A theoretical examination is made of the dynamics of transient planetary Rossby waves in the winter stratosphere forced from below, using the quasi-geostrophic, mid-latitude β-plane approximations. The response of planetary Rossby waves to a periodic forcing in the lower atmosphere is described in a model as a function of three parameters: the intensity of mean zonal wind, the wavelength of disturbance, and the period of excitation. It was found that the maximum response of the wave should take place according to the steady-state solution for a certain ratio of the wavelength to the excitation period. Periodic changes of the mean zonal wind intensity were assumed to be a source of the wave excitation and numerical time integrations of the linearized potential vorticity equation were carried out. In the present model, the results obtained agree well with the time-dependent behavior of planetary Rossby waves observed in the stratosphere during winter.
Frictional convergence due to large-scale equatorial waves discussed by Holton et al. (1971) and Yamasaki (1971) is re-examined diagnostically on the assumption that the Ekman layer solution does not extend to infinite height. It is found that frictional convergence in not singular but extreme at the critical latitude where the Coriolis frequency is equal to the wave frequency for even meridional modes, while it attains its maximum at the equator for odd modes contrary to the result by Holton et al. (1971).
The analogy index proposed in this paper experesses objectively the degree of similarity in shape and value between two kinds of distribution patterns of a physical quantity. We define this index by the following equation;s I=f(γ, E)=γ(1-E/R) where I is the analogy index, γ and E are the correlation coefficient and the root mean square difference between two kinds of patterns respectively, and R is the range of the physical quantity which forms the patterns and is a proper constant value the dimension of which is the same as the root mean square difference. R is defined by R=nδ, δ=1/2(δx+δy), where δ× and δy are respectively the standard deviation of each pattern. As a result of the consideration, the most appropriate value of R is 4δ for giving the analogy index the characteristics of the correlation coefficient r and the root mean square difference E. The verifications of the analogy index are being carried out for the surface pressure patterns and the diurnal variations of visibility at Tokyo International Airport in the warm seasons of 1966 and 1967. The analogy index is far better than the root mean square difference and somewhat better than the correlation coefficient in the case of the surface pressure patterns. On the other hand, in the case of diurnal variations of visibility, the analogy index is far better than the correlation coefficient and has almost the same accuracy as the root mean square difference. We make practical applications of the analogy index as follows. In accordance with the method used by IA. Lund (1963) and K. Abe and E. Suzuki (1969), we classify the surface pressure patterns and get the same result as obtained through synopic meteorology. Then, after verification of the 24-hour prognostic surface map, we gain the result that the analogy index is more advantageous than the correlation coefficient in showing the similarity of the pressure values.
The problem of the onset of convective motion in the fluid bounded by walls of finite thermal conductivity and finite thickness is investigated by linear analysis for two cases. In Case I we consider only the effect of the upper and lower walls, assuming the horizontal extent of fluid to be infinite. In Case II we consider only the effect of side walls with the upper and lower boundary conditions treatded in a conventional manner. In both cases, the governing equations are linearized with the Boussinesq approximation and the principle of exchange of stabilities is proved to be valid. The procedure of solving the eigenvalue probelms is described briefly. In Case I, the effect of the thickness of the walls (h) is found to be almost the same as that in the limiting case h→∞ for h larger than the depth of the fluid. As the ratio of thermal conductivity of the walls to that of the fluid (ξ) decreases, the critical Rayleigh number is reduced and the horizontal sclae of motion becomes larger. In Case II the effect of the thickness of the side walls is almost the same as that in the limiting case h→∞ for h larger than half the depth of the fluid layer. The effect of the lateral width of the fluid layer is shown very strong on the onset of motion. The calculated value of the critical Rayleigh number is compared with that obtained experimentally by Ukaji and Sawada (1969), and good agreement is obtained.
Based upon their previous studies in the concentration of deaths in winter in Japan and the West European countries, on the one hand, and, on the other hand the considerable moderation of seasonal variation in mortality, or rather “ deseasonalization ” of deaths, in the Scandinavian countries and the United States in this paper the authoresess attempt to analyze quantitatively the difference between these two types of seasonal variation in mortality and specifically the geographical difference in relationship between mortality (stroke and infant) and temperature in the three cities of London, Tokyo and New York, and they sincerely want to build up one of the groundworks necessary for long-term biometerorological forecast. For such statistical analysis, census method II and covariance analysis in the twoway layout are used. 1. As for the seasonal variation of mortality, time series analysis appears to be the effective statistical methods. Thus, census method II has been adopted to analyze a time series of stroke mortality. Generally, the time series is composed of the trend cycle (TC) the seasonal variation component (S) and the irregular component (I), but the second named alone is studied in this paper because it calls for serious considerations from the biometeorological standpoint. The time series cycle of the seasonal variation component is naturally regular in the three cities, but the amplitude is much smaller in New York than in London and Tokyo. The correlation coefficient between stroke mortality and temperature in terms of the seasonal component comes at -0.9709 for Tokyo, or slightly larger than -0.9281 for London and -0.9015 for New York. As there is some time lag between mortality and temperature, the correlation coefficients are calculated with one to five months shifted, and it is seen that the coefficient is the largest for Tokyo in case there is no time lag, and that it appears to reach the peak, if half a month is shifted, for London and New York. Details of the time series analysis with census method II will be published later. 2. Covariance analysis indicates that there is no significant difference among the three cities between the regression equation of mortality (stroke and infant) on temperature in spring and that in autumn in the 1960's, so the changes per 10°C in the death rate are calculated by average regression coefficient. Mortality is inversely related to temperature, and the increase or decrease per 10°C in the death rate for stroke turns out to be larger than that for infant mortality in the three cities. In both Tokyo and London, the rise of the death rate for stroke in autumn is considerably large, or 24.0% and 32.4%, respectively, contrasted to only 8.3% in New York (over three and four times larger, respectively). As for infants, the mortality rate decreases or increases very slightly (not more than 1.5%) in New York along with the ups and downs of temperature. The corresponding rate of increase or decrease comes at about 8-9% in London. In Tokyo, however, the infant death rate declines by about 16.0% with tempearture up 10°C and goes up by as much as 17.5% with the similar drop of temperature. The changes in death rate with the variation of temperature turn out to be the smallest in New York among the three municipalities. All this clearly indicates that central heating, widely adopted in the American city, has brought about favorable bearings upon mortality, especially that of infants who can live in the artificial climate. It is also to be noted that mortality from stroke undergoes much larger changes with the ups and downs of temperature in London than in Tokyo, and vice versa in the case of infant mortality.