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Mesospheric data were analyzed by a composite method combining phase and group velocity tracing technique and the spectra method of Stokes parameter analysis to obtain the propagation parameters of atmospheric gravity waves (AGW) in the height ranges between 63.6 and 99.3 km, observed using the MU radar at Shigaraki in Japan in the months of November and July in the years 1986, 1988 and 1989. The data of waves with downward phase velocity and the data of waves with upward phase velocity were independently treated. First, the vertical phase velocity and vertical group velocity as well as the characteristic wave period for each wave packet were obtained by phase and group velocity tracing technique. Then its horizontal wavelength, intrinsic wave period and horizontal group velocity were obtained by the dispersion relation. The intrinsic frequency and azimuth of wave vector of each wave packet were checked by Stokes parameters analysis. The results showed that the waves with intrinsic periods in the range 30 min–4.5 h had horizontal wavelength ranging from 25 to 240 km, vertical wavelength from 2.5 to 12 km, and horizontal group velocities from 15 to 60 m s−1. Both upward moving wave packets and downward moving wave packets had horizontal group velocities mostly directed in the sector between directions NNE (north-north-east) and SEE in the month of November, and mostly in the sector between directions NW and SWS in the month of July. Comparing with mean wind directions, the gravity waves appeared to be more likely to propagate along with mean wind than against it. This apparent prevalence for downstream wave packets was found to be caused by a systematic filtering effect existing in the process of phase and group velocity tracing analysis: A significant portion of upstream wave packets might have been Doppler shifted out of the vertical range in phase and group velocity tracing analysis.

Three among the existing methods of obtaining the properties (intrinsic period, wavelength, propagation direction) of atmospheric gravity waves (AGWs) were compared and studied by numerical method to simulate radar data. Three-dimensional fluctuation velocity satisfying dispersion equation and polarization relation of atmospheric gravity wave were generated, then the numerical data were analysed by these methods to obtain the properties of waves. We found that, hodograph analysis was accurate for a monochromatic wave in obtaining its wave period and propagation direction, but the analysis became erratic for the case of multiple waves' superposition. The error was especially large when data consisted of both upward propagating waves and downward propagating waves. The hodograph method became meaningful again if all the component waves propagated in the same direction and the resulting period was dominantly decided by the lowest frequency wave. Stokes parameters method would obtain statistically meaningful values of wave period and azimuth if the spreading of the azimuths among the component waves did not exceed 90° and the resulting period and azimuth were dominated by the lowest frequency wave component as well, irrespective of the vertical sense of propagation. Another method called phase and group velocity tracing technique was reconfirmed to be meaningful in measuring the characteristic wave period and vertical group and phase velocities of a wave packet: the characteristic wave period and vertical wavelength was dominated by the wave with the highest frequency among the component waves in the wave packet. Based on these numerical results, a composite procedure of data analysis for wave propagation was proposed and an example of real data analysis was presented.

We study the horizontal structure of the atmospheric gravity waves (AGW) in the height ranges between 6 and 22 km observed using the MU radar at Shigaraki in Japan, during a 3 day period in January and a 4 day period in August 1988. The data were divided by double Fourier transformation into a data set of upward moving waves and a data set of downward moving waves for independent analysis. The phase and group velocity tracing technique was applied to measure the vertical group and phase velocity as well as the characteristic period of the gravity wave packet. Then the dispersion equation of the linear theory of AGW was solved to obtain its intrinsic wave period – horizontal wavelength and horizontal group velocity – and the vertical flux of horizontal momentum associated with each wave packet was estimated to help determine the direction of the characteristic horizontal wave vector. The results showed that the waves with periods in the range of 30 min~6 h had horizontal scales ranging from 20 km to 1500 km, vertical scales from 4 km to 15 km, and horizontal phase velocities from 15 m/s to 60 m/s. The upward moving wave packets of wave period of 2 h~6 h had horizontal group velocities mainly toward east-south-east and northeast in winter, and mainly in the section between the directions of west-north-west and north in summer.

We study the momentum flux of the atmospheric motions in the height ranges between 6 and 22 km observed using the MU radar at Shigaraki in Japan during a 3 day period in January 1988. The data were divided by double Fourier transformation into data set of waves with downward- phase- velocity and data set of waves with upward-phase-velocity for independent momentum flux calculation. The result showed that both the 72 h averaged upward flux and downward flux of zonal momentum were negative at nearly each height, meaning that the upward flux was dominated by westward propagating waves while the downward flux was dominated by eastward propagating waves. The magnitude of the downward flux was approximately a factor of 1.5 larger than the upward flux for waves in the 2~7 h and 7~24 h period bands, and about equal to the upward flux in the 10–30 min and 30 min–2 h period bands. It is also observed that the vertical flux of zonal momentum tended to be small in each frequency band at the altitudes below the jet maximum (10~12 km), and the flux increased toward more negative values to reach a negative maximum at some altitude well above the jet maximum. Daily averaged flux showed tremendous variation: The 1st 24 h (quiet day) was relatively quiet, and the fluxes of the 2nd and 3rd 24 h (active days) increased sharply. Moreover, the upward fluxes of zonal momentum below 17 km in the quiet day for each period band (10~30 min, 30 min~2 h, 2~7 h, and 7~24 h) were dominantly positive, while the corresponding downward fluxes were dominantly negative, meaning that the zonal momentum below 17 km in each period band under study were dominantly eastward (propagating along the mean wind). In the active days, both the upward fluxes and downward fluxes in each frequency band were dominantly negative throughout the whole altitude range 6.1–18.95 km.

The wave packets of atmospheric gravity waves were numerically generated, with a given characteristic wave period, horizontal wave length and projection mean wind along the horizontal wave vector. Their projection phase and group velocities along the oblique radar beam (vpr and vgr), with different zenith angle θ and azimuth angle φ, were analyzed by the method of phase- and group-velocity tracing. The results were consistent with the theoretical calculations derived by the dispersion relation, reconfirming the accuracy of the method of analysis. The RTI plot of the numerical wave packets were similar to the striation patterns of the QP echoes from the FAI irregularity region. We propose that the striation range rate of the QP echo is equal to the radial phase velocity vpr, and the slope of the energy line across the neighboring striations is equal to the radial group velocity vgr of the wave packet; the horizontal distance between two neighboring striations is equal to the characteristic wave period τ. Then, one can inversely calculate all the properties of the gravity wave responsible for the appearance of the QP echoes. We found that the possibility of some QP echoes being generated by the gravity waves originated from lower altitudes cannot be ruled out.