On the Transformation and Mutual Relations of Adiabatic Charts Convenient to the Height Calculation

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Though the method of adiabatic charts has been applied to thermodynamical problems in meteorology for a long time, especially in aerology their use has been flourished remarkably during last twenty years, and in this period quick treatments of observational data of aerology and quick calculations of their heights were required, because many aerological observatories were established and at each place aerological observations were carried out several times a day. So far in meteorological circles a well known method by barometric formula has been used as procedures of height calculations for these data. (cf. 1 (i)). About twenty years ago, however, in order to reduce the complication inherent in these procedures, Stuve proposed a method to utilize adiabatic charts for this purpose, whose adoption has since prevailed quickly in the aerological circles. Moreover a few special adiabatic charts have appeared, suitable to the above requirement about the quick height calculation. At the same time some theories about height calculations on adiabatic charts and the mutual relations among these charts appeared also as below. We shall classify the recent development of these theories into the following four classes. (i) Stuve's theory to reduce the height problem of actual atmosphere on Emagram (T-logp) to that of isothermal atmosphere or dry adiabatic one. (ii) Theories of height calculation on Tephigram by Shaw, Brunt and Arakawa. (iii) Refsdal's theory of Aerogram. (iv) Yamaoka's theory for the transformation of adiabatic charts and his proposition of Taikisendzu (Atmospheric Chart). As shown in the above classification new adiabatic charts such as Aerogram and Taikisendzu have appeared recently, convenient to the height calculation on these diagrams. According to the author's opinion, contrary to the usual considerations about Tephigram, it belongs to the same family of adiabatic charts as Aerogram etc. as regards to the convenience of height calculation. Though the general theories for height calculation are described in the above classification (iii) and (iv), Yamaoka's (iv) is, however, considered to be superior to Refsdal's theory (iii). But there remains some questions to be discussed-their assumptions and mutual relations among these diagrams. In this paper we shall consider mainly these problems, and make good Yamaoka's theory, but in our paper the whole problem is treated quite differently from Yamaoka's. In 1 preliminary notes on fundamental equations and the theory for height calculation so far used are described as fundamentals for the further development of our theory. In 2 conditions to be satisfied for our aim are discussed, as the above coordinates lead to the partial differential equation of Monge-Ampere's type, its general solution being given in 3. In 4 the outline of Yamaoka's theory is described and its results are compared with ours. In 5 mutual relation among Aerogram, Taikisendzu and Tephigram is derived from our general formula and rough sketch of each case is also delivered.
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On the Transformation and Mutual Relations of Adiabatic Charts Convenient to the Height Calculation

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