北京市海淀区绿地结构功能性连接分析与构建策略研究
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摘要
城市绿地结构布局一直是风景园林学科研究的重点之一,构建具有生态价值的空间结构是城市建设的迫切需求。本文对北京市海淀区绿地网络结构功能性连接与构建策略进行研究,结合生态系统服务评估与权衡(InVEST)模型、最小费用模型等方法构建阻力面、确定连接路径;采用功能性连接指数(NL、NC、IIC、PC和dIIC)表示不同距离阈值下绿地网络结构特性。研究结果表明,整体而言,最适合海淀区绿地网络现状结构的距离阈值为2200m;此时形成了10个组分共353条路径,确立了西山、颐和园等6个需优先保护的重要节点和三条重要路径。研究进一步显示,以乔木为目标物种的林地网络和以水禽为目标物种的水域网络的破碎化程度较高,其中林地网络在西部山区、北部平原和东南城区分别形成了优势斑块结构、局部网络结构和点状组团结构。研究同时证明,通过增加10条重要连接路径可使林地网络连接度提高至原来的1.7倍,使整体结构由破碎化网络变成完整、沿多方向延伸的、稳定而具有韧性的网络结构。最后,研究针对城市绿地结构的构建提出了明确目标、确定目标物种,识别并保护重要节点及重要连接路径,增加潜在连接路径、完善绿地网络结构等策略,从而高效改善和提升城市生态品质。
Urban green space structure and pattern have been one of the highlights in Landscape Architecture studies, accompanying with urgent demands of promoting ecological spatial structures in urban construction. Focusing on functional connectivity and construction strategies of the structure of green space network in Haidian District of Beijing, this research builds resistance surface and identifies linkages through habitat quality evaluation of the InVEST Model and the simulation with the LeastCost Model, while adopting functional connectivity index(NL, NC, IIC, PC, and dIIL) to indicate the structural characteristics of green space network at varied distance thresholds. Results reveal that, on the whole, the distance threshold of 2,200 meters is most appropriate for the structure of the existing green space network of Haidian District, when 10 components and 353 linkages are identified and six important nodes and three important linkages that require a protection priority are further determined. Findings also disclose that the forest network of target tree species and that of water network of target water bird species are highly fragmented. Forest network serves in forms of dominant patch structure, local network structure, and fragmented cluster structure in the western mountainous area, the northern plain area, and the southeastern urban area, respectively. Moreover, the research proves that by introducing ten important linkages, the connectivity of forest network can be improved by 1.7 times, completing the overall structure in multiple directions and helping form a stable and resilient structure of the network. Finally, the research puts forward strategies for urban green space construction, including identifying construction objectives and target species, identifying and protecting important nodes and important linkages, and introducing possible important linkages and improving the structure of green space network, to help efficiently improve urban ecological quality.
Urban green space structure and pattern have been one of the highlights in Landscape Architecture studies, accompanying with urgent demands of promoting ecological spatial structures in urban construction. Focusing on functional connectivity and construction strategies of the structure of green space network in Haidian District of Beijing, this research builds resistance surface and identifies linkages through habitat quality evaluation of the InVEST Model and the simulation with the LeastCost Model, while adopting functional connectivity index(NL, NC, IIC, PC, and dIIL) to indicate the structural characteristics of green space network at varied distance thresholds. Results reveal that, on the whole, the distance threshold of 2,200 meters is most appropriate for the structure of the existing green space network of Haidian District, when 10 components and 353 linkages are identified and six important nodes and three important linkages that require a protection priority are further determined. Findings also disclose that the forest network of target tree species and that of water network of target water bird species are highly fragmented. Forest network serves in forms of dominant patch structure, local network structure, and fragmented cluster structure in the western mountainous area, the northern plain area, and the southeastern urban area, respectively. Moreover, the research proves that by introducing ten important linkages, the connectivity of forest network can be improved by 1.7 times, completing the overall structure in multiple directions and helping form a stable and resilient structure of the network. Finally, the research puts forward strategies for urban green space construction, including identifying construction objectives and target species, identifying and protecting important nodes and important linkages, and introducing possible important linkages and improving the structure of green space network, to help efficiently improve urban ecological quality.
引文
[1]Fu,W.,Liu,S.L.,Cui,B.S.,&Zhang,Z.L.(2009).A review on ecological connectivity in landscape ecology.Acta Ecologica Sinica,29(11),6174-6182.
