京津冀城镇用地空间结构的多分维谱分析

doi:10.18306/dlkxjz.2019.01.005

摘要/Abstract

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。

关键词: 城镇体系, 多分形, 多分维谱, 自仿射, 土地利用, 京津冀地区

Abstract:

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-Tianjin-Hebei 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.

Key words: urban system, multifractals, multifractal dimension spectrum, self-affinity, land use, Beijing-Tianjin-Hebei region

黄琳珊, 陈彦光, 李双成. 京津冀城镇用地空间结构的多分维谱分析[J]. 地理科学进展, 2019, 38(1): 50-64.

Linshan HUANG, Yanguang CHEN, Shuangcheng LI. Multifractal spectral analysis of land use structure of the Beijing-Tianjin-Hebei urban system[J]. PROGRESS IN GEOGRAPHY, 2019, 38(1): 50-64.

图/表 9

图1

表1

图2

表2

表3

图3

图4

表4

表5

参考文献 38

[1]	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. ]
[2]	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 geographical distributions. Progress in Geography, 34(3): 321-329.]
[3]	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 central plains. Acta Scientiarum Naturalium Universitatis Pekinensis, 37(6): 810-818. ]
[4]	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 Sinica, 23(6): 713-720. ]
[5]	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. ]
[6]	Allen P M.1997. Cities and regions as self-organizing systems: Models of complexity[M]. London & New York: Routledge.
[7]	Arbesman S.2012. The half-life of facts: Why everything we know has an expiration date[M]. New York: Penguin Group.
[8]	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. doi: 10.1016/j.compenvurbsys.2012.11.001
[9]	Batty M, Longley P A.1994. Fractal cities: A geometry of form and function [M]. London, UK: Academic Press.
[10]	Chen Y G.2014. Multifractals of central place systems: Models, dimension spectrums, and empirical analysis[J]. Physica A, 402: 266-282. doi: 10.1016/j.physa.2014.01.061
[11]	Chen Y G.2016. Defining urban and rural regions by multifractal spectrums of urbanization[J]. Fractals, 24(1): 1650004. doi: 10.1142/S0218348X16500043
[12]	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.
[13]	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. doi: 10.1068/b36155
[14]	Chen Y G, Zhou Y X.2004. Multi-fractal measures of city-size distributions based on the three-parameter Zipf model[J]. Chaos, Solitons & Fractals, 22(4): 793-805.
[15]	Chhabra A, Jensen R V.1989. Direct determination of the f(α) singularity spectrum[J]. Physical Review Letters, 62(12): 1327-1330. doi: 10.1103/PhysRevLett.62.1327
[16]	Encarnação S, Gaudiano M, Santos F C, et al.2012. Fractal cartography of urban areas[J]. Scientific Reports, 2: 527. doi: 10.1038/srep00527
[17]	Feder J.1988. Fractals [M]. New York: Plenum Press.
[18]	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. doi: 10.2136/sssaj1994.03615995005800020004x
[19]	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.
[20]	Gordon K.2005. The mysteries of mass[J]. Scientific American, 293(1): 40-46, 48.
[21]	Haag G.1994. The rank-size distribution of settlements as a dynamic multifractal phenomenon[J]. Chaos, Solitons and Fractals, 4(4): 519-534. doi: 10.1016/0960-0779(94)90063-9
[22]	Haken H, Portugali J.1995. A synergetic approach to the self-organization of cities and settlements[J]. Environment and Planning B: Planning and Design, 22(1): 35-46. doi: 10.1068/b220035
[23]	He S, Wang Y.2017. Revisiting the multifractality in stock returns and its modeling implications[J]. Physica A, 467: 11-20. doi: 10.1016/j.physa.2016.09.040
[24]	Huang L S, Chen Y G.2018. A comparison between two OLS-based approaches to estimating urban multifractal parameters[J]. Fractals, 26(1): 1850019. doi: 10.1142/S0218348X18500196
[25]	Ihlen E A.2012. Introduction to multifractal detrended fluctuation analysis in Matlab[J]. Frontiers in Physiology, 3: 141.
[26]	Kantelhardt J W, Koscielny-Bunde E, Rego H H, et al.2001. Detecting long-range correlations with detrended fluctuation analysis[J]. Physica A, 295(3): 441-454. doi: 10.1016/S0378-4371(01)00144-3
[27]	Kantelhardt J W, Zschiegner S A, Koscielny-Bunde E, et al.2002. Multifractal detrended fluctuation analysis of nonstationary time series[J]. Physica A, 316(1): 87-114. doi: 10.1016/S0378-4371(02)01383-3
[28]	Knox P L, Marston S A.2009. Places and regions in global context: Human geography[M]. The 5th Edition. Upper Saddle River, NJ: Prentice Hall.
[29]	Kravchenko A N, Boast C W, Bullock D G.1999. Multifractal analysis of soil spatial variability[J]. Agronomy Journal, 91(6): 1033-1041. doi: 10.2134/agronj1999.9161033x
[30]	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.
[31]	Portugali J.2000. Self-organization and the city[M]. Berlin, Germany: Springer.
[32]	Rozenfeld H D, Rybski D, Andrade Jr. D S, et al.2008. Laws of population growth[J]. PNAS, 105(48): 18702-18707. doi: 10.1073/pnas.0807435105
[33]	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. doi: 10.1371/journal.pone.0196737
[34]	Stanley H E, Meakin P.1988. Multifractal phenomena in physics and chemistry[J]. Nature, 335: 405-409. doi: 10.1038/335405a0
[35]	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. doi: 10.1016/S0378-4371(00)00606-3
[36]	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. doi: 10.1016/S0378-4371(01)00433-2
[37]	Takayasu H.1990. Fractals in the physical sciences [M]. Manchester, UK: Manchester University Press.
[38]	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. doi: 10.1068/a251175

