京津冀城镇用地空间结构的多分维谱分析
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摘要
城市形态和城镇体系都具有分形性质,但简单分形模型不能有效揭示城市系统的复杂结构特征及其背后的问题。多分形模型及分析方法是研究城市空间复杂性和描述城市异质性的有效手段。利用城镇建设用地和总建设用地的多分维谱分析,可以发现京津冀城镇体系及主要城市的空间演化问题。主要结果如下:(1)京津冀总建设用地的全局谱线不正常,代表中心区的谱线收敛过快,而代表边缘区和乡村地区的谱线收敛位置严重越界;(2)局部谱线单峰左偏,左(趋向中心区)高密、右(趋向边缘区)低疏,且右边数值越界;(3)多分维增长曲线服从二次logistic函数,但不同区域和城市的增长曲线的拐点位置不同。深入分析谱线特征及其异常根源,得出如下结论:(1)京津冀主要城市的中心区填充过密,没有太多缓冲空间,而边缘区无序扩展,需要通过规划进行优化;(2)京津冀城市生长以外延扩展模式为主,但河北省总建设用地有中心集聚迹象;(3)京津冀地区特别是主要城市用地接近饱和,土地扩展速度高峰已经过去,只有河北省部分区域例外。
Cities and urban systems both bear scale-free properties,from which no characteristic scales can be found for mathematical modeling and quantitative analysis.Therefore,fractal geometry is useful for making scaling analysis.Complex urban systems cannot be effectively described by simple fractal models,but can be characterized by multifractal theory.This paper is devoted to exploring the spatiotemporal features of urban change in the Beijing-Tianjin-Hebei region from 1995 to 2013.Using multifractal parameter spectrums,we can reveal the spatial dynamics of urbanization from the aspects of urban form and urban system.The main findings are as below:1) The spectral curves of global fractal dimension are abnormal.If q>1 and q→∞,the spectral lines quickly converge to horizontal lines;when q<0 and q→-∞,the spectral lines quickly surpass the upper limit of fractal dimension,2,which represents Euclidean dimension of embedding space.2) The spectral curves of local fractal dimension are also not entirely normal.The peaks of the f(α) curves incline to the left,and the left ends of the curves are higher than the right ends.The problem lies in that the curves go beyond the maximum value of 2.3) Fractal dimension growth curves can be described by the quadratic logistic function.Capacity parameters and inflection points of different fractal dimension growth curves are different.The main conclusions are as follows:1) The urban fringes are disorderly developed,while the central areas of the main cities in the Beijing-TianjinHebei region is overfilled with construction land,leaving little buffer space.2) The main mode of urban growth is to expand to the outside region,but there are signs of central agglomeration in the total construction land of Hebei Province.3) Land use of the main cities is close to saturation,and the speed of land expansion has peaked for Beijing and Tianjin,but not in Hebei Province yet.In short,it is necessary to optimize the land use structure in the Beijing-Tianjin-Hebei region by city planning.
Cities and urban systems both bear scale-free properties,from which no characteristic scales can be found for mathematical modeling and quantitative analysis.Therefore,fractal geometry is useful for making scaling analysis.Complex urban systems cannot be effectively described by simple fractal models,but can be characterized by multifractal theory.This paper is devoted to exploring the spatiotemporal features of urban change in the Beijing-Tianjin-Hebei region from 1995 to 2013.Using multifractal parameter spectrums,we can reveal the spatial dynamics of urbanization from the aspects of urban form and urban system.The main findings are as below:1) The spectral curves of global fractal dimension are abnormal.If q>1 and q→∞,the spectral lines quickly converge to horizontal lines;when q<0 and q→-∞,the spectral lines quickly surpass the upper limit of fractal dimension,2,which represents Euclidean dimension of embedding space.2) The spectral curves of local fractal dimension are also not entirely normal.The peaks of the f(α) curves incline to the left,and the left ends of the curves are higher than the right ends.The problem lies in that the curves go beyond the maximum value of 2.3) Fractal dimension growth curves can be described by the quadratic logistic function.Capacity parameters and inflection points of different fractal dimension growth curves are different.The main conclusions are as follows:1) The urban fringes are disorderly developed,while the central areas of the main cities in the Beijing-TianjinHebei region is overfilled with construction land,leaving little buffer space.2) The main mode of urban growth is to expand to the outside region,but there are signs of central agglomeration in the total construction land of Hebei Province.3) Land use of the main cities is close to saturation,and the speed of land expansion has peaked for Beijing and Tianjin,but not in Hebei Province yet.In short,it is necessary to optimize the land use structure in the Beijing-Tianjin-Hebei region by city planning.
