The Demarcation of Urban Development Boundary Based on the Maxent-CA Model: A Case Study of Wuxi in China

Abstract

With the rapid development of urbanization, the demarcation of the urban development boundary (UDB) is of great practical significance to curb the disorderly spread of urban land, avoid losing control of urban development space, and build a barrier to green development space. In this paper, we propose a method to support the demarcation of the UDB by combining the Maxent model and the cellular automata (CA) model. This approach comprehensively considers the relationship between urban construction suitability, neighborhood effect, spatial constraint, and random interference based on a spatio-temporal dynamic simulation. This contributes to the analysis of the driving mechanism and distribution pattern of urban expansion. According to the principle of scale expansion and centralization, the simulation result is modified to demarcate the UDB. The following conclusions are drawn: the Maxent-CA model can intuitively reflect the driving mechanism and accurately simulate urban expansion in specific cities, which contributes to demarcating the UDB. Considering that this method fully embodies the principle of combining top-down and bottom-up approaches in the demarcation of UDB, we argue that the Maxent-CA model is of vital importance for the sustainable development of the living environment and is of great reference value for territorial spatial planning.

1. Introduction

Since the reform and opening up in 1978, social economy development and urbanization in China have experienced rapid growth [1,2]. According to the seventh population census in China, the urbanization rate of the population reached 63.89% in 2020. From 2010 to 2020, the built-up area in Chinese cities increased from 40,058.01 km² to 60,721.32 km², an increase of 1.52 times. Comparatively, the urban population increased from 669.78 million to 902.20 million in a decade, which was only an increase of 0.34 times. The rate of urban expansion is much higher than that of population growth. This pattern of urban sprawl is prone to causing serious urban and rural problems, such as the occupation of high-quality cultivated land resources, tough livelihoods for land-lost farmers, a declining trend of industrial development, low land use efficiency, aggravated environmental pollution, and population hollowing issues [3,4,5,6]. Controlling the excessive urban expansion and ensuring the sustainable intensification of cultivated land [7] to achieve a green, low-carbon, efficient and intensive spatial pattern of land use have become one of the hot issues of academic research [8]. However, as the largest developing country, China is still in a period of rapid urbanization, which means that urban expansion is inevitable. Therefore, facing the contradiction between economic development and environmental pressure, China has put forward the concept of the “urban development boundary (UDB), ecological protection red line, and permanent basic farmland” in its territorial space planning to achieve a balance between urban development, ecological protection, and food security [9,10]. Among the three control lines, the UDB is an effective means to curb the disorderly spread of urban land, avoid losing control of urban development space, and build a barrier to green development space. It has become a key task in China’s territorial space planning and a primary measure used to control urban expansion.

The UDB, originally called the urban growth boundary (UGB), is a regional planning tool to protect rural areas and promote the compactness of cities [11,12]. After World War II, the rapid development of car traffic in Western countries resulted in problems such as suburban urbanization, central city recession, and disordered urban sprawl [13]. Thus, various countries began to pay attention to the coordinated development of cities and peripheral space. In 1976, the USA first applied the UGB theory to define the urban development scope in Salem [13]. Subsequently, the USA incorporated the UDB theory as a policy control tool [14] into the smart growth movement [15]. The demarcation of the UDB in the Portland metropolitan area is a typical form of integration of policy and theory [16]. Zhang [17] first introduced the UDB theory into China, but it was not until 2014 that Chinese research on the UDB turned from academic inquiry to practical implementation. The report of the 19th National Congress of the Communist Party of China in 2017 stressed the need to complete the demarcation of three control lines. In the Guiding Opinions regarding Coordinating the Delimitation and Implementation of Three Control Lines in National Spatial Planning in 2019, the General Office of the State Council, once again, emphasized the strict demarcation and implementation of three control lines, hoping to form a more scientific and orderly territorial space management system by 2035. As the maximum rigid boundary for the expansion of urban construction land, the UDB is the demarcation line between developable construction areas and forbidden construction areas. Its application is gradually being recognized and supported by the Chinese government.

The existing demarcation methods for UDB are mainly divided into two types: the reverse method and the forward method [18]. Based on the urban development suitability, the reverse method draws the forbidden development boundary to frame the suitable construction area of urban land [19,20]. This method can visually distinguish between suitable and unsuitable areas for urban construction, but it has a low degree of differentiation for the location conditions. Based on the current distribution of urban construction land, the forward method simulates urban expansion through an analysis of the driving mechanism and then demarcates the UDB. The method places demand on the training and accuracy of the model. Studies have combined the two to form a better model system, which is called the synthesis method [21,22,23]. Based on the forbidden development boundary, the synthesis method establishes a mathematical model to simulate the expansion pattern so as to demarcate the UDB. The key to simulating urban expansion lies in the selection of models, which includes the logistic regression model, artificial neural networks (ANN), the SLEUTH (slope, land use, exclusion, urban extent, transportation, and hillshade) model, the future land use simulation (FLUS) model, ant colony optimization model algorithm [24,25,26,27,28,29], and the cellular automaton (CA) model.

