黄河流域动力系统泥沙时序混沌特征分析——地理系统综合研究的一种尝试
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摘要
选取黄河头道拐、潼关、花园口和利津断面1952~2000年的泥沙含量为时序,在G-P重构相空间的基础上,分别计算了各断面泥沙时序的关联维(D2)、K2熵和Hurst指数。结果表明,各断面的最小饱和镶嵌维(m)、D2和K2熵分别为5、3.24和0.13,说明黄河流域各级系统均具有混沌特征,并且从上游到下游混沌特性逐渐增强。随着混沌特性的增强其平均可预报时间下降,头道拐断面为8年,其余断面为3年。各断面Hurst指数均大于0.68,在可预报时间内,各断面泥沙时序具有持续性下降趋势,并用2001~2004年实际数据得到了验证。文章还给出了黄河流域动力系统的一般形式,该系统至少需要8个状态变量,2个控制变量。
The sandiness content on every section of the Yellow River relates all the factors that are interactive in many ways,so it includes some evolution information of the system controlled by monitoring section.We can infer the dynamic characters of the system from the sandiness time series based on the techniques of phase space reconstruction and the picking-up methods for chaos indexes.Sandiness contents from 1952 to 2000 were chosen as the time series on Toudaoguai section,Tongguan section,Huayuankou section and Lijin section along the Yellow River.Correlation dimension(D_(2)) was calculated according to Grassberger-Procaccia arithmetic,Kolmogorov entropy(K_(2)) according to Zhao Gui-bing arithmetic,and Hurst index(H) according to Rescaled Range Analysis(R/S).The results are shown as follows:(1) The correlation dimension on Toudaoguai section is 3.24,Tongguan section is 5.69,Huayuankou section is 6.57 and Lijin section is 7.34.We can see that all the dimensions are fractal dimensions,so the dynamic systems controlled by different sections of the Yellow River basin are chaotic systems and the chaotic degrees heighten gradually from upper section to lower section.(2) Forecast time of the time series was calculated by 1/K_(2).On Toudaoguai section,the forecast time of the sandiness time series is about 8 years,and the other sections are 3 years.The more obvious the chaos is,the shorter the forecast time is.(3) Hurst indexes on all the study sections are more than 0.5, the maximum is 0.86 on Tongguan section and the minimum is 0.68 on Toudaoguai section,which indicates that the changes of the time series have persistence trends in the average forecasting time.The past trends of the time series from 1952 to 2000 on all the sections were wavelike descending,so that the future trends of the time series will go on wavelike descending too.Compared with the time series from 1999 to 2000,the future trends was validated with the time series from 2001 to 2004 on Tongguan section,Huayuankou section and Lijin section.(4) We can get some information from correlation dimensions and saturated inlay dimensions to construct useful dynamic system model.The sandiness time series on Lijin section infers the dynamic characters of the whole Yellow River basin,its correlation dimension is 7.34 and the saturated inlay dimension is 10.Therefore,the dynamic model of the whole Yellow River basin needs eight state variables and two control variables at least.A general form of the dynamic model of the whole Yellow River basin was given in this paper.