引文
陈涛.1995.豫北地区城镇体系的分形研究[D].长春:东北师范大学城市与环境学院.[Chen T.1995.Studies on fractal systems of towns in the central plains.Changchun China:College of Urban and Environmental Sciences Northeast Normal University.]
陈彦光.2015.简单、复杂与地理分布模型的选择[J].地理科学进展,34(3):321-329.[Chen Y G.2015.Simplicity complexity,and mathematical modeling of geographica distributions.Progress in Geography,34(3):321-329.]
陈彦光,周一星.2001.豫北地区城镇体系空间结构的多分形研究[J].北京大学学报(自然科学版),37(6):810-818[Chen Y G,Zhou Y X.2001.A study of multifractals measures of the spatial structure of the urban system in centra plains.Acta Scientiarum Naturalium Universitatis Pekinensis,37(6):810-818.]
刘继生,陈彦光.2003.河南省城镇体系空间结构的多分形特征及其与水系分布的关系探讨[J].地理科学,23(6)713-720.[Liu J S,Chen Y G.2003.Multifractal measures based on man-land relationships of the spatial structure of the urban system in Henan.Scientia Geographica Sinica23(6):713-720.]
汪富泉,李后强.1996.分形--大自然的艺术构造[M].济南:山东教育出版社.[Wang F Q,Li H Q.1996.Fractals:The artistic structure of nature.Jinan,China:Shandong Education Press.]
Allen P M.1997.Cities and regions as self-organizing systems:Models of complexity[M].London&New York:Routledge.
Arbesman S.2012.The half-life of facts:Why everything we know has an expiration date[M].New York:Penguin Group.
Ariza-Villaverde A B,Jimenez-Hornero F J,De Rave E G.2013.Multifractal analysis of axial maps applied to the study of urban morphology[J].Computers,Environment and Urban Systems,38:1-10.
Batty M,Longley P A.1994.Fractal cities:A geometry of form and function[M].London,UK:Academic Press.
Chen Y G.2014.Multifractals of central place systems:Models,dimension spectrums,and empirical analysis[J].Physica A,402:266-282.
Chen Y G.2016.Defining urban and rural regions by multifractal spectrums of urbanization[J].Fractals,24(1):1650004.
Chen Y G,Lin J Y.2009.Modeling the self-affine structure and optimization conditions of city systems using the idea from fractals[J].Chaos,Soliton&Fractals,41:615-629.
Chen Y G,Wang J J.2013.Multifractal characterization of urban form and growth:The case of Beijing[J].Environment and Planning B:Planning and Design,40(5):884-904.
Chen Y G,Zhou Y X.2004.Multi-fractal measures of citysize distributions based on the three-parameter Zipf model[J].Chaos,Solitons&Fractals,22(4):793-805.
Chhabra A,Jensen R V.1989.Direct determination of the f(α)singularity spectrum[J].Physical Review Letters,62(12):1327-1330.
Encarna??o S,Gaudiano M,Santos F C,et al.2012.Fractal cartography of urban areas[J].Scientific Reports,2:527.
Feder J.1988.Fractals[M].New York:Plenum Press.
Folorunso O A,Puente C E,Rolston D E,et al.1994.Statistical and fractal evaluation of the spatial characteristics of soil surface strength[J].Soil Science Society of America Journal,58(2):284-294.
Frankhauser P.1998.The fractal approach:A new tool for the spatial analysis of urban agglomerations[J].Population:An English Selection,10(1):205-240.
Gordon K.2005.The mysteries of mass[J].Scientific American,293(1):40-46,48.
Haag G.1994.The rank-size distribution of settlements as a dynamic multifractal phenomenon[J].Chaos,Solitons and Fractals,4(4):519-534.
Haken H,Portugali J.1995.A synergetic approach to the selforganization of cities and settlements[J].Environment and Planning B:Planning and Design,22(1):35-46.
He S,Wang Y.2017.Revisiting the multifractality in stock returns and its modeling implications[J].Physica A,467:11-20.
