Urban–Rural Boundary Delineation Based on Population Spatialization: A Case Study of Guizhou Province, China

Abstract

Rational delineation of urban–rural boundaries is a foundational prerequisite for holistic urban and rural development planning and rational resource allocation. However, using a single data source for urban–rural boundaries yields non-comprehensive results. To address this problem, the present study proposes a method for extracting urban–rural boundaries using multiple sources such as population data, nighttime light data, land use, and points of interest (POI) data. Considering Guizhou Province for a case study, this study presents a two-step method for identifying urban–rural boundaries. First, the random forest model was combined with the dasymetric mapping method to obtain the province’s population spatialization data with a 30-m resolution. Second, based on the spatialized population, the urban–rural boundary for Guizhou Province in 2020 was extracted using the breaking point method. This method comprehensively integrated the benefits of various data and judiciously extracted the boundaries of the main urban areas and small and medium-sized towns of each city in the study province at the same spatial scale. The stratified random sampling method revealed an average overall accuracy of 88.05%. The proposed method has high universality and application value and can be useful for accurate and practical identification of urban–rural boundaries.

1. Introduction

Rapid urbanization and the implementation of the urban–rural integration development strategy have gradually strengthened the mutual nesting and influence between urban and rural areas [1]. The traditional theory of the urban–rural dichotomy cannot fully explain the blurred boundary between the urban and rural landscapes [2]. According to the modern urban spatial structure theory represented by concentric zone theory and core-edge theory, a developed city can be categorized into three main components, namely built-up areas, the urban–rural fringe area, and the rural area [3,4]. The urban fringe area, which is located between the built-up and rural areas, has steadily become the most dynamic zone for urban development, diffusion, and sprawl [5]. Unlike homogeneous cities and countryside, the urban–rural fringes exhibit distinct attributes of transition, fluctuation, and diversity [6]. Under the influence of both urban and rural areas [7], problems such as man–land contradictions and land use conflicts have emerged in these urban fringe areas. These issues have led to several other problems such as chaotic urban and rural planning, resource misallocation, and unbalanced public services [8]. Therefore, identifying the spatial identification method of urban and rural fringe areas and reasonably delineating the urban–rural spatial boundary hold great significance for the overall planning of urban and rural development, rational resource distribution, and promotion of coordinated development of these areas [9,10].

The urban–rural fringe area is affected by factors such as population, urban size, and economy [7], which render its spatial form dynamic and constantly undergoing changes. Therefore, most studies have been conducted from the perspectives of population characteristics [11,12,13] and urban spatial morphological changes [14,15]. Population, as one of the key factors for the evolution of urban–rural boundaries, is a crucial indicator for measuring the spatial structure of cities. Previous research methods have mostly focused on qualitatively demarcating urban–rural boundaries based on population density [16,17] from the perspective of administrative or natural regions. Subsequently, various indicators closely related to human activities, such as commuting levels [11,17], socio-economic linkages [18], and infrastructure services [19,20], were used for delineating these boundaries. Some recent studies have attempted to demarcate urban–rural boundaries by using spatial positioning data such as points of interest (POI) [21,22], takeaway data [23], and locations of new residential buildings in suburbs [24].

The advancement of remote sensing technology has contributed to extensive research on the methods for determining urban spatial morphological change. Studies have integrated these methods with quantitative methods such as the breaking point method [25], information entropy method [26], and mutation detection [27] for identifying the spatial boundaries of cities. The urban–rural boundary is principally obtained by extracting the relevant indicators of spatial land morphology, such as the impervious surface index and landscape disorder degree [28,29]. The extent of urban build-up on global [30,31] and urban scales [14,32,33] has been determined. The remote sensing image data include Landsat-TM images [34], nighttime light data [30], Sentinel [15,23,35], and other sources. Convolutional [15] and deep neural network models [36] have also been used for studying urban–rural boundaries. However, being a complex socio-economic polyhedron, the formation of this urban–rural boundary is affected by various factors. When delineating boundaries, the urban fringe zone often cannot rely solely on some types of indicators such as territorial units or a given population range [7].

