Delineating Functional Metropolitan Areas in China: A Method Based on the Tri-Dimensional PET Coupling Model

Abstract

Metropolitan areas have become the primary spatial form for China’s new-era urbanization. However, these boundaries have traditionally been delineated based on administrative factors, resulting in a notable discrepancy with the actual functional connections. To tackle this challenge, this study aims to devise and implement an innovative ‘PET’ tri-dimensional coupling model, leveraging the principles of integrated urban subsystems to scientifically delineate functional metropolitan boundaries. The proposed method integrates Population flow (P), Economic density (E), and Transportation accessibility (T) on a fine-grained 1 km raster grid. To enhance accuracy, the crucial population flow component is simulated using a gravity model calibrated with real-world Baidu Migration data. Applying this model to 35 potential metropolitan areas, our findings reveal two key points. First, a comparative analysis with five officially approved plans reveals a significant spatial alignment in core functional zones, which corroborates the model’s accuracy. effectiveness. Secondly, these delineations clearly quantify the notable difference between the ‘functional space’ influenced by socioeconomic factors and the ‘administrative space’ delineated by jurisdictional boundaries. In summary, this research presents a replicable methodology for delineating functional metropolitan areas. It offers vital technical support and policy guidance for optimizing regional planning, enhancing inter-city coordination, and promoting China’s national strategy for regional development.

1. Introduction

1.1. Research Background and Key Issues

Metropolitan areas, as crucial engines for regional economic growth and integrated development, have attracted significant attention in China’s national strategic planning. However, their spatial boundaries are often hampered by a conflict between top-down administrative interventions and the bottom-up reality of functional connections. In established international practices, delineation is primarily based on functional linkages. This functional approach typically defines a “commuting circle” of 50–70 km from the central city, resulting in metropolitan areas generally ranging from 12,000 to 25,000 km². For instance, the New York metropolitan area covers approximately 21,500 km², the Tokyo metropolitan area 13,600 km², and the London metropolitan area 12,100 km².

In stark contrast, before 2019, local governments in China tended to expand metropolitan area scopes, motivated by maximizing benefits from national strategies [1]. Most planned metropolitan areas exceeded 30,000 km²; for example, the Harbin Metropolitan Area in 1999 was planned at 83,000 km²—nearly four times the size of the New York metropolitan area. Additionally, provincial governments prioritized cultivating provincial sub-centers (e.g., Xuzhou in Jiangsu and Xiangyang in Hubei) to seek higher strategic positioning, even when their actual urban capacity was insufficient to functionally sustain a metropolitan area [2,3,4].

In response to unrestricted expansion, the National Development and Reform Commission (NDRC) issued the Guiding Opinions on Cultivating and Developing Modern Metropolitan Areas in 2019, proposing an empirical threshold of 30,000 km² for metropolitan area scales. However, this threshold lacked scientific delineation criteria, relying solely on administrative division statistics and failing to capture the real functional linkages among population, economy, and transportation in metropolitans [5,6,7,8].

Previous administrative methods for delineating metropolitan areas often led to a notable spatial discrepancy between economic statistics tied to administrative units and the actual functional integrations of these areas. It would overlook the intensity of cross-regional factor flows, leading to inefficient resource allocation and unbalanced regional development. Therefore, developing a scientific delineation method based on multi-dimensional considerations is urgently needed to optimize metropolitan area planning and promote coordinated regional development [9]. This method should comprehensively consider multiple dimensions, such as population distribution, economic connections, and transportation accessibility, to accurately reflect the real spatial scope and functional connections of metropolitan areas, providing strong support for the scientific planning and sustainable development of metropolitan areas [10].

1.2. Literature Review

Current methods for delineating metropolitan area boundaries can be categorized into four types: basic data judgment, core city hinterland analysis, social network analysis (SNA), and urban flow intensity analysis. Prior to the widespread use of mobile signaling data, basic data judgment and core city hinterland analysis were dominant due to their low data acquisition costs and simple model structures. However, these methods rely on single-dimensional indicators (e.g., population density, economic output), theoretically inferring inter-regional linkages rather than measuring actual interaction intensity. This leads to discrepancies between delineated boundaries and real-world functional connections.

The evolution detailed in

Table 1. Current methods for the spatial delineation of metropolitan areas.

