地理科学进展  2016 , 35 (5): 589-599 https://doi.org/10.18306/dlkxjz.2016.05.006

研究综述

两步移动搜寻法及其扩展形式研究进展

陶卓霖12, 程杨3**

1. 北京大学城市与环境学院,北京 100871
2. 北京大学城市规划与设计学院,广东 深圳 518055
3. 北京师范大学地理学与遥感科学学院,北京 100875

Research progress of the two-step floating catchment area method and extensions

TAO Zhuolin12, CHENG Yang3*

1. College of Urban and Environmental Sciences, Peking University, Beijing 100871, China
2. School of Urban Planning and Design, Peking University, Shenzhen 518055, Guangdong, China
3. School of Geography, Beijing Normal University, Beijing 100875, China

通讯作者:  通讯作者:程杨(1982-),女,四川自贡人,副教授,主要从事健康地理学研究,E-mail: chengyang@bnu.edu.cn

接受日期:  2016-02-27

网络出版日期:  2016-05-27

版权声明:  2016 地理科学进展 《地理科学进展》杂志 版权所有

基金资助:  国家自然科学基金项目(41301164)National Natural Science Foundation of China, No.41301164

作者简介:

作者简介:陶卓霖(1990-),男,江西万载人,博士研究生,研究方向为城市与区域规划,E-mail: taozhuolin@pku.edu.cn

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摘要

两步移动搜寻法是公共服务设施空间可达性研究中的重要方法,在国内外公共服务设施布局研究中得到了广泛应用,且发展出了众多扩展形式。但国内研究中对两步移动搜寻法尤其是其扩展形式的应用还较为有限。本文对两步移动搜寻法的主要扩展形式进行系统梳理和总结,将国内外研究中提出的两步移动搜寻法扩展形式归纳为基于引入距离衰减函数的扩展、对搜寻半径的扩展、针对需求或供给竞争的扩展以及基于出行方式的扩展4类,并分析了各种扩展形式的优缺点、适用情景以及未来可能改进方向。旨在为相关研究的方法选择提供参考,促进两步移动搜寻法及其扩展形式在国内相关领域的应用和发展。

关键词: 两步移动搜寻法 ; 扩展形式 ; 距离衰减函数 ; 搜寻半径 ; 三步移动搜寻法 ; 研究进展

Abstract

Two-step floating catchment area (2SFCA) method is an important method of research on spatial accessibility to public services, which has been widely applied in studies on the spatial layout of public service facilities. Various extensions of 2SFCA have been developed. However, the application of the 2SFCA method and especially its extensions is still very limited in China. Thus, this study systematically summarizes the major extensions of the 2SFCA method. Such extensions found in existing literature can be classified into four categories. The first category focuses on the distance-decay function, replacing the dichotomous distance-decay form of the original 2SFCA by a multilevel discrete form as in the Enhanced 2SFCA, or continuous forms such as in the gravity-style, Gaussian-style, and Kernel-density-style distance-decay functions. The second category deals with the delimitation of catchment areas. The original 2SFCA form adopts a buffer-ring (BR) method delineating the catchment areas as concentric circles with certain radii of physical distance or travel time. A number of extensions have improved the BR method, including the Variable 2SFCA, the Dynamic 2SFCA, and the Multi Catchment Sizes 2SFCA. Moreover, a novel nearest-neighbor (NN) method for delineating the catchment areas by identifying a finite number of nearest facilities for each demand node has been proposed. The third category strives to improve the accuracy of 2SFCA by accounting for the competition among demand nodes or among supply nodes. The initial extension of this category is the Three-step Floating Catchment Area (3SFCA) method, following which other extensions such as the Modified 2SFCA and the Huff 2SFCA are proposed to make further improvements. The fourth category extends the travel means of the demand side, including the Multi-mode 2SFCA taking into account various potential transportation modes, and the Commuter-based 2SFCA integrating service visits and commuting behavior. The advantages and disadvantages, scenarios appropriate for their application, and potential improvements in the future of these extensions are also discussed. This study can contribute to the choice of method in relevant studies and promote the implementation and development of the 2SFCA method and extensions in relevant research fields in China.

Keywords: two-step floating catchment area method ; extension ; distance-decay function ; catchment area ; three-step floating catchment area method ; research progress

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陶卓霖, 程杨. 两步移动搜寻法及其扩展形式研究进展[J]. , 2016, 35(5): 589-599 https://doi.org/10.18306/dlkxjz.2016.05.006

TAO Zhuolin, CHENG Yang. Research progress of the two-step floating catchment area method and extensions[J]. 地理科学进展, 2016, 35(5): 589-599 https://doi.org/10.18306/dlkxjz.2016.05.006

1 引言

公共服务设施对于满足人们日益增长的物质和文化生活需要及全面提升生活品质起着至关重要的作用。因此,公共服务设施的公平配置就成为其规划和布局的重要目标(Wang et al, 2013; Dadashpoor et al, 2016),尤其是在基本公共服务均等化的政策背景下,这一目标显得更为重要。空间可达性评价方法能够识别出公共服务的稀缺区域,是衡量公共服务设施布局空间公平性的有效途径(宋正娜等, 2010; 陶卓霖等, 2015),因此也受到国内外研究的广泛关注,并开发出了丰富的方法体系(宋正娜等, 2010; Wang, 2012)。其中,两步移动搜寻法(Two-step floating catchment area method, 2SFCA)得到了广泛关注和应用,并且在后续研究中各种扩展形式层出不穷,形成了一个庞大的两步移动搜寻法模型族。在国内,近几年来两步移动搜寻法也受到越来越多的关注,在医疗(刘钊等, 2007; 胡瑞山等, 2012; 邓丽等, 2015; 付加森等, 2015)、教育(任若菡等, 2014)、养老(陶卓霖等, 2014; 赵东霞等, 2014)、绿地(魏冶等, 2014)、旅游景点(张鹏飞等, 2015)等公共设施可达性以及就业可达性(王绮等, 2015)等领域均有应用,并且对两步移动搜寻法的部分改进形式也有应用(任若菡等, 2014; 陶卓霖等, 2014; 魏冶等, 2014; 邓丽等, 2015; 张鹏飞等, 2015)。但整体而言,国内研究中对两步移动搜寻法,尤其是其扩展形式的应用还较为有限。因此,本文通过对两步移动搜寻法的主要扩展形式进行系统梳理和总结,以期为相关研究的方法选择提供参考,促进两步移动搜寻法在国内相关领域的应用和发展。

2 2SFCA的原始形式及与其他方法的比较

2SFCA最早是由Radke等(2000)提出,由Luo等(2003)进一步改进并命名为两步移动搜寻法。2SFCA的基本思想为:①对每个供给点j,搜索所有在j搜寻半径( d0)范围内的需求点(k),计算供需比 Rj;②对每个需求点i,搜索所有在i搜寻半径( d0)范围内的供给点(j),将所有的供需比 Rj加总得到i点的可达性 AiF(Luo et al, 2003):

式中:i表示需求点;j表示供给点; AiF表示根据2SFCA计算得到的需求点i的可达性; dij是需求点i和供给点j间的距离; Rj是供给点j的设施规模与搜寻半径( d0)内所服务的人口的比例; Sj表示供给点j的供给规模; Dk表示需求点k的需求规模。

另一个较常用的可达性评价方法为重力模型法,也称为潜能模型(宋正娜等, 2009)。实际上,2SFCA和重力模型法基于同一个理论框架(Luo et al, 2003),都综合考虑了设施的供给规模、需求规模和供需之间的距离关系对可达性的影响,两者的不同在于对距离因素的处理:重力模型法采用了连续型距离衰减函数,从而考虑了设施服务能力随距离衰减的特征,但并未对设施的有效搜寻半径进行限制;而2SFCA法采用二分法处理距离衰减,即在搜寻半径阈值范围内的可达性相同,而在搜寻半径范围之外则完全不可达。

此外,还有其他几种较为常用的可达性评价方法:最近距离法只考虑距离因素,未对供需点规模因素进行考虑;Huff模型考虑了设施规模和距离因素,但未考虑需求点规模;核密度法实际上与重力模型法同属一个框架,采用的距离为欧氏距离,无法考虑实际交通网络的影响,也没有考虑需求点规模(陶卓霖等, 2014)。

综上可知,在众多空间可达性评价方法中,2SFCA和重力模型法应用最为广泛,考虑的因素最为全面,模型的理论基础相似,但2SFCA得益于两步移动搜寻的思想,易于理解,可操作性更强,因此得到了更多的关注和发展,为各种可能的扩展形式提供了可行的基本框架(McGrail et al, 2009)。

3 主要扩展形式

3.1 基于引入距离衰减函数的扩展

2SFCA原始形式中对距离衰减的处理为二分法。一部分扩展形式针对距离衰减函数进行扩展,本质上是在2SFCA的搜寻半径之内再加入一个额外的距离衰减函数,具体函数形式因扩展形式而不同。

针对这类扩展,Wang(2012)提出了一个2SFCA的一般形式(Generalized 2SFCA),在模型中加入一项距离衰减函数 f(dij),用于概括和表示不同扩展中的距离衰减函数形式:

Ai=j=1nSjf(dij)k=1mDkf(dkj)(2)

式中: Ai是需求点i的可达性得分,实际含义为需求点i的平均每个需求者可达的设施资源; f(dij)是一般化的距离衰减函数;其他变量含义与式(1)一致。 f(dij)可进一步表示为:

f(dij)=g(dij),dijd00,dij>d0(3)

式中:f是一般化的距离衰减函数; dijij的距离; d0是搜寻半径,即设施的有效服务半径; g(dij)表示在搜寻半径 d0范围内的距离衰减函数。在这一框架下,可将2SFCA的各个扩展形式对距离衰减函数的改进概括为对函数 g(dij)的替代。2SFCA原始形式中将 g(dij)处理为恒等于一个常数,而在扩展形式中,函数 g(dij)可采用按距离区分权重的分段衰减形式、重力模型的距离衰减函数形式(如幂函数或指数函数等)、核密度形式或高斯形式等。下面介绍主要的几种距离衰减函数扩展形式(图1)。

(1) 增强型2SFCA

为解决2SFCA原始形式中对搜寻半径内可达性的差异未予以区分的不足,Luo等(2009)进一步提出了增强型2SFCA (Enhanced 2SFCA, E2SFCA),将搜寻半径范围内的距离衰减函数 g(dij)进行分段处理,距离越近的分段内权重越大,可达性越好。函数 g(dij)可表示为:

g(dij)=W1,dijD1,Wr,dijDr(4)

