is needed near the tropopause and the high-latitude summer mesopause in large-scale models of the atmosphere. Thus, this process may play a significant role in determining the global effects of gravity waves on the large-scale circulation.

Spectral analysis of temperature and Brunt-Vaisala frequency fluctuations observed by radiosondes

We observed profiles of the temperature, T, and Brunt-Vaisala frequency squared, N2, from 0 to 30 km in altitude using radiosondes with 150 m height resolution launched from the MU observatory, Japan (34°51′N, 136°06′), from September 27, 1986, to February 24, 1989. We analyzed vertical wavenumber spectra of the normalized temperature T/T and N2 fluctuations in the 2.0–8.5 km (troposphere) and 18.5–25.0 km (lower stratosphere) altitude ranges and compared them with model spectra based on saturated gravity wave theory. In the winter stratosphere the slope of the mean T/T spectra in the wavenumber range from 7.0×10−4 to 2.0×10−3 (cycles per meter) was very close to the −3 predicted by the model, and the spectral amplitudes were 1.3–1.9 times larger than the predicted values, which is within the possible range of variability of the model. On the other hand, in the summer stratosphere the spectral slope ranged from −2.2 to −2.4, which is more gradual than the model, and the spectral amplitudes were only 0.4 to 0.5 of the predictions. The spectral shape in the troposphere did not show a significant difference between summer and winter. The spectral amplitudes, however, exceeded the model values by factors of about 3.2 and 1.9 in winter and summer, respectively. The overall shape of the profile for fluctuations with vertical scales from 150 to 900 m was generally similar to the shape of the background value of N4, consistent with the saturated gravity wave model, but the details of the altitude variations were rather complicated. That is, just below the tropopause usually exceeded the model by a factor of 2 to 4, and it became significantly smaller than the model in the summer stratosphere and in a region above 25 km in winter.

Studies of Velocity Fluctuations in the Lower Atmosphere Using the MU Radar. Part II: Momentum Fluxes and Energy Densities

Abstract This paper describes a study of the frequency spectra, the vertical profiles of energy density, and the momentum flux of the motion field observed during a six-day campaign in March 1986 using the MU Radar in Shigaraki, Japan. Our results reveal significant differences between the mean zonal and meridional frequency spectra as well as different profiles of mean energy density with height for different frequency bands and for zonal and meridional components. The vertically averaged momentum flux exhibited considerable temporal variability and good consistency between adjacent beam pairs. A mean vertically averaged flux toward 267° was inferred, suggesting an essentially zonal drag in regions of wave dissipation. A mean frequency spectrum and height profiles of momentum flux in four frequency bands revealed a westward flux at all frequencies. Ratios of the differenced to the mean variance of radial velocity in each vertical plane suggested an ∼20%–30% excess of westward over eastward propagating wa...

Zenith-angle dependence of VHF specular reflection echoes in the lower atmosphere

Abstract We studied the characteristics of specular echoes reflected from stratified layers in the troposphere and lower stratosphere. In particular, we observed echoes at antenna-beam zenith angles, θ, from 0 ° to 28 ° in steps of 2 °. When the radar measurements were averaged over about 30 min, the zenith angle dependence of the echo power normalized by the vertical power, S (θ) , was generally the same for sufficiently intense reflection echoes. That is, the echo power was largest in the vertical direction, decreased to about − 10 dB at 6 °, and then gradually decreased to a constant level between − 15 and − 25 dB at θ ≥ 20 °. This constant level is interpreted as the isotropic turbulence scattering level S i . The width of S (θ) was significantly broader than expected for specular reflection from a perfectly horizontal layer. In order to explain this broadening, we developed two numerical models that describe statistically the slope of a reflection layer that has been distorted by vertical gravity-wave motions. With realistic gravity-wave spectra, the shape of S (θ) for θ = 0–6 ° was successfully explained. However, from 8 ° to 18 ° the observed S (θ) was enhanced by as much as 7 dB over the model. From the observations we showed that all of the reflection echoes, including the enhanced echoes at θ = 8–18 °, are probably due to the same process. Then we showed that the discrepancy with the model may be the result of our neglect of the horizontal component of gravity-wave motions, which was done in order to constrain the number of calculations.

Spectral Estimates of Gravity Wave Energy and Momentum Fluxes

The spectral characteristics of atmospheric gravity wave motions are remarkably uniform in frequency and wavenumber despite widely disparate sources, filtering environments, and altitudes of observation. This permits a convenient and useful means of describing mean spectral parameters, including energy density, anisotropy, energy and momentum fluxes, and wave influences on their environment. Our purposes here are to provide a general formulation of the mean energy spectrum, estimates of the wave energy and momentum fluxes and the flux divergences expressed as the energy dissipation rate and the induced accelerations in the lower and middle atmosphere, and a parameterization of the manner in which these quantities vary with background wind and thermal fields. Our results show spectral observations to be consistent with independent estimates of energy dissipation rates and to suggest a high degree of anisotropy of the gravity wave field under conditions of strong wave filtering by mean and low-frequency motions. The implied momentum fluxes are largely consistent with observations of mean and variable fluxes at a number of altitudes and locations as well as with the apparent needs of present general circulation models.

Frequency spectra of vertical velocity from Flatland VHF radar data

The vertical wind velocity over very flat terrain was observed every 153 s in the troposphere and lower stratosphere by the Flatland radar, near Champaign-Urbana, Illinois. Several hundred frequency spectra were calculated from all accepted 6-hour time series from March through May 1987. By stratifying the spectra in various ways we find the following: (1) The spectra were independent of altitude within the troposphere or lower stratosphere, but the spectra in the two regions differed in amplitude and frequency; (2) At a given altitude the spectra were independent of the wind shear dū/dz, the buoyancy frequency N, and the maximum wind speed below 16 km; (3) The change of spectral shape and amplitude with increasing background wind speed ū was much less than at stations near mountains. The variance of the spectra, equal to twice the vertical kinetic energy per unit mass, roughly doubled as ū increased by 10 m s−1; (4) The spectra were consistent with being due to a spectrum of gravity waves, as indicated by the sharp drop in spectral amplitude near N at small ū and by the fact that the observed change of shape with increasing ū was quite consistent with the change of shape of model Doppler-shifted gravity wave spectra; (5) The results of comparison between the observed and model spectra are consistent with an intrinsic gravity wave spectrum that is invariant with ū, dū/dz, etc., contrary to expectations from gravity wave theory; (6) The results are insensitive to the azimuthal distribution of gravity wave energy, as long as the distribution is roughly symmetrical relative to the mean flow; (7) The resulting characteristic horizontal phase velocity c* of the intrinsic frequency spectrum was about 6 m s−1 in both the troposphere and the stratosphere. The corresponding characteristic vertical wavelengths were about 3300 and 1800 m, respectively, consistent with previous estimates.

Gravity waves and convection in Colorado during July 1983

Abstract In order to gain insight into the complex dynamics of a convective system interacting with a gravity wave train, we have carried out an experiment in northeast Colorado during July and August, 1983, utilizing data from several program areas in NOAA. Pressure data from the PROFS mesonetwork of microbarograph stations were combined with velocity profiles from the Wave Propagation Laboratory UHF wind profiler (ST) radar at Stapleton Airport in Denver and convective cell location data from the NWS Limon weather radar. Several events were clearly visible in the microbarograph data, from which four (called Events A, B, C and D) in late July were selected for further study. These events differed from each other in fundamental ways. In each event the waves represent oscillations of a substantial depth of the troposphere and seem to appear and disappear together with the convective cells. In Events A and B the waves have a critical level and are probably unstable modes generated by wind shear in the jet s...