The sandiness content on every section of the Yellow River relates all the factors that are interactive in many ways,so it includes some evolution information of the system controlled by monitoring section.We can infer the dynamic characters of the system from the sandiness time series based on the techniques of phase space reconstruction and the picking-up methods for chaos indexes.Sandiness contents from 1952 to 2000 were chosen as the time series on Toudaoguai section,Tongguan section,Huayuankou section and Lijin section along the Yellow River.Correlation dimension(D_(2)) was calculated according to Grassberger-Procaccia arithmetic,Kolmogorov entropy(K_(2)) according to Zhao Gui-bing arithmetic,and Hurst index(H) according to Rescaled Range Analysis(R/S).The results are shown as follows:(1) The correlation dimension on Toudaoguai section is 3.24,Tongguan section is 5.69,Huayuankou section is 6.57 and Lijin section is 7.34.We can see that all the dimensions are fractal dimensions,so the dynamic systems controlled by different sections of the Yellow River basin are chaotic systems and the chaotic degrees heighten gradually from upper section to lower section.(2) Forecast time of the time series was calculated by 1/K_(2).On Toudaoguai section,the forecast time of the sandiness time series is about 8 years,and the other sections are 3 years.The more obvious the chaos is,the shorter the forecast time is.(3) Hurst indexes on all the study sections are more than 0.5, the maximum is 0.86 on Tongguan section and the minimum is 0.68 on Toudaoguai section,which indicates that the changes of the time series have persistence trends in the average forecasting time.The past trends of the time series from 1952 to 2000 on all the sections were wavelike descending,so that the future trends of the time series will go on wavelike descending too.Compared with the time series from 1999 to 2000,the future trends was validated with the time series from 2001 to 2004 on Tongguan section,Huayuankou section and Lijin section.(4) We can get some information from correlation dimensions and saturated inlay dimensions to construct useful dynamic system model.The sandiness time series on Lijin section infers the dynamic characters of the whole Yellow River basin,its correlation dimension is 7.34 and the saturated inlay dimension is 10.Therefore,the dynamic model of the whole Yellow River basin needs eight state variables and two control variables at least.A general form of the dynamic model of the whole Yellow River basin was given in this paper.
引文
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[26]金德龙,师长兴,陈浩,等.人为动力泥沙灾害类型及其特征研究.地理科学进展,2000,19(4):317~326.
[27]景可,等.我国土壤侵蚀与地理环境的关系.地理研究,1999,9(2):29~38.
[28]卢金发.黄河中游流域地貌形态对流域产沙的影响.地理研究,2002,21(2):171~178.
[29]陈浩,等.黄河中游流域环境要素对水沙变异的影响.地理研究,2002,21(2):179~187.
[30]卢金发.土地覆被对黄河中游流域泥沙产生的影响.地理研究,2003,22(5):571~578.
[31]王文均,叶敏,陈显维.长江径流时间序列混沌特性的定量分析.水科学进展,1994,5(2):87~94.
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[33]周寅康,包浩生,张捷.淮河流域洪涝变化混沌演化特征研究.地球信息科学,1999,1(2):8~11.
[34]周寅康,王腊春,许有鹏,等.淮河流域洪涝变化动力系统研究.地理科学,2001,21(1):41~45.
[35]魏一鸣,等.1949~1994年中国洪水灾害成灾面积的时序分形特征.自然灾害学报,1998,7(1):83~86,93.
[36]马建华,楚纯洁.花园口断面年径流量时间序列混沌特性分析.人民黄河,2006,28(1):18~20.
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[38]Grassberger P,Procaccia I.Characterization of strange attractors.Phys.Rew.Lett.,1983,50(5):346~349.
[39]Grassberger P,Procaccia I.Estimation of the Kolmogorov entropy from a chaotic signal.Phys Rew A,1983,28(4):2591~2593.
[40]Feder J.Fractals.New York:Plenum Press,1988.
[41]黄登仕,李自强.分形几何学、R/S分析与分式布朗运动.自然杂志,1990,13(8):477~482.
[42]Cohen A,Procaccia I.Computing the Kolmogorov entropy from time signals of dissipative conservative dynamicalsystem.Phys.Rev.A,.1985,31(3):1872~1882.
[43]周寅康,张捷,王腊春,等.长江下游地区近五百年洪涝序列的R/S分析.自然资源学报,1997,6(2):78~84.
[44]郝柏林.分形和分维.科学杂志,1986,38(1):9~17.
[45]Hurst H E.Long-Term Storage:An Experimental Study.London:Constable,1965.
[46]Mandelbrot B B,Van Ness J W.Fractional brownian motion,fractional noise and application.SIAM Review,1968,10:422~437.
[47]Mandelbrot B B,Wallis J R.Some long-run properties of geographysical records.Water Resources Research,1969a,5(2):321~340.
[48]Mandelbrot B B,Wallis J R.Robustness of the rescaled range R/S in the measurement of noncyclic long-run sta-tistical dependence.Water Resources Research,1969b,5(4):967~988.
[49]Mcheod A I,Hipel K W.Preservation of rescaled adjusted range.Water Resources Research,1978,14(3):491~518.
[50]Lorenz E N.Deterministic nonperiodic flow.J.Atmos.Sci.,1963,20:130~141.
