In this paper are treated some problems in estimating the continuous space-time spectra with separation into the westward and the eastward moving components using the Fourier transforms of space-time covariance functions, which are applicable to the analysis of the space-time series (aperiodic for both space and time) sampled from a limited area such as the tropical Pacific. However, at the beginning of this paper, several types of space-time spectra are also discussed in order to make clear the relation of the present study to the previous ones which have been mostly concerned with the discontinuous space-continuous time spectra of the space-time series (periodic for space but aperiodic for time) sampled globally but not locally along latitude circles. In Chapter I the s p ace-time spectra discontinuous for both space and time with separation into the westward and the eastward moving wave components are first given as the Fourier transforms of the covariance functions defined by the averages over space and time. Then the spacetime spectra discontinuous for space but continuos for time and those continuous for both space and time are derived respectively as the limiting cases of the spectra discontinuous for both space and time. The relation of the continuous to disontinuous spectra is also discussed. In the statistical approach to space-time series, the space-time spectra are defined as the Fourier tranforms of the space-time covariance functions defined by the averages over the ensembles. It is shown in Chapter II that the general type of space-time spectra appear as the sum of nine defferent types of space-time spectra. If the space-time spectra are absolutely continuous for both space and time, they have space-time spectral density functions. Statistically speaking, the continuous space-time spectra discussed in Chapter I simply mean the sample spectra of the continuous parameter space-time series which we assume to exist for continuous space and time. However in most cases the space-time series are sampled at equidistant space and time intervals, and therefore we are faced with the problem of wavenumber-frequency aliasing which will be discussed briefly. The spectra of the space-time series thus sampled are then required. to converge in some probability modes to the true spectral density functions as defined by the ensemble averags. In order for such sample spectra to be consistent estimates to the true spectral density functions, two different space-time spectral windows which smooth the sample spectra are presented. The large sample properties of such smoothed space-time spectra. ara examined and used to derive approximations to their sampling distributions based on x2-distribution. One of the mo s t important practical problems in the spectral analysis of the continuous parameter space-time series when sampled at equidistant space and time intervals will arise the fact that the very low wavenumberfrequencies appear with much greater sensitivity than others. In Chapter III, two types of high wavenumber-frequency pass filters generated by three different space-time smoothing functions are presented to eliminate the very low wavenumber-frequencies but leave the synoptic scale wave disturbances. In some cases the very high wavenumber-frequencies appear as noise rather than as signal. To eliminate such very high wavenmberfrequencies as well as the very low wavenumber-frequencies but leave the synoptic-scale wave disturbances, a type of intermediate wavenumberfrequency pass filter is also presented. The relatihnship between the filtered and the original space-time spectra is also discussed briefly.
A statistical study was made on the disturbances in the mean lower atmosphere over the tropical Pacific which appears as a well-defined integrated cloud distribution on the photo-climatological cloud picture. In the northern hemisphere summer, the photo-climato logical cloud picture shows two well-defined cloud bands separated by an equatorial cloudless region extending from west to southeast. The monthly surface pressure and wind fields indicate that the northern one of these cloud bands is associated with the Intertropical Convergence Zone (ITCZ) while the southern one is associated with the South Pacific polar trough. These two cloud bands are characterized by marked cyclonic vorticity and convergence, low steadiness of the winds, and high variances of the pressure as well as of the zonal and meridional wind components about their means. The equatorial region appears to be associated with the equatorial trough in the western Pacific and the equatorial ridge in the eastern Pacific. This region is characterized by large negative vorticity and divergence, relatively high steadiness of the winds and relatively low variances of the pressure and winds. The frequenency-spectrum analysis of the local variations in the mean fields over the Pacific indictes that a 4-5 day period is predominant north of the ITCZ and in the South Pacific trough. In the equatorial cludless region extending from west to southeast a 4-5 day period is predominant in the western Pacific while an 8-10 day period is predominant in the eastern Pacific. The space-time spectrum analysis made along latitude circles over the Pacific indicates that near 10°N, in the region of the ITCZ, westward moving easterly waves with wavelengths of 2,500 km and periods of 4-5 days are observed but they are much more predominant at 20°N. Waves of 5,000 km wavelength moving toward the east with a 6-day period are observed at 30°N, which are identified with the. North Pacific subtropical highs moving toward the east with a 5,000 km spacing. At 20°S are observed waves of 5,000 km wavelength moving toward the east with a 4-5 day period and with 10 day periods against the basic easterly currents. These may be identified as the South Pacific subtropical highs moving toward the east with a 5,000 km spacing. In the equatorial region between 10°S and 10°N waves with a 6,000 km wavelength are observed moving toward the west with 6 day and 10 day periods. These waves are identified as the equatorial anticycolones moving toward the west with a 6,000 km spacing. Finally, it is observed that the southward momentum transport by the disturbances takes place north of the ITCZ, and the northward. transport takes place south of the ITCZ, thus suggesting the convergence of the easterly momentum by the disturbances along the ITCZ. The wavenumber-frequency co-spectrum analysis shows that at 10°N the northward and southward transports of the easterly momentum take place due to the waves moving toward the west with a 4,000 km wavelength -5.5 day period and with a 2,500 km wavelength 5.5 day period, respectively, the latter corresponding to the easterly waves. The southward transport of the easterly momentum by the easterly waves is most predominant at 20°N.
According to BRADLEY, velocity changes do not agree fairly well with the PANOFSKY and TOWNSEND theory in the rough-smooth direction. This problem is reexamined by the use of BRADLEY'S data. It is concluded that the velocity profiles observed agree fairly well with those predicted by the PANOFSKY and TOWNSEND theory also in this case by a reasonable choice of roughness parameters.
The eruptive activities of Komagatake, Akita Prefecture, which were recorded during the period from September 1970 to February 1971, are especially interesting on account of some unusual phenomena involved in lava flows and explosions. The writer expressed the characteristics of the volcano's mechanism of explosion in terms of S/M, that is, the ratio of two phase amplitudes of sound and earthquake in a seismogram of explosion (Fig.6). Referring to the theoretical values of tide generating forces of Komagatake, the writer studied the nature of this activity and explained the depth of the source of explosion and its changes. The mechanism of the underground activities of Komagatake applies also to the Matsushiro earthquake swarm and activities of other volcanoes. During the eruptive activities, the “smoke-ring” was observed for the first time in Japan. Fortunately, the writer was able to observe the whole process of its formation from the crater, by means of an 8 mm cinecamera and the tapecorder. Then he carried out spectrum analysis and examined the relationship between the fluctuations of explosive energy and the seismic waves, so as to elucidate the cause of this unique phenomenon which is seldom recorded in the history of volcanoes of the world. At 14: 16 in Oct.24,1970, a pillar-like white smoke emerged out of the crater with a detonation (Fig.2-a-1). It grew with the top part gradually shaping into a horizontal ring as it became taller (Fig.2-a-2). After 12 seconds, at a height of 50meters, the ring went up alone leaving the white pillar of smoke below. The ring was about 7 meters in diameter. The air current was seen to move relatively upwards inside the ring and downwards outside it. The ring travelled up for about 20 minutes until it disappeared in the cloud (AC) about 5,000 meters high. The detonating sound of the explosion recorded o n magnetic tape was analysed by band pass filters, the results being shown in Fig.3-a,3-b. There is little difference in strength between the detonation accompanied by “smoke-ring” and that without it. Marked difference, however, is seen in the type of spectrum of the detonation between that with “smoke-ring”(Fig.4, top) and those without it. (Fig.4, middle and bottom). Sound energy is more concentrated in the lower band of frequency in the former case than in the latter.