[2]Merriam,G.(1984).Connectivity:a fundamental ecological characteristic of landscape pattern.In J.Brandt,&P.Agger(Eds.),Proceedings of the 1st Seminar of the International Association of Landscape Ecology.Roskilde,Denmark:Roskilde University Center
[3]Uezu,A.,Metzger,J.P.,&Vielliard,J.M.E.(2005).Effects of structural and functional connectivity and patch size on the abundance of seven Atlantic Forest bird species.Biological Conservation,123(4),507-519.doi:10.1.1.461.4659
[4]Sork,V.L.,&Smouse,P.E.(2006).Genetic analysis of landscape connectivity in tree populations.Landscape Ecology,21(6),821-836.doi:10.1007/s10980-005-5415-9
[5]Coulon,A.,Cosson,J.F.,Angibault,J.M.,Cargnelutti,B.,Galan,M.,Morellet,N.,…Hewison,A.J.M.(2004).Landscape connectivity influences gene flow in a roe deer population inhabiting a fragmented landscape:An individual-based approach.Molecular Ecology,13,2841-2850.doi:10.1111/j.1365-294X.2004.02253.x
[6]Urban,D.,&Keitt,T.(2001).Landscape connectivity:AGraph-Theoretic Perspective.Ecology,82(5),1205-1218.doi:10.1890/0012-9658(2001)082[1205:LCAGTP]2.0.CO;2
[7]Xie,S.L.,Lu,F.,Cao,L.,Zhou,W.Q.,&Ouyang,Z.Y.(2016).The Effect of Landscape Patterns on Avian Communities during Summer Months in Beijing’s Urban Parks.Landscape Architecture Frontiers,4(3),10-21.
[8]Shu,Y.,Hu,Y.M.,Guo,D.F.,Shan,K.,Zhu,S.Y.,&Wang,L.D.(2004).The Change of Habitat Suitable for the Red-crowned Crane in Yellow River Delta.Chinese Journal of Zoology,39(3),33-41,121.doi:10.13859/j.cjz.2004.03.009
[9]Liu,X.,Jiao,Y.M.,Wang,M.,&Zhang,K.F.(2018).Evaluation of key nodes and corridors of river and canal network in Hani Rice Terraces based on graph theory.Chinese Journal of Ecology,37(1),287-294.doi:10.13292/j.1000-4890.201801.032
[10]Chen,C.D.,Jia,Z.Y.,Wu,S.J.,Tong,X.X.,Zhou,W.Z.,Chen,R.Y.,&Zhang,C.L.(2017).A bibliometric review of Chinese studies on the application of landscape connectivity.Acta Ecologica Sinica,37(10),3243-3255.doi:10.5846/stxb201602290341
[11]Pascual-Hortal,L.,&Saura,S.(2006).Comparison and development of new graph-based landscape connectivity indices:towards the priorization of habitat patches and corridors for conservation.Landscape Ecology,21(7),959-967.doi:10.1007/s10980-006-0013-z
[12]Wu,J.J.,Li,Y.Z.,Yu,L.J.,Gao,M.,Wu,X.Q.,&Bi,X.L.(2018).Dynamic changes and driving factors of landscape connectivity for natural wetland in Yellow River Delta.Ecology and Environmental Sciences,27(1),71-78.doi:10.16258/j.cnki.1674-5906.2018.01.010
[13]Wang,M.(2017).Evaluation on the Ecology Connectivity Based on the Least Cost Distance Model-Taking the Xishan District as An Example(Master thesis).Kunming University of Science and Technology,Kunming.
[14]Chen,C,D.,Meurk,C.D.,Ignatieva,M.E.,Stewart,H.G.,&Wu,S.J.(2015).Identifying and evaluating functional connectivity for building urban ecological networks.Acta Ecologica Sinica,35(19),6414-6424.
[15]Ou,W.X.,&Yuan,W.J.(2015).Priority of red-crowned crane wintering habitat patches using landscape connectivity in the Yancheng coastal wetland.Resources Science,37(4),823-831.
