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Landscape and Urban Planning 113 (2013) 78–89

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Landscape and Urban Planning

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Research paper

Modeling the urban landscape dynamics in a megalopolitan cluster area by

incorporating a gravitational ﬁeld model with cellular automata

a,∗ b c a

Chunyang He , Yuanyuan Zhao , Jie Tian , Peijun Shi

State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal University, Beijing 100875, China

College of Resources Science & Technology, Beijing Normal University, Beijing 100875, China

Department of International Development, Community, and Environment, Clark University, 950 Main Street, Worcester, MA 01610, United States

h i g h l i g h t s

This paper proposes a new megalopolis landscape dynamic model by combining a gravitational ﬁeld model with a CA model.

The model proposed produced more accurate simulation results than the CA model, which did not account for urban ﬂows.

The model proposed is of great value for locating ‘hotspots’ of future urbanization in a megalopolis cluster area.

The model proposed can provide valuable information for regional landscape planning and environmental management in a megalopolis cluster area.

a r t i c l e i n f o a b s t r a c t

Article history: The effective modeling of the urban landscape dynamics in a megalopolitan cluster area (MCA) is essen-

Received 23 April 2012

tial to understanding its spatial evolution process. However, existing urban landscape dynamic models

Received in revised form 13 January 2013

based on cellular automata (CA) are limited in that they do not consider urban ﬂows (e.g., ﬂows of peo-

Accepted 14 January 2013

ple, material, and information) between the different cities/towns in an MCA. This paper proposes a new

megalopolitan landscape dynamic model (MLDM) that is better suited for simulating the urban land-

Keywords:

scapes in an MCA by combining a gravitational ﬁeld model (GFM) with a CA model. The GFM was used to

Beijing–Tianjin–Tangshan megalopolitan

model the influence of inter-city urban flows and to refine the transition rules of the CA model. The MLDM

cluster area

was applied to simulate the urban landscape in the MCA of Beijing–Tianjin–Tangshan, and produced more

Cellular automata model

accurate simulation results than the CA model that did not account for urban ﬂows. The MLDM-based

Gravitational ﬁeld model

Megalopolitan cluster area prediction of future landscapes suggested that urbanization will continue in the region through 2020,

Urban ﬂow especially in a few ‘hotspot’ areas. Close attention should be paid to these areas for strategic regional

Urban landscape dynamics planning and environmental protection in this heartland of China.

1. Introduction Boston, Philadelphia, and New York covers only 1.4% of US ter-

ritory but is home to 17.3% of the US population (Vicino et al.,

The term megalopolitan cluster area (MCA) refers to a region 2007). In China, the three major MCAs (Yangtze, Pearl River

comprising a considerable number of cities clustered around Delta and Beijing–Tianjin–Tangshan) comprise only 2.2% of the

the regional economic core of one or two super-large cities. country’s territory but are home to 12% of the Chinese pop-

Although these cities can signiﬁcantly differ one from another, ulation and contribute 34% of China’s gross domestic product

they are closely interconnected and have strong interactions due (GDP) (NSBC, 2010). These MCAs have become highly urban-

to the highly developed regional transportation and information ized in the past decades, and the local natural landscapes have

networks (Lang & Knox, 2009; Yao, Chen, & Zhu, 2006). MCAs been removed or considerably changed. This urbanization pro-

are often the most vigorously developing urban areas around the cess has resulted in enormous ecological and environmental issues,

world and attract a great deal of attention (Gu, Hu, Zhang, Wang, such as increased surface temperature and decreased biodiver-

& Guo, 2011; Tian, Jiang, Yang, & Zhang, 2011a; Vicino, Hanlon, sity (Chen, Li, Zheng, Guan, & Liu, 2011; Foley, DeFries, & Asner,

& Short, 2007). For example, the MCA of Washington–Baltimore, 2005; Grimm et al., 2008; Jenerette & Wu, 2001; Nikanorov,

Khoruzhaya, & Mironova, 2011; Valiela & Martinetto, 2007; Yang,

Hou, & Chen, 2011). Spatial process models are important tools for

∗ better understanding the driving forces to urban landscape dynam-

Corresponding author. Tel.: +86 10 58804498; fax: +86 10 58804498.

ics and evaluating their ecological and environmental impacts

E-mail addresses: [email protected] (C. He), [email protected] (Y. Zhao),

(Valbuena, Verburg, Bregt, & Ligtenberg, 2010). There has been

[email protected] (J. Tian), [email protected] (P. Shi).