To compensate for the lack of comprehensive data from a single data source, some scholars have attempted to use nighttime light data [37], combine two types of indicators related to population and land, and employ an empirical threshold method or classification method [38] for determining the urban boundary range. These studies have preferred to construct composite indices for unifying data types. However, obtaining unified data at the spatial scale is difficult because of the availability of various spatial data sources, which reduces the applicability of these methods [39]. By contrast, population spatialization fits population data to spatial locations by establishing relationships between the population and influencing factors. It presents the geographical distribution characteristics of the population as grid cells [40] and can display more refined spatial information in the statistical population data. To some extent, population spatialization can “bridge” spatial scale differences among different data.

Therefore, considering Guizhou Province as the study area, this study first integrated various data including those of land use, nighttime light, demographic features, POI, and topography. Using the population spatialization method and the random forest model, the multi-source data were then uniformly mapped to the grid data with a 30-m resolution to achieve the fusion of multi-source data at the same scale. Using the breaking point method, the urban–rural boundary for Guizhou Province (GZURB) was extracted based on the spatialized population. This study offers a new approach for demarcating urban boundaries.

2. Materials and Methods

2.1. Study Area

Guizhou Province (Figure 1) is situated in the southwestern region of China, spanning coordinates 24°37′–29°13′ N latitude and 103°36′–109°35′ E longitude. This province comprises nine municipal-level and 88 county-level administrative divisions. Its total land area is approximately 176,167 km². Of the total land area, approximately 61.7% is mountainous terrain, 31.1% is hilly, and only 7.5% comprises the mountainous region of Pingba. The karst landform area accounts for approximately 62% of the total area of the province. Guizhou Province is a typical mountainous region.

Over the past three decades, the urbanization rate in the study province has increased significantly. It was 23.87% in 2000, which increased to 33.81% by 2010 and reached 53.15% in 2020. In comparison, the overall urbanization rate of China increased from 36.2% in 2000 to 49.7% in 2010, which further increased markedly to 63.9% in 2020. Although the urbanization rate of the study province has not yet reached the overall level of China, its urbanization growth rate has far exceeded that of China (Figure 2). Because Guizhou Province is located in the transportation hub of southwest China and is a crucial part of the Yangtze River Economic Belt, the coordination and optimization of urban and rural spatial layouts in this province have been the research focus in related regions. Therefore, considering this province as the study area, the present study analyzed the urban–rural boundary with a decentralized distribution pattern, which is favorable for comprehending the development and change characteristics of southwest China, especially in karst landform regions.

2.2. Research Method

2.2.1. Overall Framework

This study proposes an urban–rural boundary delineation method that includes four steps: data collection and preprocessing, population spatial representation, urban–rural boundary determination, and accuracy verification (Figure 3). First, various data including those of NPP/VIIRS, land use, and POI were collected and preprocessed to construct a characteristic factor database. Second, a random forest regression model coupled with dasymetric mapping was used to generate the population spatialization data with 30-m spatial resolution in the study province. The population spatialization result was considered as the index factor, and the urban–rural boundary was extracted using the breaking point method. Finally, stratified random sampling and comparative analysis were used to verify the accuracy of the boundary division results.

2.2.2. Population Spatialization Methods

The spatial interpolation method [40] and multiple linear regression models [41,42] have been used widely in population spatialization studies. Although the spatial interpolation method can, to some extent, eliminate the influence of administrative boundaries, accurately expressing the true characteristics of the spatial distribution of a population within administrative units remains challenging. Multiple linear regression models can more accurately fit the spatial distribution of the population but are less effective when addressing data collinearity problems. By contrast, the random forest model can construct complex nonlinear relationships between the population and its auxiliary variables, leading to a high-precision spatial distribution of the population [43,44,45]. Therefore, in recent years, the random forest model has been extensively used in the spatial expression of populations. The Bierman’s 2001 model [46] is a decision tree-based ensemble learning algorithm that involves introducing the bagging algorithm for multiple random sampling into decision trees and combining the extracted multiple decision trees to complete integrated model construction [47].

Population data, POI data, and other characteristic factors constituted the foundational database. The random forest model was employed for training to predict population weight values for different factors. Leveraging dasymetric mapping [48], the actual area’s total population was spatially assigned based on the aforementioned predicted weight values to achieve a spatial representation of population quantities. Its calculation formula is as follows:

$$P_i=S_j/D_j\times D_i$$

(1)

where P_i represents the final population count for grids; S_j denotes the total statistical population of the city where grid j is located; D_j is the total weighted value of the estimated grid i in the city (autonomous prefecture); and D_i denotes the raster value of the estimated grid i.

