The change of pressure in the atmosphere due to change of temperature, such as the formation of low in land due to the solar radiation, is one of the most important cause for growth and decay of cyclone and anticyclone. The relation between pressure change and temperature change in the atmosphere is investigated. The fundamental relations are, and The former is the equation of motion and the latter is equivalent to the equation of continuity. Neglecting small quantities, we can derive following equation from them And we have one of the above solutions, This is the condition which holds for any change of temperature. From this condition, we have the relation between the pressure change and temperature change in the atmosphere as follows, where P0 is pressure on the earth surface. The relation is confirmed by various examples.
The autumn weather in the Far Eastern Asia is researched from the stand point of dynamical climatology and the results are summarized as follows. (1) Summer weather changes abruptly into autumn weather. The change of minimum air temperature at Maebasi and the alternation of pressure distribution on the synoptic chart show clearly these phenomena. (2) The above phenomena can be explained as the out break of horizontal stability due to the cooling of asiatic continent. This is proved theoretically if we assume simple model. (3) The autumn weather is considered to be influenced by the interaction of continental air mass and oceanic air mass, and if the frontal zone between these two air masses becomes sharp, the weather becomes bad and the depressions develop_??_ and progress on this zone. (4) The out flow of continental air mass from asiatic continent is the fundamental pheneomena in this season and the formation of continental high are discussed theoretically. (5) One of the typical pressure distribution in this season is “High in the North, Low in the South” This weather is considered as transitional weather from summer to autumn, and it corresponds to Baiu, i.e. the rainy seasonin June and July. (6) Thermodynamical properties of typhoon are investigated, and the kinetic energy, power, total mass of prcepitation, are estimated to be about 2×1024 ergs. 4×1010 horse power, 10×1014gr/day respectively for ordinary typhoon.
Recently H. Ertel discussed the horizontal stability of zonal circulation and derived the equation(1): Here f denotes the coriolian parameter 2ω sinφ, ρ0 the density, P0 the pressure, U0 the east component of wind velocity and n the constant in polytropic change of state. b is the Lagrangian coordinate and directed towards the north pole. In Ertel's theory is assumed the conservation of pressure in horizontal virtual displacement and this is the very reason why the term -U0∂f/∂b appears in his equation of horizontal stability, since the pressure P0 is connected with f and U0 by the relation: Thus Ertel's assumption of conservation of pressure in virtual displacement directly determines the law of change of coriolian parameter and relative wind velocity (geostrophic wind velocity) in horizontal virtual displacement. But this assumption is generally inacceptable on our rotating earth. As already pointed out by v. Helmholtz in his theory of air mass ring, it is reasonable to assume the conservation of angular momentum and potential temperature in virtual displacement on the rotating earth. Therefore the pressure does not obey the law of conservation in horizontal displacement, as is the case with the problem of vertical stability. Following v. Helmholtz's theory the present author derived the equation of horizontal stability of the atmosphere as follows: Here a is the radius of the earth, G the acceleration due to gravity, υλ the longitudinal component of velocity and Θ the potential temperature. In case of υλ_??_aωcosφ, the above equation becomes: in which some terms are also found in Ertel's equation, but there exists an essential difference between the two equations. H. Ertel applied his theory to the problem of horizontal stability of the actual atmosphere and concluded that the atmosphere is stable for horizontal displacement in a state of zonal circulation. This conclusion holds good also in the author's present paper, but in the substratosphere where the temperature gradient is reverse to that in the troposphere, horizontal instability occurs and predominant advection is expected.
Assuming that a small mass of air, which occupies a certain position, say x1, at time t, is diffused by eddy into its surrounding air within the limits of x1-s to x1+s at the next time t+τ, it was found that the eddy flux of any physical quantity per unit area for the time from t to t+τ can be calculated numerically by the formula (6), if the distribution of the quantity at time t is known. By the Simpson's 1/3 rule the formula (6) can be transformed into more convenient formula such as (71), (711), or (7111). Further these formulae can be also transformed into the formula (8), where A is the Austausch coefficient and _??_τ (x, t) the mean gradient of the distribution of the quantity for the time from t to t+τ. Fig. 3, I, II and III show how to determine the mean gradient from the curve of the distribution of the quantity, corresponding respectively to the formulae (71), (711), and (7111). In the case when τ is not small, it will be better to use the formula (13). In the tables 1 and 2 are compared the results of the theoretical and the numerical calculations for some exercises.
We investigated the correlation of the air temperature at Miyako in July and those in other months at other stations and then gained the results that the air temperature in April in the middle part of Japan, the southen part of Korea and the Central China have the intimate relation to the air temperature in July at Miyako. The correlation coefficients are +0.4_??_+0.6.