Determination of Kolmogorov Entropy of Chaotic Attractor Included in One-Dimensional Time Series of Meteorological Data

The 1970-1985 day to day averaged pressure dataset of Shanghai and the extension method in phase space are used to calculate the correlation dimension D and the second-order Renyi entropy K2 of the approximation of Kolmogorov's entropy, the fractional dimension D = 7.7-7.9 and the positive value K2 - 0.1 are obtained. This shows that the attractor for the short-term weather evolution in the monsoon region of China exhibits a chaotic motion. The estimate of K2 yields a predictable time scale of about ten days. This result is in agreement with that obtained earlier by the dynamic-statistical approach.The effects of the lag time i on the estimate of D and K2 are investigated. The results show that D and K2 are convergent with respect to i. The day to day averaged pressure series used in this paper are treated for the extensive phase space with T = 5, the coordinate components are independent of each other; therefore, the dynamical character quantities of the system are stable and reliable.     

利用一维时间序列重建动力系统的初步研究

通过对月平均气温一维时间序列作相空间拓展,和假定相空间状态变量随时间的演化方程含有线性和非线性二次项,再根据拓展后的资料进行拟合,利用最小二乘法求出各项系数,保留其方差贡献大的项,以重建动力系统.实际计算结果表明,重建的低阶动力系统有可能对月平均气温所表征的短期气候演化过程的非线性特性作出描写.     

一维气候时间序列的拓展及其相空间中浑沌吸引子维数的确定

本文利用上海和广州近百年(1873—1980)月平均气温时间序列资料,将一维气候时间序列拓展到多维相空间上去。计算结果表明,月平均气温所表示的我国季风区短期气候演化,在相空间中存在吸引子,具有分维结构,其维数分别是d=3.4和d=2.3,为奇怪吸引子。由此推论,就我国季风区气候短期变化而言,为了能在多维相空间支撑起上述奇怪吸引子,最好选取四个变量或者建立最低为四阶的动力学模式来进行描述。      

神经网络BP模型用于月降水预报的研究

采用神经网络ＢＰ型三层映射模式，以南京１９４６－１９８５年４０年月雨量为基础序列，确定三层模式的形式。通过不断调整权重系数，作出１９８６年１－１２月的月雨量长期预报，又用同样方法但改用前一个月的实测值报后一个月的月雨量作出１９８６年各月的月雨址预报。平均绝对误差分别为６．０７ｍｍ和５．７３ｍｍ。对１９９４年６、７、８、９月月雨量以４个不同的起始值进行神经网络预测，都得到１９９４年夏季南京特旱的结果，与实测结果相同。     

给定参数条件下海温脉动随机模式的混沌行为

从Ｓａｌｔｚｍａｎ海气随机气候模式出发，得到了海温脉动θ＇的Ｌａｎｇｅｖｉｎ方程以及对应的Ｆｏｋｋｅｒ－ｐｌａｎｋ方程。在给定参数条件下求数值解，得到的概率密度曲线ｐ（ｘ，ｔ）具有多个极大值，并在ｐ（ｘ，ｔ）－ｐ（ｘ，ｔ＋τ）相空间中呈现Ｃａｎｔｏｒ集合图象，表明该随机系统在上述参数条件下出现了混沌行为。     

CHAOTIC OUTPUT OF SST FLUCTUATION STOCHASTIC MODEL WITH GIVEN PARAMETERS

Starting from the Saltzman's air-sea stochastic climatic model, we have derived a langevin-type equation describing SST fluctuation and the related pokker-Plank expression, which were then numerically solved with parameters given, yielding the probability density curve P(x, t) of multiple bifurcations, with the Cantor set of images given in phase space of P(x, t) and P(x, t+τ), thereby indicating that chaotic output comes from the random system under the conditions of the above parameters.     

一维气候时间序列的李亚普诺夫指数所显示的动态系统的演化特征

本文利用广州1873—1980年共108年的月平均气温时间序列资料,在拓展了的三维相空间中,用Wolf的方法,求出了在不同参数条件下的李亚普诺夫指数λ₁。从中发现,对每一组参数,均得到λ_1,2>0（其中λ₁>λ₂）,λ₃<0。这说明我国季风区短期气候演化存在着浑沌吸引子,因而气候应该分享经历着浑沌力学行为的体系所具有的那种本征的演化特征。