[16]Chen,T.,Qin,S.N.,&Chen,Y.H.(2017).The Assessment on Woodland Network Based on Functional Connectivity of Bird’s Biological Characteristics:A Case Study in Ningxiang County,Changsha.Sichuan Journal of Zoology,36(5),489-497.doi:10.11984/j.issn.1000-7083.20160312
[17]Chen,J.,Liang,G.F.,&Ding,S.Y.(2012).Landscape connectivity analysis for the forest landscape restoration:a case study of Gongyi City.Acta Ecologica Sinica,32(12),3773-3781.doi:10.5846/stxb201108171210
[18]Government of Haidian District,Beijing.(2016).The land use planning of Beijing(2006-2020).Retrieved from http://www.bjhd.gov.cn/xxgk/auto4558_51854/auto4558_57869/201810/P020170104436568765730.pdf
[19]Bureau of Landscaping of Beijing.(2017).Urban Greening Resources of Beijing in 2016.Retrieved from http://www.bjyl.gov.cn/zwgk/tjxx/201705/t20170517_192779.html
[20]General Administration of Quality Supervision,Inspection and Quarantine of the People’s Republic of China,Standardization Administration of the People’s Republic of China.(2007).Current land use classification(GB/T 21010-2007).
[21]Government of Beijing City.(2009).The land use planning of Beijing(2006-2020).Retrieved from http://www.bjyl.gov.cn/zwgk/tjxx/201804/P020180425535648094242.pdf
[22]Government of Beijing City.(2004).The general planning of Beijing City(2004-2020).Retrieved from https://wenku.baidu.com/view/baf1bbda76eeaeaad1f33010.html
[23]Yu,K.J.(1999).Landscape Ecological Security Patterns in Biological Conservation.Acta Ecologica Sinica,19(1),10-17.
[24]Zhang,X.F.,Wang,Y.L.,&Li,Z.G.(2005).Landscape pattern optimization based upon the concept of landscape functions network:a case study in Taiwan,China.Acta Ecologica Sinica,25(7),1707-1713.
[25]Wu,C.G.,Zhou,Z.X.,Wang,P.C.,Xiao,W.F.,Teng,M.J.,&Peng,L.(2009).Evaluation of landscape connectivity based on least-cost model.Chinese Journal of Applied Ecology,20(8),2042-2048.doi:10.13287/j.1001-9332.2009.0267
[26]Bentrup,G.(2008).Conservation buffers-Design guidelines for buffers,corridors,and greenways.(General technical report SRS-109).Asheville:USDA Forest Service Southern Research Station.Retrieved from https://www.srs.fs.usda.gov/pubs/gtr/gtr_srs109.pdf
[27]Lu,C.H.(2006).Roles of animals in seed dispersal of Pinus:Areview.Chinese Journal of Ecology,25(5),557-562.
[28]Lu,C.H.(2003).Seed Dispersal by Animals(pp.138-139).Harbin:Northeast Forestry University Press.
[29]Xing,J.J.(2018).Seed Dispersal of Quercus varibilis Trees under the Mediation of Animals:From Seed to Seedling(Master thesis).Wuhan:Central China Normal University.
[30]Zhang,Y.F.,Wang,W.R.,Li,W.,Miao,X.D.,&Lu,J.Q.(2016).Effects of Thinning on Seed Dispersal by Rodents in Secondary Forest.Journal of Zhengzhou University(Natural Science Edition),48(1),67-72.
[31]Breitbac,N.,Laube,I.,Steffan-Dewenterl,I.,&B?hning-Gaese,K.(2010).Bird diversity and seed dispersal along a human landuse gradient:high seed removal in structurally simple farmland.Oecologia,162(4),965-976.doi:10.1007/s00442-009-1547-y
[32]Huang,Y.(2015).The Methodology of Bird Habitats’Making and Planning at Beijing Urban Green Spaces(Doctoral dissertation).Tsinghua University,Beijing.
[33]Chen,Z.Q.,Fu,J.P.,Zhao,X.R.,&Ding,C.Q.(2010).The Construction of Birds in Yuanmingyuan Relic Park,Beijing.Chinese Journal of Zoology,45(4),21-30.doi:10.13859/j.cjz.2010.04.011
[34]Guo,T.Y.,Yang,J.W.,Qu.Y.Y.,&Chen,W.(2010).Investigations on Diversity of Birds at the Black Bamboo Park in Beijing.Sichuan Journal of Zoology,29(6),975-980.