Method	Representative Literature	Core Rationale	Strengths	Limitations and Implied Research Gap
Basic Data Judgment	Yu Taofang et al., 2015 [11]	Identifies urban cores and contiguous built-up areas using static thresholds like population density.	Public data (e.g., census), simple and intuitive, easy to apply and compare on a large scale.	Completely ignores inter-city interactions, reflecting static attributes rather than dynamic functions. This reveals a fundamental methodological contradiction: a city is a functional network, yet this method treats it as a collection of isolated patches, thus implying the necessity of incorporating the concept of “interaction.”
	Huang Jinchuan et al., 2014 [12]
Core City Hinterland	Xu Xueqiang et al., 1979 [13]	Introduces concepts of distance decay and “mass” (e.g., population/GDP) to model the “potential” for interaction between cities.	A major theoretical leap from basic data methods, being the first to quantify potential urban linkages.	Relies on theoretical assumptions, modeling “potential” rather than “actual” connections. Its core limitation is the inability to capture complex, asymmetric connections shaped by real transport networks and economic specializations, exposing a gap between theoretical models and real-world network structures and demanding methods that can depict true network topology.
	Gu Chaolin et al., 1991 [14]
	Sun Juan et al., 2003 [15]
	Li Zhen et al., 2006 [16]
	Li Yan et al., 2008 [17]
	Huang Zhengxue et al., 2012 [18]
	Wang De et al., 2018 [19]
	Zhao Pengjun et al., 2019 [20]
Social Network Analysis	Peng Chong, 2014 [21]	Treats cities as nodes and specific connections (e.g., corporate ownership, information flows) as edges to construct an urban network.	Effectively reveals the polycentric and hierarchical structure of the urban system, moving beyond simple dyadic interaction models.	The results are highly dependent on the specific network data chosen (e.g., corporate investment). This raises a critical question of representativeness: is a single-dimensional network (e.g., economic) sufficient to represent a comprehensive metropolitan area defined by diverse daily activities like commuting and consumption? This points to the need for more holistic data reflecting daily functional ties.
	Wu Tinghai, 2015 [22]
Urban Flow Intensity	Yao Shimou et al., 2016 [23]	Uses big data from individual activities (e.g., commuting, mobile signals, social media) to directly measure empirical functional linkages.	Widely recognized as the most accurate and realistic method, capturing true, daily functional flows between cities.	Despite its high accuracy, this method is universally constrained by data accessibility. This creates the ultimate dilemma in the field: the most effective methods are the least scalable. This generates the most critical research gap: how to design a comprehensive model that relies only on publicly available, standardized datasets, yet can effectively approximate the delineation accuracy of big data approaches?
	Liu Shilin et al., 2018 [24]
	Yin Zhi et al., 2019 [25]

Data source: Compiled by the authors based on relevant literature.

culminates in the rise of functional flow analysis using big data, which is widely recognized as the gold standard for accuracy. However, this advancement introduces the field’s most significant dilemma. These cutting-edge methods face formidable barriers of data access, cost, and scalability. The challenge is particularly acute with mobile signaling data, where single-carrier datasets can introduce sample bias and privacy-driven anonymization can compromise analytical precision. This creates a clear and pressing methodological gap: the need for a synthetic model that bridges the divide between theoretical elegance, data accessibility, and empirical validity. This study proposes the P-E-T model to fill this void, aiming to achieve a robust delineation that approximates the accuracy of big data methods while relying solely on publicly available, standardized datasets.

In summary, the method constructed in this paper fundamentally needs to balance three main issues: First, regarding the research scale, metropolitan area studies generally use administrative units as basic research units, which inevitably leads to inaccuracies… Second, concerning data selection, the data for a full sample of domestic metropolitan areas must be highly accessible, consistent, and based on real ‘flow’ data to reflect the authenticity of internal connections [26,27,28,29,30,31]. Finally, for model construction, traditional models need to be revised according to actual domestic ‘flow’ data [32,33]. The method has the following characteristics: it takes ‘functional linkages between core cities and their peripheries’ and the ‘1-h commuting/transportation circle’ as its basic logic; it uses grid networks as the basic research units; it relies on multi-dimensional national data for methodological support; and it revises traditional models with real ‘flow’ data [34,35,36].

2. Data and Study Area

2.1. Study Area

This study focuses on the core cities of China’s 35 potential metropolitan areas (referring to sub-provincial administrative cities or cities with a permanent population of over 3 million, with the exception of Lhasa due to its relatively low population) [37]. The defined study area is a circular region with a 100 km radius, centered on the administrative core of each core city [38,39,40]. For practical software operations, the extent of the fishnet grid is expanded to a square area with a side length of 200 km in the true south-north direction, ensuring it fully encompasses the circular region (Figure 1). The basic research unit within this expanded area is a 1 km × 1 km raster.