式中:搜寻半径内的范围按距离分为 r段; Dr表示第 r分段; Wr表示第 r分段内的可达性权重,根据距离衰减原理,通常距离越近的分段内权重越大。例如,在Luo等(2009)的研究中,具体将30 min的搜寻半径划分为3段:0~10、10~20、20~30 min,各段的权重根据高斯函数确定(Kwan, 1998);实际结果发现E2SFCA的评价结果更符合直觉判断,且对公共服务资源匮乏地区的识别更为精确。E2SFCA方法在国内也已有一定应用,如张鹏飞等(2015)采用其对武汉市城市旅游景点可达性进行了评价。

E2SFCA的不足之处为,对距离分段的划分以及权重的确定仍存在一定主观和理想化的成分。距离分段的数量和划分标准由研究者主观决定,而权重则是根据在假设搜寻半径范围内的设施和需求点各自服从正态分布的理想条件下的高斯函数来确定,与实际情况难免会存在偏差。

(2) 重力型2SFCA

重力型2SFCA(Gravity 2SFCA, G2SFCA)采用重力模型的距离衰减函数作为2SFCA搜寻半径内的距离衰减函数 g(dij)(陶卓霖等, 2014)。重力模型是空间相互作用领域发展最为成熟的模型,对其距离衰减函数的探讨也较为丰富,较为常用的函数形式有幂函数型、指数型、对数型等(王成金, 2009; 刘瑜等, 2014)。高斯型函数形式虽也有一些研究涉及(刘瑜等, 2014),但由于2SFCA扩展形式中有一类专门命名为高斯型2SFCA,因此这里不再归类为重力型2SFCA,而是单独作为一类进行介绍。以最为常见的幂函数形式为例,扩展后的重力型2SFCA搜寻半径内的距离衰减函数 g(dij)可表示为:

g(dij)=dij-β,dijd0(5)

式中: β为距离衰减参数;其他变量与式(2)相同。例如,Wang等(2013)、陶卓霖等(2014)以及Tao等(2014)在研究中均采用重力型2SFCA度量医疗设施或养老设施的空间可达性,并对距离衰减参数 β的取值进行了敏感性分析。

重力型2SFCA将发展较为成熟的重力模型中的距离衰减函数引入到2SFCA中,从而将传统2SFCA和E2SFCA的离散型距离衰减函数改进为连续型函数(图1c)。这一改进具有以下优点:一是刻画了传统2SFCA搜寻半径内的可达性差异,从而增强了可达性评价的准确性;二是不需要像E2SFCA那样对距离进行主观性的分段,且距离衰减函数的数学表达形式更为简洁,有效提升了模型形式的可读性;三是有利于重力模型的应用和发展中在函数形式和参数设定方面积累的经验。

(3) 核密度型2SFCA

核密度型2SFCA(Kernel Density 2SFCA,KD2SFCA)由Dai等(2011) 提出,在2SFCA搜寻半径内加入核密度函数形式的距离衰减函数 g(dij),可表示为:

g(dij)=341-dijd02,dijd0(6)

式中:核密度函数的带宽参数为搜寻半径 d0, d0取值越小则距离衰减效应越强,即可达性随距离增加而减弱的趋势越强;其他变量含义同式(2)。

核密度型2SFCA与重力型2SFCA类似,都具有连续型距离衰减函数,但两者的距离衰减函数形式不同。核密度型距离衰减函数为凹函数,当距离较小时,可达性随距离的衰减速度较慢;距离越大,则衰减越快(图1e)。本文所用的幂函数形式的重力型距离衰减函数为凸函数,当距离较小时,可达性衰减较快;距离越大,则衰减越慢(图1c)。

图1   主要距离衰减函数示意图(资料来源:作者根据Wang(2012)自绘)

Fig.1   Major forms of distance-decay function (Data source: Wang (2012))

(4) 高斯型2SFCA

高斯型2SFCA(Gaussian 2SFCA, Ga2SFCA)由Dai(2010, 2011)提出,采用高斯函数作为2SFCA搜寻半径内的距离衰减函数 g(dij),可表示为:

g(dij)=e-12×dijd02-e-121-e-12,dijd0(7)

式中:各变量含义与式(2)相同。

Dai将高斯型2SFCA运用到了医疗设施(Dai, 2010)和城市绿地(Dai, 2011)的可达性评价研究中。在国内,已有学者利用高斯型2SFCA评价沈阳市城市绿地可达性(魏冶等, 2014)和就业可达性(王绮等, 2015)。

高斯型2SFCA的距离衰减函数与重力型2SFCA和核密度型2SFCA均不相同(图1d),后两种距离衰减函数中可达性衰减速率随距离的增加持续增大或减小,而高斯型距离衰减函数中的可达性衰减速率随距离的增加先加快后减慢。

(5) 对距离衰减函数选取的讨论

上述几类2SFCA扩展形式针对距离衰减函数进行改进,将2SFCA原始形式中搜寻半径内可达性无差异的二分法改进为不同类型的分段型或连续型距离衰减函数。不同扩展形式之间的差异主要在于距离衰减函数的衰减趋势不同,如E2SFCA的距离衰减函数为分段跳跃型衰减;幂函数形式的重力型2SFCA和核密度型2SFCA分别为凸型和凹型的连续衰减;而高斯型2SFCA为“S”型衰减,可达性随距离衰减速度在较近和较远阶段较慢,而在中间部分较快(Wang, 2012)。

在实际应用中,距离衰减函数形式的选取应根据案例的设施实际使用行为特点而定。最理想的状况是根据设施使用行为的实际调查确定距离衰减函数形式及相关参数值,但这往往需要耗费大量的人力和资金投入,且特定案例区域的调查结果不一定能扩展到其他区域应用,因此可操作性不强。值得注意的是,近年快速发展的手机数据、出租车轨迹数据和社交网络数据等大数据研究能对人类出行行为的距离衰减特征进行识别,从而为距离衰减函数形式的科学选取以及相应参数的标定提供有效支持(刘瑜等, 2014)。例如,齐兰兰等(2014)利用出租车轨迹数据对广州市医疗设施的出行特征进行了检验,发现医疗服务的使用行为确实符合距离衰减规律:1.5 km内人数最多,超过1.5 km后随距离增加出行人数逐渐减少。需指出的是,设施使用行为不仅受到距离衰减效应的影响,还受到设施的服务质量和收费水平、交通方式的差异以及设施使用者出行能力和经济能力等多方面因素的综合影响,因此在根据相关数据确定参数值时,应充分考虑这些因素对设施使用行为的影响。当缺乏距离衰减函数及参数值设定的充足依据时,应通过多情景分析提供更综合的结果参考,对关键参数的设定应进行敏感性分析(周慧等, 2015)。

3.2 对搜寻半径的扩展

除缺乏对搜寻半径内可达性差异的考虑外,2SFCA的另一个不足是采用单一的搜寻半径,对于所有设施和人群的搜寻半径均相同(McGrail et al, 2009)。一些研究尝试提出针对这一不足的扩展形式(Luo et al, 2012; McGrail, 2012; McGrail et al, 2014; 陶卓霖等, 2014)。

(1) 可变半径2SFCA

Luo等(2012)最早提出了一种搜寻半径可变的2SFCA扩展形式,并命名为可变半径2SFCA(Variable 2SFCA, V2SFCA)。具体做法为:在第一步搜寻,即以每个设施为中心进行搜寻时,首先设定一个初始的搜寻半径 d0,若设施在当前搜寻半径内覆盖的需求量未达到最小服务量阈值(该研究中定为50万人),则逐步增加搜寻半径直到满足这一条件,将最终得到的搜寻半径作为第一步搜寻的设施供给搜寻半径 df;而第二步搜寻,即以每一个需求点为中心进行搜寻时,与第一步类似,首先设定初始搜寻半径 t0,逐步增加搜寻半径直到需求点在当前搜寻半径内所能获取的设施资源达到给定的最小阈值(该研究中定为每3500人1名医生),将最终的搜寻半径作为第二步搜寻的需求点搜寻半径 tf

V2SFCA能够较为有效地解决采用单一搜寻半径可能遇到的两类问题:一是部分区域需求分布较为分散时,采用单一搜寻半径可能导致设施无法形成有效供给规模;二是供给分布较为分散时,采用单一搜寻半径可能导致需求点无法获取满足基本需求的公共服务资源,而在实际情况中,当设施数量很少时,需求者倾向于克服更远的距离以获取服务。但对于设施的最小服务量阈值和需求点获取的设施资源最小阈值的确定具有较大主观性,缺乏充足依据。

(2) 动态半径2SFCA

McGrail等(2014)提出了根据区域人口密度确定不同搜寻半径的扩展形式,即动态半径2SFCA(Dynamic 2SFCA, D2SFCA)。McGrail等(2014)首先根据人口密度将澳大利亚全国范围划分为主要城市(RA-1)、内部地区(RA-2)、外围地区(RA-3)、偏远地区(RA-4)和高度偏远地区(RA-5)5种类型,并根据既有调查数据和经验判断将5类地区的基本医疗服务搜寻半径依次设为30、45、70、120和200 min,并进行实证检验,发现根据人口密度的减小,逐步增大搜寻半径的方法是可行的,但上述5级搜寻半径的划分方法还较为粗略,所得结果中存在少量不合理的情况。

因此,McGrail等(2014)进一步改进了动态搜寻半径的划分方法。具体方法为,对任意相邻2类地区之间的界限进行平滑处理(例如,属于RA-4,但实际上更为邻近RA-3的需求点,设施选择行为可能与RA-3更为接近),从而进一步在5类地区的基础上划分出3个子类,划分的3个原则如下:

第一,如果需求点周边的大部分(>50%)服务设施与该需求点位于同一类型地区或位于更高级别地区,则该需求点的搜寻半径保持不变。例如,假设需求点A位于RA-4且满足本条件,则需求点A的搜寻半径仍设置为RA-4的值,即120 min。

第二,如果需求点周边的少部分(25%~50%)设施与该需求点位于同一类型或更高级别类型地区,则该需求点的搜寻半径需要进行修正(该类型搜寻半径减去其与更低一级搜寻半径之差的1/3)。例如,假设需求点B位于RA-4且满足本条件,则需求点B的搜寻半径修正为:120(RA-4半径)-50(RA-4与RA-3半径之差)×1/3=103 min。

