第四纪古气候变化非线性动力学初步研究——黄土粒度曲线的奇异谱分析

A STUDY ON NONLINEAR DYNAMICS OF PALEOCLIMATE VARIATIONS DURING QUATERNARY:SINGULAR SPECTRUM ANALYSIS OF LOESS GRAIN-SIZE RECORD

作者将奇异谱分析(SSA)引入第四纪古气候变化研究中,收到了较好的效果。奇异谱分析是一种新的时间序列分析工具,它可形成一个单边(向前)滤波器,将原时间序列有效地分解成各个主成分,其滤波系数完全由数据本身决定。由奇异谱分析确定的统计维,给出动力维上界的估计,为非线性动力学研究打下基础。分析表明,在整个第四纪,宝鸡黄土粒度曲线的统计维为19,与深海钻孔V28-239氧同位素分析结果(=18)十分接近;各主成分在地球轨道几何参数各成分中大都能找到对应关系,但均不是线性响应关系;与偏心率、地轴倾斜度和岁差有关的成分分别占46、43和6％左右;其中第一主成分还揭示出与偏心率约0.4Ma周期对应的振荡仅在2.5—1.7和0.7—0.3Ma B.P.出现。

The authors regard the Baoji loess grain-size time series, generated by employing orbital tuning approach by SPECMAP project, as a proxy of paleoclimatic variations during the Quaternary and apply Singular Spectrum Analysis (SSA) to investigate the dynamic characteristics of paleoclimate and lay foundations for nonlinear dynamics study in this field. SSA provides estimates of the statistical dimension, which gives a theoretical upper boundary for the minimal number of degrees of freedom required to describe the attractor of a dynamic system. It also gives time-domain moving-average filters determined directly by the data by means of solving eigenvectors of the embedding matrix, so that we can effectively divide the time series into principal components (PCs). The percentage of every eigenvalue out of all the eigenvalues reflects the relative weight of the PC. Those PCs describe the main physical phenomena reflected by the data and the regime changes of the dynamic system. It turns out that SSA is a new and powerful spectrum analysis for time series and a powerful descriptive tool for nonlinear dynamics in general and climate dynamics in particular. We have investigated the Baoji loess grain-size record, i.e. the profile of radio <2μm％ to >10μm％, which is considered to he a proxy indicator of winter monsoon strength. Data are sampled at a regular depth interval of 10 cm, containing 1587 raw points and corresponding to unequal time intervals. To obtain uniform samling in time, the techniques of orbital tuning approach developed by SPECMAP project is employed, followed by interpolation of the data to the new time scale. For this time series, the mean has been subtracted and the values normalized by its standard deviation. We apply this apparatus to two time spans,0.8—0.0 and 2.5—0.0 MaB.P., of Baoji grain-size time series respectively. The results are as follow: (1) 0.8—0.0 Ma. B.P. Fig. 1 shows the singular spectra for M(embedding dimension)=10,20 and 40; the corresponding window lengths (τ_w) are 10 000a, 20 000a and 40 000a. It also displays the singular spectrum for m=20 and sampling interval (τ _s)=2 000a, i.e. τ_w=40 000a. The four spectra show a similar shape, with a decrease up to k=6, followed by a floor which occurs at k=9. So we can infer the statistical dimension of this span as equal to 6. Meanwhile, we have found the first ten values of two spectra of τ_w=40 000a fit rather well, indicating that the spectra in this window length are stable. Accordingly, we choose 40 as the embedding dimension. Fig. 2 shows the PCs for m=40.and τ_s=1 000a. The average oscillation period of PC 1 (56.36％) is 0.12 Ma, corresponding to the dominant period of Earth's orbit eccentricity. PC 2(25.32％) corresponds to another period of eccentricity, 0.094Ma, though it is superim- posed by the variation of about 40 000a. PC 3(7.51) is associated with the period in about 40 000a, corresponding to the period of obliquity. PC 4(4.15％) and PC 5(2.41％) correspond to the precession-related periods; the former period is 23 000a and the latter 19 000a. The average period of PC 6 (1.04) is still associated with another period of precession, 16 000a. (2) 2.5—0.0 Ma B.P. This span extends over the entire Quaternary. We can anticipate getting a more detailed dividing of the time series. Fig. 3 shows the singular spectra for m=100(τ_s=2 000a), m=50 (τ_s=4 000a) and m=40 (τ_s=5 000a). We can see that the first nineteen values of three spectra are closely fit, and the occupancy percentage of PC 20 in total PCs is less than 0.6％, indicating one is noise component. So we infer that in the entire quaternary, the statistical dimension of Baoji loess grain-size record is equal to 19. Fig. 4 displays the PCs for m=100 and τ_B=2 000a. PC 1(15.01％) displays a clear oscillatory behavior in 2.5—1.7 and 0.7—0.3 Ma B.P., with a period of about 0.4Ma, correspondding to the most important period of eccen(?)ricity. This is an excellent result. PC 2(11.26％), 3(10.36％) and 4(9.10％) are associated with other periods of eccentricity, which are 0.12Ma, 0.099Ma and 0.095Ma respectively. They are a common characteristi.c, i.e. they mainly occurred in 1.9—1.6 and 0.6—0.2 Ma B.P. Accordingly, we hold that there were two paleoclimatic shifts in about 1.6 and 0.6 Ma B.P. PC 5(8.7％), 6(8.48％) and 7(7.4％) display about 40 000a period oscillation, associated with obliquity. They all developed better in 1.6—0.0 Ma B.P. than in 2.5—1.6 Ma B.P. PC 8(5.62％), 9(4.24％), 10(2.86％), 11(2.32％), 12(1.73％) and 13(1.59％) correspond to other obliquity-related periods. PC 14(1.19％),1％5(1.15%), 16(1.08%), 17(1.02%), 18(1.01%) and 19(0.72%) display an oscillatory behavior in the entire 2.5 Ma, with periods in range 19 000a—23 000a, known to be associated with variations of the precessional parameter. In summary, we can obtain the following conclusions: (1) Almost all critical principal components of the time series can be approximately related to a certain periodic component of variations of the Earth's orbital geometry. But the amplitude and frequency of each principal component vary with time. Therefore their responses are nonlinear in a strict sense. The results reveal that about 0.4 Ma oscillations related to the eccentricity of the Earth's orbit occurred in 2.5—1.7 and 0.7—0.3 Ma B.P., about 0.Ma oscillations mainly occurred in 1.9—1.6 and 0.6—0.2 Ma B.P., about 0.04Ma oscillations related to the obliquity developed better in 1.6—0.0 than in 2.5—1.6 Ma B.P., and the oscillations related to the precession show relative stability. (2) According to the eigenvalues of the principal factors, we estimate the three sums of principal components related to the Earth's orbit geometry elements at about 45％, 43％ and 6%% over the past 2.5 Ma. (3) Suppose the relationships between winter monsoon strength and loess grain-size ecord are relatively simple, the above variation of PCs roughly reflects the paleoclimatic regime changes and relationships between paleoclimate and astronomical forcing during the Quaternary. (4) Under the same calculating condituon(the window length is equal to 0.2Ma), during 2.5—0.0 Ma B.P. the statistical dimension of the Baoji Loess grain-size time series, which is equal to 19, is very close to that of Deep Sea Drill V28-239, which is equal to 18. It reveals that there is some common nature of paleodlimatic regime changes in inland and in ocean during the Quaternary and the two phase spaces may be similar.