年份	城镇建设用地		农村居民点用地		工矿和交通建设用地		总建设用地面积/m²
年份	面积/m²	比例	面积/m²	比例	面积/m²	比例	总建设用地面积/m²
1995	3430909489	0.2020	11154546324	0.6569	2395113056	0.1411	16980568869
2000	3541167552	0.2043	11451994392	0.6606	2343239014	0.1352	17336400957
2005	4775537679	0.2404	11709702253	0.5894	3381724968	0.1702	19866964900
2010	6517866881	0.2589	14435903946	0.5734	4222176983	0.1677	25175947809
2013	8079748079	0.3250	13273658619	0.5340	3505285674	0.1410	24858692372

年份	城镇建设用地				总建设用地
年份	D₀	D₁	D₂	D₁/D₀	D₀	D₁	D₂	D₁/D₀
1995	1.4411	1.2858	1.1949	0.8922	1.8071	1.6847	1.6062	0.9323
2000	1.4374	1.2899	1.2017	0.8974	1.8062	1.6868	1.6124	0.9339
2005	1.4623	1.3157	1.2331	0.8998	1.8135	1.6882	1.6108	0.9309
2010	1.5075	1.3781	1.3074	0.9141	1.8479	1.7248	1.6534	0.9334
2013	1.5187	1.3860	1.3122	0.9126	1.8414	1.7064	1.6316	0.9267
平均	1.4734	1.3311	1.1949	0.9032	1.8232	1.6982	1.6062	0.9314

年份	城镇建设用地				总建设用地
年份	α(0)	f(α(0))	Δα	Δf	α(0)	f(α(0))	Δα	Δf
1995	1.6481	1.4411	1.6058	0.2237	1.9823	1.8071	1.6746	0.0732
2000	1.6358	1.4374	1.6226	0.2356	1.9824	1.8062	1.6444	0.0698
2005	1.6650	1.4623	1.6595	0.2946	1.9953	1.8135	1.6789	0.1076
2010	1.6995	1.5075	1.6570	0.2467	2.0248	1.8479	1.6651	0.1239
2013	1.7123	1.5187	1.7415	0.3932	2.0414	1.8414	1.6786	0.0861
平均	1.6721	1.4734	1.6573	0.2788	2.0052	1.8232	1.6683	0.0921