Huang L S,Chen Y G.2018.A comparison between two OLS-based approaches to estimating urban multifractal parameters[J].Fractals,26(1):1850019.
Ihlen E A.2012.Introduction to multifractal detrended fluctuation analysis in Matlab[J].Frontiers in Physiology,3141.
Kantelhardt J W,Koscielny-Bunde E,Rego H H,et al.2001Detecting long-range correlations with detrended fluctuation analysis[J].Physica A,295(3):441-454.
Kantelhardt J W,Zschiegner S A,Koscielny-Bunde E,et al2002.Multifractal detrended fluctuation analysis of nonstationary time series[J].Physica A,316(1):87-114.
Knox P L,Marston S A.2009.Places and regions in globa context:Human geography[M].The 5th Edition.Upper Saddle River,NJ:Prentice Hall.
Kravchenko A N,Boast C W,Bullock D G.1999.Multifractal analysis of soil spatial variability[J].Agronomy Journal,91(6):1033-1041.
Murcio R,Masucci A P,Arcaute E,et al.2015.Multifractal to monofractal evolution of the London street network[J].Physical Review E,92,062130.
Portugali J.2000.Self-organization and the city[M].Berlin,Germany:Springer.
Rozenfeld H D,Rybski D,Andrade Jr.D S,et al.2008.Laws of population growth[J].PNAS,105(48):18702-18707.
Salat H,Murcio R,Yano K,et al.2018.Uncovering inequality through multifractality of land prices:1912 and contemporary Kyoto[J].PLoS One,13(4),e0196737.
Stanley H E,Meakin P.1988.Multifractal phenomena in physics and chemistry[J].Nature,335:405-409.
Sun X,Chen H P,Wu Z Q,et al.2001.Multifractal analysis of Hang Seng index in Hong Kong stock market[J].Physica A,291:553-562.
Sun X,Chen H P,Yuan Y Z,et al.2001.Predictability of multifractal analysis of Hang Seng stock index in Hong Kong[J].Physica A,301:473-482.
Takayasu H.1990.Fractals in the physical sciences[M].Manchester,UK:Manchester University Press.
White R,Engelen G.1993.Cellular automata and fractal urban form:A cellular modeling approach to the evolution of urban land-use patterns[J].Environment and Planning A,25(8):1175-1199.
(1)关于多分维谱线的正常状态(理想状态)与不正常状态(非理想状态)的理论基础和实际表现请参见Huang et al, 2018。
陈彦光.2015.简单、复杂与地理分布模型的选择[J].地理科学进展,34(3):321-329.[Chen Y G.2015.Simplicity complexity,and mathematical modeling of geographica distributions.Progress in Geography,34(3):321-329.]
陈彦光,周一星.2001.豫北地区城镇体系空间结构的多分形研究[J].北京大学学报(自然科学版),37(6):810-818[Chen Y G,Zhou Y X.2001.A study of multifractals measures of the spatial structure of the urban system in centra plains.Acta Scientiarum Naturalium Universitatis Pekinensis,37(6):810-818.]
刘继生,陈彦光.2003.河南省城镇体系空间结构的多分形特征及其与水系分布的关系探讨[J].地理科学,23(6)713-720.[Liu J S,Chen Y G.2003.Multifractal measures based on man-land relationships of the spatial structure of the urban system in Henan.Scientia Geographica Sinica23(6):713-720.]
汪富泉,李后强.1996.分形--大自然的艺术构造[M].济南:山东教育出版社.[Wang F Q,Li H Q.1996.Fractals:The artistic structure of nature.Jinan,China:Shandong Education Press.]
Allen P M.1997.Cities and regions as self-organizing systems:Models of complexity[M].London&New York:Routledge.
Arbesman S.2012.The half-life of facts:Why everything we know has an expiration date[M].New York:Penguin Group.
Ariza-Villaverde A B,Jimenez-Hornero F J,De Rave E G.2013.Multifractal analysis of axial maps applied to the study of urban morphology[J].Computers,Environment and Urban Systems,38:1-10.
Batty M,Longley P A.1994.Fractal cities:A geometry of form and function[M].London,UK:Academic Press.
Chen Y G.2014.Multifractals of central place systems:Models,dimension spectrums,and empirical analysis[J].Physica A,402:266-282.
