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《Chinese Journal of Atmospheric Sciences》 1992-06
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On the Seasons of General Atmospheric Circulation and their Abrupt ChangesPart I:General Concept and Method

Zeng Qingcun Zhang Bangjin(Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100080)  
This is the first paper of our series of papers on the seasons of general atmospheric circulation and their abrupt changes. General concept, theory and method which are suitable to the division of seasons and the definition of abruptness of their transitions are developed based on objective and quantitative. Firat of all, the measure of similarity of two fields is defined by their coefficient of correlation, and the measure of their difference by the normalized root-mean-square deviation. In the cases of typical winter field Fw and typical summer field Fs, taking F'w≡FW = F* and F'≡F-F*, where F *≡(Fw+ Fs )/2, the correlation coefficient, Rw(t), between F'(t) and F'K and the associated normalized roormean-square deviation, dw(t), can be taken as suitable measures of the similarity and difference between F ' and the typical winter regime, respectively. Because there is certain relationship between Rw(t) and dw2(t), one can analyze only Rw in most cases. We have: (1 ) Winter regime is defined as 1≤Rw (t)0.5, summer regimeas -1≤Rw(t)- 0.5, and transitional seasons as -0. 5Rw (t) 0. 5. (2) Denoting the lengths of winter and spring (transition from winter to summer.) as Tw and tw, respectively, then 1-τ/Tw is a measure of the abruptness of the transition from winter to summer. We have τw. = 0, and 1-τw/Tw,= 1, if the transition is of ideal abruptness (discontinuous function); while τw=1/2, and 1 -τw/Tw,= 1/2, if the seasonal cycle is given by a harmonic function; but 1 -τw,/Tw.《1/2,if the transition is a slow process, for example, 1 -τw/Tw = 0 if τw=Tw. (3) The intensity of season of an individual year can be represented by Rw(t)[||F '||/|| Fw|| ], where Fw is the climatological mean of Fw for a long enough period. In the case of nonexistence of typical fields, we can only define the persistency and abruptness of transition by calculating the time-lag correlation coefficient and normalized root-mean-square deviation Rτ(t)and dτ(t), respectively, where τ is the interval of time lag. However such definitions are not clear enough unless some other additional criteria are also introduced. Finally, some differences between the regional climate and the climate of larger area are also indicated in the paper.Some applications of the theory to individual years and climatological mean state will be presented in the following paper of our series.
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