第三,如果需求点周边的极少数(<25%)设施该需求点位于同一类型或更高级别类型地区,则该需求点的搜寻半径也需修正(该类型搜寻半径减去其与更低一级搜寻半径之差的2/3)。例如,假设需求点C位于RA-4且满足本条件,则需求点C的搜寻半径修正为:120(RA-4半径)-50(RA-4与RA-3半径之差)×2/3=87 min。

D2SFCA在经过上述修正后(这里将修正后的方法称为Modified D2SFCA, MD2SFCA)得到的可达性评价结果更为恰当,但MD2SFCA的操作过程过于复杂,在实际中推广应用难度较大,相比之下D2SFCA的可操作性更强。总之,D2SFCA和MD2SFCA所提出的动态半径改进具有较强的实际意义,尤其适用于城市与农村地区混合的案例区域研究。

(3) 多级半径2SFCA

不同于McGrail等(2014)从需求角度根据人口密度划分动态的搜寻半径,陶卓霖等(2014)从供给角度出发,根据设施规模的不同,设定多级搜寻半径,这项扩展形式可称为多级半径2SFCA(Multi Catchment Sizes 2SFCA, MC2SFCA)。该研究在养老设施的案例中指出,规模不同的设施可能具有不同搜寻半径,通常规模越大,搜寻半径也会更大,从而将养老设施划分为大型(多于300个养老床位)、中型(100~300个床位)和小型(100个床位以下),参照已有研究对老年人口选择入住养老设施时的可接受距离,将搜寻半径依次设为2.0、1.0、0.5 h。研究结果发现采用多级半径后的MC2SFCA评价结果比采用单一半径的2SFCA更为合理。

事实上,除了规模因素外,公共服务设施的权属性质等属性也可能对其搜寻半径产生影响。以北京市养老设施为例,市属的公办养老设施以及规模较大的民办养老设施,往往面向全市范围接受老人入住,因此搜寻半径较大;而区属、乡镇或街道属的公办养老设施,服务范围可能限于各自管辖范围;规模较小的民办养老设施的市场范围也可能仅限于本地。

(4) 最近设施型2SFCA

Jamtsho等(2015)指出,2SFCA及其现有改进形式中,对设施服务范围的刻画都采用缓冲区—环形的方法(Buffer-Ring Method),隐含假设是某一需求点会从其搜寻半径内的所有设施中进行选择。该研究认为这一假设在现实中往往难以满足,因此提出了任意需求点仅从搜寻半径内最近的一定数量(备选设施数量)设施中进行选择的设施服务范围方法(Nearest-Neighbor Method),从而构建了最近设施型2SFCA(Nearest-Neighbor 2SFCA, NN2SFCA)这一扩展形式。

在实际应用中,需求点备选设施数量的确定应根据具体案例中的需求点与设施分布情况及其之间的交通网络而确定,既可以对全部需求点设定相同的备选设施数量,也可类似于服务半径那样设定为可变的。例如,Jamtsho等(2015)在研究不丹的医疗设施时,分析发现在一些区域,离需求点第三近的设施距离较远,而将备选设施数量设为1又不精确,因此将备选数量设为2。

(5) 对合理设定搜寻半径的讨论

这类扩展形式从公共服务设施搜寻半径的角度对模型结构提出了重要改进,为公共服务可达性的科学评价作出了有益尝试。但整体上对搜寻半径的类型划分及具体数值的确定仍存在一定主观性,需要更多研究辅助选取参数。事实上,公共服务设施搜寻半径可从2个方面来确定:一是根据设施使用者实际愿意承受的出行距离;二是根据相关政策和规划的目标。国外已有很多研究关注了医疗设施的服务范围,如Allan(2014)以及Mazumdar等(2014)对相关研究进行了总结,但目前国内在这方面的研究还很不足。

最后,在上述已有搜寻半径的扩展形式之外,本文再提出一种可能的扩展形式:即设施服务范围的界定既不按照传统的缓冲区—环形方法,也不按照NN2SFCA中的Nearest-Neighbor方法,而是按照行政范围来划分(Administrative Boundary Method)。在中国现行制度安排下,公共服务设施的配置通常是以特定行政单元为主体,对设施的服务范围也通常根据行政范围加以限制。因此采用行政范围划分的方法可能更适合中国的实际情况。需要指出的是,公共服务设施的搜寻半径受到多方面因素的共同作用,设施所承担的职能差异及其产生的设施层级性、设施供需分布及其空间相互作用方式,以及消费者获取服务的行为特点等因素都会对设施的搜寻半径产生影响,需要后续研究进行更深入地探讨。

3.3 针对需求或供给竞争的扩展

(1) 三步移动搜寻法(3SFCA)

Wan等(2012)、Bell等(2013)先后提出了2SFCA的扩展形式,且都命名为3SFCA(Three-step Floating Catchment Area),但两者的内涵并不相同。Wan等(2012)的3SFCA所增加的第三步搜寻考虑当一个需求点的搜寻半径内存在多个设施时,设施之间存在的竞争效应。该模型认为,在上述情况下,当需求点的一部分需求已经被一个设施满足,再从其他设施竞争资源时应将这部分已经满足的需求扣除,否则会高估规模较大的需求点的可达性,并认为在2SFCA基础上增加对设施间竞争效应的考虑能够提升模型的合理性。而Bell等(2013)提出的3SFCA对模型增加的第三步搜寻的含义是:将E2SFCA的评价得分合并为更大的人口单元,实质性改进较小。因此,后文中3SFCA专指Wan等(2012)提出的3SFCA。

3SFCA的具体实现是在传统的两步移动搜寻过程之前,增加一步包括全部需求点和设施在内的搜寻,计算需求点 i与设施 j之间的选择权重(Selection Weight),用于衡量位于同一需求点搜寻半径之内的多个设施之间的竞争效应:

式中: Gij表示需求点 i与设施 j之间的选择权重; TijTik分别表示需求点 i选择设施 j和设施 k的权重,权重根据高斯函数分配。后续计算中,以E2SFCA(式(4))为基础,在权重 Wr的基础上再乘以选择权重 Gij。事实上,3SFCA也可在其他对距离衰减函数进行扩展的模型上进行选择权重的改进,例如重力型2SFCA、高斯型2SFCA、核密度型2SFCA等。

在Wan等(2012)提出3SFCA之后,其他一些研究在其基础之上提出进一步改进。Delamater(2013)通过3SFCA与E2SFCA的系统比较,认为Wan等(2012)提出的3SFCA高估了设施之间的竞争效应,并提出改进形式(Modified 2SFCA)。

(2) 改进型2SFCA

Delamater(2013)指出,在2SFCA及其现有改进形式中,均隐含着一个假设,即所有的设施供给点在空间上都得到最优配置以满足系统内的需求,从而表现为根据现有的2SFCA模型族的评价结果,每个需求点的可达性得分乘以其需求规模并加总后恒等于设施总规模,并意味着所有的设施资源都得到了充分利用。而这一假设在现实世界中很难成立。因此,Delamater(2013)提出了改进型2SFCA(Modified 2SFCA, M2SFCA)(注:改进型2SFCA的命名是为了与提出该改进的原文献保持一致,但该命名方式并不能准确反映这项改进形式的特点。后文中优化型2SFCA的命名方式也与此类似。)这一重要扩展形式,允许设施的空间配置存在次优情况,即存在部分设施资源无法分配到需求点从而无法得到有效利用,前面提到的可达性得分的需求规模加权总和相较于总供给规模会存在一定损耗。该问题可归纳为:2SFCA及其现有改进形式虽然较好地度量了可达性(Accessibility)这一概念,但对设施资源的可用性(Availability)却缺乏考虑,而M2SFCA正是在可达性的基础上实现了对可用性的度量。

虽然M2SFCA放宽了2SFCA及其现有改进形式中的一项重要假设条件,使得模型更加符合现实条件,但其模型形式却较为简单:

Ai=j=1nSjf(dij)f(dij)k=1mDkf(dkj)(9)

式中:各项变量含义均与式(2)相同;M2SFCA与Wang(2012)提出的2SFCA一般化框架(式(2))的差异在于在分子处多乘以一次距离衰减函数 f(dij)。额外增加的这项 f(dij)反映了设施所处区位的可达性状况,正是该指标影响了设施的资源是否能得到充分利用。还应注意到,只有在一种完全理想条件下,系统内全部设施资源都能够得到充分利用,即达到完全最优的系统状态。这个理想条件为,需求点与设施点之间不存在空间分离,不仅要求需求点和设施点的相互重叠,还要求每个需求点和设施点所代表的需求和资源都集中在一个点上。此外,Delamater(2013)提出的M2SFCA对距离衰减函数的处理是采用E2SFCA的形式,事实上也可采用其他形式替换。

(3) 胡弗型2SFCA

Luo(2014)指出,人们选择服务设施时综合考虑出行成本和设施点服务能力2个方面的因素,而3SFCA中扩展的选择权重 Gij中,未考虑设施供给方面的因素对设施选择行为的影响。因此有必要对3SFCA的选择权重变量进行修正,以综合考虑出行成本和设施点服务能力2个方面因素对出行选择的影响。Luo(2014)引入经典的胡弗模型(Huff model)来刻画选择权重变量,从而提出了胡弗型2SFCA(Huff 2SFCA, H2SFCA)这一扩展形式:

HGij=Sjdij-βSkdik-β(10)

式中: HGij表示采用Huff模型修正的选择权重变量;其他变量含义与式(2)相同。值得注意的是,Luo(2014)构建的模型中采用了较常用的幂函数作为选择权重变量中的距离衰减函数,实际应用中可根据需要和实际情况采用不同的距离衰减函数形式。

(4) 优化型2SFCA

不同于传统2SFCA中通过以设施为中心搜寻在半径内的需求点,并将搜寻半径内的需求点的总需求作为该设施的潜在使用者,Ngui等(2011)提出了优化型2SFCA(Optimized 2SFCA, O2SFCA),采用各设施在前一年的实际使用者数量(在该案例中为医疗设施,使用者为就医人数)作为设施的潜在使用者数量,从而改进了对同一设施资源可能面临来自多个需求点的竞争,是对传统2SFCA的一个有益补充。但优化型2SFCA需要较好的数据基础,数据的可获取性是该方法在实际应用中推广所面临的一个问题。

