Chin. Geogra. Sci. 2014 Vol. 24 No. 6 pp. 751–762
doi: 10.1007/s11769-014-0678-1
Springer
Science Press
www.springerlink.com/content/1002-0063
A Comparative Study of Methods for Delineating Sphere of Urban Influence: A Case Study on Central China
WANG Hao1, 2, DENG Yu1, TIAN Enze3, WANG Kaiyong1
(1. Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China; 2. University of Chinese Academy of Sciences, Beijing 100049, China; 3. Harvard University Graduate School of Design, Cambridge 02138,
USA)
Abstract: A number of urban and regional plans have been developed with the advancement of urbanization and regional integration,
among which the delineation of sphere of urban influence and improvement of integration between the city and its hinterland have become vital important for guiding practices. In terms of delineating sphere of urban influence, existing studies have been focused on
static study by using single year data or single method, resulting in a lack of time-series longitudinal analysis or comprehensive analysis
based on multiple methods. This study emphasizes on comparing two methods from both the theoretical and empirical perspective. Both
gravity model and improved field model are applied to the selected study area for measurements and comparison, to explore their
strengths and weaknesses. A research framework for comprehensive analysis on delineating sphere of urban influence is proposed. In the
end, the differences of delineating methods are illustrated and the feasibility of comprehensive analysis is discussed. Recommendations
are provided for selecting appropriate methods for delineating sphere of urban influence or developing regional hierarchy system plans
and urban spatial structure schemes.
Keywords: gravity model; improved field model; sphere of urban influence; regional planning; central China
Citation: Wanghao, Deng Yu, Tian Enze, Wang Kaiyong, 2014. A comparative study of methods for delineating sphere of urban influence: A case study on central China. Chinese Geographical Science, 24(6): 751–762. doi: 10.1007/s11769-014-0678-1
1
Introduction
With rapid socio-economic development, the effect of
urban attraction and radiation has grown extensively.
Individual cities, which scatter around growth hubs,
have built closer relationships with each other and
gradually evolved into urban agglomerations or other
more advanced forms (Lu, 1995; Fang, 2008). At present, as a major form of regional development, urban
agglomeration has been incorporated into the national
strategic development schemes, such as the urban agglomeration emerged in Changjiang (Yangtze) River
Delta (Luo and Shen, 2007), Zhujiang (Pearl) River
Delta (Hu, 2006) and Wuhan metropolitan area (Liu et
al., 2009). In order to improve regional competitiveness,
promote co-operation among cities and effectively take
advantage of the core cities′ role in resources allocation,
it is necessary to identify the relationships among cities
and regions and make the best use of supportive policies
(Lu, 2002).
Sphere of urban influence is fundamentally associated
with the identification of urban agglomeration, the improvement of comprehensive competitiveness of core
cities, and the development of urban hierarchy and supportive policies (Pan et al., 2008). Related theories concerning sphere of urban influence include Central Place
Theory (Christaller, 1933), Breaking-point Theory (Reilly,
1929) and Field Theory (Wang and Chen, 2004). The
Received date: 2013-01-07; accepted date: 2013-05-27
Foundation item: Under the auspices of National Natural Science Foundation of China (No. 40901088)
Corresponding author: DENG Yu. E-mail: [email protected]
© Science Press, Northeast Institute of Geography and Agroecology, CAS and Springer-Verlag Berlin Heidelberg 2014
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basic definition of sphere of urban influence was put
forward through the Central Place Theory. Following
that, more and more revisions were made to the Central
Place Theory. Breaking-point Theory and Field Theory
were developed. Since the 1980s, globalization has become an important aspect of urban and regional study.
In the meantime, World City Theory (Friedmann, 1986),
Network Cities Theory (Batten, 1995), Heartland and
Hinterland Theory (McCann, 1982) and Nation State
Theory (Ohmae, 1995) were developed, which further
clarified and enriched the notion, characteristics and
formation mechanism of sphere of urban influence.
Studying sphere of urban influence is not only to make
clear of the relationship between city and its hinterland,
but also to pay close attention to how the urban-region
system plays its important role in regional and global
level.
There are four methods for delimitating sphere of urban influence: empirical analysis, gravity model, breaking-point model and field model. Comparatively, the
results of empirical analysis are more accurate and
credible; but data collection is more complicated. Also,
there is a lack of detailed commuting data between cities.