2.2.3. Methods of Urban–Rural Boundary Delimitation

Methods such as information entropy, mutation detection, and breaking point analysis [49,50] have been widely used for delineating urban–rural boundaries. The information entropy method requires that a reasonable threshold is selected and exposed to some subjectivity [26]. The mutation detection method focuses on a single factor, whereas the breaking point method offers a clear inflection point for outlining urban–rural boundaries [7]. Hence, the breaking point analysis method was adopted in this study for identifying these boundaries. The breaking point theory [51], proposed by P.D. Converse in 1949, postulates that the population size of and distance between two cities determine the attraction between those cities. The fundamental principle involves identifying the distance decay mutation peak for each element in the same direction as the breaking point; the calculation formula is as follows:

$$d_A=\frac{D_{AB}}{1+\sqrt{P_B/P_A}}$$

(2)

where d_A is the distance from the breaking point to the city; D_AB represents the distance between two cities; and P_A and P_B are the population size values of the two cities, respectively.

The fracture point is determined by calculating the maximum distance attenuation value as follows:

$$D_i=\max (\frac{\left|x_{ij}-x_{i(j+1)}\right|}{{\displaystyle \sum \left|x_{ij}-x_{i(j+1)}\right|/N}})$$

(3)

where D_i is the maximum distance attenuation value on the ith profile line, x_ij is the jth sequence eigenvalue on the ith profile line, and x_i(j+1) is the (j + 1)th sequence eigenvalue on the ith profile line.

2.2.4. Accuracy Verification Methods

This study examined the accuracy of both population spatialization and urban–rural boundary delineation. Because the population spatialization results directly affect urban–rural boundary delineation, we conducted an error analysis of population spatialization by employing three evaluation indicators: root mean square error (RMSE), relative root means square error (%RMSE), and mean absolute error (MAE). Population spatialization results were compared and analyzed with datasets such as WorldPop and LandScan to assess the accuracy of these results. The accuracy of urban–rural boundary demarcation was verified using stratified random sampling and comparative analysis.

3. Data Sources and Processing

We used a comprehensive array of data sources, including land use data, administrative divisions, normalized difference vegetation index (NDVI), digital elevation model (DEM), NPP/VIIRS and DMSP/OLS nighttime light remote sensing data, demographic statistics, meteorological information (including precipitation and temperature data), POI data, road networks, river data, and population datasets from WorldPop and LandScan.

Table 1. Data and sources.

Data Type	Data Name	Data Year	Scale/Resolution	Data Sources
Vector data	GlobeLand30	2020	30 m	https://www.webmap.cn (accessed on 9 February 2023)
	Administrative division data	2019	1:1,000,000	https://www.webmap.cn (accessed on 15 December 2022)
	Rivers	2019	1:1,000,000	https://www.webmap.cn (accessed on 26 December 2022)
	Roads	2020	1:1,000,000	https://www.openstreetmap.org (accessed on 26 December 2022)
	POI data	2020	-	https://lbs.amap.com (accessed on 15 January 2023)
Raster data	DEM	2020	30 m	https://www.gscloud.cn (accessed on 20 November 2022)
	Meteorological data	2020	1 km	https://data.tpdc.ac.cn (accessed on 18 December 2022)
	NDVI	2020	Spatial resolution: 250 m Temporal resolution: 16 days	https://ladsweb.modaps.eosdis.nasa.gov (accessed on 10 November 2022)
	NPP/VIIRS	2020	500 m	https://www.ngdc.noaa.gov/eog/dmsp.html (accessed on 28 December 2022)
	DMSP/OLS	2020	1 km	https://payneinstitute.mines.edu (accessed on 29 December 2022)
	WorldPop	2020	100 m	https://www.worldpop.org (accessed on 29 November 2022)
	LandScan	2020	1000 m	https://landscan.ornl.gov (accessed on 23 June 2023)
Statistical data	Population census data	2020	-	http://www.stats.gov.cn (accessed on 5 November 2022) https://www.guizhou.gov.cn (accessed on 7 November 2022)

presents the data and their sources.