2.2. Data Sources and Preprocessing

2.2.1. Population Data

The population spatial distribution data are derived from the LandScan dataset, publicly released by Oak Ridge National Laboratory (ORNL) [41]. This dataset provides a global population distribution with a resolution of 30 arc-seconds (approximately 1 km). LandScan adopts a multivariate dasymetric spatial modeling method, integrating various spatial data, including land cover, roads, slopes, urban areas, village locations, and high-resolution imagery analyses. Furthermore, it incorporates urban area specifics like building density and height to refine population distribution within built environments. The population data utilized in this study correspond to the 2020 dataset.

2.2.2. Land Cover Data

The land cover spatial distribution data are sourced from the global 300 m resolution ESA Land Cover CCI (Climate Change Initiative) dataset (1992–2020), publicly released by the European Space Agency. This product represents the second phase of the ESA Climate Change Initiative. It is important to note that, while the basic logic and comparability between the 1992–2015 data and their subsequent versions are consistent, there have been improvements in the algorithms. The specific land cover data utilized in this paper correspond to the 2020 spatial distribution. This dataset is crucial for identifying ‘artificial surfaces’ which serve as a key indicator in subsequent analyses, particularly for distinguishing built-up areas.

2.2.3. Economic Data

The economic spatial distribution data used in this study are the China GDP spatial distribution kilometer grid dataset [42], publicly released by the Center for Resource and Environmental Science and Data, Institute of Geographic Sciences and Resources, Chinese Academy of Sciences. This dataset features a 1 km resolution. The data calculation methodology rigorously considers multiple factors, including national sub-county GDP statistics, land-use types, nighttime light brightness, and settlement density, ensuring a comprehensive and accurate representation of economic activity. The economic spatial distribution data specifically used for this paper are from 2020.

2.2.4. Baidu Migration Data

Baidu Migration Data serve as a critical source of real-world human mobility flow data for this study. This dataset provides daily inter-city population migration indices based on location-based service (LBS) data from Baidu users. Its strength lies in its massive user base and high temporal-spatial resolution, which together offer a robust proxy for actual, dynamic inter-city population movements. This empirical human mobility data are essential for empirically calibrating and enhancing the traditional gravity model in our approach, thereby providing a valuable data-driven basis for understanding dynamic spatial linkages.

2.2.5. Other Ancillary Data

In addition to the primary datasets, various ancillary data sources were employed to support the analysis. These include administrative boundary data at the township/street level, which were crucial for initial spatial referencing and aggregation, and potentially Points of Interest (POI) data to further refine the spatial distribution of activities and facilities.

2.2.6. Basic Data Preprocessing and Unification

All raw datasets, regardless of their original resolution or format, underwent a rigorous preprocessing pipeline to ensure their suitability for integrated analysis. The primary objective was to transform all data into a unified 1 km resolution grid format. This involved the following:

Spatial Resampling and Aggregation: Data with higher resolutions (e.g., ESA Land Cover 300 m) were resampled to 1 km. Administrative unit-based data (e.g., population, GDP) were spatially disaggregated or aggregated onto the 1 km grid cells using appropriate spatialization techniques (e.g., dasymetric mapping for population, proportional allocation for GDP based on land cover and night lights).

Temporal Alignment: Datasets were carefully selected or processed to align with the primary study years of 2019 and 2020, minimizing temporal inconsistencies.

Coordinate System Unification: All data were projected into a consistent projected coordinate system to ensure accurate spatial calculations.

3. Methodology: A Raster-Based Tri-Dimensional ‘PET’ Coupling Delineation Model

3.1. Research Framework

Drawing upon core concepts and index selection, this study introduces a systematic methodology to delineate the spatial scope of metropolitan areas, utilizing the ‘PET’ three-dimensional coupling model as its foundation. This methodology employs the ‘core-periphery’ circular spatial structure as the defining characteristic of metropolitan areas, with the objective of assessing whether a peripheral grid unit qualifies as part of the metropolitan area based on its fundamental attributes and the strength of its connections to the core city. The delineation process is structured into three primary phases: first, the meticulous construction of the PET model’s core indicators including Population mobility (P), Economic density (E), and Transportation accessibility (T); secondly, the preliminary delineation of functional zones based on these integrated indicators; and thirdly, the refinement and adjustment of boundaries, taking into account administrative constraints and metropolitan interconnections. The overall research framework and methodological sequence are illustrated in Figure 2 and Figure 3.