C. He et al. / Landscape and Urban Planning 113 (2013) 78–89 79

a great need for models that can effectively simulate the urban once established, may not be effectively applied to a different study

landscape dynamics of MCAs to support the urban/regional plan- area; and (3) the physical meaning of the model is not so clear.

ning and the sustainable development in these areas (Berling-Wolff Urban ﬂow refers to the frequent interﬂows of people, mate-

& Wu, 2004a; Wu & David, 2002; Wu, 2010). rial, information, capital, and technologies among a cluster of

At present, the simulation of urban landscape dynamics mainly cities/towns (Zhu & Yu, 2002). There exists a variety of trans-

relies on four types of models (Berling-Wolff & Wu, 2004a; Parker, portation networks including highways, expressways, waterways

Manson, Janssen, Hoffmann, & Deadman, 2003). The ﬁrst type and airways within and between the urban areas in an MCA. The

describes urban structure and morphology in a qualitative way; socio-economics of the cities/urban areas of different sizes strongly

most models of this type were developed before the 1940s, includ- interact with each other, collectively driving the regional develop-

ing concentric zone model, sector model, and multiple nuclei model ment of an MCA. Therefore, urban ﬂows often play a signiﬁcant role

(He, Okada, Zhang, Shi, & Li, 2008). The second type is built upon in the evolution of an MCA (Gu et al., 2011; Limtanakool, Schwanen,

Newton’s theory of gravity, and focuses on depicting the spatial & Dijst, 2007; Seto & Fragkias, 2005). Urban ﬂow intensity char-

interactions between different entities. Typical examples include acterizes the strength of the inﬂuence from the centralization

the gravity model (Foot, 1981) and the Lowry model (Harris, 1985). and decentralization of the cities in an MCA. Zhu and Yu (2002)

The third type uses differential equations to represent the spatial deﬁned the concept of urban ﬂow intensity and used it in analyz-

process; the models of this type were initially proposed in the 1970s ing the urban ﬂows in the HuNingHang megalopolitan cluster. Cao

with the system dynamic models being representative (Gilbert & and Wang (2007) analyzed the intensity of the urban ﬂows in a

Troitzsch, 1999). The last type includes the discrete dynamic mod- city cluster of Northeast China. These studies have suggested that

els that have ﬂourished since the 1970s; the best known examples urban ﬂow intensity is an effective indicator of the strength of the

include cellular automata (CA) (Santé, García, Miranda, & Crecente, socioeconomic interactions between the member cities/towns in

2010) and multi-agent system (Parker et al., 2003) models. CA a megalopolitan cluster area (Derudder & Taylor, 2005; Yao et al.,

models have been widely applied to simulate urban landscape 2006).

dynamics in the past two decades (Berling-Wolff & Wu, 2004b; He The gravitational ﬁeld model (GFM) was ﬁrst proposed by

et al., 2006a; He, Okada, Zhang, Shi, & Zhang, 2006b; He et al., 2008). Lagrange in 1773 to measure the gravitational inﬂuence of a planet

Numerous works have successfully demonstrated the capability of from a distance (Stewart, 1947). In the 1940s, Stewart adopted the

CA models in representing the complex process of urban landscape GFM to represent the inﬂuence of population as a function of dis-

evolution (Barredo, Kasanko, McCormick, & Lavalle, 2003; Fang, tance and applied it for the ﬁrst time in socioeconomic research

Gertner, Sun, & Anderson, 2005; Li & Yeh, 2002; Mitsova, Shuster, (Brown, 1982; Gardiner, Martin, & Tyler, 2011; Stewart, 1941,

& Wang, 2011; Sui & Zeng, 2001). However, a CA model typically 1942, 1947). In the 1980s, Friedman (1986) treated an MCA as an

assumes that the regional pattern change is an aggregate of the urban ﬁeld in which the spatial inﬂuence of one city on another

local changes, and simulates the evolution of an urban ecosystem is inversely related to the distance between them. Liang (2009)

based merely on local interactions (Qi et al., 2004). This approach employed the GFM to calculate the local/regional impact of 670

focuses on micro individual cells and often neglects the links and Chinese cities with non-agricultural populations exceeding 80,000.

interactions between cells and the macro spatial patterns (Qi et al., Wu, Zhang, Jin, & Deng (2009) used a GFM to study the spatial

2004). In addition, the ‘bottom-up’ construction of traditional CA interactions among 18 cities in the coastal area of eastern China

models usually prevents them from fully capturing the macro-scale during 1991–2002, by analyzing the economic, population, and

socioeconomic driving forces of urban landscape dynamics (Ward, transportation data. Most recently, Wang, Deng, Liu, & Wang (2011)

Murray, & Phinn, 2000; White & Engelen, 1997; White & Engelen, used a GFM to investigate the urban expansion in central China from

2000). Therefore, researchers have attempted to extend and 1990–2007. These studies have shown that GFMs are effective in

enhance traditional CA models by incorporating socioeconomic representing the spatial interactions among cities. However, a GFM

models. For instance, White and Engelen (2000) linked a CA model alone is inadequate for representing the complex spatial processes

with a regional development model to simulate the evolution of of the urban landscape evolution in an MCA because it cannot well

urban landscapes for the entire country of the Netherlands. Wu capture the micro-scale dynamics.

and David (2002) integrated hierarchical theory with a CA model This paper presents a new megalopolitan landscape dynamic

to simulate the urban landscape dynamics in the metropolitan model (MLDM) that can better model the urban landscape dynam-

area of Phoenix, AZ, USA. He et al. (2008) incorporated a potential ics in MCAs. The model basically integrates a GFM with a CA model.

model with a CA model to simulate the landscape dynamics in the In the MLDM, the demand for urban land in an MCA is ﬁrst esti-

Beijing metropolitan area. Most recently, Kuang (2011) coupled a mated based on the socioeconomic data. Then, a GFM is employed