Because of the diversity of data sources, different data types were first standardized to the Lambertian projection uniformly and then resampled to a 30-m resolution. The primary data processing steps are as follows:

(1)

Nighttime Light Data: Using the constant target area method [52] NPP/VIIRS and DMSP/OLS images were subjected to oversaturation correction, continuity correction, and outlier processing, along with mutual substitution between continuous year images. Following logarithmic transformation [53], a function relationship was established for digital number (DN) values between the two images to ensure consistency in the correction results for nighttime light data of Guizhou Province in 2020 (Figure 4).

(2)

Land use data: Using the GlobeLand30 dataset, land use data for Guizhou Province were extracted, and the proportions of various land cover types in each district were evaluated. Based on the results, we calculated the cultivated land index, grassland index, shrubland index, forest index, water index, and artificial surface index.

(3)

Urban Nighttime Light Index and Human Settlements Index: We constructed the corrected urban nighttime light index VANUI [54] and the human settlements index HSI by comprehensively using nighttime light data and the NDVI vegetation index, respectively.

(4)

DEM: The moving window method and the mean variation point method [55] were used for identifying the optimal statistical unit for topographic relief in the study area. Additionally, the proportion factor of a flat land area in the study area [56] was incorporated to calculate topographic relief.

(5)

Meteorological data: ArcGIS version 10.8 software was used to query, screen, and calculate the annual average precipitation and temperature for each district in the study province.

(6)

POI: Fourteen types of POI data were obtained from the open API platform of Amap for 2020, and kernel density analyses were performed to calculate the average kernel density for each district.

(7)

River and road data: Leveraging existing datasets and the Euclidean distance method, we computed the straight-line distance between each point and the nearest river and road and determined the mean value of Euclidean distance.

(8)

NDVI: Based on MOD13Q1 data, the administrative division data of Guizhou Province were used to crop the NDVI image data for each time period. Subsequently, the average values of NDVI images in 2020 were calculated using a raster calculator.

To alleviate the impact of different scales and dimensions, the Min–Max data standardization method was applied to normalize various indicators and compile a database of population spatialization characteristic factors (

Table 2. Database of population spatialization characteristic factors.

Source of the Characteristic Factor	Name of the Characteristic Factor
GlobeLand30	Cultivated land index
	Forest index
	Grassland index
	Shrubland index
	Water index
	Artificial surface index
Nighttime light data	Average brightness of night lights
NDVI	Average value of
	NDVI index
NDVI and nighttime light data	VANUI
	HSI
DEM	DEM
	Slope
	Aspect
	relief amplitude
River and road data	Distance from the road
	Distance from the river
Meteorological data	Annual average temperature
	Annual average precipitation
POI data	Kernel density of POI data

).

4. Results and Discussion

4.1. Results of Population Spatialization

By referring to the database of population spatialization characteristic factors, statistical mean data were correlated with the districts in the study province using ArcGIS version 10.8. To construct a fundamental dataset, the population density data from the 2020 census for each district were used as the dependent variable, whereas the database of characteristic factors was used as the independent variable. The corresponding random forest model was constructed using the R programming language. The data were categorized into training and test sets, accounting for 70% and 30%, respectively (

Table 3. Parameter setting of the random forest model.

Parameter Name	Parameter Value
Number of decision trees	100
Maximum number of features during partitioning	Auto
Minimum number of samples for leaf nodes	1
Maximum depth of the tree	10
Sampling rule	With replacement
Out of bag estimation	Yes

).

Initially, the model for the relationship between independent variables and population density was established. The model was then applied to the characteristic factor data at a 30-m grid scale, which yielded the initial population grid data on the basis of the random forest model prediction, known as the grid weight eigenvalue. To ensure alignment of the grid data with the actual district population, dasymetric mapping was performed to allocate the actual city population based on weight values. Subsequently, the total number of weight values in each city or state was tallied, and the grid’s population count was computed using the ratio of actual population data to the total number of weight layers, which resulted in the final population spatialization outcome (Figure 5).