Therefore, empirical analysis is often used as testing and
complementary method (Du, 2001). The gravity model,
which is built upon the partitions of urban hierarchy
levels, mainly focuses on the dynamic change of urban
hierarchy levels by analyzing spatial characteristics of
sphere of urban influence and urban system (Huff and
Lutz, 1995). Breaking-point model outperforms the
other methods in studying the interaction between two
different places, because it could clearly delineate two
essential elements of spatial interaction in a concise
manner. However, this method can not delimitate the
boundary directly and needs to take natural and human
elements into consideration, which further increases the
subjectivity of this model (Wang, 2005). The traditional
field model simply applies a single index for the urban
strength and merely considers the diffusion of urban
field effect to occur in an ideal space while ignoring the
anisotropy of spatial expansion (Deng et al., 2010).
In summary, none of the above methods could outweigh the others at all merits. All existing scholarly
works are primarily based on single year dataset with
single method, which lacks dynamic and comprehensive
analysis. Based on these concerns, this study would set
up a comprehensive analysis framework by combing
gravity model and improved field model and conducting
dynamic analysis based on three points in 1990, 2000
and 2007. We first compare these two models by analyzing their similarities and differences. Then we apply
these two models separately to delimitate sphere of urban influence from a comparative analysis perspective
and eventually propose a comprehensive analysis framework for studying the sphere of urban influence and its
dynamic characteristics. The ultimate goal of this preliminary study is to provide recommendations for selecting appropriate method for delineating sphere of
urban influence and developing regional hierarchy system plans and urban spatial structure schemes.
2
Materials and Methods
2.1 Study area
The central China is a comprehensive concept which
combines several aspects of geography, economy and
administration. Therefore, its area varies at different
times. At present the central China refers to six provinces, which are Shanxi, Henan, Hubei, Hunan, Anhui
and Jiangxi (Su and Wei, 2006) (Fig. 1). The central
China was an important part in regional development
framework. But its development pace slowed down
since the imbalanced development strategy was carried
out in the late 1970s, especially in the 1990s when strategic policies such as ′Great Western Development
Strategy′ and ′Northeast Area Revitalizing Plan′ were
implemented. The central China stayed on the ′policy
edge′ for a long time, and fell into the embarrassing
situation of ′central collapse′ (Zhu, 2007). In order to
promote the development of the central region, the state
issued the strategy of ′Rise of Central China′ in 2004.
Since then, the Central China has witnessed rapid development in economic growth.
According to Chinese Urban Construction Statistical
Yearbook 2007 (NBSC, 2008), there were 83 prefecture-level cities and 88 county-level cities in the central
China at the end of 2007, of which the urban population
and GDP accounted for 41% and 60% of the whole region respectively. Overall, there are plenty of small cities compared to megacities in the central China. Referring to the six provinces respectively, there are 11 prefecture-level cities and 11 county-level cities in Shanxi
Province, 18 prefecture-level cities and 20 county-level
cities in Henan Province, 16 prefecture-level cities and 6
WANG Hao et al. A Comparative Study of Methods for Delineating Sphere of Urban Influence: A Case Study on Central China 753
Fig. 1
Location of central China
county-level cities in Anhui Province, 13 prefecturelevel cities and 24 county-level cities in Hubei Province,
14 prefecture-level cities and 16 county-level cities in
Hunan Province, 11 prefecture-level cities and 11
county-level cities in Jiangxi Province. Wuhan urban
agglomeration and the central plain urban agglomeration
are two important growth poles in the central China. The
former consists of 6 prefecture-level cities and 3 countylevel cities lead by Wuhan City, while the latter consists
of 9 prefecture-level cities lead by Zhengzhou City.
Both two urban agglomerations are promoted as national strategic level in National Major Function Oriented Zoning.
2.2 Index selection
We aim to build a comprehensive index system for measuring urban economic strength. We consider that the
scale of an urban area represents its economic development level. Whether a central place can provide more
commodities and services for its peripheral area is also
related to the urban economic development level. Only
when the central place achieves high economic level,
can the potential difference be created between the central place and its peripheral area, and can various kinds
of population, commodities, information and technology
be attracted to flow between them. We measure the
economic development level in both direct and indirect
terms. For direct measurement, we focus on comprehensive economic situation, market, employment and investment. Comprehensive economic situation refers to
the regional GDP and the industrial structure. However,
GDP only represents economic development level superficially. In order to measure economic development
level more comprehensive and veritably, we add the
indexes of employment and market. The index of investment serves as a direct indicator for economic
growth. Other than economic development indexes, we
select indirect measurement including non-agricultural
population, education, medical service and infrastructure in order to understand the complexity of regional
development. It is assumed that only when economic
development achieves a certain level can the regional
government put more efforts and resources into improving education, medical service and infrastructure.