CA model with an artiﬁcial neural network model to simulate the to model the urban ﬂows within the MCA. Next, the GFM is incor-

urban landscape changes in the Beijing–Tianjin–Tangshan region, porated in deﬁning the transition rules of a CA model to more

China. These researches have signiﬁcantly enhanced the ability of accurately map the potential new urban cells that are to meet

CA models to accurately simulate landscape dynamics in an urban the urban land demand of the MCA. A case study was conducted

area. by applying the model to simulate the urban landscape dynamics

However, most of the existing models are focused on one single in the Beijing–Tianjin–Tangshan megalopolitan cluster area (BTT-

city and not suitable for modeling the urban landscape dynamics in MCA) of China for the time period of 1990–2009 and to predict the

an MCA. In order to solve this problem, Li and Liu (2006) proposed ‘hotspot’ areas that are highly likely to experience rapid urbaniza-

an extended CA model in which the transition rules were deter- tion from 2009 to 2020.

mined by using a case-based reasoning (CBR) technique. The idea is

to build a case library based on the geographical data including land

use/cover, and then determine the state of a cell state according to 2. Description of the MLDM

the proximity between the cell and the cases in the library calcu-

lated. The advantages of this model include not having to deﬁne the The objective of the MLDM is to consider not only the evolution

transition rules and being possibly able to simulate for complex sit- of individual land cells, but also urban ﬂows between the differ-

uations. The disadvantages include: (1) the model accuracy is highly ent cities/towns in an MCA. Landscape dynamics in an MCA can

sensitive to the representativeness of the case data; (2) the model, be regarded as a self-organizing process inﬂuenced by broad-scale

environmental, geographical, and socioeconomic factors (Barredo

80 C. He et al. / Landscape and Urban Planning 113 (2013) 78–89

2.1. Estimating the demand for urban land

Core city

Sub -core city

At present, several non-spatial models are available for estimat-

Major city ing the demand for urban land in an MCA during a given time period,

including the linear programming model (Wang, Yu, & Huang,

Other cities

2004), the regression analysis models (López, Bocco, & Mendoza,

Road

Influence of urban flows beyond the 2001; He et al., 2008), and the system dynamic models (He et al.,

neighborhood (arrow thickness

2006a,b). The regression analysis models are merited for the rel- represents the urban flows of cities at

different hierarchical levels)

atively simple calculations and fewer parameters required. López

Non-urban landscape occupied in the

process of urban landscape evolution et al. (2001) suggested that the population residing in an urban area

is highly correlated with its size. Therefore, historical data on the Urban landscape

Neighborhood

size of an urban area can be regressed on its population and the

space

regression model can be further used to predict the future demand

Fig. 1. The conceptual model. for urban land based on population growth data. Please refer to

section 3.4 for further details.

2.2. Defining the influence of urban flows on landscape evolution

As discussed by Liang (2009) and Wang et al. (2011), an MCA

can be regarded as a ﬁeld of urban ﬂow intensity, which decreases

et al., 2003; He et al., 2008). The MLDM assumes that the evolution

over distance from the city centers. We adopted this concept and

of the urban landscape in an MCA is shaped by the regional demand

used the GFM to quantify the inﬂuence of urban ﬂows on the land-

for urban lands and the potential conversion of a non-urban land

scape evolution in an MCA. According to Liang (2009), the inﬂuence

cell to an urban cell is co-determined by local neighborhood fac-

of urban ﬂows on a non-urban cell (x, y) at time t ( Ii,x,y) can be

tors (from a CA model perspective) and the inter-city urban ﬂows

expressed as follows:

within the MCA. The model therefore integrates a GFM with a CA

t Fi

model so that the inﬂuence of urban ﬂows can be modeled by the Ii,x,y = (1)

D x,y,x ,y

former while that of local neighborhood factors can be modeled by ( i i)

the latter (Fig. 1). t

where Ii,x,y is the intensity of the urban ﬂow from city i at cell (x,

The MLDM consists of three parts: (1) the estimation of demand D

y); (x,y,xi,yi) is the Euclidean distance from the city center (xi, yi) to

for urban land in an MCA; (2) a GFM-based deﬁnition of the inﬂu-

the cell (x, y); and Fi is the urban outﬂow from city i. As suggested

ence of inter-city urban ﬂows on the urban landscape evolution;

by Zhu and Yu (2002) and Yao et al. (2006), Fi can be calculated as

and (3) the prediction of future urban land cells by considering the

follows:

urban flow influence defined in (2) in framing the transition rules

F = N

× E

of the CA model (Fig. 2). i i i (2)

Urban flow of core cities Suitability

Urban flow of sub-core cities Gravational Neighborhood effect Urban flow of major cities field model

Urban flow of other cities Inherited attribute

Ecological constraints Urban flow influence Local driving forces Population

Economy Driving forces Resistant forces

Regional factors Local factors

Statistical model Cellular automata model Demand-supply balance Urban landscape demand Urban landscape supply

Urban land area Urban land location

Urban landscape dynamics

Fig. 2. Flowchart of the megalopolitan landscape dynamic model.

