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The non-stationary characteristics of the climate system have been widely recognized. The occurrence of this non-stationary phenomenon is caused by the hierarchical structure of the climate system. As a high-level system, the external driving forcing changes with time, which leads to the non-stationary phenomenon of atmospheric movement. Slow feature analysis (SFA) method can extract the slow-changing features from fast-changing non-stationary signal. The SFA has been applied to attribution analysis of the climate system. In this paper, we use the SFA method to extract the driving force signal from the non-stationary time series obtained by the Henon mapping model to test its extraction capability. Then we extract the external driving force signal from Beijing monthly average temperature time series, and analyze the scale characteristics and physical mechanism of external driving forcing signals combined with wavelet transform. The results show that the long-period external driving forcing signal and the short-period external driving forcing signal jointly work on the climate system. At the same time, the long-period external driving forcing signal also works on short-period external driving forcing signal. This work contributes to understanding the hierarchical characteristics of the climate system.
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Keywords:
- climate system /
- hierarchy /
- driving force signal /
- slow feature analysis (SFA)
[1] Schmutz C, Luterbacher J, Gyalistras D, Xoplaki E, Wanner H 2000 Geophys. Res. Lett. 27 1135
Google Scholar
[2] Stern D I, Kaufmann R K 2000 Clim. Change 47 411
Google Scholar
[3] Yang P C, Zhou X J, Bian J C 2000 J. Geophys. Res. Atmos. 105 12253
Google Scholar
[4] Slonosky V C, Jones P D, Davies T D 2001 Int. J. Climatol. 21 63
Google Scholar
[5] Tsonis A A 1996 Nature 382 700
Google Scholar
[6] 杨培才, 卞建春, 王革丽, 周秀骥 2003 科学通报 48 1470
Google Scholar
Yang P C, Bian J C, Wang G L, Zhou X J 2003 Chin. Sci. Bull 48 1470
Google Scholar
[7] 杨培才, 周秀骥 2005 气象学报 63 556
Google Scholar
Yang P C, Zhou X J 2005 Acta. Meteor. Sinica 63 556
Google Scholar
[8] O’Neill RV 1988 Scales and Global Change: Spatial and Temporal Variability in Biospheric and Geospheric Processes (New York: John Wiley) p29
[9] 林振山 1990 北京大学学报(自然科学版) 26 355
Google Scholar
Lin Z S 1990 Acta Scientiarum Naturalium Universitatis Pekinensis 26 355
Google Scholar
[10] Wiedermann, Marc, Donner, Reik V, Handorf, Doerthe, Kurths, Juergen, Donges, Jonathan F 2017 Int. J. Climatol. 37 3821
Google Scholar
[11] Konen W, Koch P https://arxiv.org/pdf/0911.4397.pdf [2021-12-21]
[12] 潘昕浓, 王革丽, 杨培才 2017 物理学报 66 080501
Google Scholar
Pan X N, Wang G L, Yang P C 2017 Acta Phys. Sin. 66 080501
Google Scholar
[13] Yang P C, Zhou X J, Wang G L, Zhang F 2016 Clim. Dyn. 46 3197
Google Scholar
[14] Wang G L, Yang P C, Zhou X J 2016 Theor. Appl. Climatol. 124 985
Google Scholar
[15] Wiskott L, Sejnowski T J 2002 Neural Comput 14 715
Google Scholar
[16] Berkes P, Wiskott L 2005 J. Vision 5 579
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Google Scholar
[18] Takens F 1981 Lect. Notes Math. 898 366
[19] 迟洪钦, 吴忠英 1994 上海交通大学学报 5 96
Chi H Q, Wu Z Y 1994 J. Shanghai Jiaotong Univ. 5 96
[20] 张宾, 李月, 卢金 2004 吉林大学学报(信息科学版) 22 4
Google Scholar
Zhang B, Li Y, Lu J 2004 J. Jilin Univ. (Information Science Edition) 22 4
Google Scholar
[21] 张勇, 关伟 2009 物理学报 58 756
Google Scholar
Zhang Y, Guan W 2009 Acta Phys. Sin. 58 756
Google Scholar
[22] 范开宇, 王革丽, 李超, 潘昕浓 2018 气候与环境研究 23 287
Google Scholar
Fan K Y, Wang G L, Li C, Pan X N 2018 Climatic and Environmental Research 23 287
Google Scholar
[23] 范开宇 2018 硕士学位论文 (成都: 成都信息工程大学)
Fan K Y 2018 M. S. Thesis (Chengdu: Chengdu University of Information Technology) (in Chinese)
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图 1 (a) 基频信号
$ \left\{n\left(t\right)\right\} $ ; (b) 调制信号$ \left\{m\left(t\right)\right\} $ ; (c) 时变参数$ \left\{a\left(t\right)\right\} $ (蓝线)与其调制信号(包络)M(红线)Figure 1. (a) Fundamental frequency signal
$ \left\{n\left(t\right)\right\} $ ; (b) modulation signal$ \left\{m\left(t\right)\right\} $ ; (c) time-varying parameter$ \left\{a\left(t\right)\right\} $ (blue line) and its modulation signal (envelope) M (red line).