3.4 基于出行方式的扩展

(1) 多交通模式2SFCA

Mao等(2013)考虑了获取公共服务时可能采取不同交通模式的情况,提出了多交通模式2SFCA(Multi-mode 2SFCA, MM2SFCA),采用多交通模式之间的加权平均交通时间,对传统2SFCA中单一交通模式的交通时间进行了修正。通过与单一交通模式2SFCA的实证比较研究发现,多交通模式2SFCA更能够反映需求人群在交通能力方面的异质性。更重要的是,多交通模式2SFCA在实际应用中的可操作性较强,尤其是在交通方式较为丰富、公共交通系统较为发达的城市区域更加具有应用前景。

(2) 基于通勤的2SFCA

Fransen等(2015)提出了基于通勤的2SFCA(Commuter-based 2SFCA, CB2SFCA),以考虑通勤行为对公共服务可达性的影响。在CB2SFCA中,需求数量不再是传统2SFCA中那样固定不变,而是根据通勤行为而有所变动,在一天之中需求个体的位置是可能变化的。CB2SFCA的第一步搜寻是以设施为中心进行:

Rk=Sknij(11)

式中: Rk表示设施 k的供需比; Sk表示设施 k的资源规模; tijtiktkj表示下标中相应的前一个地点到后一个地点的交通时间; tf表示设施的服务范围阈值,即搜寻半径; td表示需求者由于通勤而愿意额外付出的最大绕道时间阈值,即由于要通勤而需绕道前往设施的时间减去直接前往设施的时间; nij表示从 ij的实际通勤人数。类似地,第二步搜寻以需求点为中心,可表示为:

Ai=Rk(12)

式中: Ai为可达性得分;其他变量含义如式(11)。CB2SFCA能够为通勤行为与公共服务设施使用行为相互衔接的情况提供更准确的衡量,但需要任意2个研究单元之间的通勤人数,在实际应用中如此高的数据要求很难满足。

4 总结与展望

本文总结了国内外最近研究进展中对2SFCA的14种扩展形式,并归纳为4种扩展类型,分别为:基于引入距离衰减函数的扩展,对搜寻半径的扩展,针对需求或供给竞争的扩展以及基于出行方式的扩展。将这4种类型共14种扩展形式及其主要扩展内容和典型文献总结为表1

表1   2SFCA主要扩展形式

Tab.1   Major extensions of 2SFCA

扩展类型扩展形式主要扩展内容典型文献
基于引入距离衰减函数的扩展Enhanced 2SFCA对搜寻半径范围内的距离衰减函数按距离进行分段Luo等(2009)
Gravity 2SFCA在搜寻半径范围内加入重力模型的距离衰减函数,如幂函数、指数函数、对数函数等Wang等(2013)、Tao等(2014)
Gaussian 2SFCA在搜寻半径范围内加入高斯函数型距离衰减函数Dai(2010, 2011)
Kernel Density 2SFCA在搜寻半径范围内加入核密度函数型距离衰减函数Dai等(2011)
对搜寻半径的扩展Variable 2SFCA分别调整两步搜寻的半径,以使得设施的搜寻半径内覆盖足够需求规模、需求点的搜寻半径内能获取基本的设施资源规模Luo等(2012)
Dynamic 2SFCA根据各区域人口密度,设定不同的搜寻半径,适用于城乡混合的案例区域McGrail等(2014)
Multi Catchment Sizes 2SFCA根据设施规模等级设定不同搜寻半径,规模越大的设施搜寻半径越大陶卓霖等(2014)
Nearest Neighbor 2SFCA不同于传统2SFCA中采用的缓冲区-环形搜寻半径划定方法,提出需求点仅从最近的一定数量设施中进行选择的搜寻半径划定方法Jamtsho等(2015)
针对需求或供给竞争的扩展Three-step Floating Catchment Area增加一步搜寻,计算需求点与设施之间的选择权重(Selection Weight),用于衡量位于同一需求点搜寻半径之内的多个设施之间的竞争效应Wan等(2012)
Modified 2SFCA允许设施的空间配置存在次优情况,即存在部分设施资源无法分配到需求点从而无法得到有效利用,具体扩展是在E2SFCA模型分子处多乘以一次距离衰减函数fdijDelamater(2013)
Huff 2SFCA采用Huff模型,对3SFCA的选择权重变量进一步修正,以综合考虑出行成本和设施点服务能力两方面因素对出行选择的影响Luo(2014)
Optimized 2SFCA采用各设施在前一年的实际使用者数量作为设施的潜在使用者数量,改进了对同一设施资源可能面临的来自多个需求点的竞争Ngui等(2011)
基于出行方式的扩展Multi-mode 2SFCA采用多交通模式之间的加权平均交通时间对传统2SFCA中单一交通模式的交通时间进行了修正Mao等(2013)
Commuter-based 2SFCA考虑通勤行为对公共服务可达性的影响,假设需求数量不再是传统2SFCA中那样固定不变,而是根据通勤行为而有所变动Fransen等(2015)

新窗口打开

进一步将扩展形式之间的关系概括为图2。在基于引入距离衰减函数的扩展类型中,E2SFCA仍属于离散型距离衰减函数的扩展,而其他3种扩展形式属于连续型距离衰减函数。对搜寻半径的扩展类型中,V2SFCA、D2SFCA和MC2SFCA仍然继承了2SFCA原始形式中缓冲区—环形的设施搜寻范围划定方法,而NN2SFCA提出了新的仅考虑最近一定数量设施的Nearest Neighbor搜寻范围划定方法,在3.2的小结中,本文也提出了另一种适用于中国国情的基于行政范围的搜寻范围划定方法。针对需求或供给竞争的扩展类型中,3SFCA是最早做出尝试的扩展,随后M2SFCA和Huff 2SFCA都是在其基础上提出了进一步发展,而Optimized 2SFCA属于另一类扩展方式。基于出行方式的扩展类型中,MD2SFCA和CB2SFCA分别从不同角度作出了改进。不同类型的扩展形式之间也能够同时组合应用,后3类扩展形式大多是在基于引入距离衰减函数的扩展的基础上构建的,在未来研究中后3类扩展之间也可以尝试相互结合,从而进一步提升可达性评价的准确性。

图2   2SFCA主要扩展形式的关系示意图

Fig.2   Relationships between major extensions of 2SFCA

由于2SFCA方法在医疗设施领域应用最为广泛,最早也是在医疗设施的研究中提出,因此本文中涉及的2SFCA扩展形式同样大部分是在医疗设施布局研究中发展出来的。但这些扩展形式的适用范围并不局限于医疗设施,而是如同已有应用案例中表现出的那样,在各类公共设施中都具备应用价值。然而,各种2SFCA扩展形式适用于哪种公共设施并不可一概而论,既受到设施特点的影响,也受到具体研究区域对设施使用安排的影响。研究者在选择适用的方法时,应对这两方面进行分析,再结合2SFCA各种扩展形式所作改进的特点进行选择。本文总结的2SFCA扩展形式的4个维度为应用研究中的方法选择提供了基本框架。

本文对广泛应用的2SFCA方法及其丰富的扩展形式进行了系统梳理和总结,并且分析了各扩展形式的优缺点、适用情景以及未来可能的改进方向,这些扩展形式从公共服务设施空间可达性的不同方面,或者是对同一方面提出了不同的改进,研究者可根据具体案例特点选择合适的一种扩展形式或多种扩展形式相结合,从而更准确地度量公共服务设施空间可达性。

The authors have declared that no competing interests exist.


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针对贫困区基础教育资源分布中 出现的教育资源空间配置不合理等问题,以连片特困区——武陵山片区的重庆市黔江区为例,以自然村尺度进行测算,重点研究并解决了贫困区教育资源空间布局现 状的评估技术,以及两步移动搜寻法在农村贫困山区的关键技术改进和实现,并从供给和需求角度出发评价了教育资源的空间可达性。结果表明两步移动搜寻法适用 于评估贫困山区教育资源的空间配置状况和分布情况;研究区教育可达性较高的地区不及需求总数的30%,分布在地形相对平坦,海拔较低的地区,服务范围内的 学校多为中心校和实验小学,师资和占地面积优势大,但整体可达性并不理想。为相关部门有效配置教育资源,提出了"跑教"提升师资力量和恢复原有教学点等合 理化建议。

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针对贫困区基础教育资源分布中 出现的教育资源空间配置不合理等问题,以连片特困区——武陵山片区的重庆市黔江区为例,以自然村尺度进行测算,重点研究并解决了贫困区教育资源空间布局现 状的评估技术,以及两步移动搜寻法在农村贫困山区的关键技术改进和实现,并从供给和需求角度出发评价了教育资源的空间可达性。结果表明两步移动搜寻法适用 于评估贫困山区教育资源的空间配置状况和分布情况;研究区教育可达性较高的地区不及需求总数的30%,分布在地形相对平坦,海拔较低的地区,服务范围内的 学校多为中心校和实验小学,师资和占地面积优势大,但整体可达性并不理想。为相关部门有效配置教育资源,提出了"跑教"提升师资力量和恢复原有教学点等合 理化建议。
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[J]. Progress in Geography, 28(6): 848-854.]

https://doi.org/10.11820/dlkxjz.2009.06.003      URL      Magsci      [本文引用: 1]      摘要

<p>空间可达性是评价医疗设施布局合理与否的重要指标,传统的医疗设施空间可达性评价,或者从医疗服务供需状况着手,或者从供需双方之间距离因素着手,均无法全面评价居民实际所能获取的医疗资源。本文采用基于潜能模型的评价方法对江苏省如东县医疗设施空间可达性进行分析研究,该方法综合考虑了医疗设施服务能力、居民点人口数量、医疗设施与居民点之间的出行阻抗。研究表明,通过选取合适的出行摩擦系数,该方法能够较为全面准确地测度较小研究单元的医疗设施空间可达性,辅以GIS技术,可以很直观地揭示研究区域内医疗设施空间可达性差异,结合公共卫生管理部门制定的医疗资源配置标准,还可较为准确判定缺医地区,为政府相关部门规划决策提供依据。</p>
[9] 宋正娜, 陈雯, 张桂香, . 2010.

