On the Coherence between Progressive and Retrogressive Waves and a Partition of Space-Time Power Spectra into Standing and Traveling Parts

Space-Time Spectral Analysis and its Applications to Atmospheric Waves

“…(3). However, his estimates were not statistically meaningful, since a frequency band mean was not taken, as was pointed out by Hayashi (1973), Tsay (1974) andPratt (1976). On the other hand, Hayashi (1971Hayashi ( , 1977bHayashi ( , 1981b's method enables one to estimate spacetime cross spectra by use of time spectral analysis methods such as the lag correlation method, the direct Fourier transform method and the maximum entropy method depending on the length of the record.…”

Modified Methods of Estimating Space-Time Spectra from Polar-Orbiting Satellite Data

“…These spectra are correctly estimated by the frequency transform method with a correction for the uneven time increments (top), whereas they are aliased without this correction (middle). They are also aliased by the ordinary method (Hayashi, 1971) of space-time spectral analysis (bottom).…”

“…On the other hand, Hayashi (1980) modified the conventional method of Hayashi (1971) in order to estimate space-time spectra correctly from asynoptic satellite data which are sampled at the same local time. When these data are regarded as spatial data, the wavenumber m is shifted by the frequency * (see Fig.…”

“…In addition, the coherence Cohm , *(w) between eastward and westward moving components (Hayashi, 1977(Hayashi, , 1979) is given by List 2 The power spectra of standing (WS) and traveling (wt) wave components are given by use of this coherence as…”

“…However, as pointed out by Hartmann (1976), a direct application of the conventional methods (e.g. Hayashi, 1971) of space-time spectral analysis to polar-orbiting satellite data suffers from serious errors in the spectra of waves with periods shorter than 5 days or so. This is because these data are sampled at the same local time but different hours of the day due to the earth's rotation relative to the orbit of the satellite (see Fig.…”