The CA model assigns a value of 0 or 1 to each unitary cell according to its binary state after spatial cellularization. Based on certain state transition rules, the spatial evolution of the next time series is carried out considering the states of other cells that form a specific neighborhood relationship with a single cell [30,31]. This model has the advantages of spatio-temporal dispersion, spatial interaction, and local temporal causality. It can achieve spatial interaction in the adjacent hierarchical structure [32] and effectively integrate the geographical driving factors of urban expansion [33]. Therefore, it has been widely applied in the study of urban expansion and UDB demarcation [34,35,36,37]. However, the CA model has the disadvantage of being unable to obtain model parameters from images of a single period and a single class, so it cannot explain the variable mechanism well. In addition, if only the neighborhood effect is considered in the spatio-temporal dynamic simulation, the simulation result will be far different from the complex process of real urban expansion. Therefore, existing studies on the CA model usually aim to explore state transition rules to improve the simulation accuracy [38]. Combining the CA model with other intelligent algorithms, such as SD-CA [34], SLEUTH-CA [27], Markov-CA [39], and other models, tends to give simulation results that are more similar to real urban expansion.

This paper attempted to combine the CA model and Maxent model to study the spatial simulation of urban expansion. Based on the partial constraint information of the unknown distribution, the Maxent model can select the probability distribution with the maximum information entropy under the constraint condition, which has the most uncertainty from random events [40]. The Maxent model has been widely applied in the field of species habitat assessment [41,42]. This model can automatically obtain the weight coefficients of variables from images of a single period and a single class, which contributes to reflecting the driving mechanism and formulating state transition rules. Combined with the CA model, on the one hand, it can make up for the disadvantage that the CA model cannot obtain the model parameters from images of a single period and a single class. On the other hand, it can give full play to the advantages of both models and greatly improve the simulation accuracy. At present, only a few studies on the Maxent-CA model have proved its practical value. Lin combines the Maxent-CA model and multiperiod dynamic programming algorithm to propose a novel method for the scientific optimization of nature reserves [43]. Tan constructs the SD-Maxent-CA model for dynamic simulation of natural forests to present its potentiality in future land use simulation [44]. However, only a few scholars have used the Maxent-CA model to make empirical studies in urban expansion simulation. Zhang firstly applied the Maxent-CA model to simulate urban expansion in China [45]. The results show that the model performs well in simulating the land use of a single class. However, this study only simulates urban expansion at a large regional scale (China) from a macro perspective without conducting model verification for a specific small regional scale. Additionally, the resolution of this study is 1 km, so the variability and uniqueness of urban expansion in small regions tend to be missed. Chen verified that the Maxent-CA model can simulate a more compact land pattern [46] but did not explore more practical value in the field of UDB demarcation. In view of this, this paper simulated urban land expansion based on the Maxent-CA model to propose a new approach to demarcate the UDB. It can provide a scientific basis and decision reference for the demarcation of the three zones and three lines in China.

This paper selected Wuxi city as the study area and applied the Maxent-CA model to simulate urban expansion in a small region. From the perspective of both natural and socioeconomic conditions, 11 environmental variables were selected. The maximum entropy probability was calculated based on the new range of urban land in Wuxi from 2005 to 2015. Under dual control of the constraint condition and the maximum expansion area in the CA model, this study simulated the range of urban expansion in 2035 and demarcated the UDB of Wuxi using the synthesis method. In this way, we were able to delve into the mechanisms by which relevant environmental variables drive urban expansion as well as explore a more scientific method of demarcating the UDB. This study aimed to provide a decision-making reference for improving the urban construction layout, coordinating urban and rural development, and promoting economical and intensive land use.

2. Materials and Methods

2.1. Study Area

Wuxi (119°33′–120°38′ E, 31°07′–32°02′ N) is located in Jiangsu Province in Eastern China. It is a vital part of the Yangtze River Delta city cluster and contributes to regional development by undertaking economic radiation from Shanghai and driving the industrial upgrade of the hinterland. Wuxi has a total area of 4627.47 km², including five districts (Liangxi, Binhu, Huishan, Xishan, and Xinwu) and two county-level cities under its jurisdiction (Jiangyin and Yixing) (Figure 1). The topography of Wuxi is mainly plain. The city has a dense network of rivers, with the Yangtze River to the north and Taihu Lake to the south. The humid subtropical monsoon climate in this area gives Wuxi four distinct seasons and sufficient precipitation. The excellent location and climate conditions have led to Wuxi becoming one of the most economically developed cities in China. In 2020, Wuxi’s GDP totaled CNY 123,748 billion with a per capita GDP of CNY 165,777, ranking first in Jiangsu Province and second in China. The urbanization rate of the permanent resident population reached 82.8%.

The rapid development of the economic level and urbanization led to the rapid expansion of construction land in Wuxi. Between 2010 and 2020, the built-up area expanded from 348.50 km² to 563.41 km² (an increase of 61.67%), while the permanent resident population grew from 6.38 million to 7.46 million (an increase of only 17.07%), which meant that land urbanization occurred much faster than population urbanization in Wuxi. In terms of the pattern of construction land expansion, although the urban expansion in Wuxi between 1990 and 2005 was dominated by edge expansion and infilling expansion, its small-area patches were obviously reduced [47]. Between 2005 and 2015, the density of urban land patches decreased from 0.44 to 0.22, which means that the pattern of urban expansion became more fragmented. The efficiency of land development needs to be improved urgently.