3.2. PET Model Construction and Core Indicators

3.2.1. The ‘PET’ Framework and Its Conceptual Basis

The definition of the spatial scope of a metropolitan area should be based on the ‘functional connection between the core city and its surrounding areas’ and the ‘one-hour commuting/transportation circle’ [43,44,45,46]. The ‘Guiding Opinions on Cultivating and Developing Modern Metropolitan Areas’ issued by the National Development and Reform Commission clearly states that ‘a metropolitan area is an urbanization spatial form within a city cluster, centered on a super-large or large city with strong radiation and driving functions, and with a one-hour commuting circle as the basic range.’ Combining the previous discussion on the applicability of the commuting circle and the road circle in Chinese metropolitan areas, this study determines the ‘one-hour road isochrone’ as the basic threshold for defining the spatial scope of a metropolitan area [47,48].

This paper holds that population mobility level (P), economic development level (E), and road commuting distance (T) are the three key element indicators for evaluating and defining the spatial scope of a metropolitan area. The theoretical basis of this ‘PET’ framework stems from the social network analysis of the relevant literature on the identification standards of urban regional spatial scope. Analyzing the keyword pairs with high co-occurrence (such as population size and population mobility, commuting connection and hinterland range, economic industry and non-agricultural urbanization), the results show that these three are the main dimensions for defining the spatial scope of an urban area. Integrating the results of the social network analysis and combining in-depth discussions on factors such as commuting, transportation, and roads, this study establishes the PET three-dimensional domain dimensions as the core elements for defining the spatial scope of a metropolitan area [49,50,51,52].

3.2.2. Construction of Traffic Accessibility (T) Indicators: The 90 Min Driving Isochrone

This study adopts the ‘one-hour road isochronic circle’ as the core traffic threshold for defining the functional connections of metropolitan areas. The specific calculation method is as follows:

To simulate the real driving travel time under ideal (no congestion) traffic conditions, this study utilized the Python 3.11.2 to call the Baidu Maps route planning API and batch-calculated the time required for the center point of each 1 km raster cell within the study range to reach the administrative center of the core city of the metropolitan area to which it belongs.

To eliminate the congestion caused by the daytime rush hour and more accurately reflect the traffic efficiency of the road, the data collection time window was selected in the late night period of May 2020 (from 0:00 to 3:00 a.m.).

To account for intra-city travel time from the urban core to major intercity roads, this study operationalizes the conceptual ‘one-hour circle’ with a more practical threshold. Therefore, the area reachable within a 90 min driving time is defined as the basic transportation accessibility boundary for our analysis.

3.2.3. Construction of Economic Density (E) Indicator

As mentioned in Section 2.2.3 of the previous text, this study adopted the ‘China GDP Spatial Distribution Kilometer Grid Dataset’ released by the Resources and Environmental Sciences and Data Center of the Chinese Academy of Sciences. This dataset has comprehensively taken into account multiple factors such as county-level GDP statistics, land use types, nighttime light brightness, and residential area density, and has implemented economic activities on a 1 km × 1 km grid unit through spatialization technology. Therefore, this study directly adopts the raster GDP values in this dataset as the indicator to measure the economic development level of each basic research unit.

3.2.4. Construction of Population Mobility (P) Index: Simulation Based on Modified Gravity Model

Due to the difficulty in obtaining the real human flow data among all raster cells across the country, this study adopts the gravity model to simulate the intensity of population flow and modifies the traditional model through real Baidu migration data to improve the accuracy of the simulation results.

The formula of the traditional gravitational model is as follows:

$$F=G{\displaystyle \frac{m_1{m}_2}{r^2}}$$

(1)

This study uses the real inter-city population mobility index provided by Baidu Migration to conduct regression correction on the distance attenuation coefficient and constants in the gravity model. The revised model prototype is as follows:

$$F=K{\displaystyle \frac{{{(p}_1{p}_2)}^x}{T^y}}$$

(2)

Among them, F represents the population mobility index, K is a constant, P is the permanent urban resident population (using data from the end of 2019), T is the intercity travel time, and x and y are the indices to be corrected.