公共服务设施空间可达性及其度量方法

[J]. 地理科学进展, 29(10): 1217-1224.

https://doi.org/10.11820/dlkxjz.2010.10.009      URL      Magsci      [本文引用: 2]      摘要

<p>空间可达性度量既可用于评价公共服务设施空间布局的合理性,也可用于比较规划方案的优劣。公共服务设施空间可达性度量需要针对不同设施特有的空间布局目标,选取与之相适应的可达性评价因子,并采用合适的度量方法展开,对此进行专题研究的文献并不多见。本文一方面在对公共服务设施按照时效性、接受性、数量、等级性进行分类的基础上,系统阐述如何针对不同设施进行空间布局目标设定和可达性评价因子选取;另一方面将主要的度量方法分为比例法、最近距离法、基于机会累积的方法、基于空间相互作用的方法,并对各类方法的应用领域及优缺点予以分析比较,同时以潜能模型、两步移动搜寻法为例探讨相关方法在公共服务设施空间可达性度量中的应用;最后在对上述研究总结评述的基础上,本文指出多等级设施空间可达性、从需求者的活动规律考虑空间可达性、针对各类设施的综合空间可达性以及相关度量方法与GIS的集成等主题值得投入更多关注。</p>

[Song Z N, Chen W, Zhang G X, et al.2010.

Spatial accessibility to public service facilities and its measurement approaches

[J]. Progress in Geography, 29(10): 1217-1224.]

https://doi.org/10.11820/dlkxjz.2010.10.009      URL      Magsci      [本文引用: 2]      摘要

<p>空间可达性度量既可用于评价公共服务设施空间布局的合理性,也可用于比较规划方案的优劣。公共服务设施空间可达性度量需要针对不同设施特有的空间布局目标,选取与之相适应的可达性评价因子,并采用合适的度量方法展开,对此进行专题研究的文献并不多见。本文一方面在对公共服务设施按照时效性、接受性、数量、等级性进行分类的基础上,系统阐述如何针对不同设施进行空间布局目标设定和可达性评价因子选取;另一方面将主要的度量方法分为比例法、最近距离法、基于机会累积的方法、基于空间相互作用的方法,并对各类方法的应用领域及优缺点予以分析比较,同时以潜能模型、两步移动搜寻法为例探讨相关方法在公共服务设施空间可达性度量中的应用;最后在对上述研究总结评述的基础上,本文指出多等级设施空间可达性、从需求者的活动规律考虑空间可达性、针对各类设施的综合空间可达性以及相关度量方法与GIS的集成等主题值得投入更多关注。</p>
[10] 陶卓霖, 程杨, 戴特奇. 2014.

北京市养老设施空间可达性评价

[J]. 地理科学进展, 33(5): 616-624.

https://doi.org/10.11820/dlkxjz.2014.05.003      URL      Magsci      [本文引用: 7]      摘要

发展养老服务是当前中国社会建设中的重要部分。近年来,北京市养老设施发展迅速,但是由于快速的人口老龄化,北京市养老设施的供给仍难以满足老年人口对养老设施的需求。对北京市养老设施空间可达性进行科学评价是进行合理空间配置的基础,具有重要的现实意义。本文基于GIS技术,应用改进的两步移动搜索法,对北京市养老设施的空间可达性进行了测算,并重点对1小时单一有效服务半径和按养老设施规模划分的三级有效服务半径这两种情形进行了比较分析。结果表明,后者对北京市养老设施的空间可达性评价更具合理性。本文对空间可达性的测算结果识别出了北京市各区域养老设施的稀缺程度,为养老设施的空间布局提出了政策性建议。

[Tao Z L, Cheng Y, Dai T Q.2014.

Measuring spatial accessibility to residential care facilities in Beijing

[J]. Progress in Geography, 33(5): 616-624.]

https://doi.org/10.11820/dlkxjz.2014.05.003      URL      Magsci      [本文引用: 7]      摘要

发展养老服务是当前中国社会建设中的重要部分。近年来,北京市养老设施发展迅速,但是由于快速的人口老龄化,北京市养老设施的供给仍难以满足老年人口对养老设施的需求。对北京市养老设施空间可达性进行科学评价是进行合理空间配置的基础,具有重要的现实意义。本文基于GIS技术,应用改进的两步移动搜索法,对北京市养老设施的空间可达性进行了测算,并重点对1小时单一有效服务半径和按养老设施规模划分的三级有效服务半径这两种情形进行了比较分析。结果表明,后者对北京市养老设施的空间可达性评价更具合理性。本文对空间可达性的测算结果识别出了北京市各区域养老设施的稀缺程度,为养老设施的空间布局提出了政策性建议。
[11] 陶卓霖, 程杨, 戴特奇, . 2015.

基于公平最大化目标的2020年北京市养老设施布局优化

[J]. 地理科学进展, 34(12): 1609-1616.

https://doi.org/10.18306/dlkxjz.2015.12.009      URL      [本文引用: 1]      摘要

北京市正快速步入老龄化社会, 机构养老作为一种重要的养老模式,对其布局公平性和合理性的研究具有重要的科学和现实意义。本文首先预测了自然增长状态下2020年北京市老龄人口的空间 分布,然后建立设施布局优化模型,该模型以各需求点到养老设施的可达性差异最小化为目标;并采用粒子群优化算法求解,对北京市养老设施进行以公平最大化为 目标的布局优化。研究结果表明,在公平最大化的目标下,首都功能核心区和城市功能拓展区(即中心城区)所提供的机构养老资源不能完全满足本地需求。城市发 展新区在满足当地的机构养老需求之外,还将为中心城区提供大量机构养老服务,生态涵养发展区在满足本地需求的基础上还可为其他地区提供少量机构养老服务。 该布局导向与《北京市养老设施专项规划》提出的布局建议相一致,且符合中心城区用地紧张、郊区自然环境较舒适的现实情况。研究结果能为养老政策的制定提供 科学建议,所采用的方法也能为其他类型公共服务设施的布局优化提供借鉴。

[Tao Z L, Cheng Y, Dai T Q, et al.2015.

Spatial optimization of residential care facility locations in 2020 in Beijing: Maximum equity in accessibility

[J]. Progress in Geography, 34(12): 1609-1616.]

https://doi.org/10.18306/dlkxjz.2015.12.009      URL      [本文引用: 1]      摘要

北京市正快速步入老龄化社会, 机构养老作为一种重要的养老模式,对其布局公平性和合理性的研究具有重要的科学和现实意义。本文首先预测了自然增长状态下2020年北京市老龄人口的空间 分布,然后建立设施布局优化模型,该模型以各需求点到养老设施的可达性差异最小化为目标;并采用粒子群优化算法求解,对北京市养老设施进行以公平最大化为 目标的布局优化。研究结果表明,在公平最大化的目标下,首都功能核心区和城市功能拓展区(即中心城区)所提供的机构养老资源不能完全满足本地需求。城市发 展新区在满足当地的机构养老需求之外,还将为中心城区提供大量机构养老服务,生态涵养发展区在满足本地需求的基础上还可为其他地区提供少量机构养老服务。 该布局导向与《北京市养老设施专项规划》提出的布局建议相一致,且符合中心城区用地紧张、郊区自然环境较舒适的现实情况。研究结果能为养老政策的制定提供 科学建议,所采用的方法也能为其他类型公共服务设施的布局优化提供借鉴。
[12] 王成金. 2009.

中国交通流的衰减函数模拟及特征

[J]. 地理科学进展, 28(5): 690-696.

https://doi.org/10.11820/dlkxjz.2009.05.006      Magsci      [本文引用: 1]      摘要

<p>交通流具有随距离延伸而不断衰减的空间属性,距离衰减规律是交通地理学的重要议题。基于空间&ldquo;流&rdquo;距离衰减研究进展的评述,本文构筑了交通流距离衰减规律的主要可能函数模型,包括指数模型、Pareto模型、常对数模型、平方指数模型、开方指数模型,采用中国城际交通流包括公路客流、铁路客流、铁路货流和航空客流,分别对5种距离衰减模型进行了模拟并对比分析,从中识别出最佳的距离衰减函数是Pareto模型。然后,重点分析了各种交通流距离衰减函数的参数差异和地理内涵,并采用时间序列的交通流进行模拟,考察距离衰减函数的主要参数变化,并解释其地理内涵,同时绘制了交通流累计率曲线和分配率曲线,对各种交通方式的距离衰减函数模型、主要函数参数和距离衰减规律进行论证和解释。</p>

[Wang C J.2009.

Function simulation and regularity of distance decay of inter-urban traffic flow in China

[J]. Progress in Geography, 28(5): 690-696.]

https://doi.org/10.11820/dlkxjz.2009.05.006      Magsci      [本文引用: 1]      摘要

<p>交通流具有随距离延伸而不断衰减的空间属性,距离衰减规律是交通地理学的重要议题。基于空间&ldquo;流&rdquo;距离衰减研究进展的评述,本文构筑了交通流距离衰减规律的主要可能函数模型,包括指数模型、Pareto模型、常对数模型、平方指数模型、开方指数模型,采用中国城际交通流包括公路客流、铁路客流、铁路货流和航空客流,分别对5种距离衰减模型进行了模拟并对比分析,从中识别出最佳的距离衰减函数是Pareto模型。然后,重点分析了各种交通流距离衰减函数的参数差异和地理内涵,并采用时间序列的交通流进行模拟,考察距离衰减函数的主要参数变化,并解释其地理内涵,同时绘制了交通流累计率曲线和分配率曲线,对各种交通方式的距离衰减函数模型、主要函数参数和距离衰减规律进行论证和解释。</p>
[13] 王绮, 修春亮, 魏冶, . 2015.

基于高斯两步移动搜索法的沈阳市就业可达性评价

[J]. 人文地理, 30(2): 78-82.

https://doi.org/10.11820/dlkxjz.2014.04.005      URL      [本文引用: 2]      摘要

将高斯两步移动搜索方法引入到就业可达性测度研究中,在证明方法有效性的同时,也对研究案例沈阳市中心城区的就业可达性空间格局、形成机理进行了分析,并提出相应的调控策略。结果显示,沈阳市中心城区的就业可达性在空间上并非均匀分布,而是呈现为明显的中心—外围格局。形成这一格局的机理有:1单中心的城市形态;2城市规划的功能性布局;3居住的郊区化;4旧城改造与政策性住房;5地理要素的空间阻隔。提出用足规划手段促进产业与人口均衡化布局、旧城改造与政策性住房的合理落位、完善城市交通,破除路径障碍与培育多中心城市空间结构等调控策略。

[Wang Q, Xiu C L, Wei Y, et al.2015.