Although it is not possible to cover every single aspect
of economic development, we try to build a comprehensive index system in this study. Twenty-five indexes are
selected to measure urban influence from the above
eight aspects, i.e., comprehensive economic situation,
market, employment, investment, population, education,
medical service and infrastructure (Table 1).
2.3 Data sources
Data are mainly obtained from the Chinese Urban Construction Statistical Yearbook 1990; 2000; 2007 (NBSC,
1991; 2001; 2008). Other data sources include Chinese
Population and Employment Statistical Yearbook 1990;
2000; 2007 (NBSC, 1991; 2001; 2008), China County
Statistical Yearbook 1990; 2000; 2007 (NBSC, 1991;
2001; 2008), Chinese Construction Statistics Yearbook
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Table 1 A comprehensive index system for measuring urban economic strength
Index
Sub-index
Comprehensive
economic situation
Market
GDP (104 yuan), Per captia GDP (104 yuan), GDP per square kilometer (104 yuan), Output value of primary industry (104
yuan), Output value of secondary industry (104 yuan), Output value of tertiary industry (104 yuan), Output value of industry
(104 yuan)
Commercial sale amount (104 yuan)
Employment
Employee amount, Registered jobless population, Salary per captia (yuan)
Investment
Fixed investment (104 yuan), Foreign direct investment on contract (104 yuan), Foreign direct investment in reality (104 yuan)
Population
Non-agriculture population, Non-agriculture population per square kilometer
Education
Amount of primary school, Amount of middle school
Medical service
Amount of hospital, Amount of doctors, Amount of doctors per 104 captia
Infrastructure
Gas usage percent (%), Public transportation vehicles in every 104 people, Urban construction area (km2), Percent of urban
construction area in total area (%)
1990; 2000; 2007 (NBSC, 1991; 2001; 2008). When
necessary, synthesis of data is performed. The spatial
data in this study are based on the electronic version of
the county-level boundary map of China at the scale of
1∶100 000 000 provided by National Geomatics Center
of China (Albers Secant Conic Projection).
2.4 Methods
Both gravity model and improved field model require an
index to represent the urban influence and to measure
the comprehensive impact of urban external radiation.
Therefore, this study would hinge on an appropriate selection of urban influence indexes. As discussed above,
we focus on establishing a comprehensive urban influential index system by employing 25 indexes from eight
aspects. Then we apply the indexes system on the central China for three time points 1990, 2000 and 2007,
providing groundwork for delimitating sphere of urban
influence and other related analysis (Wang et al., 2011).
2.4.1 Gravity model
In this study, we apply the widely adopted gravity model
to demonstrate the regional interaction (distance coefficient is normally assigned as 2). Obviously, the interaction is proportioned to the urban scale and inversely to
the distance (Taaffe, 1962). The specific formula is
shown as follows:
Fij  G
Si S j
rij2
(1)
where Fij is the interaction between city i and city j; G is
the gravity constant; Si and Sj are urban influence index
of city i and city j respectively; rij is the distance between city i and city j.
Using gravity model we first outline gravitational
boundaries of various cities by judging the distances
between the spatial points and their adjacent cities, and
then delimitate the sphere of urban influence. The results of adopting this method are fully consistent with
the improved huff model (Huff and Lutz, 1995). The
classification of urban influential indexes is the basis of
urban hierarchical layering and the prerequisite to delimitate sphere of urban influence. The Central Place
Theory argues that a system of centers (core cities)
emerges in all hierarchy levels and higher-order centers
encompass and carry out all functions/services supplied
by lower-order centers. Laying urban hierarchy by urban
influential indexes could delimitate the sphere of urban
influence accurately across all-level cities in the region,
which is useful for grasping dynamic varying laws of
urban hierarchy from the perspective of spatial changes
of sphere of urban influence.
2.4.2 Improved field model
Traditionally, it is considered that the diffusion effect of
urban field model only occurs in an ideal space, resulting in an overlook of the anisotropy of field extension in
space. In fact, a logical and reasonable measurement of
diffusion effect of urban field model is essential for delimitating the sphere of urban influence accurately.
Given this inadequacy, we adopt the improved field
model based on the measurement of regional accessibility (Wang et al., 2011). The method is as follows:
Fki 
Zk
Tki
(2)
where Fki is the field intensity of city k on point i; Zk is
the urban influence index of city k; Tki is the time cost
from city k to point i.
As Fig. 2a shows, the sphere of urban influence of a
WANG Hao et al. A Comparative Study of Methods for Delineating Sphere of Urban Influence: A Case Study on Central China 755
single city is confined within its outer boundaries. Any
point within the region could be radiated by all the cities.