2.2. Data

(1)

Land use data

Land use data from Wuxi were vector data obtained from the Resource and Environment Science and Data Center (RESDC) of the Chinese Academy of Sciences (CAS) (http://www.resdc.cn/, accessed on 23 December 2021), and the years 2005, 2015, and 2020 were selected as the time nodes. The classification accuracy of the original data was as high as 95% [48], allowing the extraction of the secondary land class of “the built-up area above the county” and “other construction land such as industrial and mining, roads, airports, special land” as urban land in Wuxi. Meanwhile, the “water area” and “forest land” in the primary land class can be extracted as vital components of the urban land-restricted area.

(2)

Resource and environmental data

SRTM digital elevation model (DEM) data from Jiangsu Province (90 m × 90 m) and the spatial distribution dataset of the normalized difference vegetation index (NDVI) (1 km × 1 km, 2015) were obtained from RESDC. The DEM data were used to calculate the index of the surface relief and aspect. A 1:4,000,000 map of soil types in the Yangtze River Delta region (2013) was obtained from the Cold and Arid Regions Environmental and Engineering Research Institute (CAREERI) of the CAS. The soil types were classified into seven categories: iron bauxite, alfisols, primary soil, semi-hydromorphic soil, anthropogenic soil, lake–reservoir, and river. The ecological protection red line and permanent basic farmland data were sourced from the Wuxi Natural Resources Bureau as essential components of the urban land restriction area.

(3)

POI and network data

Using web crawling, we obtained the distribution data for points of interest (POI) and road network data from Wuxi on the Baidu map. The POI data included transportation facilities, medical care, science and culture education, enterprise companies, government agencies, and other categories. Data cleaning was needed to remove irrelevant information to ensure authenticity and unification, and spatial processing was achieved through coordinate transformation. The road network data were in shapefile format and included county roads, provincial roads, national roads, expressways, and high-speed railways. Due to the limitation of multivariate data collection, the year of network big data was unified as 2019.

(4)

Socioeconomic data

Spatial data related to China’s gross domestic product (GDP) (1 km × 1 km, 2015) and population (1 km × 1 km, 2010) were obtained from the RESDC. Permanent resident population data from 2006 to 2020 were taken from the Wuxi Statistical Yearbook.

The coordinate system was set as a Krasovsky ellipsoid. Tools for resampling and extracting by mask were used to unify the resolution (30 m × 30 m) and range size (3234 rows × 3553 columns) of the raster data.

2.3. Method

2.3.1. Index System

Urban expansion is a spatiotemporal evolution process involving the joint action of various natural and human factors [49,50]. This study selected 11 environmental variables as influencing factors of the urban expansion mechanism, considering both natural conditions and socioeconomic conditions. In terms of natural conditions, the attributes of the urban underlying surface affect the construction cost of urban land and the geographical locations of buildings, while the vegetation coverage and soil type affect the selection of urban development land [25]. All of these factors play a role in guiding the spatial layout of urban expansion. Thus, the surface relief, aspect, NDVI, and soil type were selected as evaluation indexes. In terms of socioeconomic conditions, due to the impact of traffic accessibility, urban expansion near major traffic arteries is significantly faster than that in other areas [51,52,53]. The closer the area is to large-scale transport stations, the more prominent the direct demand for urban land is. This indirectly affects infrastructure construction, industrial development, and population agglomeration through the multiplier effect, further expanding the demand for urban land [54]. Therefore, distances to roads (including county roads, provincial roads, national roads, highways, and high-speed railways), transport stations (including airports, ports, railway stations, metro stations, and bus stations), infrastructure (including hospitals, schools, parks, and squares), industrial enterprises, and government departments at all levels were selected. Additionally, the economic level and population are positive independent factors for most types of urban expansion [45,54]. Economic development and population growth can accelerate the transformation of non-urban land, which was characterized by the gross domestic product (GDP) and population distribution in this paper (

Table 1. Specific details of environmental variables in the Maxent-CA model.

Type	Variable	Abbreviation	Min	Max	Unit
Natural conditions	Surface relief	relief	0	175	m
	Aspect	aspect	0	360	°
	NDVI	NDVI	0.008	0.9
	Soil type	soil	Iron bauxite: 1; alfisols: 2; primary soil: 3; semi-hydromorphic soil: 4; anthropogenic soil: 5; lake–reservoir: 6; river: 7
Socio-economic conditions	Distance to road	road	0	13,872.1	m
	Distance to transport station	traffic	0	13,754.7	m
	Distance to infrastructure	infra	0	15,171.5	m
	Distance to industrial enterprise	indus	0	15,540.8	m
	Distance to government department	gov	0	13,738.7	m
	GDP density	GDP	834	248,673	yuan/km2
	Population density	pop	501.3	10,949.5	pop/km2

, Figure 2).

