This paper concerns the parameter model which is used in the numerical weather prediction. The expression of the atmospheric motion with a finite number of parameters can never satisfy the original equations of motion and the thermodynamic equation completely for all the levels of the atmosphere, but it can only fulfill the equations approximately. The prognostic equations in the parameter model, therefore, are derived in such a way that the deviations of the parameterized solution of motion from the real solution of equations may become minimum for the domain concerned. Along this line, non-filtered prognostic equations in three-parameter model were derived with the use of the variational principle, and then those for the balanced system of equations were obtained by filtering the prognostic equations.
After resolving the contour heights at the 500 and 1000 mb levels into Fourier series, daily estimates have been made for all possible interaction terms, including the upward transfer of energy into the upper atmosphere, during a one year period from October 1962 to September 1963. It was found that (1) the release of available potential energy is maximum for the wave of wave number 3 in the lower atmosphere, presumably this conversion process is related to the diabatic effect due to the land and sea distribution, (2) the release of available potential energy is almost compensated for by the export of energy to the upper atmosphere, which is largely accomplished by the ultra-long waves of wave numbers 2 and 3, (3) the kinetic energy of the ultra-long waves is partly supplied from all the other waves through nonlinear interaction. An examination of the monthly mean values of the interaction terms in January and February 1963, when the pronounced "blocking" persisted over the northern hemisphere, revealed that "blocking" plays an important part in maintaining the general circulation of the atmosphere. In section 5 will be presented the power spectrum of each interaction term, in order to study the nature of the fluctuations in the energy cycle of the atmosphere.
The downdraft produced by falling waterdrops was measured, using a vertical U-shaped tube. The results showed the magnitude of the downdraft to be much less than expected, even though the measurements included the downdraft produced by the dragforce of the falling drops and that resulting from their negative buoyancy. It was also found that the magnitude of the two components was approximately equal. With regard to the negative buoyancy resulting from the weight of raindrops, it was proposed that, in a parcel of air which contains falling raindrops, air resistance is exerted on each drop individually rather than on the parcel of air as a whole. If this should be the case, it would easily explain why the magnitude of the downdraft produced by individual raindrops is so much less than expected.
The cold air domes which can be analysed inside of the "polar air mass" moved over the Japan Sea, bringing extremely heavy snow fall to lee side coastal region. General feature of sinking cold air is verified by the decreasing volume in the upper part of cold dome, and at the same time the ascent motion is found in surrounding air mass. The temperature in the uppermost part of this cold dome, however, decreases while it passes over the Japan Sea, resulting in a destabilizing of stratification. It is suggested that the upward motion and compensating convergence are caused by a strong supply of heat from the sea surface amounting to more than 1000ly day-1 as the superior cold air covers the warmer sea.
Internal gravity waves caused in the fluid with vertical density gradient passing over a solitary barrier are studied. The patterns of gravity waves numerically computed for the cases of the internal Froude number of 0. 25, 0.20 and 0.125 are compared well with the experimental results obtained by R. Long (1955). On the other hand, the drag coefficient CD is derived analytically from a linearized equation and is given by CD∞1/Fi(1-3/4H2/b2Fi2), where Fi is the Froude number, H the depth of channel and b the characteristic scale of height of the mountain barrier. This formula is checked by the numerical computation with a complete form of non-linear equation.
A computational model for large scale motions which extends to the stratosphere is designed. The model has the tropopause and ground surface, and is favorable in treating the interaction between the tropospheric and stratospheric motions. A special σ-coordinate in the vertical is used, and the tropopause is assumed to be a material surface at which dσ/dt vanishes. Fundamental equations of the model are illustrated, and energetical considerations are given. Particular interest is put in the interaction of kinetic energy between the troposphere and the stratosphere in the short term evolution of the atmospheric motion. Calculation based on the actual data is made for the vertical transfer of kinetic energy through the tropopause. Analytical solutions of perturbations superimposed on the basic tonal current are obtained for barotropic and baroclinic models and compared with those of p-coordinate system. The kinetic energy transport in vertical as well as control of the false westward retrogression of the ultra-long wave, due to the non-vanishing vertical mean divergence in the troposphere, are shown. Modification of the criterion of baroclinic instability due to the existence of the stratosphere is discussed.