2.5Ma 以来古气候变化的混沌吸引子

利用2.5Ma以来经过时标调谐的宝鸡黄土剖面的粒度比值曲线,等时距(1000a)地重构了具2500个样本容量的时间序列。作者在分析此时间序列所记录的古气候变化的混沌特征后发现:2.5Ma以来的古气候是具有有限个自由度的复杂的混沌系统,吸引子关联维数为3.8,饱和嵌入维数为11,它的以最大Lyapunov指数和二阶Renyi熵表征的可预报时效(误差增大一倍所需时间)分别为0.66—0.76Ma和6600—7100a。已有的研究证明该剖面古气候时间序列的大部分时间区间受地球轨道参数的驱动,表明2.5Ma以来的古气候是一种混沌的与周期性的混合式振荡的动力系统。

CHAOTIC ATTRACTORS OF PALEOCLIMATIC VARIATIONS SINCE 2.5 Ma B. P.

In this paper, the nonlinear characteristics of paleoclimatic dynamic system in the last 2.5 Ma B.P. has been studied by using chaotic method. The number of major factors that affect the climatic system of the Earth and the time scale for effectively forecasting future climatic changes are given. The relation between the parameter of Earth's orbit and the chaotic attractors is also discussed. Using the chaotic method to study paleoclimate, a key problem is to establish a new n-dimension vector space through a time series of singular variable shifting for a given time lag of T and then recover the past climatic dynamic system within this new space. The attractor characteristics contained in paleoclimatic system can be determined by calculating the association function of attractors in the n-dimension phase space, the association dimension and the saturation dimension. Moreover, the dynamic behaviour of paleoclimatic system and its foreteling are discriminated by studying the Lyapunov index λ₁ and order-2 Renyi entropy. The curve of grain-size series of Baoji loess profile which has undergone the modulation of time scale has been used to analyse the chaotic feature of paleoclimatic changes by selecting 2500 sample points with equal time interval（1000a）. The calculated result shows that paleoclimatic evolution in the last 2.5Ma B.P. is a complex chaotic system with finite degrees of freedom, the association dimension of the attractor is 3.8, the saturation dimension is 11. Its predictability time scales （the time needed when the error becomes doubling） indicated by the largest Lyapunov characteristic exponents and the order-2 Renyi extropy are 0.66—0.76 Ma and 6600-7100 a respectively. The result confirms that about 90 percent of 2.5 Ma time series is driven by the parameters of the terrestrial orbit and shows the shifting dynamic system having chaotic and periodic characteristics. This characteristics of paleoclimate in China Loess Plateau can be compared with the record of deep-sea deposits （the association dimension of paleoclimatic attractor in oxygen record in V28-238 core is 3.1, in the eastern Atlantic core 4.2）. It is considered that there are at least 4 variables （the most will be 11） in paleoclimatic dynamic system, measured by one thousand year time interval, controlling the climatic evolution. These variables correspond to some cycles of parameters of Earth's orbit and the changes in the icesheet of Arctic.