[51]E.N.洛伦兹.混沌的本质.刘式达,刘式适,严中伟译.北京:气象出版社,1997.
[52]Rckmanm J P.Ergodc theory of chaos and strange attractors.Review Modern Physics,1985,57:617~655.
[53]周寅康,付重林,王腊春,等.淮河流域洪涝变化可预报时间研究.自然灾害学报,1999,8(4):118~122.
[54]谢正栋,等.淮河流域洪水的分形特征及可预报时间研究.南京大学学报(自然科学版),2003,39(1):113~119.
[55]赵晶,徐建华.1950~1997年我国洪涝灾害成灾面积的分形特征研究.自然灾害学报,2003,12(2):31~35.
[56]http//www.yellowriver.gov.cn/lib/ggl/2005-08-24/jj_160400119297.html.
[57]黄建平,衣育红.利用观测资料反演非线性动力模型.中国科学(B),1991,(3):331~336.
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[2]吴传钧,张家桢.我国20世纪地理科学发展回顾及新世纪前景展望.地理学报,1999,54(5):385~390.
[3]陆大道.关于地理学“人—地系统”理论研究.地理研究,2002,21(2):135~145.
[4]陆大道.中国地理学发展若干值得思考的问题.地理学报,2003,58(1):2~8.
[5]葛全胜,吴绍洪,朱立平,等.21世纪中国地理学发展的若干思考.地理研究,2003,22(4):406~415.
[6]倪绍祥.地理学综合研究的新进展.地理科学进展,2003,22(4):335~341.
[7]杨勤业,郑度,吴绍洪,等.20世纪50年代以来中国综合自然地理学研究进展.地理研究,2005,24(6):899~910.
[8]蔡运龙,陆大道,周一星,等.地理科学的中国进展与国际趋势.地理学报,2004,59(6):803~810.
[9]宋长青,冷疏影.21世纪中国地理学综合研究的主要领域.地理学报,2005,60(4):546~552.
[10]黄秉维.自然地理学一些主要的趋势.地理学报,1960,26(3):149~154.
[11]《黄秉维文集》编辑组.自然地理工作六十年———黄秉维文集.北京:科学出版社,1993.
[12]黄秉维,郑度,赵名茶.现代自然地理.北京:科学出版社,1999.
[13]美国国家航空和宇航管理局地球系统科学委员会.地球系统科学.陈泮勤等译.北京:地震出版社,1992.
[14]黄秉维.可持续发展战略的理论基础———建立地球系统科学的基本设想.中国环境报,1996-04-13.
[15]黄秉维.论地球系统科学与可持续发展战略科学基础.地理学报,1996,51(4):350~356.
[16]黄秉维.区域可持续发展的理论基础———陆地系统科学.地理学报,1996,51(5):445~453.
[17]杨勤业.地理综合研究与陆地系统科学———祝黄秉维院士八十五寿辰.地理研究,1997,16(4):1~6.
[18]《地理学报》编辑部.地球系统科学———庆贺黄秉维院士八十五华诞.地理学报,1998,53(1):1~12.
[19]吕金虎,陆君安,陈士华.混沌时间序列分析及其应用.武汉:武汉大学出版社,2002.
[20]赵贵兵,石炎福,等.从混沌时间序列同时计算关联维和Kolmogorov熵.计算物理,1999,16(3):309~315.
[21]马建华,管华.系统科学及其在地理学中的应用.北京:科学出版社,2002.
[22]许炯心.黄河下游历史泥沙灾害的宏观特征及其与流域因素和人类活动的关系———历史气候及植被因素的影响.自然灾害学报,2001,10(2):7~11.
[23]许炯心.黄河下游历史泥沙灾害的宏观特征及其与流域因素和人类活动的关系———人类活动、历史地震及地形因子的影响.自然灾害学报,2001,10(3):7~12.
[24]许炯心.流域因素与人类活动对黄河下游河道输沙功能的影响.中国科学(D辑),2004,38(8):775~781.
[25]许炯心.无定河流域侵蚀产沙过程对水土保持措施的响应.地理学报,2004,59(6):972~981.
[26]金德龙,师长兴,陈浩,等.人为动力泥沙灾害类型及其特征研究.地理科学进展,2000,19(4):317~326.