2.3.2. Suitability Evaluation of Urban Construction Based on the Maxent Model

Maxent (version 3.4.1) (CBC, New York, NY, USA) [55], under the Java runtime environment, is a type of software based on the principle of maximum entropy. According to the known distribution information ($X$) (Figure 2) of the new points of urban land, by taking the environmental variable ($Y$) as the constraint condition, the influence probability of $Y$ on the distribution of $X$ can be calculated. The probability distribution ($X^{\prime }$) with the largest information entropy and the most uniform distribution in the probability model will be obtained [56], which means that the urban land distribution results will be the most stochastic.

$$H\left(X,Y\right)=-{{\displaystyle \sum }}_{i=1}^{n}p\left(x_i,y_i\right)\log p\left(x_i,y_i\right),$$

(1)

$$X^{\prime }=argmaxH\left(X,Y\right),$$

(2)

The 11 environmental variables were set to ASCII format, while 516,542 new urban land points were set to CSV data in the form of latitude and longitude coordinates. Considering the possibility of overfitting, a random sample of the new points was taken before importing them into Maxent software. In order to explore the extent to which different numbers of samples affect the accuracy of the Maxent model, 500, 600, 800, 1000, 2000, 5000, and 10,000 sample points were selected randomly. Subject to the same environmental constraints, a comparative analysis was carried out to determine the optimal number of samples.

To improve the accuracy of the results, the sample data were divided into two parts, 75% of the points were randomly selected for model training and the remaining 25% were selected for the resulting test. The software’s built-in jackknife test can assist with interpreting the contribution and importance of each environmental variable to urban expansion, of which the output file is in logistic format. The software also creates the Receiver Operating Characteristic Curve (ROC) to verify the model, and the area under ROC (AUC) can be used to evaluate the accuracy of the Maxent model. The AUC usually ranges from 0.5 to 1.0, with larger values indicating that the model is more accurate [57], while an AUC of 0.5 is judged to be of no reference value, and an AUC of 1.0 is judged to indicate a perfect prediction. Accordingly, the evaluation criteria can be set as follows: 0.5–0.6 for fail, 0.6–0.7 for poor, 0.7–0.8 for fair, 0.8–0.9 for good, and 0.9–1.0 for excellent. Only when the AUC values of both training data and test data reach good or excellent levels can the results of the Maxent model be incorporated into the CA model for further analysis.

2.3.3. Simulation of Urban Expansion Based on the CA Model

Permanent Resident Population Forecast

In the study of urban expansion simulation, the maximum expansion area is generally regarded as the termination threshold of circular iterations for the CA model and is one of the basic building blocks of the model. However, the latest plan for Wuxi is the Master Plan for Land Use of Wuxi (2006–2020), developed in 2011, which is not applicable to the simulation of Wuxi’s urban expansion in 2035. Moreover, the new round of territorial spatial planning has not yet been completed, so relevant data on the future urban land planning of Wuxi are not available. Therefore, from the perspective of population and land use, this study used the permanent resident population from 2006 to 2020 as the database to forecast the population size and urban land demand of Wuxi in 2035.

According to the existing urban land area and permanent resident population data, the per capita urban land area of Wuxi in 2015 was 118.55 m². Referring to the Standard of Climatic Regionalization for Architecture (GB50178-93) and the Code for Classification of Urban Land Use and Planning Standards of Development Land (GB50137-2011), Wuxi is located in climate zone III, so its ideal urban land area per capita was set as 110 m² based on the principle of regulated development and reasonable expansion. By using this value, the maximum urban land area required to accommodate the above population in 2035 can be obtained. Combined with the setting of 900 m² per cell, the urban land area can be converted into a corresponding number of cells, which is used as the termination threshold of circular iterations.

In order to improve the accuracy of population forecast, three population forecasting methods, namely the comprehensive growth rate method, the unitary linear regression, and the GM (1, 1) grey prediction model, were used in this study to calculate the average result. In particular, the comprehensive growth rate method follows the expected indicators of the Wuxi 14th Five-year Plan for Population Development to set the annual growth rate of the permanent resident population as 1.4%. The grey prediction passed the quasi-smooth test $\rho \left(t\right)$ and the quasi-exponential law test $\sigma \left(t\right)$, indicating that the population forecast is feasible. Detailed results are shown in

Table 2. Prediction of the urban expansion scale for Wuxi in 2035.

Method	Population/Thousand People	Area/m2	Raster Number	Accuracy
Comprehensive growth rate	9194.77	1011.42	1,123,805
Unitary linear regression	9640.30	1060.43	1,178,259	R2 = 0.9371
GM (1, 1) model	10,064.83	1107.13	1,230,146	δ = 2.14%
Average	9633.30	1059.66	1,177,403

. The average urban land raster obtained was 1,177,403, and this was used in the subsequent CA model.

CA Model

The CA model, with distinct spatio-temporal coupling characteristics, is especially suitable for the dynamic simulation of complex geographical systems, such as urban expansion. There are three important components to be considered in the construction of the CA model: the neighborhood effect, spatial constraint, and random interference. The neighborhood effect can control the self-organizing behavior of the model and thus influence the formation of a complex system [58,59]. The spatial constraint describes the areas where urban land development is prohibited, while random interference is used to simulate random and unpredictable factors. The state transition rule serves as the core that determines the relationship between the transition probability of urban land and the neighborhood effect, spatial constraint, and random interference [33].