Evaluation of job accessibility of Shenyang using Gaussian based 2-step floating catchment area method

[J]. Human Geography, 30(2): 78-82.]

https://doi.org/10.11820/dlkxjz.2014.04.005      URL      [本文引用: 2]      摘要

将高斯两步移动搜索方法引入到就业可达性测度研究中,在证明方法有效性的同时,也对研究案例沈阳市中心城区的就业可达性空间格局、形成机理进行了分析,并提出相应的调控策略。结果显示,沈阳市中心城区的就业可达性在空间上并非均匀分布,而是呈现为明显的中心—外围格局。形成这一格局的机理有:1单中心的城市形态;2城市规划的功能性布局;3居住的郊区化;4旧城改造与政策性住房;5地理要素的空间阻隔。提出用足规划手段促进产业与人口均衡化布局、旧城改造与政策性住房的合理落位、完善城市交通,破除路径障碍与培育多中心城市空间结构等调控策略。
[14] 魏冶, 修春亮, 高瑞, . 2014.

基于高斯两步移动搜索法的沈阳市绿地可达性评价

[J]. 地理科学进展, 33(4): 479-487.

https://doi.org/10.11820/dlkxjz.2014.04.005      URL      Magsci      [本文引用: 3]      摘要

基于高斯两步移动搜索法,进行沈阳市绿地可达性分析。在揭示研究区内绿地可达性空间格局的同时,探索这一新方法的实际应用价值。结果显示:① 沈阳市绿地可达性整体上具有北高南低、东高西低的空间分布特征,4 个高值区与3 个低值区可清晰识别;高值区域主要分布在核心城区的近外围,低值区域主要分布于核心城区与城市的西部及南部远郊。② 沈阳市绿地可达性空间格局十分不平衡,具有较强的空间极化特征,70%以上的街道绿地可达性低于全市平均水平,只有少数街道呈现较高的可达性,人口与绿地的空间不匹配是造成不平衡的主要因素。③ 根据可达性评价结果,提出了实施空间优化策略,促进绿地服务均等化的相关建议。该方法能够较好地揭示城市绿地系统与人口相互作用的规律,未来还应进一步与客观实际结合,使之更加具体化和实用化。

[Wei Y, Xiu C L, Gao R, et al.2014.

Evaluation of green space accessibility of Shenyang using Gaussian based 2-step floating catchment area method

[J]. Progress in Geography, 33(4): 479-487.]

https://doi.org/10.11820/dlkxjz.2014.04.005      URL      Magsci      [本文引用: 3]      摘要

基于高斯两步移动搜索法,进行沈阳市绿地可达性分析。在揭示研究区内绿地可达性空间格局的同时,探索这一新方法的实际应用价值。结果显示:① 沈阳市绿地可达性整体上具有北高南低、东高西低的空间分布特征,4 个高值区与3 个低值区可清晰识别;高值区域主要分布在核心城区的近外围,低值区域主要分布于核心城区与城市的西部及南部远郊。② 沈阳市绿地可达性空间格局十分不平衡,具有较强的空间极化特征,70%以上的街道绿地可达性低于全市平均水平,只有少数街道呈现较高的可达性,人口与绿地的空间不匹配是造成不平衡的主要因素。③ 根据可达性评价结果,提出了实施空间优化策略,促进绿地服务均等化的相关建议。该方法能够较好地揭示城市绿地系统与人口相互作用的规律,未来还应进一步与客观实际结合,使之更加具体化和实用化。
[15] 张鹏飞, 蔡忠亮, 张成, . 2015.

基于E2SFCA的城市旅游景点的潜在空间可达性分析

[J]. 测绘地理信息, 40(1): 76-79.

URL      [本文引用: 2]     

[Zhang P F, Cai Z L, Zhang C, et al.2015.

Potential spatial accessibility to urban scenic spots based on E2SFCA

[J]. Journal of Geomatics, 40(1): 76-79.]

URL      [本文引用: 2]     

[16] 赵东霞, 韩增林, 王利, . 2014.

基于两步移动搜寻法的城市居家养老服务设施可达性研究: 以大连市沙河口区低龄老年人为例

[J]. 地域研究与开发, 33(6): 27-32.

Magsci      [本文引用: 1]      摘要

基于ArcGIS的两步移动搜寻法可以解决设施(供给)与人口(需求)的空间分布差异性及两者可跨越区界的潜在相互作用。通过对大连市沙河口区常住居家低龄老年人与养老服务设施空间可达性进行实证研究,利用两步移动搜寻法获取各服务设施到人口聚居点的可达性数值并利用MapInfo绘制成图,得出89个社区供需间潜在的空间可达性呈现优秀、良好、一般和较差4种结果,为大连沙河口区针对低龄老年人居家养老服务设施的发展规划提供辅助决策支持,也展现了两步移动搜寻法在公共服务空间可达性评价方面的作用。

[Zhao D X, Han Z L, Wang L, et al.2014.

Accessibility research about urban in-home service facilities for the elderly based on two-step mobile research: Taking low-aging elder people in Shahekou District of Dalian as an example

[J]. Areal Research and Development, 33(6): 27-32.]

Magsci      [本文引用: 1]      摘要

基于ArcGIS的两步移动搜寻法可以解决设施(供给)与人口(需求)的空间分布差异性及两者可跨越区界的潜在相互作用。通过对大连市沙河口区常住居家低龄老年人与养老服务设施空间可达性进行实证研究,利用两步移动搜寻法获取各服务设施到人口聚居点的可达性数值并利用MapInfo绘制成图,得出89个社区供需间潜在的空间可达性呈现优秀、良好、一般和较差4种结果,为大连沙河口区针对低龄老年人居家养老服务设施的发展规划提供辅助决策支持,也展现了两步移动搜寻法在公共服务空间可达性评价方面的作用。
[17] 周慧, 蔡忠亮, 张鹏飞, . 2015.

增强型两步移动搜索模型的参数灵敏度研究

[J]. 测绘地理信息, 40(5): 65-69, 75.

https://doi.org/10.14188/j.2095-6045.2015.05.019      URL      [本文引用: 1]      摘要

采用局部灵敏度分析方法,结合可视化技术,以深圳市就医可达性为例对E2SFCA模型的3个主要参数——距离衰减指数(β)、划分子区域大小(Sub_Size)、极限搜索距离(Catchment_Size)的灵敏度进行分析。研究结果表明,3个参数的取值对可达性评价结果都有着不同程度的影响,其中Catchment_Size的影响最为明显,Sub_Size和β的取值也与Catchment_Size的大小有关。

[Zhou H, Cai Z L, Zhang P F, et al.2015.

Parameter sensitivity study of the enhanced two-step floating catchment area model

[J]. Journal of Geomatics, 40(5): 65-69, 75.]

https://doi.org/10.14188/j.2095-6045.2015.05.019      URL      [本文引用: 1]      摘要

采用局部灵敏度分析方法,结合可视化技术,以深圳市就医可达性为例对E2SFCA模型的3个主要参数——距离衰减指数(β)、划分子区域大小(Sub_Size)、极限搜索距离(Catchment_Size)的灵敏度进行分析。研究结果表明,3个参数的取值对可达性评价结果都有着不同程度的影响,其中Catchment_Size的影响最为明显,Sub_Size和β的取值也与Catchment_Size的大小有关。
[18] Allan D P.2014.

Catchments of general practice in different countries: A literature review

[J]. International Journal of Health Geographics, 13(1): 32.

URL     

[19] Bell S, Wilson K, Bissonnette L, et al.2013.

Access to primary health care: Does neighborhood of residence matter

[J]. Annals of the Association of American Geographers, 103(1): 85-105.

https://doi.org/10.1080/00045608.2012.685050      Magsci      摘要

Neighborhood social and physical contexts have the ability to impact health and health behaviors of residents. One neighborhood characteristic that remains underexamined in the research is access to health care resources. This research examines potential (geographical) access to primary health care in the city of Mississauga, Ontario, Canada. A modification of the two-step floating catchment area method that better suits the study of locally relevant natural neighborhood units is presented. Potential access to health care is measured in each of Mississauga's neighborhoods considering several spatial and aspatial (i.e., social) characteristics of the population and of physicians, including the raw abundance of physicians, languages spoken by physicians and patients, and whether physicians are accepting new patients. Neighborhood-level results are compared to census tracts. The results of this analysis reveal that potential access significantly differs between neighborhoods for all spatial and aspatial dimensions of access. Accessibility is considerably reduced for linguistic minorities and for those who might not have a dedicated family physician as compared to the general population. This research contributes to the existing body of literature on neighborhoods and health by demonstrating the utility of an alternative methodology for developing a more comprehensive understanding of access to health care within natural geographical neighborhoods.
[20] Dadashpoor H, Rostami F, Alizadeh B.2016.

Is inequality in the distribution of urban facilities inequitable: Exploring a method for identifying spatial inequity in an Iranian city

[J]. Cities, 52: 159-172.

URL      [本文引用: 1]     

[21] Dai D J.2010.

Black residential segregation, disparities in spatial access to health care facilities, and late-stage breast cancer diagnosis in metropolitan Detroit

[J]. Health & Place, 16(5): 1038-1052.

https://doi.org/10.1016/j.healthplace.2010.06.012      URL      PMID: 20630792      [本文引用: 1]      摘要

This study evaluates the role of black residential segregation and spatial access to health care in explaining the variation in late-stage diagnosis of breast cancer in metropolitan Detroit. Data pertaining to female breast cancer from 1998 to 2002 are obtained from the Michigan Cancer Surveillance Program. An isolation index is used to assess black segregation. The 2-step floating catchment area approach integrated with a Gaussian function is used to estimate the health care access. While socioeconomic factors at ZIP code level are controlled, ordinary least squares and spatial lag models are used to explore the association between the rates of late-stage diagnosis and segregation and health care access. Results suggest that living in areas with greater black segregation and poorer mammography access significantly increases the risk of late diagnosis of breast cancer. Disadvantaged populations including those with low socioeconomic status or sociocultural barriers tend to experience high rates of late diagnosis. Findings emphasize the need for heightened screening, surveillance, and intervention programs in these areas. Copyright 2010 Elsevier Ltd. All rights reserved.
[22] Dai D J.2011.