Field intensity might overlap in space due to factors of
city location and urban influential index. Classifying
spatial points by maximum membership principle helps
determine the extent of membership for each point. On
the other hand, we connect points in equal field intensity
and constitute the sphere of urban influence of given
cities by combining the outer boundaries of single cities′
influence sphere, as shown in Fig. 2b.
After determining the sphere of urban influence, we
analyze the dynamic changes in both the scope and the
size of sphere of urban influence and interpret the development trend and interrelated intensity between cities
within urban agglomerations. Then we select four indicators to identify the patterns of urban spatial organization, i.e. levels of sphere of urban influence in core cities, overlapping areas of sphere of urban influence, the
relationship between overlapping areas of sphere of urban influence and regional average overlapping areas,
and the completeness of urban system. The overlapping
sphere of urban influence indicates a shared public hinterland between two or more cities. It demonstrates a
connection among these cities and the connection is dependent on the size of overlapping areas. By this way,
we measure the interaction intensity among cities and
further clarify the basic patterns, characteristics and development trends of urban spatial morphology.
2.4.3 Integrated study
The improved field model, which chooses sphere of urban influence as study object from the microscopic perspective, extends the study area from sphere of urban
influence groups to urban cluster and agglomeration,
and helps analyze its internal spatial structure and evolution characteristics. The gravity model primarily studies the changes of macro-scale urban hierarchy system
and hinterland, with an emphasis on a city′s escalation
or decline in the urban hierarchy from the spatial perspective. In this study, an integrated method is adopted
by combining the advantages of these two methods. The
study method is shown in Table 2.
First, by using the improved field model we identify
the types of urban agglomeration as a mosaic or a string
type. Then we classify the urban agglomeration into
inner city and outer city based on the size of overlapping
area of urban influence and its connection with core cities.
Thirdly, following the idea of hierarchy of urban influence indexes in gravity model, we study the hierarchy of
different types of cities within the urban agglomeration.
Finally, using gravity model we determine the subordinate relationship between different types of cities within
urban agglomeration and identify their hinterland area.
Fig. 2 Spatial pattern of sphere of urban influence based on improved field model
Table 2 Method and scheme of comprehensive study
Step one
Step two
Step three
Step four
Methods
Spatial distribution of
urban agglomerations
Improved field model
Relationship with core
cities
Improved field model
Hierarchy of cities within the
urban agglomeration
Gravity model
Hinterland and relationship of cities
within the urban agglomeration
Gravity model
Standards
Spatial form
Achievement
Mosaic type; string type
Connection type with
core cities
Inner cities; outer cities
Hierarchy of urban influence
indexes
Hierarchy of different types of
cities
Spatial distribution of sphere of urban
influence
Hinterland and relationship of different
types of cities
Objective
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Chinese Geographical Science 2014 Vol. 24 No. 6
Compared with studies using single model, we are able to
understand some laws and knowledge by applying integrated study, which provides a new method for identifying the development stage and characteristics of urban
agglomeration.
3 Comparison of Theoretical Differences
Between Gravity Model and Field Model
In general, gravity model, based on urban hierarchy
from the central place theory, discusses the evolution of
sphere of urban influence and the difference of urban
functions at different hierarchies, while improved field
model focuses on identifying the intensity between cities as well as the characteristics and patterns of urban
spatial morphology. Through a comprehensive comparison of these two methods, we are able to find out
their differences.
3.1 Differences in theoretical basis
Similarly to Central Place Theory, the gravity model
introduces the Newton gravity formula into urban spatial partition. It assumes that the interaction between
regions is in direct proportion to the urban spatial scale
and in inverse proportion to the distance. Unlike gravity
model, improved field model is based on the urban field
theory regarding the urban regional system as ′urban
field′. The field energy difference between core cities
and the surrounding hinterland leads to ′fluid′ flow in
the field. Downward flowing field energy decreases as
the distance to the core city increases and finally diminishes to zero. In terms of theoretical basis, the gravity
model requires taking into account the interaction between cities and enlarges the study area to the whole
space. On the other hand, improved field model requires
investigating the changes in field intensity in different
city centers and paying attention to the changes of individual cities′ hinterland. The gravity model therefore has
a macroscopic view while improved field model is more
microcosmic.
3.2 Differences in theoretical hypothesis
The gravity model would have to identify the differences between cities before it delimitates the sphere of
urban influence. It theoretically assumes that cities at
different levels undertake different functions and that
there exists a hierarchy of sphere of urban influence. As
a result, we could only delimitate the sphere of urban
influence on the premise of a clearly defined urban hierarchy. On the contrary, improved field model only
emphasize on the relationship between city and its hinterland.