The simulation process used in this study is based on the assumption that the CA model contains only a binary transformation; that is, it only contains two cellular attributes (urban land and non-urban land). Only the possibility of the conversion from non-urban land to urban land was considered. After the study area was rasterized with a resolution of 30 m, urban land was defined as 1 and non-urban land as 0, giving each cell its state $S_x^t$ at a specific time step $t$. Its state $S_x^{t+1}$ at the next time step can be affected by multiple factors, which can be expressed as follows.

$$S_x^{t+1}=f\left(S_x^t, M_x^t, N_x^t, L_x^t, R_x^t\right),$$

(3)

where $M_x^t$ represents the transition potential of the cell driven by environmental variables, namely the urban construction suitability obtained by the Maxent model; $N_x^t$ represents the neighborhood coefficient, namely the urban development intensity of the cellular neighborhood; $L_x^t$ represents the spatial constraint of the restricted area on the cell; and $R_x^t$ represents random interference.

For the neighborhood structure applied by the CA model, the Moore type is one of the most frequently used neighborhood structures. It consists of 8 surrounding cells, which, except for the central cell, are arranged in a 3 × 3 grid structure. The neighborhood coefficient $N_x^t$ can be expressed as:

$$N_x^t=\frac{\sum con\left(S_x^t=1\right)}{8},$$

(4)

Combined with the urban construction suitability and neighborhood effect, the global transition probability of each cell can be calculated.

$$p_x^t=M_x^t+wN\ast N_x^t,$$

(5)

where $wN$ represents the weight coefficient of neighborhood effect.

Thus, the final probability of cellular transition $P_x^t$ is shown as:

$$P_x^t=exp\left[\alpha \left(\frac{p_x^t}{p_{x.max}^t}-1\right)\right]\ast R_x^t\ast L_x^t,$$

(6)

where $\alpha$ represents the diffusion coefficient, and $p_{x.max}^t$ represents the maximum global transition probability in each iteration loop, which is continuously updated in each subloop.

The spatial constraint of the CA model mainly includes four restricted areas: the water area, forest land, ecological protection red line, and permanent basic farmland in Wuxi. The water area and forest land data were extracted from the Wuxi land use data. The four data layers were merged and set as the forbidden construction area of urban land in the CA model, as shown by the following formula:

$$L_x^t=\left\{\begin{array}{c}1, \mathrm{not} \mathrm{subject} \mathrm{to} \mathrm{restricted} \mathrm{zones}\hfill \\ 0, \mathrm{subject} \mathrm{to} \mathrm{restricted} \mathrm{zones}\hfill \end{array}\right.,$$

(7)

According to $P_x^t$ in each iteration loop, the model updated the cellular state as well as counting the number $stepNUM$ of cells whose state changed to urban land and the total number $sumNUM$ of cells whose state was urban land in this iteration. When the $sumNUM$ was equal to or greater than the iteration threshold, that is, when the total size of urban land exceeded the maximum urban land area calculated by permanent resident population forecast, the model stopped. The distribution result of urban land at this time was taken as the prediction result for urban expansion in Wuxi in 2035.

2.3.4. Identification of Three Urban Expansion Types

In order to quantitatively describe the characteristics and distribution pattern of urban expansion in Wuxi in 2035, this study converted the new urban land data into vector format and extracted the common edge according to the spatial attributes. The ratio between the length of the common edge and the total perimeter of each patch was used as the basis for classification [52,60]. The new urban land patches were divided into three urban expansion types, infilling, edge expansion, and outlying, for visual display [61].

$$P=\frac{l_c}{l},$$

(8)

where $l_c$ represents the length of the common edge between a new urban patch and an old urban patch, and $l$ represents the total perimeter of the new urban patch. The value of $P$ ranges from 0 to 1. The infilling expansion has $0.5<P\le 1$, which is characterized as old urban land surrounding more than half of the new urban area. The edge expansion has $0<P\le 0.5$, which refers to the development of new urban land spreading outward from the edge of an old urban area and surrounded by less than 50% old urban area. The outlying expansion has $P=0$, which indicates that there is no common edge between the new urban land and old urban land.

The above methods can be integrated into the following research process (Figure 3).

3. Results

3.1. Analysis of the Maxent Model

3.1.1. Influence of the Sample Size on the Model Accuracy

Under the same environmental constraints, different numbers of sample points were randomly selected to predict the maximum entropy distribution. The AUC values of the training data set and test data set are shown in

Table 3. Accuracy of the Maxent model with different sample sizes.

	Sample Size	600	800	1000	2000	5000	10,000
11 environment variables	AUC of the training data set	0.825	0.822	0.816	0.786	0.739	0.685
	AUC of the test data set	0.809	0.811	0.813	0.779	0.734	0.684
8 environment variables	AUC of the training data set	0.825	0.817	0.814	0.785	0.738	0.685
	AUC of the test data set	0.784	0.806	0.805	0.777	0.734	0.692

. The results show that when the sample size exceeded 1000, the model accuracy decreased as the sample size increased, and when the sample size was between 800 and 1000, the AUC values of both were greater than 0.8, indicating that the Maxent model can predict urban expansion well. The follow-up results on the mechanism of environmental variables show that the best result was obtained with a sample size of 800. This value was applied to subsequent simulations to ensure the high accuracy of the Maxent-CA model.