Racial/ethnic and socioeconomic disparities in urban green space accessibility: Where to intervene

[J]. Landscape and Urban Planning, 102(4): 234-244.

https://doi.org/10.1016/j.landurbplan.2011.05.002      Magsci      [本文引用: 2]      摘要

Access to green spaces is important to physical activities and public health, yet one concern remains as to whether the disparities in green space access exist. This study aimed to (1) introduce an approach to quantify potential spatial accessibility to green spaces in a Geographic Information Systems (GIS) environment: and (2) evaluate the racial/ethnic and socioeconomic disparities in green space access. Urban green spaces (n = 890) in metropolitan Atlanta, Georgia were collected from the Atlanta Regional Commission. A Gaussian-based two-step floating catchment area method was adapted to assess the spatial accessibility to green spaces at the census tract level. The Ordinary Least Squares (OLS) model and the spatial lag model were used to evaluate the racial/ethnic and socioeconomic disparities. Results suggest that the spatial accessibility to green spaces in Atlanta was not evenly distributed. Both models show that neighborhoods with a higher concentration of African Americans had significantly poorer access to green spaces (P < 0.05). Asian population had significantly poor access in the OLS model but not in the spatial lag model. Poor access was present in socioeconomically disadvantaged areas as well. Findings can be used for the city and regional planners to target the specific areas for green space development in order to elucidate the disparities. (C) 2011 Elsevier B.V. All rights reserved.
[23] Dai D J, Wang F H.2011.

Geographic disparities in accessibility to food stores in southwest Mississippi

[J]. Environment and Planning B: Planning and Design, 38(4): 659-677.

https://doi.org/10.1068/b36149      URL      摘要

Disparities in accessibility to healthy food are a critical public-health concern. Poor access to reasonably priced, nutritious, and good-quality food may lead to poor diet and increase the risks of health problems such as obesity, diabetes, and cardiovascular diseases. This research advances the popular two-step floating catchment area (2SFCA) method by incorporating a kernel density (KD) function to form the ‘KD2SFCA method’. The study applies the method to measure the spatial access to food stores in southwest Mississippi, and examines the interaction between the spatial access and nonspatial factors. The research shows that neighborhoods with higher scores of urban socioeconomic disadvantage actually have better spatial accessibility to food stores; but higher percentages of carless households and lower income in some neighborhoods may compromise overall accessibility. Neighborhoods with stronger cultural barriers tend to be associated with poorer spatial accessibility. The study clearly differentiates spatial and nonspatial factors in access inequalities, and thus helps policy makers to design corresponding remedial strategies.
[24] Delamater P L.2013.

Spatial accessibility in suboptimally configured health care systems: A modified two-step floating catchment area (M2SFCA) metric

[J]. Health & Place, 24: 30-43.

https://doi.org/10.1016/j.healthplace.2013.07.012      URL      PMID: 24021921      [本文引用: 4]      摘要

The floating catchment area (FCA) family of metrics employ principles from gravity-based models to incorporate supply, demand, and distance in their characterization of the spatial accessibility of health care resources. Unlike traditional gravity models, the FCA metrics provide an output in highly interpretable container-like units (e.g., physicians per person). This work explores two significant issues related to FCA metrics. First, the Three Step Floating Catchment Area is critically examined. Next, the research shows that all FCA metrics contain an underlying assumption that supply locations are optimally configured to meet the needs of the population within the system. Because truly optimal configurations are highly unlikely in real-world health care systems, a modified two-step floating catchment area (M2SFCA) metric is offered to address this issue. The M2SFCA is built upon previous FCA metrics, but allows for spatial accessibility to be discounted as a result of the suboptimal configuration of health care facilities within the system. The utility of the new metric is demonstrated through simulated data examples and a case study exploring acute care hospitals in Michigan.
[25] Fransen K, Neutens T, De Maeyer P, et al.2015.

A commuter-based two-step floating catchment area method for measuring spatial accessibility of daycare centers

[J]. Health & Place, 32: 65-73.

https://doi.org/10.1016/j.healthplace.2015.01.002      URL      PMID: 25638791      [本文引用: 2]      摘要

This paper puts forward a commuter-based version of the two-step floating catchment area (2SFCA) method, which has gained acceptance in studies on spatial health care accessibility. Current implementations of the 2SFCA method are static in that they consider centroid-based night-time representations of the population. The proposed enhancement to the 2SFCA approach addresses this limitation by accounting for trip-chaining . The presented method is illustrated in a case study of accessibility of daycare centers in the province East Flanders in Belgium. The results show significant spatial differences in accessibility between the original and commuter-based version of the 2SFCA (CB2SFCA). They highlight the importance of giving heed to more complex travel in cases where the need for detailed accessibility calculations is apparent.
[26] Jamtsho S, Corner R, Dewan A.2015.

Spatio-temporal analysis of spatial accessibility to primary health care in Bhutan

[J]. ISPRS International Journal of Geo-Information, 4(3): 1584-1604.

https://doi.org/10.3390/ijgi4031584      URL      [本文引用: 3]      摘要

Geographic information systems (GIS) can be effectively utilized to carry out spatio-temporal analysis of spatial accessibility to primary healthcare services. Spatial accessibility to primary healthcare services is commonly measured using floating catchment area models which are generally defined with three variables; namely, an attractiveness component of the service centre, travel time or distance between the locations of the service centre and the population, and population demand for healthcare services. The nearest-neighbour modified two-step floating catchment area (NN-M2SFCA) model is proposed for computing spatial accessibility indices for the entire country. Accessibility values from 2010 to 2013 for Bhutan were analysed both spatially and temporally by producing accessibility ranking maps, plotting Lorenz curves, and conducting spatial clustering analysis. The spatial accessibility indices of the 205 sub-districts show great disparities in healthcare accessibility in the country. The mean- and median-based classification results indicate that, in 2013, 24 percent of Bhutan鈥檚 population have poor access to primary healthcare services, 66 percent of the population have medium-level access, and 10 percent have good access.
[27] Kwan M P.1998.

Space-time and integral measures of individual accessibility: A comparative analysis using a point-based framework

[J]. Geographical Analysis, 30(3): 191-216.

https://doi.org/10.1111/j.1538-4632.1998.tb00396.x      URL      [本文引用: 1]      摘要

ABSTRACT Conventional integral measures of accessibility, although valuable as indicators of place accessibility, have several limitations when used to evaluate individual accessibility. Two alternatives for overcoming some of the difficulties involved are explored in this study. One is to adapt these measures for evaluating individual accessibility using a disaggregate, nonzonal approach. The other is to develop different types of measures based on an alternative conceptual framework. To pursue the former alternative, this study specifies and examines eighteen gravity-type and cumulative-opportunity accessibility measures using a point-based spatial framework. For the latter option, twelve space-time accessibility measures are developed based on the construct of a prism-constrained feasible opportunity set. This paper compares the relationships and spatial patterns of these thirty measures using network-based GIS procedures. Travel diary data collected in Columbus, Ohio, and a digital data set of 10,727 selected land parcels are used for all computation. Results of this study indicate that space-time and integral indices are distinctive types of accessibility measures which reflect different dimensions of the accessibility experience of individuals. Since space-time measures are more capable of capturing interpersonal differences, especially the effect of space-time constraints, they are more &ldquo;gender sensitive&rdquo; and helpful for unraveling gender/ethnic differences in accessibility. An important methodological implication is that whether accessibility is observed to be important or different between individuals depends heavily on whether the measure used is capable of revealing the kind of differences the analyst intends to observe.
[28] Luo J.2014.

Integrating the Huff model and floating catchment area methods to analyze spatial access to healthcare services

[J]. Transactions in GIS, 18(3): 436-448.

https://doi.org/10.1111/tgis.12096      URL      [本文引用: 3]      摘要

Abstract Analysis of spatial access to healthcare services is critical for effective health resource planning. Gravity-based spatial access models have been widely used to estimate spatial access to healthcare services. Among them, the floating catchment area (FCA) methods have been proved to be informative and helpful to the designation of Health Professional Shortage Areas (HPSAs). This article integrates the Huff Model with the FCA method to articulate population selection on services. Through the proposed approach, population demand on healthcare services is adjusted by a Huff Model-based selection probability that reflects the impacts of both distance impedance and service site capacity. The new approach moderates the over- or under-estimating of population demand that occurred with previous methods. Furthermore, the method uses a continuous distance impedance weight function instead of the arbitrarily defined subzones of previous studies. A case study of spatial access to primary care in Springfield, MO, showed that the proposed method can effectively moderate the population demand on service sites and therefore can generate more reliable spatial access measures.
[29] Luo W, Qi Y.2009.

An enhanced two-step floating catchment area (E2SFCA) method for measuring spatial accessibility to primary care physicians

[J]. Health & Place, 15(4): 1100-1107.

https://doi.org/10.1016/j.healthplace.2009.06.002      URL      PMID: 19576837      [本文引用: 2]      摘要

This paper presents an enhancement of the two-step floating catchment area (2SFCA) method for measuring spatial accessibility, addressing the problem of uniform access within the catchment by applying weights to different travel time zones to account for distance decay. The enhancement is proved to be another special case of the gravity model. When applying this enhanced 2SFCA (E2SFCA) to measure the spatial access to primary care physicians in a study area in northern Illinois, we find that it reveals spatial accessibility pattern that is more consistent with intuition and delineates more spatially explicit health professional shortage areas. It is easy to implement in GIS and straightforward to interpret.
[30] Luo W, Wang F H.2003.

Measures of spatial accessibility to health care in a GIS environment: Synthesis and a case study in the Chicago region

[J]. Environment and Planning B: Planning and Design, 30(6): 865-884.

URL      [本文引用: 2]     

[31] Luo W, Whippo T.2012.

Variable catchment sizes for the two-step floating catchment area (2SFCA) method

[J]. Health & Place, 18(4): 789-795.

https://doi.org/10.1016/j.healthplace.2012.04.002      URL      PMID: 22560115      [本文引用: 3]      摘要

Abstract Government efforts designed to help improve healthcare access rely on accurate measures of accessibility so that resources can be allocated to truly needy areas. In order to capture the interaction between physicians and populations, various access measures have been utilized, including the popular two-step floating catchment area (2SFCA) method. However, despite the many advantages of 2SFCA, the problems associated with using fixed catchment sizes have not been satisfactorily addressed. We propose a new method to dynamically determine physician and population catchment sizes by incrementally increasing the catchment until a base population and a physician-to-population ratio are met. Preliminary application to the ten-county region in northern Illinois has demonstrated that the new method is effective in determining the appropriate catchment sizes across the urban to suburban/rural continuum and has revealed greater detail in spatial variation of accessibility compared to results using fixed catchment sizes. Copyright 漏 2012 Elsevier Ltd. All rights reserved.
[32] Mao L, Nekorchuk D.2013.

