一维气候时间序列所包含的浑沌吸引子的Kalmogorov熵的确定

DETERMINATION OF THE KOLMOGOROV ENTROPY OF A CHAOTIC ATTRACTOR INCLUDED IN THE ONE-DIMENSIONAL TIME SERIES OF METEOROLOGICAL DATA

摘要:

本文采用上海16年(1970—1985年)逐日平均气压资料,用相空间延拓的方法,计算了它的关联维D和Kalmogorov熵的近似值二阶Renyi嫡K₂。得到D=7.7～7.9,为分数值,K₂约为0.1,是一正数值。证明我国季风区短期天气吸引子是一种浑沌运动。由K₂数值直接估计可预报时间T=(1K₂)约为十天,与早期动力统计学方法所得的可预报时间尺度相一致。 本文计算中,考察了相空间拓展时延滞τ的效应。计算结果表明:关联维D和K₂对τ均是收敛的。对本文所用上海逐日平均气压序列,用延滞τ=5延拓的相空间,各坐标分量是相互独立的,系统动力学特征量是稳定可靠的。

Abstract:

The 1970-1985 daily-averaged pressure dataset of Shanghai is used to calculate its associated dimension D and the second-order Reiyi entropy, K₂, as the approximation of Kolmogorov's entropy, in terms of the phase space continuation, indicating the fractional dimension D = 7.7-7.9 and positive K₂≈0.1.This shows that the attractor for the short-term weather evolution in the monsoon region of China exhibits a choatic motion.The direct estimate of K₂ yields a roughly 10-day scale of the lead time T= (1/K₂) ,a result which is in agreement with that obtained earlier by the dynamic-statistical approach.Examined during the continuation of phase space is the effect of the lag time τ.Calculations show that D and K₂ are convergent with respect to τ.The daily averaged pressure series employed are treated by the continuation of phase space with τ=5, with the coordinate components independent of each other, and the dynamically characteristic quantity of the system is found stable and thus reliable.