C. He et al. / Landscape and Urban Planning 113 (2013) 78–89 81

where Ni stands for the internal function (the ability of city i in (x, y) from being converted to urban use. The random perturbation

an MCA to support itself), which can be fairly well represented by term Vx,y can be constructed as:

the city’s GDP per employee. Ei denotes the external function (the t a

Vx,y = 1 + [− ln(rand)] (9)

ability of city i to support other cities in the MCA), which can be

represented by totaling the external functions of all the economic

where rand (0 < rand < 1) is a random variable and a is an adjustable

sectors of city i as follows (Yao et al., 2006; Zhu & Yu, 2002):

parameter representing the magnitude of the random perturba-

m tion. To keep the calculation manageable while incorporating urban

Ei = Eij (3) ﬂows into the transition rule of a CA model, the probability x,y for

a non-urban cell to be converted into an urban cell can then be j=1

expressed as:

where E is the output function of a speciﬁc economic sector (j) of

ij m−n

city i, and m is the number of sectors in city i. E is calculated as ij t P = W × t t

x,y i Si,x,y + Wm−n+1 × Nx,y

follows because it is effective and the data required to calculate for

i=1

it are usually available: G m−1

j t t t t

E = G − G × + W × I − W × J × EC × V ij ij i G (4) i i,x,y m x,y r,x,y x,y

i=m−n+2 r=1

where Gij is the number of employees in economic sector j of city (10)

i, Gi is the number of employees in all the economic sectors of city

m−nW ×t S

i, Gj is the number of employees in economic sector j of the entire where i=1 i i,x,y is the suitability for the conversion at time

MCA, and G is the total number of employees of the MCA. If Eij ≤ 0, t. i,x,y is a standardized suitability score [0, 100] based on the

. . .

the economic sector j of city i has no output function and Eij is given consideration of a number (i = 1, , m – n) of factors. m is the total

a value of 0. If Eij > 0, it means that the economic sector j of city i number of weights and m – n is the number of suitability factors. Wi

has an output function for the other cities in the MCA because the denotes the weight associated with each factor. x,y represents the

− proportion of employees in the sector j of city i is larger than that of neighborhood effect for cell (x, y) at time t and Wm n + 1 is its asso-

m−1 t

the entire MCA. In other words, the sector j is more centralized in W × I

ciated weight. The term i=m−n+2 i i,x,y quantiﬁes the overall

city i than the other cities/towns in the MCA and therefore has an urban ﬂow inﬂuence from all the cities/towns in an MCA, in which

output function to support the other cities in the MCA. A larger Eij Ii,x,y is the urban ﬂow inﬂuence from the cities of a comparable

value indicates a stronger output function for the economic sector size k and Wi is the corresponding weight. Jx,y is the continuity

j of city i (Yao et al., 2006). attribute of cell (x, y) and Wm is its weight. These weights (W1, W2,

When a land cell is inﬂuenced by the urban ﬂows from cities . . ., Wm) are used to represent the relative importance of the fac-

of similar sizes, the maximum inﬂuence is accounted (Wang et al., tors that drive or resist urban landscape changes. r=1 ECr,x,y is the

2011). Thus, for a non-urban cell (x, y), the urban ﬂow inﬂuence product of a few binary variables used to represent the ecological

(Ik,x,y) from a number (s) of cities with a comparable size of k, can constraints on the urban landscape change, such as being located

be expressed as: in an area of nature reserve or water protection. ECr,x,y will have a

value of 0 if cell (x, y) is preserved due to constraint r.

I = I , I , . . . , I

k,x,y max( k1,x,y k2,x,y ks,x,y) (5)

Neighborhood size is essential in running a CA model, as it

should well deﬁne the extent of interactions between land uses and

2.3. Calculating the probability of land change

the scale of the land dynamics of an ecosystem (Caruso, Rounsevell,

& Cojocaru, 2005). According to Barredo et al. (2003), He et al. (2008)

According to Barredo et al. (2003), He et al. (2008) and White

and White and Engelen (2000), a neighborhood in the MLDM is a

and Engelen (2000), the urban landscape evolution in an MCA can

circular area around the cell of interest with a radius of ﬁve cells.

be understood as a complex process determined simultaneously

This deﬁnition of neighborhood is believed to be appropriate for

by driving forces, resistant forces, and random perturbation. In the

capturing the local urban cells’ agglomeration effect (Chen, Gong,

MLDM, the driving forces primarily include: (1) land suitability, (2)

He, Luo, & Tamural, 2002). The neighborhood effect Nx,y can be

the contextual effect of a local neighborhood, and (3) the macro-

quantiﬁed as:

level urban ﬂows from the different cities in an MCA. t

t t Uc

The probability Px,y for cell (x, y) to be converted into urban use

N = A ×

x,y C (11)

at time t can be expressed as: c

t t t t

Px,y = f ( Dx,y, Rx,y, Vx,y) (6) t

where Uc indicates whether a cell at the distance C from cell (x, y)

t D t t is urban. Uc will have a value of 1 if it is urban and 0 if not. A is a

R V

where x,y, x,y, and x,y represent the driving forces, resis- t

scalar used to linearly standardize Nx,y into the range of [0, 100].

tant forces, and random perturbation inﬂuencing the land change, t

t Once the probability PK,x,y for cell (x, y) to be converted into

respectively. Dx,y can be further expressed as:

urban use from a type z is determined, the evolution of the urban

t t t t

D = f

x,y ( Sx,y, Nx,y, Ix,y) (7) landscape can be simulated with respect to the total demand for

urban land. To simplify the computation of the model, we can gen-

t S t t

where x,y stands for the suitability, and Nx,y and Ix,y represent

erally classify the various land use types into urban and non-urban,

the neighborhood effect and the urban ﬂow intensity, respectively.

t and only model the conversion processes from one generalized type

The resistant force Rx,y can be considered a function of two vari-

to the other. Competition for space among different types of land

ables as follows:

use does not need to be considered because almost all the consump-

t t t tion of non-urban lands in our study area is for urban development.