[35]Wang,L.J.,Ji,J.W.,&Li,T.Y.(2012).A field survey on bird diversity and seasonal changes at the Beihai Park in Beijing.Journal of Hubei University(Natural Science),34(3),298-303.doi:10.3969/j.issn.1000-2375.2012.03.012
[36]Chen,Y.,Qiao,F.,&Jiang,L.(2016).Effects of Land Use Pattern Change on Regional Scale Habitat Quality Based on InVESTModel-A Case Study in Beijing.Acta Scientiarum Naturalium Universitatis Pekinensis,52(3),553-562.doi:10.13209/j.0479-8023.2016.057
[37]Chu,L.,Zhang,X.R.,Wang,T.W.,Li,Z.X.,&Cai,C.F.(2018).Spatial-temporal evolution and prediction of urban landscape pattern and habitat quality based on CA-Markov and InVESTmodel.Chinese Journal of Applied Ecology,29(12),4106-4118.doi:10.13287/j.1001-9332.201812.013
[38]Corlett,R.T.(2009).Seed dispersal distances and plant migration potential in tropical East Asia.Biotropica,41(5),592-598.doi:10.1111/j.1744-7429.2009.00503.x
[39]Qi,K,.&Fan,Z.Q.(2016).Evaluation method for landscape connectivity based on graph theory:a case study of natural forests in Minqing County,Fujian Province.Acta Ecologica Sinica,36(23),7580-7593.doi:10.5846/stxb201507301599
[40]Teng,M.J.(2011).Planning Ecological Security Patterns in a Rapidly Urbanizing Context:A Case Study in Wuhan,China(Doctoral dissertation).Huazhong Agricultural University,Wuhan.
(1)图论是数学中一门研究图形的理论,其利用数学结构来分析两个事物之间的关系。
(1)In mathematics,Graph Theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
(2)《北京城市总体规划(2016—2035)》中规定:“三山五园是对位于北京西北郊、以清代皇家园林为代表的各历史时期文化遗产的统称。三山指香山、玉泉山和万寿山,五园指静宜园、静明园、颐和园、圆明园和畅春园。”
(2)According to the Master Plan of the City of Beijing(2016-2035), the"three great mountains and five marvelous gardens"is a collective reference of the cultural heritages located in the northwest suburbs of Beijing,which are represented by various imperial gardens built in the Qing Dynasty."Three great mountains"refer to the Fragrant Hills,the Jade Spring Hill,and the Longevity Hill;"the five marvelous gardens"refer to the Jingyi Garden, the Jingming Palace, the Summer Palace, the Yuanmingyuan Park,and the Garden of Everlasting Spring.
(3)具体算法参见参考文献[11]。
(3)See Ref.[11] for more details of the algorithm.
[2]Merriam,G.(1984).Connectivity:a fundamental ecological characteristic of landscape pattern.In J.Brandt,&P.Agger(Eds.),Proceedings of the 1st Seminar of the International Association of Landscape Ecology.Roskilde,Denmark:Roskilde University Center
[3]Uezu,A.,Metzger,J.P.,&Vielliard,J.M.E.(2005).Effects of structural and functional connectivity and patch size on the abundance of seven Atlantic Forest bird species.Biological Conservation,123(4),507-519.doi:10.1.1.461.4659
[4]Sork,V.L.,&Smouse,P.E.(2006).Genetic analysis of landscape connectivity in tree populations.Landscape Ecology,21(6),821-836.doi:10.1007/s10980-005-5415-9
[5]Coulon,A.,Cosson,J.F.,Angibault,J.M.,Cargnelutti,B.,Galan,M.,Morellet,N.,…Hewison,A.J.M.(2004).Landscape connectivity influences gene flow in a roe deer population inhabiting a fragmented landscape:An individual-based approach.Molecular Ecology,13,2841-2850.doi:10.1111/j.1365-294X.2004.02253.x
[6]Urban,D.,&Keitt,T.(2001).Landscape connectivity:AGraph-Theoretic Perspective.Ecology,82(5),1205-1218.doi:10.1890/0012-9658(2001)082[1205:LCAGTP]2.0.CO;2
[7]Xie,S.L.,Lu,F.,Cao,L.,Zhou,W.Q.,&Ouyang,Z.Y.(2016).The Effect of Landscape Patterns on Avian Communities during Summer Months in Beijing’s Urban Parks.Landscape Architecture Frontiers,4(3),10-21.