3.3 Differences in theoretical emphasis
The gravity model is developed on the premise that
there are cities at different levels and each level would
have been assigned different functions correspondingly.
By adopting this method, studies on sphere of urban
influence address the changes of urban hierarchy from
the spatial perspective. Based on the decreasing field
intensity over distance, improved field model delimitates the boundary of a city′s hinterland by determining
the threshold value.
3.4 Differences in theoretical processing
In this study, the selection of aggregate indicator as the
index of urban scale inevitably leads to the possibility of
a negative index. In order to remove the negative indexes, models are processed in a flexible way. The gravity model delimitates the sphere of urban influence by
outlining the boundary between pairs of cities, in which
the ratio formula is adopted and the negative indexes are
removed by stretching the projection. Contrarily, improved field model delimitates sphere of urban influence
by measuring the field intensity of all cities, thereby the
negative indexes are removed by adding a fixed constant
to all urban indexes to ensure that the minimum index is
non-negative. When this method is adopted, the sphere
of urban influence of each city would not be affected.
3.5 Differences in theoretical expression
The sphere of urban influence is defined in the gravity
model by obtaining the equal gravitation lines between
cities in the whole area. The sphere of urban influence
of each city will be determined automatically after the
isolines are delineated. In improved field model, however, the sphere of urban influence is defined by determining the threshold of each urban field. In general,
areas with field intensity higher than the threshold
would be considered as the hinterlands of the corresponding city. From what has been discussed above, we
could say that the sphere of urban influence of each city
has different field intensity in improved field model,
which could be shown in 3D map. Yet the sphere of urban influence in gravity model can not be presented in
3D maps for the reason that in the isoline-based gravity
WANG Hao et al. A Comparative Study of Methods for Delineating Sphere of Urban Influence: A Case Study on Central China 757
model, the region within influential spheres of each city
is basically homogeneous.
4 Comparison of Empirical Study by Different Methods
4.1 Similarities
A city has a closer connection with the sphere of urban
influence, namely its hinterland, than other places.
Based on our study of an improved field model, we find
that some hinterlands interact with each other, indicating
that two or more cities share a common hinterland. It
suggests a relationship between cities that share common hinterland. And their correlation extent depends on
the size of the overlapping area. An area can be defined
as the inner city of the core city if its sphere of urban
influence has direct intersection with the core city; otherwise, it would be regarded as the outer city. Taking all
the cities of different connection types in 2007 as example, we find that 77 cities in total have direct interaction
with their core cities, among which 14 inner cities are
associated with Wuhan City. The number of cities that
have indirect interaction with the core cities is 33, 18 of
which are associated with Zhengzhou City (Table 3).
According to the results of the gravity model, cities
tend to decline in urban hierarchy system if they are
adjacent to big cities, especially if they are provincial
capitals. In this study, we notice this trend in both the
Central plain urban agglomeration and the Wuhan urban
agglomeration. From 1990 to 2000, we find that cities at
Table 3
the third level that have declined in urban hierarchy
system include, Kaifeng, Jiaozuo and Xuchang (in Henan Province), which are adjacent to Zhengzhou (the
capital of Henan Province), and Jiujiang (in Jiangxi
Province), which is a city near Nanchang (the capital of
Jiangxi Province). At the fourth city level, Jinzhong, a
city adjacent to the provincial capital Taiyuan in Shanxi
Province, is also found to have declined in the hierarchy.
From 2000 to 2007, a similar trend has been found in
the following cities: Xiantao, which is adjacent to Wuhan in Hubei Province, as well as Xinxiang, Anyang,
Pingdingshan and Luohe (in Henan Province), which are
close to Zhengzhou. The results of our study are consistent with Stabler′s study on Saskatchewan (Stabler et al.,
1992). He argues that the customers could easily bypass
the smaller cities and directly approach to the big center
cities for better services due to improved highway system and increasing use of vehicles. This also partially
explains why some smaller cities have declined in the
urban hierarchy system.
