The statistical discrimination theory was first proposed by C. R. Rao (1948) and has been widely applied to the several domains of scientific classification. Its theoretical development has been due to the work of C. R. Rao, S. S. Wilks, J. G. Bryan and others. It was recently applied to meteorological classifactory preciction by R. G. Miller (1962-1964) and by the present author (1963-1965) almost concurrently. In this paper, a simple optimum linear discrimination function is firstly investigated for the case containing several qualitative or categorical variables only, based on the joint probability dis-tribution (i. e., multi-variate binomial distribution) defined by A. S. Krishnamoorthy (1951) and by the author (1966). Secondly the quantification procedure maximizing the correlation ratio between classified predictand variable Y and categorical set of predictor variable X used for classification (of Y), which has already been shown by C. Hayashi and S. Chino, is taken into account through com-bining it with a linear discriminant function. Lastly, several explanatory examples are shown for qualitative prediction of the rain state and the occurrence or non-occurrence of snowslide by using the effective presaged predictors.
In order to measure the wind fluctuations in the layer the height of which is 500 m above the ground, a bi-directional vane mounted on a captive ballon cable has been developed. Vertical and lateral wind fluctuations are detected by the bi-vane and magnetic compass. Signals of these quantities are transmitted to the surface and recorded. Response characteristics have been investi-gated in a wind tunnel. The distance constant of vane, U/ωnξ(U is wind speed, ωn is frequency of the natural oscillation and ξ is the damping ratio) has been measured and found to be ap-proximately 1.6 m. In preliminary observations, spectra of the vertical and lateral wind fluctua-tions have been measured for the frequency ranges from 0.05 to 1.0 Hz. Intensities of the fluctuations and the maximum frequencies np of the logarithmic vertical spectra have been measured in the layer below 500 m.
The three dimensional structure of large-scale disturbances found in the lower stratosphere and the upper troposphere in the equatorial Pacific is studied in detail by power spectral and synoptic analyses, using the special upper-air observations during the period April through July 1962. It is found that the sharp spectral peak of the meridional component of the wind near the 4.5-day period in the upper troposphere and the lower stratosphere is caused by the westward movement of large-scale eddies which are centered over the equator and penetrating through the tropopause with their axes tilting westward with height. A spectral method of estimating vertical and horizontal transports of energy is devised, by which energy flux is obtained from the correlation between horizontal wind and temperature or the tilt of phase lines. It is shown that the westward tilt of vertical phase lines or poleward transport of heat indicates the upward transport of wave energy. The large-scale waves in the upper troposphere provide the lower stratosphere with energy of the order of 6 ergs per cm2 sec and the vertical convergence of energy of the order of 1 erg per cm2 sec km occurs at the levels from 15 to 20 km. In the lower stratosphere horizontal convergence of wave energy occurs near the equator.
The time evolution of symmetric meridional motions in various unstable baroclinic circular vortices in an incompressible and inviscid fluid is studied by numerical integration of the hydrodynamic equations as an initial value problem. The fluid is bounded in a rectangular domain. Several types of the initial balanced state are considered. All the types belong to Ooyama's (1966) Class (C) vortices, i. e., there exist negative eigenvaues of the stability tensor somewhere in the domain. The results of the numerical experments demonstrate the sufficiency of the above condition for an unlimited growth of the meridional motion from certain types of initial disturbances. The growth rate of the meridional motion primarily depends on the smallest eigenvalue of the stability tensor, but it also depends on the ratio of the smallest to the largest eigenvalue in the domain. When the ratio is small, the growth of the meridional motion becomes very sensitive to the choice of initial perturbations. The preferred orientation of the meridional motion coincides with that expected from the linear theory which assumes no boundaries. When only a part of the domain is unstable, the development of the meridional motion is confined within the unstable subdomain. The direction of energy transformations between the meridional kinetic energy and the zonal kinetic energy and between the meridional kinetic energy and the potential energy is discussed.
The wind distribution over a strait was analyzed by numerical techniques. We assume the surface friction, large roughness length over land and small one over sea. The numerical results based on a simple shape channel show a stronger wind over a strait comparing to that over land. When we assume the height of land in addition to the surface friction, these features are shown more clearly.
A parabolic flow between two horizontal parallel plates is considered, when the lower plate is heated and the upper plate is cooled uniformly. When the temperature difference between the top and bottom of the fluid layer exceeds a critical value, roll-type convection occurs with the axes parallel to the mean flow. The governing equations are solved numerically using the Boussinesq approximation for the range of Rayleigh number, 3 Rac_??_Ra_??_7 Rac, where Rac is the value of the Rayleigh number at which infinitesimal perturbations can be just maintained. The Prandtl number is taken as 0.713. In all cases investigated, the system achieves a steady state. The thus calculated distribution of the velocity component in the direction of the mean flow agrees well with Mori and Uchida's experiment (1966) for Ra=4.69 Rac and the Reynolds number=513. The agreement between the calculated and experimental temperature fields is rather poor however. For the range of Rayleigh numbers considered, the non-dimensional Nusselt number is found to vary in proportion to the 0.328 power of the Rayleigh number, very close to the 1/3 power variation predicted on dimensional reasoning for the Benard-Rayleigh convection problem.
The results of analysis of the data collected on the concentrations of the ice-forming and other forms of nuclei in a few places in India (Delhi, Calcutta, Bombay, Lonavla and Poona) have been presented. The ice-forming nuclei have varied generally inversely with the chloride nuclei at Delhi, Bombay and Poona. The ice-forming and hygroscopic nuclei have shown negative correlation at Delhi. The ice-forming and non-hygroscopic nuclei have varied on parallel lines at Poona. The relatively large value of the ice-forming nuclei noticed at Delhi as compared to that at Calcutta has been seen reflected in the high value of the non-hygroscopic nuclei observed in that region. The observations have suggested that the main source for the ice-forming nuclei in the regions measured is the land. The possibility of the continental dust being responsible for the observed ice nuclei counts in the maritime air has been pointed out.
Clouds over the Indochina Peninsula were observed by a 16 mm time-lapse movie camera, utilizing a passenger jet on 1 Oct. 1965. The aerial cloud pictures were analyzed by the stereoscopic method. The results of the analysis were compared with a satellite picture which was taken almost at the same time as that of the observation time. Because the resolving power of the satellite picture was poor compared with that of the aerial cloud pictures, it was difficult to identify individual clouds, however a good correlation was obtained between the brightness in the satellite picture and the cloud amount calculated from the aerial cloud pictures.