3.1.2. The Contribution and Importance of Variables

Eight hundred random sample points were used for the trial operation of the Maxent model. The contributions and importance of 11 environmental variables to the maximum entropy distribution of urban land in Wuxi are shown in

Table 4. Preliminary results for the contribution and importance of each environmental variable.

Variable	Contribution (%)	Importance (%)
road	27.74	20.56
NDVI	23.51	22.86
pop	13.99	11.37
indus	10.80	9.99
traffic	9.04	11.06
relief	8.75	2.77
gov	3.63	11.32
soil	1.14	2.67
GDP	0.58	3.34
infra	0.55	3.03
aspect	0.28	1.04

. The contribution covers the variable interaction, while the importance reflects the dependent influence of a single environmental variable on the maximum entropy distribution.

The results show that the contributions and importance of the aspect, infra, and GDP are relatively low. It is speculated this is due to the predominantly plain topography, the generally developed economy, and the perfect infrastructure of Wuxi. The homogenization of regional nature leads to homogeneity in the construction conditions. After excluding these three low-value variables, the new index system was applied to the model. The AUC values of the training data set and test data set were 0.817 and 0.806, respectively, indicating that the model is credible. The final results are shown in

Table 5. Final results for the contribution and importance of environmental variables.

Type	Variable	Contribution (%)	Importance (%)
Natural conditions	NDVI	22.69	22.91
	relief	6.24	3.11
	soil	0.55	3.64
Socio-economic conditions	road	30.23	17.24
	indus	16.07	9.53
	traffic	11.38	14.63
	gov	7.38	17.52
	pop	5.46	11.43

.

Among the eight environmental variables, the more prominent contributors are road (30.23%), NDVI (22.69%) and indus (16.07%), with a total contribution of 68.99%, indicating that these three variables play key roles in the systematic model of variable interaction. While the single variables with large influences are the NDVI (22.91%), gov (17.52%), and road (17.24%), the importance of traffic, indus, and pop fluctuate around 10–15%, which means that their influences on the model are basically equal. Overall, the contributions and importance of socioeconomic conditions are higher than those of natural conditions, indicating that the urban expansion process in Wuxi is more likely to be affected by human socioeconomic activities. In addition, the contributions of gov and pop are obviously lower than their importance levels, while the contributions of road and indus are significantly higher than their importance levels, indicating that a system with variable interaction will reduce the roles of gov and pop in the model, and conversely, the roles of road and indus will increase.

The model also outputs the jackknife test of the variables’ regularized training gain (Figure 4), where the dark bar represents the extent to which the environment variable affects the model when used in isolation. The traffic is found to have the highest gain and therefore appears to represent the most useful information. The light bar represents the extent to which the environment variable decreases the gain the most when it is omitted, where the shorter the bar is, the more indispensable the presence of the environment variable is to the gain in results. The NDVI has the shortest bar, indicating that the NDVI contains the most information that is not present in the other variables and has the greatest impact on the prediction results when it changes alone.

3.1.3. The Relationship between the Probability Distribution of Urban Land and Variables

The response curve can reflect the relationship between the existence probability and environmental variables, that is, the quantitative change between the probability distribution of urban land and environmental variables (Figure 5). The interpretation of the response curve provides a deeper understanding of the relationship between the dependent and independent variables. A probability of greater than 0.5 indicates that the numerical interval of the environmental variable contributes to urban expansion and vice versa.

The response curve of soil shows that the patches of anthropogenic soil (code 5) are most likely to be covered by urban expansion, while the possibility of the patches of lake–reservoir (code 6) being converted into urban land decreases sharply, which is consistent with general cognition. The NDVI response curve shows an increasing and then decreasing trend, with the optimum range for facilitating urban expansion being between 0.2 and 0.6. When the vegetation coverage is higher than a certain level, the patches are not suitable for urban development. The relief curve shows that areas with a topographic difference of more than 10 degrees are also not suitable. In terms of socioeconomic conditions, 1500 to 9000 people per square kilometer is a relatively optimal range for urban expansion, and 2000 people per square kilometer is the optimal density. The response curves of gov, indus, road, and traffic all show non-linear negative correlations with the probability of urban expansion decreasing with an increasing distance.

3.1.4. Maximum Entropy Distribution of Urban Land Based on the Maxent Model

High values of information entropy in the maximum entropy distribution of urban land in Wuxi (Figure 6) are mainly found in the central urban areas of Wuxi city, Jiangyin city, and Yixing city, indicating that future urban expansion will tend to occur in these places which already have the foundation for urban development and where the dense populations and convenient transportation are conducive to urban expansion. The low information entropy in the scattered areas of Jiangyin city and most areas of Yixing city, on the other hand, make it difficult for these areas to be reached by urban economic radiation due to their distance from the existing urban land, resulting in a lower rate of urban development. Additionally, the information entropy of water areas, such as Taihu Lake, is extremely low, which reflects the constraint of the water environment on urban expansion in Wuxi.