Rx,y = f ( Jx,y, ECx,y) (8)

The simulation of the urban landscape dynamics in an MCA follows

t t

J P where x,y is the continuity attribute for cell (x, y) to maintain its a repetitive computational workﬂow. K,x,y is calculated for each

t t

current land use or cover state (z) at time t. ECx,y is the ecological cell, and the cell with the highest K,x,y value is labeled as a future

constraint (e.g., located in an reservation area) that prevents a cell urban cell with high conﬁdence. If the estimated total demand for

82 C. He et al. / Landscape and Urban Planning 113 (2013) 78–89

urban land in the simulated period cannot be satisﬁed by changing Mainland China, respectively (NSBC, 2010). Since China imple-

that cell into urban use, another iteration begins. The loop continues mented its open-door policy in the 1970s, the BTT-MCA has

until the total area of urban land reaches the demand. experienced tremendous urbanization (Kuang, 2011; Tan et al.,

2005).

A series of land use/cover maps (1990, 2000, and 2009) for the

3. Applying the MLDM to simulate the urban landscape BTT-MCA were used in this study. All of these maps were pro-

dynamics in the BTT-MCA, China duced from the classiﬁcation of Landsat TM/ETM+ images of good

quality and have six land use/cover classes (urban land, cropland,

3.1. Study area and data grassland, forest, water, and others). Socioeconomic data (e.g., pop-

ulation, GDP, and number of employees in each economic sector)

The study area of BTT-MCA is located in the North China Plain from the National Statistics Bureau of China (NSBC) were also col-

◦ ◦

with a latitude range of 38 28 N to 41 05 N and a longitude lected and included in our modeling. A digital elevation model was

◦ ◦

range of 115 25 E to 119 53 E. It has a total spatial area of about obtained from the International Scientiﬁc Data Service Platform

55,774.5 km and accounts for 0.5% of the total area of China. The (http://datamirror.csdb.cn/dem/ﬁles/ys.jsp, accessed 02.02.12) to

BTT-MCA consists of 43 cities and towns, including Beijing, Tianjin, represent the regional topography, and a number of geographi-

Tangshan, Qinhuangdao, and Langfang (Fig. 3). Beijing is the cap- cal information system (GIS) data layers were also collected from

ital of China and the political and cultural center of the country the National Administration of Surveying, Mapping, and Geoin-

as well. Tianjin is the third largest city and the largest port city in formation of China, including administrative boundaries, rivers,

North China. Beijing and Tianjin are under the direct jurisdiction road networks, city centers, airports, and coastal ports. All the GIS

of the central government, and are regarded as the ‘dual core’ of data were georegistered to the Albers Conical Equal Area projec-

the BTT-MCA (Tan, Li, Xie, & Lu, 2005). In 2009, the urban popu- tion and the raster datasets were resampled to have the same

lation and the GDP of the BTT-MCA were 20.68 million and 2250 cell size of 300 m (1228 columns, 969 rows), which was sufﬁ-

billion Chinese Yuan, accounting for 6.61% and 3.33% of the totals for cient to capture the detailed information about urban landscape

Fig. 3. The study area.

C. He et al. / Landscape and Urban Planning 113 (2013) 78–89 83

(a) made for urban CA models with the development of two types

100% of calibration methods (Li & Yeh, 2002). One of them is based on

90% mathematical and/or statistical analysis, such as logistic regression

80% (Wu, 2002) and artiﬁcial neural networks (Kuang, 2011). The other

70% type are the trial and error approaches, including visual tests (Ward

60% et al., 2000), landscape metrics comparisons (Berling-Wolff & Wu,

50% 2004b), and computer simulation comparisons (He et al., 2008).

40% As suggested by Chen et al. (2002) and He et al. (2008), an adap-

30% tive Monte Carlo approach was chosen to automatically calibrate

20% the parameters in the MLDM. This approach is mainly driven by

10% data and avoids subjective determination of the weights used in the

0% transition rules of the CA model. Speciﬁcally, a Monte Carlo samp-

Proportion of urban population l Core city Sub-core city Major cities Other cities

ling process was used to search for the optimal combinations of

(b) weights that resulted in the most accurate simulation results. Since

40% all the weights in a transition rule should total to 1, the calibration

35% process can be expressed as follows:

30%

Objective function max A(w1, w2, · · ·, wm) (13) 25% m

20%

Constrained condition wk = 1 (14) 15% k=1

10%

Proportion of GDP where wk is the weight for factor k and A is a measure of agreement

between the simulation result and the reality. We chose the kappa

0% index for A because it is widely recognized as an effective mea-

Core city Sub-core city Major cities Other cities

sure of accuracy for remote sensing classiﬁcations. As suggested by

Chen et al. (2002) and He et al. (2008), up to 500 iterations were

Fig. 4. Socioeconomic discrepancies between the cities in the

conducted to achieve the best performance. Although the simula-

Beijing–Tianjin–Tangshan megalopolitan cluster area in 2009.

tion was computationally intensive, it was manageable with the

strong computing power of our workstations.

dynamics while keeping the volume of computation manageable

The 2000 and 2009 urban land use maps were used to cali-

(Kuang, 2011).

brate the MLDM by treating the 1990 map as the starting point.