The population spatialization results (Figure 5) were achieved by integrating multi-source data, including nighttime light, land use, and POI data. These results revealed a population distribution pattern, characterized by a high population density in the primary urban areas and a relatively low density in the surrounding regions, in the study province. Of note, the population was concentrated in the central and northwest parts of Guizhou Province, with the eastern and southern areas exhibiting sparser populations. Population was significantly concentrated in major urban areas within cities, with Guiyang City, the provincial capital, being the primary center.

4.2. Accuracy of Population Spatialization Data

We extracted corresponding data for our study area from the WorldPop and LandScan datasets and comparatively assessed the population spatialization dataset, using MAE, RMSE, and %RMSE values as index factors (

Table 4. Precision comparison of the population spatialization results.

Data Year	Dataset	MAE	RMSE	%RMSE
2020	Population spatialization	6675.60	29,294.23	6.66
	WorldPop	53,795.71	89,286.58	20.29
	LandScan	46,776.30	94,433.72	21.46

). The simulation accuracy of the WorldPop dataset, LandScan dataset, and the population spatialization method applied in this study was 79.71%, 78.54%, and 93.34%, respectively, which indicated relatively high accuracy of the population spatialization method.

4.3. Identification of Urban–Rural Boundaries Based on Population Spatialization

This study considered the urban–rural fringe boundary as the urban–rural boundary. Leveraging population spatialization data and the breaking point theory, the population density of the study province in 2020 was computed and the spatial boundary between the urban and rural populations within the province was successfully delineated.

Once the population spatialization data met the required accuracy standards, we aimed to locate the urban–rural boundary. To achieve this objective, we initiated a meticulous process, which is outlined below.

Considering the unique characteristics of each city in Guizhou Province, the geometric center point of each city was selected as the reference origin. Starting from the east, we drew 360 cross-sectional lines at 1° intervals, thereby encircling the city’s perimeter. These lines intersected with the urban–rural division index factor, yielding 360 cross-sectional data columns containing population data. Based on the data in these columns, we calculated the maximum distance attenuation value from these columns (Figure 6).

Next, the distance attenuation value from the cross-sectional line to the corresponding spatial grid was linked through attribute fields for identifying the grid position of the breaking point. Considering the distance between the breaking point and the city center, we excluded any anomalous mutation values and connected the breaking points. Finally, the urban–rural boundary was delineated for the nine cities in the study province (Figure 7).

The extraction results (Figure 7) unveiled that this approach could precisely extract urban boundaries of the nine cities and effectively identify small towns with dispersed distributions within each city. Moreover, this approach showed enhanced recognition of the core areas. An analysis of the spatial distribution of the provincial population revealed that the development of urban population spatial boundaries in each city follows a pattern characterized by a central core and multiple sub-cores.

4.4. Discussion on the Accuracy of GZURB

4.4.1. Accuracy Validation Based on the Stratified Random Sampling Method

Landsat 8 OLI_TIRS remote sensing images from 2020 (https://www.gscloud.cn/) were used as the foundational map. A random sampling method was applied to assess the accuracy of the extracted boundary data. In total, 1000 sample points were randomly selected from the GZURB-designated urban and non-urban areas in the urban–rural boundary dataset of the study province. GZURB accuracy was verified by calculating the sample point number in the urban and non-urban areas. The number of random sampling points falling within the urban and non-urban areas was recorded for constructing a confusion matrix. Four indicators, namely overall accuracy (OA), kappa coefficient, producer accuracy (PA), and user accuracy (UA), were used to assess whether the classification results were accurate and consistent.

As shown in

Table 5. Accuracy verification of GZURB.

	Urban	Non-Urban	Total	UA
Urban	788	27	815	96.69%
Non-urban	212	973	1185	82.11%
Total	1000	1000	2000	-
PA	78.80%	97.30%	-	-
OA		88.05%
kappa		0.716

, the proposed method achieved a UA and PA of 96.69% and 78.80%, respectively, for the urban area and 82.11% and 97.30%, respectively, for the non-urban area. The OA and the kappa coefficient of GZURB reached 88.05% and 0.761, respectively, which indicated high classification accuracy of the dataset.