[8]Shu,Y.,Hu,Y.M.,Guo,D.F.,Shan,K.,Zhu,S.Y.,&Wang,L.D.(2004).The Change of Habitat Suitable for the Red-crowned Crane in Yellow River Delta.Chinese Journal of Zoology,39(3),33-41,121.doi:10.13859/j.cjz.2004.03.009
[9]Liu,X.,Jiao,Y.M.,Wang,M.,&Zhang,K.F.(2018).Evaluation of key nodes and corridors of river and canal network in Hani Rice Terraces based on graph theory.Chinese Journal of Ecology,37(1),287-294.doi:10.13292/j.1000-4890.201801.032
[10]Chen,C.D.,Jia,Z.Y.,Wu,S.J.,Tong,X.X.,Zhou,W.Z.,Chen,R.Y.,&Zhang,C.L.(2017).A bibliometric review of Chinese studies on the application of landscape connectivity.Acta Ecologica Sinica,37(10),3243-3255.doi:10.5846/stxb201602290341
[11]Pascual-Hortal,L.,&Saura,S.(2006).Comparison and development of new graph-based landscape connectivity indices:towards the priorization of habitat patches and corridors for conservation.Landscape Ecology,21(7),959-967.doi:10.1007/s10980-006-0013-z
[12]Wu,J.J.,Li,Y.Z.,Yu,L.J.,Gao,M.,Wu,X.Q.,&Bi,X.L.(2018).Dynamic changes and driving factors of landscape connectivity for natural wetland in Yellow River Delta.Ecology and Environmental Sciences,27(1),71-78.doi:10.16258/j.cnki.1674-5906.2018.01.010
[13]Wang,M.(2017).Evaluation on the Ecology Connectivity Based on the Least Cost Distance Model-Taking the Xishan District as An Example(Master thesis).Kunming University of Science and Technology,Kunming.
[14]Chen,C,D.,Meurk,C.D.,Ignatieva,M.E.,Stewart,H.G.,&Wu,S.J.(2015).Identifying and evaluating functional connectivity for building urban ecological networks.Acta Ecologica Sinica,35(19),6414-6424.
[15]Ou,W.X.,&Yuan,W.J.(2015).Priority of red-crowned crane wintering habitat patches using landscape connectivity in the Yancheng coastal wetland.Resources Science,37(4),823-831.
[16]Chen,T.,Qin,S.N.,&Chen,Y.H.(2017).The Assessment on Woodland Network Based on Functional Connectivity of Bird’s Biological Characteristics:A Case Study in Ningxiang County,Changsha.Sichuan Journal of Zoology,36(5),489-497.doi:10.11984/j.issn.1000-7083.20160312
[17]Chen,J.,Liang,G.F.,&Ding,S.Y.(2012).Landscape connectivity analysis for the forest landscape restoration:a case study of Gongyi City.Acta Ecologica Sinica,32(12),3773-3781.doi:10.5846/stxb201108171210
[18]Government of Haidian District,Beijing.(2016).The land use planning of Beijing(2006-2020).Retrieved from http://www.bjhd.gov.cn/xxgk/auto4558_51854/auto4558_57869/201810/P020170104436568765730.pdf
[19]Bureau of Landscaping of Beijing.(2017).Urban Greening Resources of Beijing in 2016.Retrieved from http://www.bjyl.gov.cn/zwgk/tjxx/201705/t20170517_192779.html
[20]General Administration of Quality Supervision,Inspection and Quarantine of the People’s Republic of China,Standardization Administration of the People’s Republic of China.(2007).Current land use classification(GB/T 21010-2007).
[21]Government of Beijing City.(2009).The land use planning of Beijing(2006-2020).Retrieved from http://www.bjyl.gov.cn/zwgk/tjxx/201804/P020180425535648094242.pdf
[22]Government of Beijing City.(2004).The general planning of Beijing City(2004-2020).Retrieved from https://wenku.baidu.com/view/baf1bbda76eeaeaad1f33010.html
[23]Yu,K.J.(1999).Landscape Ecological Security Patterns in Biological Conservation.Acta Ecologica Sinica,19(1),10-17.
[24]Zhang,X.F.,Wang,Y.L.,&Li,Z.G.(2005).Landscape pattern optimization based upon the concept of landscape functions network:a case study in Taiwan,China.Acta Ecologica Sinica,25(7),1707-1713.
[25]Wu,C.G.,Zhou,Z.X.,Wang,P.C.,Xiao,W.F.,Teng,M.J.,&Peng,L.(2009).Evaluation of landscape connectivity based on least-cost model.Chinese Journal of Applied Ecology,20(8),2042-2048.doi:10.13287/j.1001-9332.2009.0267
[26]Bentrup,G.(2008).Conservation buffers-Design guidelines for buffers,corridors,and greenways.(General technical report SRS-109).Asheville:USDA Forest Service Southern Research Station.Retrieved from https://www.srs.fs.usda.gov/pubs/gtr/gtr_srs109.pdf
[27]Lu,C.H.(2006).Roles of animals in seed dispersal of Pinus:Areview.Chinese Journal of Ecology,25(5),557-562.