By comparison, we have found the similarity of these
two models. The changes of inner cities′ positions in the
urban levels in the field model works in a similar way to
the ′closeness′ situation in the gravity model. While the
former is based on the size of common hinterland of
core cities in urban agglomeration areas, the latter depends on the distance to core cities. From 2000 to 2007,
for instance, cities in these two urban agglomerations
that have escalated or remained stable in the urban hierarchy are those who have an average overlapping area
All the cities of different connection types in 2007
Connection type
Number
Definition standard
Cities
No connection
58
No intersection
with other cities
Ruijin, Yongzhou, Changning, Leiyang, Wugang, Jinggangshan, Hengyang, Hongjiang,
Shaoyang, Jian, Huaihua, Jishou, Fuzhou, Gaoan, Zhangjiajie, Shangrao, Changde, Dexing,
Jinshi, Shishou, Honghu, Lichuan, Songzi, Dongshi, Huangshan, Jingzhou, Anqing,
Chizhou, Ningguo, Tongcheng, Tongling, Guangshui, Suizhou, Zaoyang, Liuan, Xinyang,
Shiyan, Chuzhou, Huainan, Zhumadian, Tianchang, Mingguang, Fuyang, Wugang, Bangbu,
Shangqiu, Bozhou, Yongji, Hejin, Houma, Fuyang, Linfen, Linzhou, Huozhou, Lüliang,
Yangquan, Shuozhou, Datong
Direct connection
77
Direct intersection
with leading cities
Wuhan-Xianning-Qianjiang-Xiantao-Huanggang-Hanchuan-Yingcheng-Xiaogan-Anlu-Macheng-Daye-Dongzhou-Huangshi-Tianmen-Dongzhou, Changsha-Xiangtan-Zhuzhou-LiuyangMiluo, Taiyuan-Gujiao-Jinzhong-Xinzhou, Hefei-Chaohu, Zhengzhou-Xinzheng-XinmiYinyang-Kaifeng-Xinxiang-Gongyi-Jiaozuo, Nanchang-Fengcheng, Lianyuan-LengshuijiangLoudi, Xiaoyi-Fenyang-Jiexiu, Sanmenxia-Yuncheng-Lingbao, Huaibei-Yongcheng-Suzhou,
Yichang-Yidong-Dangyang, Jiujiang-Ruichang, Chenzhou-Zixing, Nankang-Ganzhou, YichunXinyu, Yuanjiang-Yiyang, Jingdezhen-Leping, Yueyang-Linxiang, Xiangfan-Yicheng, Danjiangkou-Laohekou, Dengzhou-Nanyang, Anyang-Hebi, Luohe-Zhoukou
Indirect connection
33
Indirect intersection with leading
cities
Liling, Pingxiang, Xiangxiang, Shaoshan (Changsha), Wuhu, Maanshan, Xuancheng (Hefei), Changge, Xuchang, Yuzhou, Pingdingshan, Ruzhou, Dengfeng, Weihui, Huixian, Qinyang, Jiyuan, Jincheng, Gaoping, Changzhi, Lucheng, Yima, Yanshi, Luoyang, Mengzhou
(Zhengzhou), Yuanping (Taiyuan), Zhangshu (Nanchang), Xiangcheng, Jieshou (Luohe),
Zhijiang, Jingmen, Zhongxiang (Yichang), Wuxue (Jiujiang)
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Chinese Geographical Science 2014 Vol. 24 No. 6
of over 600 km2 with the core cities. Likewise, other
inner cities in the field model that have declined or
stayed stable in urban hierarchy are similar to the
′nearness′ situation in the gravity model (Table 4). Apparently, whether one city is ′close′ or ′near′ to the core
city is simply determined by distance. In reality, however, this has represented two different types of relationship with the core cities. ′Closeness′ means that the
city is adjacent to core cities. On the one hand, cities of
this type would be the first to be radiated by the core
cities; on the other hand, resources in these cities would
flow to the core cities due to a centripetally gravitational
force. Thus cities close to the core cities are affected by
both gravitational force and radiation effect. In contrast
to the ′closeness′ situation, cities close to the core cities
are only affected by gravitational force with a relatively
alienated relationship with the core cities. In improved
field model, the size of overlapping area with the core
cities could reflect the extent of affinity between cities.
In this regard, a certain level of similarity exists in these
two models.
4.2 Differences
There are three crucial differences in the results of these
two models. First, since the sphere of urban influence
determined by the gravity model seamlessly covers all
study area, the influential sphere of each city only shares
border with its own hinterland. In improved field model,
however, cities are only connected to those cities which
they share common hinterland with because of the existence of blank areas. Thus we can easily distinguish urban agglomerations that maintain close inner relationship through this comparison. Secondly, the gravity
model could only delineate the hinterlands of all cities at
level six in the existing urban hierarchy, but the size of
hinterland differs greatly from what has been determined by improved field model. There are two reasons
for this difference: 1) whether the sphere of urban influence covers all study area; 2) cities in the gravity
model could only serve as level six functions. In the
Table 4
central plain urban agglomeration area, for example, the
size of sphere of urban influence of Zhengzhou at level
six is pretty much the same or even smaller than those
of surrounding cities in the gravity model. Comparatively, the size of Zhengzhou′ s hinterland area determined by urban functions in improved field model takes
a great advantage over other cities (Fig. 3). Thirdly, the
gravity model only considers the relationship between
the center and peripheries. But the sphere of urban influence of high-level cities may include low-level cities.