4.4.2. Accuracy of Superimposed Remote Sensing Image Data

To further assess the accuracy of GZURB, a comparative analysis was conducted using World Imagery (WB_2020_R01) for ascertaining the consistency of the study dataset. Data from the seventh national population census revealed that Guiyang, Zunyi, and Bijie were the top three most populous cities within Guizhou Province, having permanent populations of 5.987, 6.6067, and 6.8996 million, respectively. Consequently, these cities were selected as focal points for a detailed evaluation of the extraction performance of GZURB, and a comprehensive urban–rural boundary division map was employed.

The primary urban zones along with certain dispersed small towns within the study area were successfully identified and delineated (Figure 8). This approach enabled effective delineation between urban and non-urban areas on the basis of distinctions arising from varying spatial configurations of urban boundaries. In the heart of Guiyang, which has a relatively dense population (Figure 8a), the urban–rural demarcation could be accurately identified using the proposed method, despite the complexity of the urban boundary in the region. Specifically, in the intricate urban periphery, the proposed methodology exceled in conveying the intricate spatial nuances of this region. Despite the scattered distribution of Zunyi (Figure 8b) and Bijie (Figure 8c), which primarily comprise small towns, the boundary identification approach advocated in this study yielded remarkable outcomes for the peripheries of these smaller municipalities.

Through analysis of the accuracy of urban boundary extraction in the study province, we noted that the boundary delineation results for the main urban areas were superior to those for the small towns. To delve into this phenomenon, we ranked different characteristic factors in population spatialization for each city (prefecture) in the study area in terms of their importance (Figure 9); POI data exhibited the highest feature importance of 25.300%. The results further indicated that POI data are crucial in delineating the urban boundary, particularly in urban core recognition, whereas factors such as slope, rainfall, and shrubland data have relatively limited impact.

The POI data encompass various sectors, including retail, education, and healthcare, and offer noteworthy advantages in reflecting the spatial distribution characteristics of urban structures. Figure 10 presents the distribution of the POI kernel density in Guizhou Province in 2020. As depicted, the POI distribution in the core areas of each city was relatively dense. The POI density decreased considerably near the boundaries of built-up areas and small towns, with the number of POI points declining from urban centers to urban edges and rural areas. Higher POI data density in the primary urban areas positively correlated with the finer urban–rural boundary division results, which contributed to highly accurate boundary recognition. This result aligns closely with those of previous research [12,22].

In recent years, with the widespread use of smartphones, data such as social media data [57], LBS data [58,59], and mobile phone data [60] have been applied for population spatialization. However, their study areas are generally urban-based due to the difficulties in obtaining these data on a large scale, which limits their use in large-scale population spatialization.

In summary, the proposed urban–rural boundary delineation method proved to be highly accurate in recognizing boundaries in the key urban areas of Guizhou Province. This delineation effectively captured the study area’s boundary range, thereby precisely reflecting the spatial boundary between the urban and rural populations in the study province in 2020.

The method can also be applied to other areas, especially those without sophisticated spatial databases. At the same time, the results of population spatialization based on multi-source data can be applied to evaluate the spatial rationality of urban infrastructures such as medical service facilities and parks.

5. Conclusions

The method for extracting the urban–rural boundary proposed in this study comprehensively considers data from different sources and spatializes them into a unified grid unit. Considering Guizhou Province in China as the research area, we included data from multiple sources, such as POI data, nighttime light data, and population data. By applying the random forest model and dasymetric mapping method, a spatial distribution model of Guizhou Province’s population in 2020 was constructed and the spatial data of the population with a 30-m resolution were obtained. The stratified random sampling method exhibited that the OA of the proposed urban–rural boundary extraction method was 88.05%, with a kappa coefficient of 0.761.

Based on the population spatialization method, this paper used the advantages of various data, such as nighttime light data, DEM, and population, and the extracted urban-rural boundaries were more accurate. The remote sensing images used have a short acquisition period, other data are easy to obtain, and the process is simple, which can ensure the timeliness of urban–rural boundary extraction. In the future, we will expand the testing area by extracting the urban–rural boundaries of other provinces and regions in China and the whole of China and share the existing research results through databases and other forms. Geographic data, such as mobile phone data and building data, will be added to improve the accuracy of urban–rural boundary extraction. Identifying how to integrate multi-source data to accurately reflect the spatial change characteristics of the population and realize more accurate urban–rural boundary demarcation will be the focus of future research.