Chen Y G.2016.Defining urban and rural regions by multifractal spectrums of urbanization[J].Fractals,24(1):1650004.
Chen Y G,Lin J Y.2009.Modeling the self-affine structure and optimization conditions of city systems using the idea from fractals[J].Chaos,Soliton&Fractals,41:615-629.
Chen Y G,Wang J J.2013.Multifractal characterization of urban form and growth:The case of Beijing[J].Environment and Planning B:Planning and Design,40(5):884-904.
Chen Y G,Zhou Y X.2004.Multi-fractal measures of citysize distributions based on the three-parameter Zipf model[J].Chaos,Solitons&Fractals,22(4):793-805.
Chhabra A,Jensen R V.1989.Direct determination of the f(α)singularity spectrum[J].Physical Review Letters,62(12):1327-1330.
Encarna??o S,Gaudiano M,Santos F C,et al.2012.Fractal cartography of urban areas[J].Scientific Reports,2:527.
Feder J.1988.Fractals[M].New York:Plenum Press.
Folorunso O A,Puente C E,Rolston D E,et al.1994.Statistical and fractal evaluation of the spatial characteristics of soil surface strength[J].Soil Science Society of America Journal,58(2):284-294.
Frankhauser P.1998.The fractal approach:A new tool for the spatial analysis of urban agglomerations[J].Population:An English Selection,10(1):205-240.
Gordon K.2005.The mysteries of mass[J].Scientific American,293(1):40-46,48.
Haag G.1994.The rank-size distribution of settlements as a dynamic multifractal phenomenon[J].Chaos,Solitons and Fractals,4(4):519-534.
Haken H,Portugali J.1995.A synergetic approach to the selforganization of cities and settlements[J].Environment and Planning B:Planning and Design,22(1):35-46.
He S,Wang Y.2017.Revisiting the multifractality in stock returns and its modeling implications[J].Physica A,467:11-20.
Huang L S,Chen Y G.2018.A comparison between two OLS-based approaches to estimating urban multifractal parameters[J].Fractals,26(1):1850019.
Ihlen E A.2012.Introduction to multifractal detrended fluctuation analysis in Matlab[J].Frontiers in Physiology,3141.
Kantelhardt J W,Koscielny-Bunde E,Rego H H,et al.2001Detecting long-range correlations with detrended fluctuation analysis[J].Physica A,295(3):441-454.
Kantelhardt J W,Zschiegner S A,Koscielny-Bunde E,et al2002.Multifractal detrended fluctuation analysis of nonstationary time series[J].Physica A,316(1):87-114.
Knox P L,Marston S A.2009.Places and regions in globa context:Human geography[M].The 5th Edition.Upper Saddle River,NJ:Prentice Hall.
Kravchenko A N,Boast C W,Bullock D G.1999.Multifractal analysis of soil spatial variability[J].Agronomy Journal,91(6):1033-1041.
Murcio R,Masucci A P,Arcaute E,et al.2015.Multifractal to monofractal evolution of the London street network[J].Physical Review E,92,062130.
Portugali J.2000.Self-organization and the city[M].Berlin,Germany:Springer.
Rozenfeld H D,Rybski D,Andrade Jr.D S,et al.2008.Laws of population growth[J].PNAS,105(48):18702-18707.
Salat H,Murcio R,Yano K,et al.2018.Uncovering inequality through multifractality of land prices:1912 and contemporary Kyoto[J].PLoS One,13(4),e0196737.
Stanley H E,Meakin P.1988.Multifractal phenomena in physics and chemistry[J].Nature,335:405-409.
Sun X,Chen H P,Wu Z Q,et al.2001.Multifractal analysis of Hang Seng index in Hong Kong stock market[J].Physica A,291:553-562.
Sun X,Chen H P,Yuan Y Z,et al.2001.Predictability of multifractal analysis of Hang Seng stock index in Hong Kong[J].Physica A,301:473-482.
Takayasu H.1990.Fractals in the physical sciences[M].Manchester,UK:Manchester University Press.
White R,Engelen G.1993.Cellular automata and fractal urban form:A cellular modeling approach to the evolution of urban land-use patterns[J].Environment and Planning A,25(8):1175-1199.
(1)关于多分维谱线的正常状态(理想状态)与不正常状态(非理想状态)的理论基础和实际表现请参见Huang et al, 2018。
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