Accordingly, we find that there is a certain rule by
which low-level cities at the peripheries of high-level
cities′ influence show the escalating or declining trend
in urban hierarchy system. Compared with the gravity
model, no other city within the sphere of urban influence is determined by improved field model and the
relationship between cities is interactive.
4.3 Integrated study
According to the results of improved field model, the
internal structure can be defined as two types, i.e., the
mosaic type and the string type, depending on the significant difference in its internal structure. The basic
spatial characteristic of the mosaic type is that the noneading cities rim the leading city′s influential boundary
or loosely disperse in the leading city′s spheres of influence without any connection to other cities. The
non-leading cities look like many irregular small polygons embedded on the edge or scattered in the middle of
the only large polygon. There is always a strong leading
city in the urban agglomeration of this type, overwhelmingly dwarfing all other cities in the urban hierarchy. The Wuhan urban agglomeration is of a typical
mosaic type. The basic spatial characteristic of the string
type, by comparison, is that the non-leading cities in the
city group closely string up in an enormous number.
Albeit a relatively stronger leading city in the group, the
other cities also have their own strength and they develop
on the same track as the leading one. The central plain
urban agglomeration is of a typical string type (Fig. 4).
Hierarchy of escalation and decline in two urban agglomerations
Change of level
Intensity with big cities
Level escalation
2
Average overlap area is over 600 km
Average overlap area is less than 600 km2
Xinzheng, Ezhou
Xinmi
Level kept stable
Yingyang, Xiaogan, Daye, Huangshi
Kaifeng, Kongyi, Jiaozuo,
Xianning, Huanggang, Anlu
Level decline
Xiantao
Xinxiang, Qianjiang,
Hanchuan, Yingcheng,
Macheng, Tianmen, Chibi
WANG Hao et al. A Comparative Study of Methods for Delineating Sphere of Urban Influence: A Case Study on Central China 759
Fig. 3 Comparison of sphere of urban influence based on gravity Model and improved field model
Fig. 4 Comparison of urban agglomerations between mosaic type and string type based on improved field model
Taking Wuhan and the central plain urban agglomerations as examples, we hereby conduct a further comparative analysis on these two types of urban agglom-
erations (the mosaic type and the string type) by integrating the gravity model and improved field model.
First we find that some inner cities directly linked to
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Chinese Geographical Science 2014 Vol. 24 No. 6
Zhengzhou also have connection with some outer cities.
These inner cities have more strength and higher rankings (mostly are on level four) in the urban hierarchy. In
the Wuhan urban agglomeration, Wuhan plays a predominant role and the inner cities connected to Wuhan
differ in size and levels in the urban hierarchy. Nevertheless, inner cities in the Wuhan urban agglomeration,
mostly on level five and six, do not connect to other
cities.
From the study of urban agglomeration′ s internal
evolution process, we find that all the seven inner cities
were affected by the second-level influence of Zhengzhou in the central plain urban agglomeration in 2000.
Four inner cities were under the third-level influence
and the other two were on the boundary of the thirdevel urban influential sphere of Zhengzhou. Two inner
cities were within the fourth-level urban influential
sphere and no city within the urban influence sphere is
at level 5 or lower. The number of cities affected by
Zhengzhou reduces gradually when influential level
declines, especially beyond level 4. In 2007, there were
still seven cities within the second-level urban influential sphere, six within the third-level urban influential
sphere as well as one, i.e., Gongyi, on the boundary of
the third-level urban influential sphere of Zhengzhou
and Luoyang. There was only one city within the fourthevel influential sphere, but none at level five or lower.