Thirteen of the most important impact factors were incorporated

3.2. Calculating the inﬂuence of urban ﬂows between cities in the

in the MLDM, including the inﬂuence of the urban ﬂows from all

BTT-MCA, China

the four categories of cities, slope, distances to highways, railways,

expressways, coastlines, airports, harbors, and city centers, neigh-

Based on their socioeconomic characteristics in 2009, the 43

borhood effect, and continuity attribute. Since it is understandable

cities/towns in the BTT-MCA were classiﬁed into four categories:

that the inﬂuence of urban ﬂows was dynamic, and therefore it was

(1) the primary core city of Beijing, (2) the secondary core city of

modeled for 1990, 2000 and 2009 in order to simulate the urban

Tianjin, (3) the major cities of Tangshan, Langfang, and Qinhuang-

landscape change during 1990–2000, 2000–2009 and 2009–2020.

dao, and (4) the other smaller cities and towns (Fig. 4). The inﬂuence

Because these factors were measured in different units, they were

of the urban ﬂows from the cities in each category was calculated

all scaled into the range of [0, 100]. Urban landscape dynamics

from the GIS data using Eq. (1). The inﬂuence values were subse-

were simulated for the periods of 1990–2000 and 2000–2009, with

quently standardized into the range of [0, 100] using the following

500 different sets of weights for the 13 impact factors. The sim-

formula and the resultant maps are displayed in Fig. 5.

ulated urban landscapes for 2000 and 2009 based on each set of

− I weights were compared with the actual urban landscapes in these

min

Is = × 100 (12)

two years. The most accurate simulation results achieved a kappa I − I

max min

index value of 0.81 and 0.82 for 2000 and 2009, respectively.

where I is the standardized influence of an urban flow influence,

s The set of weights that produced the most accurate simula-

I is the raw minimum inﬂuence value while I is the raw

min max tion results (Fig. 6) are displayed in Table 1. As suggested by Santé

maximum.

et al. (2010), the single use of Kappa index is not enough to assess

the urban spatial patterns generated by CA models. So we per-

3.3. Model calibration and urban landscape simulation from formed the further accuracy assessment of the simulated results

1990 to 2009 using Moran I index by referring to the relative works of Wu (2002)

and Liu, Li, Liu, He, & Ai (2008b). It was found the Moran I values

Calibration and validation are critical for the performance of CA of the simulated urban pattern in 2000 and 2009 are 0.93 and 0.96,

models because it largely depends on the appropriateness of the respectively, close to the actual urban pattern’s 0.97 and 0.99. Over-

transition rules, which typically involve several important parame- all, the simulation results by the MLDM matched the actual urban

ters (Wu, 2002; Straatman, White, & Engelen, 2004). The calibration landscapes quite well, although some small-scale details were not

of the MLDM is usually conducted based on reliable historical effectively captured. To assess their importance to the model, the

data, which hopefully facilitates the effective simulation of future inﬂuence of the urban ﬂows was excluded from consideration in

urban landscape dynamics (Wu, 2002). However, the calibration a test simulation for both periods. The highest kappa index val-

and validation of urban CA models are in fact rather challenging ues for the two year were both below 0.8, 0.75 and 0.78 for 2000

due to the complexity of urban landscape evolution processes and and 2009, respectively. Meanwhile, their Moran I values are 0.89

the numerous combinations of parameters involved (Verburg, De in 2000 and 0.93 in 2009, also more different to the actual’s 0.97

Nijs, Ritsema van Eck, Visser, & De Jong, 2004). Progress has been and 0.99 than the simulated results with urban ﬂow. The lower

84 C. He et al. / Landscape and Urban Planning 113 (2013) 78–89

Fig. 5. Inﬂuence of urban ﬂows (from the different cities) on urban landscape dynamics within the Beijing–Tianjin–Tangshan megalopolitan cluster area, China, 2009.

Fig. 6. Model calibration and urban landscape simulation in the Beijing–Tianjin–Tangshan megalopolitan cluster area, China (1990–2009).

C. He et al. / Landscape and Urban Planning 113 (2013) 78–89 85

Table 1

Calibrated weights for the periods of 1990–2000 and 2000–2009.