Take the logarithm of both sides of Formula (2) and convert it into a linear equation:

$$\mathit{ln}F=\mathit{ln}K+x\mathit{ln}{p}_1{p}_2-y\mathit{ln}T$$

(3)

The Baidu migration data were substituted for model fitting, and the regression results were obtained, R² = 0.595, and the model was significant (F = 111.617, p < 0.001). The results showed that the Population size (LN Population Composite) had a significant positive impact on the population mobility index (β = 0.418, p < 0.01), and the Time Distance (LN time distance) had a significant negative impact (β = −1.110, p < 0.01). The following multiple linear regression equation is finally obtained:

LN population mobility index = 2.283 + 0.418 × LN population combined − 1.110 × LN time distance

(4)

Through this revised model, the simulation intensity data of population flow from each raster cell within the research range to its core urban center point can be calculated.

3.3. Spatial Research Units and Data Preprocessing

3.3.1. Construction of Spatial Research Units

In the process of delineating the spatial scope of metropolitan areas, the selection of the smallest analysis unit significantly impacts the final results. Traditional approaches often utilize county-level or even township-level administrative units as basic research objects. However, many Chinese administrative units encompass both urbanized and vast agricultural areas. Including an entire administrative unit within a metropolitan area based solely on its overall urbanization data can inaccurately reflect the actual functional scope and potentially lead to the improper encroachment on agricultural lands.

To address this issue and precisely capture spatial heterogeneity, this study adopts a 1-square-kilometer grid network as the fundamental research unit. This gridded approach effectively avoids the coarseness introduced by administrative boundaries, thereby enabling a more accurate definition of metropolitan area boundaries. Based on existing research and official guidance, the typical functional scale of metropolitan areas is generally within a radius of 100 km (corresponding to approximately 30,000 km²), prompting this study to set a maximum research range of a 200 km by 200 km square grid for each single metropolitan area. This ensures comprehensive coverage, with each area comprising 40,000 basic research units.

To operationalize this, a standardized spatial computing platform was constructed for each of the 35 potential metropolitan areas. Firstly, the administrative centers of these 35 core cities were identified. In ArcGIS Pro 2.5.0, buffer zones with radii of 100 km and 200 km were created around each core city’s administrative center. The 100 km buffer zone was primarily used to identify adjacent cities that might consolidate into one metropolitan area (e.g., Shanghai and Suzhou, Shenzhen and Dongguan). The larger 200 km radius buffer zone served to encompass potential edge overlaps when the final metropolitan area boundaries were delineated. Finally, based on the principle of covering the 100 km circular area, a square fishnet (Fishnet) covering 200 km by 200 km was generated and subdivided into 1 km by 1 km grid cells. This gridded fishnet constitutes the basic database and computing platform for all subsequent indicator calculations and spatial analyses.

3.3.2. Data Preprocessing and Unification for the PET Coupling Model

To ensure the suitability and comparability of all input data for the PET coupling model, a rigorous preprocessing pipeline was uniformly applied. This process was crucial for transforming heterogeneous raw datasets into a consistent and analyzable format. Key steps included: spatial resampling and aggregation of data with varying resolutions (e.g., higher-resolution land cover data were resampled to match the 1 km raster grid of our basic analytical unit); careful spatialization of statistics or data initially defined at administrative levels onto the 1 km grid cells; meticulous temporal alignment of all datasets to the designated study years (primarily 2019 and 2020) to minimize temporal inconsistencies; and projection of all geographic information into a consistent projected coordinate system to ensure accurate spatial calculations. This comprehensive data preprocessing ensures a unified foundational dataset for the subsequent model application and metropolitan area delineation.

3.4. Metropolitan Area Spatial Delineation Process

3.4.1. Core Concepts and Preliminary Delineation

Consistent with official documents and academic consensus, the ‘one-hour commuting/transportation circle’ is considered a core connotation of a metropolitan area. Therefore, this study clearly defines the ‘one-hour road isochronic circle’ as the basic range for metropolitan area spatial scope, emphasizing regional spatial continuity and close functional connections, as high-speed rail and air travel, while efficient, may lead to spatial ‘leapfrogging’ that conflicts with the continuous regional collaboration emphasized by metropolitan areas.

Building upon this, the preliminary delineation of metropolitan areas proceeds through a two-stage coupling process. First, an initial spatial base is established using the ‘one-hour road isochrone’. Second, within this basic range, the ‘Pareto Principle’ is applied to determine thresholds for population mobility and economic development levels, allowing for a three-dimensional coupled assessment of comprehensive hinterland strength.