图 2 (a) 真实外强迫信号
$ \{{s}_{1}(t)\} $ ; (b) 非平稳时间试验序列$ \{{y}_{1}(t)\} $ ; (c) SFA方法提取得到的外强迫$ \{{as}_{1}(t)\} $ (蓝线)及其包络 M(红线); (d) 外强迫$ \{{as}_{1}(t)\} $ (红线)及真实外强迫信号$ \{{s}_{1}(t)\} $ (蓝线)比较Figure 2. (a) The true driving force signal
$ \{{s}_{1}(t)\} $ ; (b) the testing non-stationary time series$ \{{y}_{1}(t)\} $ ; (c) the driving force signal extracted by SFA method$ \{a{s}_{1}(t)\} $ (blue line) and its modulation signal (envelope) M (red line); (d) the driving force signal extracted by SFA method$ \{a{s}_{1}(t)\} $ (red line) and the true driving force signal$ \{{s}_{1}(t)\} $ (blue line).
图 3 北京月平均气温外强迫信号的提取与分析流程图
Figure 3. Flow chart of extraction and analysis of driving force signal of monthly mean temperature of Beijing.
图 4 (a)—(f)北京月平均气温外强迫信号特征尺度
$ {S}_{1} $ —$ {S}_{6} $ 对应的信号分量Figure 4. (a)–(f) Signal components corresponding to the characteristic scale
$ {S}_{1} $ –$ {S}_{6} $ of the driving force signal of monthly mean temperature in Beijing.
图 5 尺度分量
$ {S}_{6} $ (黑线)与调制信号$ {M}_{1} $ (红线)比较Figure 5. Comparison of scale component signal
$ {S}_{6} $ (black line) and modulated signal$ {M}_{1} $ (red line).
图 6 利用尺度分量
$ {S}_{6} $ (蓝线)来拟合尺度分量$ {S}_{1} $ (黑线)得到结果${S}_{1}''$ (红线)Figure 6. Use the scale component signal
$ {S}_{6} $ (blue line) to simulate the scale component signal$ {S}_{1} $ (black line) to obtain the result${S}_{1}''$ (red line).
图 7 气候系统的层次结构示意图
Figure 7. Schematic diagram of the hierarchy of the climate system.
表 1 北京月平均气温时间序列外强迫信号小波分析周期频率及谐波关系
Table 1. Periods and frequencies of the driving force signal of temperature extracted by SFA method of Beijing.
