Behaviors of internal inertio-gravity waves (IIGW) near Jones' critical levels are studied theoretically in view of a possible origin of turbulence layers in the middle atmosphere. The inertial effect associated with the earth's rotation cannot be neglected when time constant of the wave is large. Assuming that the vertical shear and Coriolis factor are constant, exact solutions of IIGW are obtained from inviscid and linear equations. The asymptotic expressions are derived by means of the Liouville-Green method developed by Olver (1974) which leads to an exact dispersion relation near the critical levels. Two important features about critical level problem of IIGW are found from the dispersion relation: valve effect across the Jones' critical levels in somewhat different sense from Grimshaw (1975, 1980), and presence of a pair of turning levels between both Jones' critical levels. Coupling these features, we predict that IIGW is absorbed or reflected by the Jones' critical levels depending on the direction of wave-front. The absorption rate and the thickness of turbulence layer produced by critical level breakdown increase as the wave-fronts tend to direct to the zonal direction, on the other hand IIGW is substantially reflected when they direct to the meridional direction. With increase of basic Richardson number the turning levels approach asymptotically the critical levels, so that turbulence layers inside the critical levels become thinner than those outside them. These features vanish in the case of non-inertial gravity waves. The relation between IIGW and turbulence layers is calculated to compare with the turbulence layers observed in the stratosphere and to have information on IIGW's propagating upwards to the mesosphere and the thermosphere. In general, thickness of the turbulence layers associated with IIGW's is thinner than that associated with non-inertial gravity waves for common mesoscale wavelength domain.
We examine the stability of a baroclinic layer between two unbounded barotropic layers in a model neglecting β -effect. Without using geostrophic approximation, calculations are made for an extended range of the Rossby number, and for the Richardson number=0.5 and 50. For the large Rossby number the solutions in the barotropic layer may be sinusoidal (gravity wave). Then, we invoke " radiation condition" to choose between the gravity wave propagating upwards and the one propagating downwards. For the comparison, same calculations are made under the condition that horizontal rigid walls exist at both boundaries of the baroclinic layer. The results of the calculations show that the nature of the disturbances is not drastically modified by the alteration of the boundary condition, although values of growth rate and phase velocity of the disturbances are to some extent changed. With an increase of the Rossby number, one of two critical points (i.e.a level at which U(z)-cγ =f/k or -f/k) appears in the baroclinic layer. However, for either boundary condition it is found that for more increased value of the Rossby number, steering level of the disturbances approaches to a boundary of the baroclinic layer, so that both critical points can not appear at the same time in the baroclinic layer.
Analytic properties and asymptotic behaviour of the Fourier-Laplace transformed Green's function for the linear initial-value problem of the barotropic disturbance in the complex frequency-plane are investigated. Singularities of this Green's function are classified into three types; poles whose positions are determined by the usual eigenvalue problems; a pole which comes from the singularity of the governing equation; a cut which corresponds to the continuous mode and is drawn between two branch points whose positions are decided by the maximum and the minimum value of the basic flow. Further it is shown that this Green's function asymptotically goes to zero in any direction of the complex frequency plane in reciprocal proportion to the absolute value of the complex frequency.
On the basis of the transformed Eulerian-mean equation which includes Eliassen-Palm flux divergence or quasi-geostrophic potential vorticity transport for large-scale extratropical motions, a transformed energy conversion equation is derived for further understanding of the wave-zonal flow interaction. The transformed mean energy conversion equation is readily derived from the transformed mean equation. In order to obtain the transformed eddy energy conversion equation consistent with the transformed mean energy conversion equation, an attempt is made to transform the eddy equation, and the transformed energy conversion equation is constructed for both mean motion and eddy motion. It is shown that there is no conversion between the mean available potential energy and the eddy available potential energy formally in the transformed energetics. The transformed energy conversion equation is applied to some theoretical problems such as Eady's baroclinic instability, upward propagating stationary planetary wave incident on a critical level and upward propagating planetary wave packet. For Eady's problem, the transformed energetics explicitly describes the significance of the existence of horizontal boundaries which is known to be essential to baroclinic instability. The behavior of energy conversion is simpler in the transformed energetics than in the ordinary energetics for the critical level problem and the wave packet problem since the transformed energy conversion equation does not include originally the term irrelevant to the net influence on the budget of energy in the result. The new form based on the transformed equation is useful to understand the circumstances that the wave-mean flow interactions occur although there are some limitations in the energetics itself.