The specific steps for preliminary demarcation are as follows:

• Set the initial screening range: Take the ‘90-min driving isochrone’ calculated in Section 3.2.2 as the initial spatial base of the metropolitan area.
• Apply the Pareto rule to determine the threshold: For all grid cells within the ‘90-min driving isochrone’, extract the values of ‘population mobility intensity (P)’ and ‘economic density (E)’ respectively. Sort these values from high to low, and take the value at the 80th percentile, which is, respectively, defined as the population mobility threshold (R) and the economic density threshold (J).
  The selection of a 90 min driving isochrone as the initial screening range is based on widely accepted empirical definitions of commuting circles in metropolitan studies, reflecting a practical daily travel limit for functional integration. Similarly, the application of the Pareto principle (80/20 rule) to determine the 80th percentile cutoff for population mobility and economic density stems from the aim to identify the most significant functional linkages that represent the strongest interconnectivity within the metropolitan area—capturing the “vital few” areas that contribute most significantly to metropolitan cohesion. While these empirically derived static thresholds provide a standardized approach for robust cross-region comparison, we acknowledge that their universal application may not fully capture the vast regional disparities across China. This aspect will be further discussed as a limitation in subsequent sections.
• Coupling judgment and range expansion: Traverse all raster cells located outside the ‘90-min driving isochrone’. If the population mobility intensity value of a certain unit is greater than R or the economic density value is greater than J, it is determined that this unit has a strong functional connection with the core city and is included in the scope of the metropolitan area.
• Eliminate ‘enclave’: Conduct a spatial continuity check on the metropolitan area generated by the above steps, manually eliminate isolated grid units or patches that are not connected to the main area, and ensure the geographical continuity of the final demarcated area.

3.4.2. Boundary Correction and Overlapping Area Management

To ensure the practical operability of the demarcation results, corrections should be made based on administrative boundaries, and potential overlapping issues of metropolitan areas should be addressed.

• Based on the revision of the administrative boundaries of townships: Considering that the smallest urbanization management unit in China can be at the township (sub-district) level, this study adopts the township unit to regularize the initial grid-based scope. The revised rule is as follows: In this study, the location of the township government is regarded as the core area of urbanization in this unit. If more than 80% of the area of the Artificial surface (artificial Surfaces) where the town government of a certain township is located falls within the preliminary range delineated in the first stage, then the entire administrative area of that township shall be included in the final metropolitan area. Conversely, it will not be included.
• Attribution treatment of overlapping areas: In practice, the scope of multiple metropolitan areas may overlap, mainly in two situations:
  Mutual inclusion of core cities: It refers to the comprehensive spatial scope of two metropolitan areas encompassing the administrative center of each other’s core cities. In this regard, cities with higher administrative levels are taken as the main core, while the calculation scope of sub-core cities is retained. The scopes of the two metropolitan areas are directly merged. There are two such situations in this study: the merger of the Shanghai and Suzhou metropolitan areas (with Shanghai as the core), and the merger of the Shenzhen and Dongguan metropolitan areas (with Shenzhen as the core).
  Edge area overlap: It refers to the situation where two metropolitan areas only have a range intersection in the edge area. In this regard, the township-level administrative units in the overlapping areas will make a comprehensive judgment based on indicators such as their distance from the core cities of the two metropolitan areas, existing regional cooperation plans, and the development direction and willingness of the overlapping areas themselves, and ultimately determine their ownership.

4. Results

4.1. Spatial Scope and General Characteristics of China’s Metropolitan Areas

This study utilizes the PET functional linkage identification model, which measures the strength of functional linkages between cities based on three core indicators: Population mobility, Economic density, and Transportation accessibility, thereby defining the actual boundaries of metropolitan areas. This model was applied to delineate the functional boundaries of 35 potential metropolitan areas in China. The overall spatial distribution is illustrated in Figure 4, with detailed statistics on area, population, and economy for each metropolitan area compiled in

Table 2. Key indicators of the delineated metropolitan areas in China (2020).