Factors Weights for 1990–2000 simulation Weights for 2000–2009 simulation

Slope 0.03 0.06

Distance to highway 0.09 0.02

Distance to railway 0.06 0.04

Distance to expressway 0.01 0.12

Distance to coastline 0.04 0.01

Distance to airports and harbors 0.01 0.09

Distance to city centers 0.05 0.02

Urban ﬂow inﬂuence of core city 0.09 0.1

Urban ﬂow inﬂuence of sub-core city 0.01 0.12

Urban ﬂow inﬂuence of major cities 0.04 0.05

Urban ﬂow inﬂuence of other towns 0.14 0.12

Neighborhood effect 0.25 0.19

Continuity attribute 0.18 0.06

accuracy indicates the signiﬁcance of accounting for urban ﬂows where y stands for the urban population and x stands for a year

in the simulation. The simulations that do not account for urban relative to 1990 (e.g., x = 6 for 1995). The regression was found to

ﬂows tend to overestimate the roles of neighborhood effect and have a very strong predictive power, with an r of 0.97.

the transportation networks in driving the urban landscape evolu- Subsequently, another regression model (Eq. (16)) was devel-

tion in an MCA. For example, the MLDM accounting for urban ﬂows oped based on the historical data (1990–2009) on the urban

suggested that, in 2000, newly converted urban lands were dis- population and the corresponding total area of urban land in the

tributed more around Beijing than around the other pre-existing BTT-MCA (Fig. 8):

urban areas [Fig. 6(a2)]. This is a much more accurate represen-

y = . x − .

3 27 3171 05 (16)

tation of the actual situation than what was produced by the CA

model that did not consider urban ﬂows which showed a relatively

where y stands for the total area of urban land and x stands for the

uniform distribution of newly converted urban lands around all

total urban population. This regression model was also found to

the pre-existing urban areas [Fig. 6(a1)]. The MLDM accounting for 2

have a rather strong predictive power (r = 0.99).

urban ﬂow inﬂuence also correctly suggested that the newly con-

The historical and predicted data of urban population, GDP, and

verted urban lands were mainly located around Tianjin and the

urban land area for the BTT-MCA are summarized in Table 2.

northeast of Beijing in 2009 [Fig. 6(b2)].

Future urban landscapes in the BTT-MCA were simulated for

2009–2020 using the calibrated MLDM and the estimated future

3.4. Prediction of urban landscape dynamics from 2009 to 2020 demand for urban land. Fig. 9 displays the simulated urban land-

scapes for 2015 and 2020, which clearly suggest a continuing

The ability to predict the future urban landscape in the BTT- urbanization in the region. Fig. 10 highlights the areas in the BTT-

MCA is very important. In order to predict the future landscape in MCA that are likely to be converted into urban use before 2020,

the study area using the proposed MLDM, we ﬁrst estimated the mainly including the northeast of Beijing, the east of Tianjin, and

future demand for urban land based on population growth data the outskirts of Langfang. Such foreseeable rapid urbanization in

(1990–2009) for the BTT-MCA (Fig. 7). A linear regression model the BTT-MCA may create or intensify environmental and ecolog-

(Eq. (15)) was built to predict urban population on year: ical problems, such as air pollution, biodiversity reduction, and

local/regional climate change (Chen et al., 2002, 2011). Therefore,

= . x + .

39 17 1257 27 (15) the highlighted areas deserve closer attention for a more effective

management of this heartland of China.

2200

4000 y = 3.27 x –3171.05

2 2000 y = 39.17 x + 1257.27 3500 R = 0.99 R 2 = 0.97 ) 2 1800 3000

1600 2500

1400 2000 Urban population (10,000s) l Urban landscape area (km 1200 1500

1000 1000

0 2 4 6 8 101214161820 1300 1500 1700 1900 2100

Time Urban population (10,000s)

Fig. 7. Linear regression of urban population on year in the Fig. 8. Linear regression of urban land area on population in the

Beijing–Tianjin–Tangshan megalopolitan cluster area, China. Beijing–Tianjin–Tangshan megalopolitan cluster area, China.

86 C. He et al. / Landscape and Urban Planning 113 (2013) 78–89

Table 2

Urban population, gross domestic product (GDP), and urban land area in the Beijing–Tianjin–Tangshan megalopolitan cluster area, China (1990–2020).

Year Urban population (10,000s) GDP (billions of Yuan) Urban land area (km )

1990 1356.83 246.62 1296.09

2000 1626.1 748.21 2094.75

2009 2068.32 2250.45 3609.90

2015 2275.82 3857.78 4270.88

2020 2471.69 6686.50 4911.38

Fig. 9. Simulated urban landscape dynamics in the Beijing–Tianjin–Tangshan megalopolitan cluster area, China (1990–2020).

C. He et al. / Landscape and Urban Planning 113 (2013) 78–89 87

Fig. 10. ‘Hotspot’ areas of future urbanization in the Beijing–Tianjin–Tangshan megalopolitan cluster area, China (by 2020).