[28]Lu,C.H.(2003).Seed Dispersal by Animals(pp.138-139).Harbin:Northeast Forestry University Press.
[29]Xing,J.J.(2018).Seed Dispersal of Quercus varibilis Trees under the Mediation of Animals:From Seed to Seedling(Master thesis).Wuhan:Central China Normal University.
[30]Zhang,Y.F.,Wang,W.R.,Li,W.,Miao,X.D.,&Lu,J.Q.(2016).Effects of Thinning on Seed Dispersal by Rodents in Secondary Forest.Journal of Zhengzhou University(Natural Science Edition),48(1),67-72.
[31]Breitbac,N.,Laube,I.,Steffan-Dewenterl,I.,&B?hning-Gaese,K.(2010).Bird diversity and seed dispersal along a human landuse gradient:high seed removal in structurally simple farmland.Oecologia,162(4),965-976.doi:10.1007/s00442-009-1547-y
[32]Huang,Y.(2015).The Methodology of Bird Habitats’Making and Planning at Beijing Urban Green Spaces(Doctoral dissertation).Tsinghua University,Beijing.
[33]Chen,Z.Q.,Fu,J.P.,Zhao,X.R.,&Ding,C.Q.(2010).The Construction of Birds in Yuanmingyuan Relic Park,Beijing.Chinese Journal of Zoology,45(4),21-30.doi:10.13859/j.cjz.2010.04.011
[34]Guo,T.Y.,Yang,J.W.,Qu.Y.Y.,&Chen,W.(2010).Investigations on Diversity of Birds at the Black Bamboo Park in Beijing.Sichuan Journal of Zoology,29(6),975-980.
[35]Wang,L.J.,Ji,J.W.,&Li,T.Y.(2012).A field survey on bird diversity and seasonal changes at the Beihai Park in Beijing.Journal of Hubei University(Natural Science),34(3),298-303.doi:10.3969/j.issn.1000-2375.2012.03.012
[36]Chen,Y.,Qiao,F.,&Jiang,L.(2016).Effects of Land Use Pattern Change on Regional Scale Habitat Quality Based on InVESTModel-A Case Study in Beijing.Acta Scientiarum Naturalium Universitatis Pekinensis,52(3),553-562.doi:10.13209/j.0479-8023.2016.057
[37]Chu,L.,Zhang,X.R.,Wang,T.W.,Li,Z.X.,&Cai,C.F.(2018).Spatial-temporal evolution and prediction of urban landscape pattern and habitat quality based on CA-Markov and InVESTmodel.Chinese Journal of Applied Ecology,29(12),4106-4118.doi:10.13287/j.1001-9332.201812.013
[38]Corlett,R.T.(2009).Seed dispersal distances and plant migration potential in tropical East Asia.Biotropica,41(5),592-598.doi:10.1111/j.1744-7429.2009.00503.x
[39]Qi,K,.&Fan,Z.Q.(2016).Evaluation method for landscape connectivity based on graph theory:a case study of natural forests in Minqing County,Fujian Province.Acta Ecologica Sinica,36(23),7580-7593.doi:10.5846/stxb201507301599
[40]Teng,M.J.(2011).Planning Ecological Security Patterns in a Rapidly Urbanizing Context:A Case Study in Wuhan,China(Doctoral dissertation).Huazhong Agricultural University,Wuhan.
(1)图论是数学中一门研究图形的理论,其利用数学结构来分析两个事物之间的关系。
(1)In mathematics,Graph Theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
(2)《北京城市总体规划(2016—2035)》中规定:“三山五园是对位于北京西北郊、以清代皇家园林为代表的各历史时期文化遗产的统称。三山指香山、玉泉山和万寿山,五园指静宜园、静明园、颐和园、圆明园和畅春园。”
(2)According to the Master Plan of the City of Beijing(2016-2035), the"three great mountains and five marvelous gardens"is a collective reference of the cultural heritages located in the northwest suburbs of Beijing,which are represented by various imperial gardens built in the Qing Dynasty."Three great mountains"refer to the Fragrant Hills,the Jade Spring Hill,and the Longevity Hill;"the five marvelous gardens"refer to the Jingyi Garden, the Jingming Palace, the Summer Palace, the Yuanmingyuan Park,and the Garden of Everlasting Spring.
(3)具体算法参见参考文献[11]。
(3)See Ref.[11] for more details of the algorithm.