地区	年份	城镇建设用地						总建设用地
地区	年份	D₀	D₁	D₂	D₁/D₀	D₂/D₁		D₀	D₁	D₂	D₁/D₀	D₂/D₁
北京市	1995	1.4662	1.3575	1.3246	0.9259	0.9758		1.6934	1.5817	1.5292	0.9340	0.9668
	2000	1.4154	1.3408	1.3126	0.9473	0.9790		1.7100	1.5983	1.5436	0.9347	0.9658
	2005	1.4745	1.4137	1.3903	0.9587	0.9835		1.7331	1.6264	1.5826	0.9384	0.9731
	2010	1.4740	1.4054	1.3802	0.9535	0.9820		1.7390	1.6256	1.5789	0.9348	0.9712
	2013	1.5558	1.5079	1.4917	0.9692	0.9893		1.7630	1.6497	1.6122	0.9357	0.9773
	平均	1.4772	1.4051	1.3799	0.9509	0.9819		1.7277	1.6163	1.5693	0.9355	0.9708
天津市	1995	1.4168	1.3258	1.2835	0.9357	0.9681		1.7598	1.6730	1.6163	0.9507	0.9661
	2000	1.4153	1.3306	1.2915	0.9402	0.9706		1.7500		1.6676	1.6113	0.9529	0.9663
	2005	1.4658	1.3912	1.3587	0.9491	0.9767	1.7759		1.6927	1.6436	0.9531	0.9710
	2010	1.5183	1.4488	1.4205	0.9542	0.9805	1.8017		1.7185	1.6714	0.9538	0.9726
	2013	1.5091	1.4430	1.4141	0.9562	0.9800	1.7887		1.7035	1.6566	0.9524	0.9725
	平均	1.4651	1.3879	1.3537	0.9471	0.9752	1.7752		1.6911	1.6399	0.9526	0.9697
河北省	1995	1.3666	1.2432	1.1689	0.9097	0.9402	1.7815	1.6649	1.5917	0.9345	0.9561
	2000	1.3730	1.2515	1.1787	0.9115	0.9419	1.7799		1.6634	1.5928	0.9346	0.9575
	2005	1.3943	1.2745	1.2051	0.9140	0.9456	1.7871		1.6699	1.5988	0.9344	0.9575
	2010	1.4522	1.3338	1.2668	0.9185	0.9498	1.8257		1.7050	1.6357	0.9339	0.9594
	2013	1.4567	1.3425	1.2796	0.9216	0.9531	1.8172		1.6890	1.6217	0.9295	0.9602
	平均	1.4086	1.2891	1.2198	0.9151	0.9461	1.7983		1.6784	1.6082	0.9334	0.9581

地区	年份	城镇用地					总建设用地
地区	年份	α(q)	f(α(q))	Δα	Δf		α(q)	f(α(q))	Δα	Δf
北京市	1995	1.6558	1.4662	1.3039	0.3908		1.8587	1.6934	1.2182	0.1128
	2000	1.5371	1.4154	1.1037	0.4278		1.8750	1.7100	1.2329	0.1191
	2005	1.5763	1.4745	1.1152	0.4844		1.9037	1.7331	1.2554	0.2103
	2010	1.5909	1.4740	1.1052	0.4435		1.9182	1.7390	1.2742	0.1650
	2013	1.6479	1.5558	1.2286	0.6240		1.9568	1.7630	1.2733	0.2655
	平均	1.6016	1.4772	1.1713	0.4741		1.9025	1.7277	1.2508	0.1745
天津市	1995	1.5496	1.4168	1.1546	0.2314		1.8673	1.7598	1.1171	0.1183
	2000	1.5393	1.4153	1.0927	0.2522		1.8515		1.7500	1.1170	0.0538
	2005	1.5847	1.4658	1.1214	0.3926	1.8858		1.7759	1.1379	0.1557
	2010	1.6404	1.5183	1.2077	0.3709	1.9124		1.8017	1.1446	0.2058
	2013	1.6174	1.5091	1.1413	0.4349	1.9042		1.7887	1.1383	0.1910
	平均	1.5863	1.4651	1.1435	0.3364	1.8842		1.7752	1.1310	0.1449
河北省	1995	1.5442	1.3666	1.5365	0.0878	1.9515	1.7815	1.6511	-0.0181
	2000	1.5477	1.3730	1.5502	0.1061	1.9538		1.7799	1.6227	-0.0182
	2005	1.5699	1.3943	1.5452	0.1246	1.9614		1.7871	1.7057	-0.0172
	2010	1.6330	1.4522	1.6453	0.1116	2.0006		1.8257	1.7070	0.0492
	2013	1.6335	1.4567	1.6931	0.2151	2.0119		1.8172	1.7163	-0.1211
	平均	1.5857	1.4086	1.5941	0.1290	1.9759		1.7983	1.6806	-0.0251