4. Conclusion and discussion to upgrade the MLDM in our future research in hope to achieve

an even higher accuracy. Third, the MLDM currently does not yet

The urban landscape dynamics in an MCA are driven by many consider the behaviors of different stakeholders (e.g., government,

factors on different scales. Socioeconomic interactions in form of enterprises, and individuals) for their inﬂuence on the landscape

urban ﬂows between the cities and towns in an MCA play an impor- evolution of an MCA, but has the potential to incorporate them by

tant role in shaping its landscape evolution. Present CA models drawing ideas from the newly developed agent-based urban land-

focusing on a single city often fail to account for the inﬂuence of scape simulation models (Fontaine & Rounsevell, 2009; Li & Liu,

urban ﬂows and are therefore inadequate for accurately simulat- 2007; Tian, Ouyang, Quan, & Wu, 2011b; Valbuena et al., 2010).

ing the urban landscapes in MCAs. This paper proposed an MLDM Fourth, although the proposed MLDM indirectly considers the inﬂu-

that enhances a CA model by accounting the inﬂuence of urban ence of macro-factors by incorporating the socio-economic data

ﬂows with the aid of a GFM. and urban planning information (e.g., the distribution of reserva-

After calibrated, the MLDM was able to simulate the urban land- tion zones), it remains to be a research challenge to fully consider

scape dynamics in the BTT-MCA, China, more accurately than the the macro level socioeconomic and political factors due to their

CA model that does not consider urban flows. The kappa index complexity and difficulty to be quantified. Lastly, it is a limitation

values for the simulated urban landscapes increased from 0.75 to of the present MLDM that more detailed land uses/covers are not

0.81 in 2000 and 0.78 to 0.82 in 2009, respectively. The simulation differentiated in the urban ﬂow calculation or suitability evalua-

results suggested a continuing urban growth in the BTT-MCA and tion. Future research efforts will be spent to upgrade the model

showed that the future urbanization is most likely to take place by allowing the consideration of more detailed land uses/covers

in the northeast of Beijing, the east of Tianjin, and the outskirts of (White & Engelen, 2000).

Langfang. Close attention should be paid to these areas to effectively Nevertheless, the MLDM is of great value to effective

detection, study and solve the problems associated with such urban urban/regional planning and environmental management (He,

expansions in hope for a sustainable development in the region. Tian, Shi, & Hu, 2011). This study has shown that accounting

The highly accurate simulation of urban landscape dynamics the inﬂuence of urban ﬂows improves the MLDM and makes it

is rather challenging due to the complexity of an MCA. The pro- more effective; the kappa index values for the simulation results

posed MLDM certainly needs to be further tested and improved in increased from 0.75 to 0.81 in 2000 and 0.78 to 0.82 in 2009, respec-

a number of ways. First of all, further research should be done to tively. It is clear that urban ﬂows have signiﬁcant impact on the

determine the sensitivity of the simulation result to the number landscape evolution and regional development in an MCA. So the

of iterations in the model calibration. Second, it should be pointed interaction and synergic development between cities/towns should

out that the linear transition rules have limitations in capturing be adequately considered in urban and regional planning. More-

the complexity of urban landscape dynamics. More advanced tech- over, highways, expressways, urban ﬂows from core cities, and

niques have been adopted to deﬁne complex transition rules in neighborhood effects were found to be relatively stronger forces

the recent years including support vector machine (Yang, Li, & Shi, in shaping in the landscape of an MCA. We can possibly control the

2008), kernel-based non-linear technique (Liu, Li, Shi, Wu, & Liu, evolution of the urban landscape by, for example, strategically pla-

2008a), ant intelligence (Liu et al., 2008b), and ant colony opti- cing the new transportation infrastructure, and regulating on the

mization (Li, Lao, Liu, & Chen, 2011). These techniques may be used growth and clustering of the towns surrounding the major cities of

88 C. He et al. / Landscape and Urban Planning 113 (2013) 78–89

Beijing and Tianjin. The simulation result also suggested that the Jenerette, G. D., & Wu, J. (2001). Analysis and simulation of land-use change in the

central Arizona-Phoenix region, USA. Landscape Ecology, 16, 611–626.

‘hotspots’ of future urbanization will be located in northeast of Bei-

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jing, east of Tianjin, and in the outskirts of Langfang. Agricultural

Beijing–Tianjin–Tangshan Metropolitan Area. Journal of Geographical Science,

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Li, X., Lao, C., Liu, X., & Chen, Y. (2011). Coupling urban cellular automata with ant

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Acknowledgments Journal of Geographical Information Science, 20, 1109–1136.

Li, X., & Liu, X. (2007). Deﬁning agents’ behaviors to simulate complex residential

development using multicriteria evaluation. Journal of Environmental Manage-

This research was supported by the Natural Science Founda-

ment, 85, 1063–1075.

tion of China (Grant Nos. 41222003 & 40971059), the National Li, X., & Yeh, A. G. O. (2002). Neural-network-based cellular automata for simulat-

ing multiple land use changes using GIS. International Journal of Geographical

Basic Research Program of China (Grant No. 2010CB950901), and

Information Science, 16(4), 323–343.

the National High-Tech Research Program of China (Grant No.

Liu, X., Li, X., Shi, X., Wu, S., & Liu, T. (2008). Simulating complex urban develop-

2009AA122004). We would like to express our respects and grat- ment using kernel-based non-linear cellular automata. Ecological Modelling, 211,

169–181.

itude to the anonymous reviewers and editors for their valuable

Liu, X., Li, X., Liu, L., He, J., & Ai, B. (2008). A bottom-up approach to discover tran-

comments and suggestions on improving the quality of the paper.

sition rules of cellular automata using ant intelligence. International Journal of

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