3.2. Analysis of the Maxent-CA Model

3.2.1. The Simulation of Urban Expansion Based on the Maxent-CA Model

A total of 252 iterations of the Maxent-CA model were used to generate 1,184,450 urban cells to simulate the urban expansion of Wuxi in 2035. From the perspective of the overall distribution pattern of urban land, the total scale of urban land is expected to reach 1066.01 km² in 2035. The new urban land is predicted to be mainly distributed in the center of Wuxi city and the subcentral urban area of Jiangyin city and scattered in the subcenter of Yixing city. The northern parts surrounded by the Yangtze River and the eastern parts adjacent to the Taihu Lake Basin are expected to be the key areas for future development (Figure 7) while adhering to the bottom line of ecological protection. From the perspective of urban expansion types (

Table 6. Urban expansion types of Wuxi in 2035.

Type	Outlying Expansion	Edge Expansion	Infilling Expansion	Total
Area (km2)	11.08	87.30	132.40	230.78
Percent (%)	4.80	37.83	57.37	100.00

), 57.37% of the new urban land is predicted to be infilling expansion concentrated in the Jiangyin High-tech Industrial Development Zone (mainly in Chengdong Street) and the Wuxi Airport Development Zone (mainly in Shuofang Street and Hongshan Street), mostly clustered in blocks; 37.83% of the new urban land is predicted to be edge-expansion, mainly distributed in the Huishan Economic Development Zone, Anzhen Street (the eastern part of the Xishan Economic Development Zone) and the corridor of the Huyi Highway between Qianqiao Street and Hu Dai Town; and only 4.80% is predicted to be outlying expansion, with the typical areas such as Zhouzhuang Town and Changjing Town developing as node towns on the main traffic routes.

In general, urban expansion basically spreads outwards around the distribution range of the old urban land and focuses on the transition of non-urban land surrounded by original urban land to meet the requirements of vacant landfilling, patch integration, and concentrated contiguity. New municipalities such as the Kegang–Huangtu Cluster, Donggang–Xibei Cluster and Zhangzhu–Hufu Cluster are predicted to develop in integrated clusters, integrating into the overall urban development and connecting three main urban areas through the Taihu–Yangtze River Development Axis and the Taihu Bay Science and Technology Innovation Belt. This simulation may allow the co-construction and sharing of public services and infrastructure, promoting more compact and intensive urban spatial development.

3.2.2. The Demarcation of the UDB

Based on the urban expansion simulation results obtained by the Maxent-CA model, this study used the Guidelines for the Compilation of the Municipal Territorial Spatial Master Plan (Trial Implementation) issued by the Ministry of Natural Resources as a reference to conduct vacant landfilling, patch deletion, and plot merging on the simulation results. Originally, the enclosed area within a single closure line was more than 30 hectares in size. Restricted areas, such as water areas, forest land, ecological protection red line areas, and permanent basic farmland were not filled in as necessary avoidance areas. Finally, the patches of node towns or special towns with small areas were kept. Based on the above three points, the demarcation results of the UDB are shown in Figure 8. The area of urban land is 1066.01 km², slightly exceeding the threshold of 1059.66 km² obtained from the forecast of the permanent resident population by 0.60%. After strict correction, the area of urban land within the rigid UDB is 1053.46 km², which is approximately 99.41% of the maximum expansion area. On the whole, the results are in line with the study’s expectations.

In general, the predicted UDB of Wuxi in 2035 meets the requirements of the urban spatial development strategy proposed in the Wuxi Territorial Spatial Master Plan (2021–2035). This UDB mainly covers the Xinwu New District in the southeast of the main urban area of Wuxi, the Xidong urban area in the east, the Huishan urban area in the north, and the new urban area on the periphery of the Jiangyin sub-city, along with the old urban area of Yixing city. It focuses on guiding the construction activities of industrial development zones, such as high-tech industries, advanced manufacturing, and productive services. Meanwhile, the demarcation of the UDB also strictly abides by the constraint rules of restricted areas, preserving a certain amount of ecological space and agricultural space for urban development. By reserving ecological nodes such as Taihu Lake Basin, Yangtze River Wetland in Jiangyin, and National Forest Park in Yixing and avoiding permanent basic farmland, the pressure on Wuxi’s ecosystem is alleviated, providing a guarantee for the city’s sustainable development.

4. Discussion and Conclusions

4.1. Discussion

4.1.1. The Accuracy of the Maxent-CA Model

In order to ensure the feasibility of the Maxent-CA model, we used land use data from 2005 and 2015 to simulate the urban expansion of Wuxi in 2020, using the Maxent-CA model and logistic-CA model, respectively. In particular, the land use data from Wuxi in 2020 were sourced from the RESDC, from which the actual area of the extracted urban land was determined to be 874.69 km². According to the setting of 900 m² per cell, the actual number of cells corresponding to the urban land of Wuxi in 2020 was 971,873, and this was used as the termination threshold of the circular iteration. The results showed the Kappa index of the Maxent-CA model was 93.87% and that of the logistic-CA model was 90.56%. In terms of spatial distribution (Figure 9), the logistic-CA model showed a more fragmented distribution of urban land, with more small urban patches in remote areas. The Maxent-CA model showed a more concentrated and contiguous distribution of urban land, effectively controlling the disorderly spread of urban land. This could provide technical support for the demarcation of a complete, scientifical, concise, and easily implemented UDB. The comparison proved that the Maxent-CA model was applicable to the prediction of the land use pattern. The results of the model were credible for the urban expansion simulation and UDB demarcation of Wuxi in 2035.