Measuring spatial accessibility to healthcare for populations with multiple transportation modes

[J]. Health & Place, 24(6): 115-122.

https://doi.org/10.1016/j.healthplace.2013.08.008      URL      PMID: 24077335      [本文引用: 2]      摘要

Few measures of healthcare accessibility have considered multiple transportation modes when people seek healthcare. Based on the framework of the 2 Step Floating Catchment Area Method (2SFCAM), we proposed an innovative method to incorporate transportation modes into the accessibility estimation. Taking Florida, USA, as a study area, we illustrated the implementation of the multi-mode 2SFCAM, and compared the accessibility estimates with those from the traditional single-mode 2SFCAM. The results suggest that the multi-modal method, by accounting for heterogeneity in populations, provides more realistic accessibility estimations, and thus offers a better guidance for policy makers to mitigate health inequity issues.
[33] Mazumdar S, Feng X Q, Konings P, et al.2014.

A brief report on Primary Care Service Area catchment geographies in New South Wales Australia

[J]. International Journal of Health Geographics, 13(1): 38.

https://doi.org/10.1186/1476-072X-13-38      URL      PMID: 25292210      摘要

Background To develop a method to use survey data to establish catchment areas of primary care or Primary Care Service Areas. Primary Care Service Areas are small areas, the majority of patients resident in which obtain their primary care services from within the geography. Methods The data are from a large health survey (n =267,153, year 2006–2009) linked to General Practitioner service use data (year 2002–2010) from New South Wales , Australia. Our methods broadly follow those used previously by researchers in the United States of America and Switzerland, with significant modifications to improve robustness. This algorithm allocates post code areas to Primary Care Service Areas that receive the plurality of patient visits from the post code area. Results Consistent with international findings the median Localization Index or the median percentage of patients that obtain their primary care from within a Primary Care Service Area is 55% with localization increasing with rurality. Conclusions With the additional methodological refinements in this study, Australian Primary Care Service Areas have great potential to be of value to policymakers and researchers.
[34] McGrail M R.2012.

Spatial accessibility of primary health care utilising the two step floating catchment area method: An assessment of recent improvements

[J]. International Journal of Health Geographics, 11(1): 50.

https://doi.org/10.1186/1476-072X-11-50      Magsci      [本文引用: 1]     

[35] McGrail M R, Humphreys J S.2009.

Measuring spatial accessibility to primary care in rural areas: Improving the effectiveness of the two-step floating catchment area method

[J]. Applied Geography, 29(4): 533-541.

https://doi.org/10.1016/j.apgeog.2008.12.003      URL      Magsci      [本文引用: 2]      摘要

<h2 class="secHeading" id="section_abstract">Abstract</h2><p id="">Quantifying spatial accessibility in relation to the provision of rural health services has proven difficult. This article critically appraises the two-step floating catchment area (2SFCA) method, a recent solution for measuring primary care service accessibility across rural areas of Victoria, Australia. The 2SFCA method is demonstrated to have two fundamental shortcomings &ndash; specifically the use of only one catchment size for all populations, and secondly the assumption that proximity is undifferentiated within a catchment (especially problematic when the catchment is large). Despite its advantages over simple population-to-provider ratios, the 2SFCA method needs to be used with caution.</p>
[36] McGrail M R, Humphreys J S.2014.

Measuring spatial accessibility to primary health care services: Utilising dynamic catchment sizes

[J]. Applied Geography, 54(4): 182-188.

https://doi.org/10.1016/j.apgeog.2014.08.005      URL      [本文引用: 5]      摘要

The two-step floating catchment area (2SFCA) method continues to be a popular measure of spatial accessibility, especially in relation to primary-level health care. Despite its popularity, most applications of the 2SFCA method are limited by the utilisation of only a single catchment size within a small geographic area. This limitation is significant to health policies which are mostly applied at the state or national scale. In this paper, a five-level dynamic catchment size was trialled within the 2SFCA method to all of Australia, with a population's remoteness used to delineate increasing catchment sizes. Initial trial results highlighted two perverse outcomes which were caused by sudden changes in catchment sizes between each level. Further refinement led to trialling an additional three-level catchment sub-type to the 2SFCA method, which created a smoother transition between remoteness levels. This study has demonstrated an effective approach to dynamically apply variable and more appropriate catchment sizes into different types of rural areas, which for the first time enables the 2SFCA method to be suitable for national-level access modelling and its potential application to health policy.
[37] Ngui A N, Apparicio P.2011.

Optimizing the two-step floating catchment area method for measuring spatial accessibility to medical clinics in Montreal

[J]. BMC Health Services Research, 11(1): 166.

https://doi.org/10.1186/1472-6963-11-166      URL      PMID: 21745402      [本文引用: 2]      摘要

We first computed catchments around existing medical clinics of Montreal Island based on the shortest network distance. Population nested in dissemination areas were used to determine potential users of a given medical clinic. To optimize the method, medical clinics (supply) were weighted by the number of physicians working in each clinic, while the previous year's medical clinic users were computed by ten years age group was used as weighting coefficient for potential users of each medical clinic (demand).The spatial accessibility score (SA) increased considerably with the optimisation method. Within a distance of 1 Km, for instance, the maximum clinic accessible for 1,000 persons is 2.4 when the conventional method is used, compared with 27.7 for the optimized method. The t-test indicates a significant difference between the conventional and the optimized 2SFCA methods. Also, results of the differences between the two methods reveal a clustering of residuals when distance increases. In other words, a low threshold would be associated with a lack of precision.Results of this study suggest that a greater effort must be made ameliorate spatial accessibility to medical clinics in Montreal. To ensure that health resources are allocated in the interest of the population, health planners and the government should consider a strategy in the sitting of future clinics which would provide spatial access to the greatest number of people.Accessibility to medical clinics is a contentious issue both in the third world [1-3] and in developed countries [4-6]. Poor access to medical clinics may result in people with simple health problems not consulting a health professional and subsequently developing more complex conditions with irreversible consequences [7]. The Canada Health Act (CHA) recognizes the importance of access to healthcare and states that all Canadians are entitled to receive medical services without barriers or restrictions. At the same time, Canadian provincial hea
[38] Radke J, Mu L.2000.

Spatial decompositions, modeling and mapping service regions to predict access to social programs

[J]. Geographic Information Sciences: A Journal of the Association of Chinese Professionals in Geographic Information Systems, 6(2): 105-112.

https://doi.org/10.1080/10824000009480538      URL      摘要

ABSTRACT Although social programs intend to provide equal access for all, in the final evaluation, fairness of the distribution of services is usually dictated by location. Measuring and predicting access to social services can help these programs adjust and better accommodate under-served regions. A method is proposed which delineates the service area of providers delivering social services and produces a probability metric that maps the equity of the program of services for each household. We begin with a computationally trivial method for delineating service areas, map the probability of households being served, and propose an adjustment process, an allocation, to level access to services. We argue such methods can serve to better locate service providers and insure equity when implementing social programs.
[39] Tao Z L, Cheng Y, Dai T Q, et al.2014.

Spatial optimization of residential care facility locations in Beijing, China: Maximum equity in accessibility

[J]. International Journal of Health Geographics, 13(1): 33.

https://doi.org/10.1186/1476-072X-13-33      URL      PMID: 25178475      摘要

Background The residential care system is rapidly developing and plays an increasingly important role in care for the elderly in Beijing. A noticeable disparity in the accessibility to
[40] Wan N, Zou B, Sternberg T.2012.

A three-step floating catchment area method for analyzing spatial access to health services

[J]. International Journal of Geographical Information Science, 26(6): 1073-1089.

https://doi.org/10.1080/13658816.2011.624987      URL      [本文引用: 4]      摘要

Gravity-based spatial access models have been widely used to estimate spatial access to healthcare services in an attempt to capture the interaction of various factors. However, these models are inadequate in informing health resource allocation work due to their inappropriate assumption of healthcare demand. For the purpose of effective healthcare resource planning, this article proposes a three-step floating catchment area (3SFCA) method to minimize the healthcare-demand overestimation problem. Specifically, a spatial impedance-based competition scheme is incorporated into the enhanced two-step floating catchment area (E2SFCA) method to account for a reasonable model of healthcare supply and demand. A case study of spatial access to primary care physicians along the Austin鈥揝an Antonio corridor area in central Texas showed that the proposed method effectively minimizes the overestimation of healthcare demand and reflects a more balanced geographic pattern of spatial access than E2SFCA. In addition, by us...
[41] Wang F H.2012.

Measurement, optimization, and impact of health care accessibility: A methodological review

[J]. Annals of the Association of American Geographers, 102(5): 1104-1112.

https://doi.org/10.1080/00045608.2012.657146      URL      PMID: 23335813      [本文引用: 4]      摘要

Despite spending more than any other nation on medical care per person, the United States ranks behind other industrialized nations in key health performance measures. A main cause is the deep disparities in access to care and health outcomes. Federal programs such as the designations of Medically Underserved Areas/Populations and Health Professional Shortage Areas are designed to boost the number of health professionals serving these areas and to help alleviate the access problem. Their effectiveness relies first and foremost on an accurate measure of accessibility so that resources can be allocated to truly needy areas. Various measures of accessibility need to be integrated into one framework for comparison and evaluation. Optimization methods can be used to improve the distribution and supply of health care providers to maximize service coverage, minimize travel needs of patients, limit the number of facilities, and maximize health or access equality. Inequality in health care access comes at a personal and societal price, evidenced in disparities in health outcomes, including late-stage cancer diagnosis. This review surveys recent literature on the three named issues with emphasis on methodological advancements and implications for public policy.
[42] Wang F H, Tang Q.2013.

Planning toward equal accessibility to services: A quadratic programming approach

[J]. Environment and Planning B: Planning and Design, 40(2): 195-212.

https://doi.org/10.1068/b37096      URL      [本文引用: 3]      摘要

In the literature various accessibility indices have been developed to assess the relative ease by which the locations of services (supply) can be reached from a residential (demand) location. In this paper we address the planning problem: how the resources can be redistributed to achieve the highest equality of accessibility to the service providers. In particular, a quadratic programming approach is used to minimize the variance of accessibility scores across demand locations by readjusting the amounts of service supplies. Two case studies—job access in Columbus, OH and primary healthcare access in Chicago, IL—are used to illustrate the method. The result suggests that in order to achieve better equality of accessibility, peripheral areas, in general, need additional supplies to compensate for their less-central locations, and some central city areas also need to add supplies to accommodate high demands by the high population density there. Keywords: accessibility index, equal accessibility, quadratic programming, job access, health-care access

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