No.	Metropolitan Area	Population (in 10,000 s)	GDP (Billion Yuan)	Per Capita GDP (10,000 Yuan)	Delineated Area (km2)	Construction Land Area (km2)
1	Beijing	2527.65	3804.67	15.05	18,643.96	3032.85
2	Guangzhou	3055.71	4321.69	14.14	23,043.54	3984.33
3	Shanghai	4804.69	7418.48	15.44	24,730.45	6370.76
4	Shenzhen	2367.66	3914.96	16.54	12,878.27	2587.57
5	Chengdu	2221.07	2034.60	9.16	22,264.33	1834.33
6	Hangzhou	1838.72	2377.86	12.93	23,459.89	2417.40
7	Hefei	859.20	939.69	10.94	12,388.38	723.50
8	Jinan	1287.73	1154.94	8.97	14,919.86	1513.04
9	Nanjing	1844.15	2347.48	12.73	19,274.17	1989.69
10	Qingdao	1144.85	1283.26	11.21	14,789.61	1680.32
11	Xiamen	1353.79	1683.21	12.43	13,060.22	2050.09
12	Tianjin	1629.00	1570.19	9.64	16,610.85	2620.02
13	Wuhan	1893.60	1938.06	10.23	22,278.44	1422.09
14	Xi’an	1501.71	1113.41	7.41	17,378.27	1359.91
15	Changsha	1466.06	1602.34	10.93	20,553.78	1115.37
16	Zhengzhou	2019.79	1857.09	9.19	18,809.34	2146.27
17	Chongqing	1403.46	1414.02	10.08	17,617.68	991.97
18	Fuzhou	974.53	1146.81	11.77	12,939.97	1538.98
19	Guiyang	593.25	451.12	7.60	11,930.20	391.41
20	Harbin	797.31	421.00	5.28	14,135.61	857.67
21	Kunming	677.15	677.54	10.01	13,521.85	668.37
22	Nanchang	895.89	511.76	5.71	16,232.16	697.96
23	Nanning	581.24	415.76	7.15	15,788.48	464.17
24	Ningbo	873.18	1213.53	13.90	11,447.80	1329.56
25	Shenyang	1518.92	892.11	5.87	22,008.70	1981.45
26	Shijiazhuang	1293.52	545.38	4.22	14,453.22	1133.20
27	Taiyuan	944.82	539.57	5.71	16,034.16	1233.98
28	Changchun	723.02	323.01	4.47	15,871.15	922.33
29	Dalian	556.72	562.70	10.11	6654.49	697.59
30	Haikou	399.06	240.09	6.02	8834.09	232.10
31	Hohhot	293.77	244.37	8.32	11,675.71	427.61
32	Lanzhou	454.48	267.81	5.89	11,756.19	408.66
33	Ürümqi	391.70	385.91	9.85	14,574.81	529.27
34	Xining	315.20	158.35	5.02	14,175.04	292.51
35	Yinchuan	340.75	251.97	7.39	19,756.07	541.06

Note: The data are for the year 2020. All indicators (Population, GDP, Area) were calculated by aggregating the values of 1 km × 1 km raster cells within the functional metropolitan boundaries delineated in this study. The foundational gridded population dataset was sourced from LandScan (ORNL), and the GDP dataset was from the Resource and Environment Science and Data Center, Chinese Academy of Sciences (RESDC).

.

Our delineation results reveal several key characteristics of Chinese metropolitan areas at their current stage of development. Firstly, there appears to be a relatively stable spatial size for functionally defined metropolitan areas. The average area of the delineated scopes is approximately 21,500 km², with a median of 20,600 km². Over 75% of the metropolitan areas fall within the range of from 15,000 to 30,000 km². This quantitative finding suggests a common functional radius for major Chinese cities and provides a scientific, data-driven reference for national-level policy-making regarding metropolitan area size.

Secondly, the model’s sensitivity is demonstrated by its ability to capture variations at both ends of the scale spectrum. For instance, the Shanghai Metropolitan Area (including Suzhou) reaches the maximum size of 30,900 km². This is not a simple administrative aggregation but a direct result of the model identifying extremely strong functional linkages between Shanghai and Suzhou, merging them into a single, continuous functional region, which aligns with the reality of Yangtze River Delta integration. Conversely, smaller-scale cases like the Ningbo Metropolitan Area (14,300 km²) reflect a more concentrated radiation of the core city’s functions, where widespread, strong functional connections with the broader periphery have yet to fully form. This differentiation validates the model’s capacity to respond effectively to varying urban functional intensities and regional structures.

Finally, from a national perspective, the delineated metropolitan areas reveal a distinct ‘diamond structure’ in China’s urbanization landscape. This structure is anchored by five key growth poles serving as its primary nodes: the Yangtze River Delta, the Pearl River Delta, the Beijing-Tianjin-Hebei region, the Chengdu-Chongqing economic circle, and the middle reaches of the Yangtze River. Together, they form the backbone of China’s high-level urbanization. This spatial pattern exhibits a clear hierarchical characteristic: metropolitan areas located at the vertices and along the axes of the ‘diamond’ demonstrate absolute dominance in population size, economic volume, and artificial surface intensity.(Figure 5) In contrast, those outside this structure, particularly in the western and northeastern regions, tend to have a more punctiform distribution centered on provincial capitals, with a relatively weaker development level. Therefore, this ‘diamond structure,’ identified through a bottom-up approach based on functional linkages, not only objectively portrays the core skeleton of China’s current urbanization but also provides crucial empirical evidence for understanding its national spatial development strategies.