[27]景可,等.我国土壤侵蚀与地理环境的关系.地理研究,1999,9(2):29~38.
[28]卢金发.黄河中游流域地貌形态对流域产沙的影响.地理研究,2002,21(2):171~178.
[29]陈浩,等.黄河中游流域环境要素对水沙变异的影响.地理研究,2002,21(2):179~187.
[30]卢金发.土地覆被对黄河中游流域泥沙产生的影响.地理研究,2003,22(5):571~578.
[31]王文均,叶敏,陈显维.长江径流时间序列混沌特性的定量分析.水科学进展,1994,5(2):87~94.
[32]王良健,彭补拙.分形方法在洪涝灾害预测中的应用———以广西梧州为例.地理科学,1998,18(3):242~248.
[33]周寅康,包浩生,张捷.淮河流域洪涝变化混沌演化特征研究.地球信息科学,1999,1(2):8~11.
[34]周寅康,王腊春,许有鹏,等.淮河流域洪涝变化动力系统研究.地理科学,2001,21(1):41~45.
[35]魏一鸣,等.1949~1994年中国洪水灾害成灾面积的时序分形特征.自然灾害学报,1998,7(1):83~86,93.
[36]马建华,楚纯洁.花园口断面年径流量时间序列混沌特性分析.人民黄河,2006,28(1):18~20.
[37]Packard N H,Crutchfield J R,Farmer J D,et al.Geometry from a time series.Phys.Rew.Lett,.1980,45(9):712~716.
[38]Grassberger P,Procaccia I.Characterization of strange attractors.Phys.Rew.Lett.,1983,50(5):346~349.
[39]Grassberger P,Procaccia I.Estimation of the Kolmogorov entropy from a chaotic signal.Phys Rew A,1983,28(4):2591~2593.
[40]Feder J.Fractals.New York:Plenum Press,1988.
[41]黄登仕,李自强.分形几何学、R/S分析与分式布朗运动.自然杂志,1990,13(8):477~482.
[42]Cohen A,Procaccia I.Computing the Kolmogorov entropy from time signals of dissipative conservative dynamicalsystem.Phys.Rev.A,.1985,31(3):1872~1882.
[43]周寅康,张捷,王腊春,等.长江下游地区近五百年洪涝序列的R/S分析.自然资源学报,1997,6(2):78~84.
[44]郝柏林.分形和分维.科学杂志,1986,38(1):9~17.
[45]Hurst H E.Long-Term Storage:An Experimental Study.London:Constable,1965.
[46]Mandelbrot B B,Van Ness J W.Fractional brownian motion,fractional noise and application.SIAM Review,1968,10:422~437.
[47]Mandelbrot B B,Wallis J R.Some long-run properties of geographysical records.Water Resources Research,1969a,5(2):321~340.
[48]Mandelbrot B B,Wallis J R.Robustness of the rescaled range R/S in the measurement of noncyclic long-run sta-tistical dependence.Water Resources Research,1969b,5(4):967~988.
[49]Mcheod A I,Hipel K W.Preservation of rescaled adjusted range.Water Resources Research,1978,14(3):491~518.
[50]Lorenz E N.Deterministic nonperiodic flow.J.Atmos.Sci.,1963,20:130~141.
[51]E.N.洛伦兹.混沌的本质.刘式达,刘式适,严中伟译.北京:气象出版社,1997.
[52]Rckmanm J P.Ergodc theory of chaos and strange attractors.Review Modern Physics,1985,57:617~655.
[53]周寅康,付重林,王腊春,等.淮河流域洪涝变化可预报时间研究.自然灾害学报,1999,8(4):118~122.
[54]谢正栋,等.淮河流域洪水的分形特征及可预报时间研究.南京大学学报(自然科学版),2003,39(1):113~119.
[55]赵晶,徐建华.1950~1997年我国洪涝灾害成灾面积的分形特征研究.自然灾害学报,2003,12(2):31~35.
[56]http//www.yellowriver.gov.cn/lib/ggl/2005-08-24/jj_160400119297.html.
[57]黄建平,衣育红.利用观测资料反演非线性动力模型.中国科学(B),1991,(3):331~336.
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