The number of cities within different urban influential
spheres appeared to drop drastically from the higher
level to the lower. Generally speaking, Zhengzhou affects the inner cities within the second and third-level
urban influential sphere, which means that it exerts less
effect on under-third-level functions which might work
independently. Therefore, these inner cities relying on
the radiation of Zhengzhou are to a certain extent capable of independent development as well. In the Wuhan
urban agglomeration, on the other hand, all the 12 inner
cities were within the second-level urban influential
sphere of Wuhan in 2000, six of which were within the
third-level urban influential sphere and two on the
boundary of the third-level urban influential sphere between Wuhan and other cities. In addition, five cities
were within the fourth-level urban influential sphere,
two on the boundary and the other two within the fifthevel urban influential sphere. Compared with Zhengzhou, the inner cities in the Wuhan urban agglomeration
also presented a declining trend on urban functions, but
starting at level five. In 2007, all 14 inner cities were
within urban influential sphere of Wuhan, 10 within the
third-level urban influential sphere, two on the boundary,
another 10 within the fourth-level urban influential
sphere and two on the boundary as well, while there are
six cities within the fifth-level urban influential sphere.
Therefore, the influence of Wuhan extended downward
to the low-level cities and posed more impact on inner
cities than Zhengzhou in general. It is worth noticing
that Wuhan shades the entire urban agglomeration and
limits all other inner cities′ functions.
When it comes to the urban functions of the inner cities, we could find that a third-level city in the central
plain urban agglomeration usually has five or more hinterland cities. There were three third-level cities of this
type in 2000 and two in 2007. A fourth-level city would
have two or more hinterland cites. There were eight
fourth-level cities in this type in 2000 and 11 in 2007. A
fifth-level city usually has one or more hinterland cities.
There were eight fifth-level cities in this type in 2000
and nine in 2007. In the Wuhan urban agglomeration,
except for Wuhan itself, the number of hinterland cities
within the third-level urban influential sphere is up to
five, which is smaller than the counterpart number in the
Central plain urban agglomeration. Three cities could
undertake the third-level functions in 2000 while the
number reduced to two in 2007. In 2000, there was only
one city that could undertake the fourth-level functions
and had the sphere of urban influence. This number increased from one to two in 2007. Plus, there were only
one or two hinterland cities under the impact of these
fourth-level cities. Similarly, except for Wuhan itself,
there were two cities that could undertake the fifth-level
function and have hinterland cities in both 2000 and
2007, and up to one hinterland city would be affected by
these fifth-level cities. It can be seen that the Central
plain urban agglomeration has a clearer urban hierarchy
system in which the coordinate relationship between
core city and its hinterland cities is perceptible, and all
the inner cities have their own functions in this system.
Since Wuhan plays a dominant role in the Wuhan urban
agglomeration, both the number of cities within each
level of urban influential sphere and the hinterland cities
that belong to them are smaller than that of the Central
plain urban agglomeration. Additionally, a much-weakened
city-city interaction would be spotted in the Wuhan urban agglomeration, and all cities are significantly influ-
WANG Hao et al. A Comparative Study of Methods for Delineating Sphere of Urban Influence: A Case Study on Central China 761
enced by Wuhan.
From the discussion above, we can see that two types
of urban agglomeration, i.e., mosaic type and string type,
differ greatly not only in patterns but also in urban internal structure and hierarchy system. It means that the
impact of the core cities on the inner cities and the function undertaken by the inner cities are significantly different.
5
Conclusions
The gravity model focuses on macro-level change of
urban hierarchy system and its hinterland. It analyzes
and predicts the city′s escalation and decline in urban
hierarchy at each level from the spatial perspective.
However, improved field model chooses sphere of urban
influence as the study object from the micro perspective.
It extends the study area from sphere of urban influence
group to urban agglomeration. It also further analyzes
the spatial structure and evolution characteristics of urban agglomerations.
On the one hand, inner cities have a close relationship
with the core cities in improved field model. And their
changes in urban hierarchy system are similar to the
′closeness′ situation in the gravity model. On the other
hand, the spheres of urban influence delimitated by
these two models have significant differences not only
in the size of its spatial coverage, but also in the spatial
patterns within the urban hierarchy system.
Based on a comparison between these two models,
we conduct a comprehensive study on two types of urban agglomeration, which are the mosaic type and the
string type. Then we choose urban spatial characteristics
as the study object in different study regions and finally
discuss the impacts of core cities on the inner cities
within the urban agglomeration. It is found that these
impacts are to be determined by the functions undertaken by those inner cities.
In terms of delineating sphere of urban influence, existing studies have been focusing on static study using
single year data or single method, resulting in a lack of
time-series longitudinal analysis or comprehensive
analysis based on multiple methods. Comprehensive
studies help obtain results and knowledge that can not
be acquired by single model methods, and result in a
more profound understanding of how urban agglomerations are developed. Inspired by the comprehensive
study of multiple models, this study is committed to the
improvement of a single model. For example, we improve the way we measure the spatial distance in the
gravity model and add the dimension of urban hierarchy
into improved field model.
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