4.1.2. Further Analysis

Through an in-depth analysis of the Maxnet-CA model, the original urban land in 2015 was found to occupy 928,127 cells whose states remained as urban land in 2020, accounting for an absolute proportion of the simulation results and therefore bringing a high Kappa index. In contrast, 48,634 cells were shown to be incorrectly simulated and 49,993 cells exceeded the actual scope of urban land. Combined with Figure 10, further spatial analysis of the simulation results revealed that the “actual, not simulated” area (Figure 10a) is mainly distributed in the peripheral area separated from the original urban land, and the “simulated, not actual” area (Figure 10b) is mainly concentrated in the central area surrounded by the original urban land. This indicates that the model has a degree of deviation when simulating the outlying expansion of urban land. It is actually more applicable to the small study area where urban expansion is mainly characterized by a cluster-like distribution and central infilling. The reason is that urban development is a dynamic and open evolution process and outlying expansion tends to follow policy-oriented guidance [52], which is more uncertain and complex. The Maxent-CA model summarizes the land transition rules based on the distribution characteristics of existing urban land, so it cannot fully predict future urban development.

On the other hand, the inadequate protection of key ecological restricted areas is also a major reason affecting the accuracy. The model result shows that 25,550 cells in the restricted area (52.53% of “actual, not simulated” area) were occupied by urban land in 2015, including about 22.99 km² of water area, forest land, ecological protection red line area, and permanent basic farmland area that is not actually protected (such as Huishan National Forest Park shown in Figure 10c). As a result, the simulation process has an error of 25,550 cells in advance, which impacts the accuracy of the results. The Maxent-CA model in this paper strictly prohibits urban expansion within the restricted areas to protect the key ecological reserves, which ensures the scientifical and reasonable demarcation of UDB.

Additionally, while the Maxent-CA model took full advantage of the Maxent model’s advantage of automatically obtaining weight coefficients from images of a single period and a single class, it also exposed the model’s shortcomings. Actually, the land use planning and management tend to involve the interactive transformation of multiple land use types [45,62]. Thus, the Maxent-CA model would have limitations in practical application. Meanwhile, it was difficult to obtain all the data at 30 m resolution directly. The non-spatial data used in this paper, such as GDP and population distribution, were generally only counted to county-level administrative regions, which had a large resolution. There was a possibility of errors caused by loss of details in the process of resampling to 30 m.

In general, the future study needs to consider the influence of political decisions and human activities on urban expansion more comprehensively. Using an improved model and data with higher resolution, more accurate simulation results are expected to be obtained to improve the practical value of the Maxent-CA model in UDB demarcation. Through the demarcation of UDB, we hope to effectively protect the ecological land, rationalize the layout of functional urban land, and control urban expansion.

4.2. Conclusions

In this study, a Maxent-CA model was constructed to demarcate the UDB. The model not only integrates the advantage of the Maxent model by automatically obtaining the weight coefficients of independent variables from images of a single period and a single class but also the advantage of the CA model by realizing spatio-temporal dynamic simulation in neighborhood structure. Based on the Maxent-CA model, this study took a typical rapidly urbanizing city (Wuxi) as the study area, land use data from 2005 and 2015 as the dependent variable, and selected environmental variables as the index system. The model was used to simulate the urban expansion of Wuxi in 2035 to demarcate the UDB, demonstrating the value of the Maxent-CA model in urban master planning. The results show that:

(1)

The Maxent-CA model proposed in this paper can be applied to demarcate the UDB of specific cities. This study comprehensively considered the relationship between the urban construction suitability, neighborhood effect, spatial constraint, and random interference of urban expansion and fully embodied the principle of combining top-down and bottom-up UDB demarcation approaches in the land use master plan.

(2)

The Maxent-CA model can intuitively reflect the driving mechanism of urban expansion. From the perspective of the importance of a single variable, NDVI and gov were found to have higher influences. However, road and indus were shown to contribute more to the model influenced by the interactions between variables. Moreover, the response relationship between urban expansion and environmental variables is complex and non-linear.

(3)

The expansion of new urban land is dominated by the infilling expansion type, followed by edge expansion, with outlying expansion being the least common. The accuracy of the model was shown to decrease when simulating outlying expansion and in situations where the key ecological restricted areas were not adequately protected. Future study needs to consider the influence of political decisions and human activities on urban expansion more comprehensively. The relevant departments should pay attention to the phenomenon of urban land occupation and coordinate the scale of urban and rural land.

Under the current urban spatial planning system in China, the policy criteria, methods, and management systems of boundary demarcation for urban and rural planning, land use planning, development priority zones, and so on vary among different administrative departments due to their different requirements. The method of demarcating the UDB based on the Maxent-CA model proposed in this paper has great potential. More in-depth research should be conducted in the future to explore the reference value of the Maxent-CA model in territorial spatial planning.