The semiannual oscillation of the mean zonal wind in the equatorial middle atmosphere is investigated by using a zonally averaged two-dimensional model. In the model, the following mechanisms are included: Easterlies just after the solstices at the stratopause level are due to meridional wind producing nonlinear advection of the easterly momentum in the summer hemisphere. Westerlies just after the equinoxes are due to the momentum deposit by Kelvin waves. The semiannual oscillation at the mesopause level is due to the selective transmission of internal gravity waves through the stratopause level semiannual oscillation (cf. Dunkerton, 1982a, b). We discuss the following two cases; (1) the case which does not include the acceleration due to gravity waves but includes Rayleigh friction in the mesosphere, (2) the case which does not include Rayleigh friction in the mesosphere but includes the acceleration due to gravity waves. In both cases, we can obtain a semiannual zonal wind oscillation at the 50km level over the equator. But, in Case (1), there appears upward propagation of the westerly wind at the equinox. In Case (2), we can obtain a semiannual oscillation with amplitude 7m/sec at the mesopause level, as well as that at the stratopause level over the equator. However, in both cases, there remain constant westerly winds at 30-40km level over the equator, and the amplitude of the semiannual oscillation at the stratopause level is small at 10° latitude. These results imply that the easterly acceleration due to planetary waves may be important in obtaining more realistic semiannual zonal wind oscillation.
A step-like increase in the 850mb zonal mean westerlies over the equatorial Southern Hemisphere (3.75°-11.25°S, 90°E-180°) occurred between 22-30 December 1978. This event was used to subjectively define the onset for the 1978-79 Southern Hemisphere monsoon. During the onset period, widespread increases in 850mb cross-equatorial northerlies occurred over the western Pacific between 120°E and the dateline, reflecting the intensified low-level Hadley circulation after the onset. Over the maritime continent (Sumatra, Borneo, New Guinea), the large-scale apparent heating rate (Q1) decreased considerably from the preto post-onset phase. By contrast, drastic intensification in Q1 heat sources took place near Cape York Peninsula and the equatorial South Pacific east of Australia, with a maximum heating rate of about 4°C per day at 447mb. The spatial distribution of the large-scale apparent moisture sources (Q2) exhibits a parallel feature to that of the Q1 pattern for both the pre- and post-onset phases. An approximate inverse relationship exists between the large-scale apparent vorticity sources (Z) at 850 and 200mb over the Southern Hemisphere monsoon region. For example, near Cape, York Peninsula, large positive Z values at 850mb are contrasted with pronounced negative Z values at 200mb after the onset.
The seasonal and the intraseasonal behaviors of the deep convective clouds are investigated by using the activity index devised in Part I of this paper. The monthly mean distributions for the period from May through August 1979 have revealed many seasonal characteristics which have been inferred in the past from the cloudiness or from the outgoing longwave radiation (OLR). The latitudinal change of the distribution has clearly shown the northward advance of the convective area over the Southeast Asia, the formation of the highly convective area which brings the Bai-u (Mei-yu in Chinese) rain, and the northward shift of the convective belt associated with ITCZ over the western Pacific. The latitude-time section of the above activity has revealed the existence of the major intraseasonal variation with the 30- to 40-day periodicity. Over the Indo-China peninsula and the Bay of Bengal, it appears in the form of the repetitive progressions from the equatorial South Indian Ocean. The more detailed analysis using the band-pass filter has revealed that there also exists a southward-progressing component which comes down from the Tibetan Plateau. Moreover, it turned out that the similar situation also occurs over the western Pacific. The composite analysis performed on the wind variation at 850mb level verified that the above 30- to 40-day variation is associated with the active/break cycle of the Indian monsoon. When the monsoon westerly is most intensified over India, the enhanced deep convection appears over the region ranging from the northeastern India to the Philippines. In contrast, the suppressed condition appears over the equatorial Indian Ocean and the Tibetan Plateau. Furthermore, it turned out that the convective activity associated with ITCZ is also intensified at this stage over the tropical western Pacific.