成分
${{S} }_{{n} }$周期
${{P} }_{{n} }$/a频率
${{f} }_{{n} }$谐波关系 物理背景 $ {S}_{1} $ $ {P}_{1}=3.2 $ $ {f}_{1}=0.312 $ 基频分量 东太平洋海温 $ {S}_{2} $ $ {P}_{2}=5.8 $ $ {f}_{2}=0.172 $ $ {f}_{2}=2{f}_{3} $ $ {S}_{3} $ $ {P}_{3}=11.6 $ $ {f}_{3}=0.086 $ 基频分量 the Hale cycle $ {S}_{4} $ $ {P}_{4}=13.8 $ $ {f}_{4}=0.072 $ $ {f}_{4}\approx $$ 3{f}_{3}-4{f}_{5} $ $ {S}_{5} $ $ {P}_{5}=21.3 $ $ {f}_{5}=0.047 $ 基频分量 the Schwabe cycle $ {S}_{6} $ $ {P}_{6}=42.7 $ $ {f}_{6}=0.023 $ ${P}_{6}=2{P}_{5}$ 太阳双黑
子周期2倍
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表 2 模拟尺度分量
${S}_{1}'$ —${S}_{6}'$ 与真实尺度分量信号$ {S}_{1} $ —$ {S}_{6} $ 比较Table 2. Comparison of analog scale component signal
${S}_{1}'$ –${S}_{6}'$ and real scale component signal$ {S}_{1} $ –$ {S}_{6} $ 成分${{S} }_{{n} }$ $R$/% ${{D} }_{ {{s} }' }/{{D} }_{{s} }$ ${{S} }_{ {{1} } }$ 60.5 0.94 ${{S} }_{ {{2} } }$ 78.4 1.05 ${{S} }_{ {{3} } }$ 90.6 1.08 ${{S} }_{ {{4} } }$ 93.4 1.11 ${{S} }_{ {{5} } }$ 99.3 1.05 ${{S} }_{ {{6} } }$ 99.8 1.01
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[1] Schmutz C, Luterbacher J, Gyalistras D, Xoplaki E, Wanner H 2000 Geophys. Res. Lett. 27 1135
Google Scholar
[2] Stern D I, Kaufmann R K 2000 Clim. Change 47 411
Google Scholar
[3] Yang P C, Zhou X J, Bian J C 2000 J. Geophys. Res. Atmos. 105 12253
Google Scholar
[4] Slonosky V C, Jones P D, Davies T D 2001 Int. J. Climatol. 21 63
Google Scholar
[5] Tsonis A A 1996 Nature 382 700
Google Scholar
[6] 杨培才, 卞建春, 王革丽, 周秀骥 2003 科学通报 48 1470
Google Scholar
Yang P C, Bian J C, Wang G L, Zhou X J 2003 Chin. Sci. Bull 48 1470
Google Scholar
[7] 杨培才, 周秀骥 2005 气象学报 63 556
Google Scholar
Yang P C, Zhou X J 2005 Acta. Meteor. Sinica 63 556
Google Scholar
[8] O’Neill RV 1988 Scales and Global Change: Spatial and Temporal Variability in Biospheric and Geospheric Processes (New York: John Wiley) p29
[9] 林振山 1990 北京大学学报(自然科学版) 26 355
Google Scholar
Lin Z S 1990 Acta Scientiarum Naturalium Universitatis Pekinensis 26 355
Google Scholar
[10] Wiedermann, Marc, Donner, Reik V, Handorf, Doerthe, Kurths, Juergen, Donges, Jonathan F 2017 Int. J. Climatol. 37 3821
Google Scholar
[11] Konen W, Koch P https://arxiv.org/pdf/0911.4397.pdf [2021-12-21]
[12] 潘昕浓, 王革丽, 杨培才 2017 物理学报 66 080501
Google Scholar
Pan X N, Wang G L, Yang P C 2017 Acta Phys. Sin. 66 080501
Google Scholar
[13] Yang P C, Zhou X J, Wang G L, Zhang F 2016 Clim. Dyn. 46 3197
Google Scholar
[14] Wang G L, Yang P C, Zhou X J 2016 Theor. Appl. Climatol. 124 985
Google Scholar
[15] Wiskott L, Sejnowski T J 2002 Neural Comput 14 715
Google Scholar
[16] Berkes P, Wiskott L 2005 J. Vision 5 579
[17] Packard N H, Crutchfield J P, Shaw R S 1980 Phys. Rev. Lett. 45 712
Google Scholar
[18] Takens F 1981 Lect. Notes Math. 898 366
[19] 迟洪钦, 吴忠英 1994 上海交通大学学报 5 96
Chi H Q, Wu Z Y 1994 J. Shanghai Jiaotong Univ. 5 96
[20] 张宾, 李月, 卢金 2004 吉林大学学报(信息科学版) 22 4
Google Scholar
Zhang B, Li Y, Lu J 2004 J. Jilin Univ. (Information Science Edition) 22 4
Google Scholar
[21] 张勇, 关伟 2009 物理学报 58 756
Google Scholar
Zhang Y, Guan W 2009 Acta Phys. Sin. 58 756
Google Scholar
[22] 范开宇, 王革丽, 李超, 潘昕浓 2018 气候与环境研究 23 287
Google Scholar
Fan K Y, Wang G L, Li C, Pan X N 2018 Climatic and Environmental Research 23 287
Google Scholar
[23] 范开宇 2018 硕士学位论文 (成都: 成都信息工程大学)
Fan K Y 2018 M. S. Thesis (Chengdu: Chengdu University of Information Technology) (in Chinese)
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