The critical condition of microphysical parameters for the formation of a typical "bimodal" drop size-distribution in cumuli composed of cloud droplets and drizzle sized drops, through which cloud droplets explosively grow into raindrops by coalescence, is investigated by using an axisymmetric cumulus model. To meet this purpose, the evolutional process of droplets in the clouds with different dynamical properties is carefully examined. The detailed analysis of the result strongly suggests the existence of a general critical condition for the formation of the typical "bimodal" drop size-distribution. The condition is simply expressed in terms of mean radius and dispersion of droplets. In well developed clouds, dynamically active, the critical condition is met almost during the developing stage of the cloud at levels far below the highest cloud top, and the explosive growth of droplets together with the development of intense downdraft by nonlinear interaction between cloud dynamics and microphysics finally gives rise to a sudden outbreak of rainfall characterized by heavy, short-lived and localized features, large raindrops, higher rainfall efficiency and so on. On the other hand, in small-scale cumuli, which are less active, the growth of droplets is fairly gradual since the critical condition is barely satisfied near the midst of the mature stage almost in the uppermost layer of the cloud. This lower growth rate of droplets together with the high evaporation rate in the decaying stage of the cloud is an important mechanism of the precipitation process in small cumuli characterized by relatively light rainfall, smaller raindrops, smaller rainfall efficiency, and so on. Careful consideration is given to the cumulus model.
An unforced air flow cloud chamber was designed to produce a very stable supercooled cloud. Ice crystals grown in such a stable cloud are large in size but are small in growth rate. Surface markings and inside patterns of them are less complicated than natural snow crystals although the dependence of the crystal habit on temperature is identical with the established result.
Ice crystals grown in a supercooled cloud at temperatures from -4 to-1.5°C in a cloud chamber of the type of unforced air flow have been studied, with the following findings: All of them are plates in shape, which are categorized into a sector plate (-4.0∼-2.5°C), a fern-shaped plate (-3.0∼2.0°C) and a plate with a scalloped periphery (-2.0∼1.5°C), and the rate of growth in the a-axis direction increases as the temperature approaches the melting point. The three types of crystals have a multilayered and plate construction in common. The most conspicuous in the layered construction is the plate with a scalloped periphery, which is characterized by the direction of growth of the tip of a branch that is not always parallel to an a-axis, the number of such branch being vast.
In order to incorporate the radiative process into a dynamical model for forcasting the development of fog or stratiform cloud, a method of calculating the rate of radiative temperature change has been developed by applying the P3-approximation method to a foggy atmosphere. We took into account absorption, scattering, and scattering and absorption of solar radiation by ozone, air molecules and water droplets, respectively, in the visible region, absorption of solar radiation by the near infrared bands of water vapor, and scattering and absorption of solar radiation by water droplets in the near infrared region. In the infrared region, we considered absorption and emission of thermal radiation by 6.3μm and rotational bands of water vapor, 15μm band of carbon dioxide and continuum band of water dimer as well as scattering, absorption and emission of thermal radiation by water droplets. Comparisons of the flux divergence estimated by the present method with that by the discrete ordinates method of high accuracy showed that the accuracy of this approximation is sufficient for the estimation of radiative effects on the evolution of fog or stratus.
Tropospheric and stratospheric air samples were collected over Japan since 1978, and analyzed for CF2Cl2, CFC13 and N20 by a GC-ECD method. Mean volume mixing ratios in the troposphere were 282 ppt for CF2Cl2, 162 ppt for CFC13, and 310 ppb for N20 during October 1978 to March 1979. It was also found that the mean mixing ratios of CF2Cl2 and CFCl3 increased by about 20% from 1979 to 1983. The volume mixing ratios of CF2Cl2, CFCl3 and N20 in the lower stratosphere decreased with increasing altitude in accordance with the vertical profiles calculated from a photochemical theory.
The lagged correlations between the annual frequency of typhoon formations and monthly sea surface temperature in the North Pacific were examined. The lagged correlations were low even in the months near the period of typhoon formations. The largest correlation coefficients appeared in October of two years before. The regions of significant positive correlation are located in the eastern Equatorial Pacific. The northwestern part of the North Pacific showed negative correlation. In general, the values of the negatvie correlations were small in magnitude compared to the positive correlations.