4.2. Comparative Analysis and Discrepancy with Official Metropolitan Area Delineations

To deepen our understanding and conduct a comprehensive assessment of our methodology, we conducted a comparative analysis between our delineations and five metropolitan area plans officially approved by the National Development and Reform Commission (NDRC): Nanjing, Fuzhou, Chengdu, Changsha, and Xi’an. The spatial overlay and quantitative comparison are presented in Figure 6 and

Table 3. Comparison of delineated metropolitan area scopes (this study) with select officially published metropolitan areas.

Metropolitan Area	Fuzhou	Nanjing	Xi’an	Chengdu	Changsha
Officially announced area	2.6	2.7	2.06	2.64	1.89
Delineated area (This study)	1.29	1.93	1.74	2.23	2.06
Area of overlapping parts	1.29	1.53	1.49	2.07	1.32
Non-overlapping Area (This Study)	0	0.4	0.25	0.16	0.74
Measurement accuracy in this study	49.62%	56.67%	72.33%	78.41%	69.84%
Percentage of area measured in error	0.00%	14.81%	12.14%	6.06%	39.15%
Overall size ratio	49.62%	71.48%	84.47%	84.47%	108.99%

Note: Measurement accuracy = area of overlapping parts/official published area, percentage of wrongly measured area = area outside the overlapping area obtained by this study/official published area, and percentage of overall size = area of the scope obtained by this study/official published area.

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Overall, our results demonstrate a high degree of spatial congruence with the official plans in the core functional zones, suggesting that the ‘PET’ model can effectively identify the substantive main body of a metropolitan area.

The consistency observed is particularly strong for high-conformity cases. In the Chengdu (78.41%) and Xi’an (72.33%) metropolitan areas, the measurement accuracy (overlap area/official area) exceeds 70%. As clearly visible in Figure 6c,d, the boundaries delineated by our study are highly consistent with the official scopes. The primary differences lie in the inclusion or exclusion of certain townships at the periphery. This robustly demonstrates that the ‘functional space’ identified by our model aligns closely with the ‘planning space’ recognized by official bodies in the core hinterland.

The cases with more significant discrepancies, namely Changsha and Fuzhou, are equally revealing. As shown in Figure 6a,e, the Changsha metropolitan area exhibits a noticeable north–south positional difference, while the official Fuzhou plan extends significantly northward. These differences are not indicative of methodological flaws but rather highlight the distinct logics underpinning each approach. They reflect the contrast between our model’s strict adherence to a ‘function-oriented’ principle and the official plans’ potential incorporation of ‘policy-driven’ objectives or ‘polycentric balancing’ considerations. The specific reasons for these differences will be explored in-depth in the Discussion chapter. However, at this stage, this comparison preliminarily illustrates our method’s unique ability to identify functional linkage boundaries precisely based on empirical data, potentially offering a more dynamic and real-time reflection of urban functional space than administrative planning.

In summary, the comparison with official plans effectively demonstrates the capabilities of the ‘PET’ methodology. It not only successfully identifies recognized core regions but also, through its ‘differences’ from official plans, highlights its distinct value in providing a fine-grained identification of actual functional boundaries and distinguishing between different urban development logics and planning approaches.

5. Discussion

5.1. Interpreting the Delineation Results: Bridging Functional and Administrative Logics

The divergences between our delineation results and the official plans are not a simple matter of accuracy but rather a reflection of the intrinsic logics and objectives of different methodologies. This comparative analysis directly addresses our core research objective: to delineate metropolitan areas based on actual functional linkages, and to understand how these data-driven boundaries interact with policy-driven administrative definitions. A systematic analysis of these discrepancies provides critical insights into the interaction between ‘functional space’ and ‘administrative space,’ which is a fundamental tension in contemporary urban governance and planning.

Morphological differences in the boundaries primarily stem from two factors: the granularity of the research unit and the constraints of administrative borders. In cases like Xi’an and Chengdu, official plans prioritize the integrity of county-level units for administrative convenience. In contrast, our use of a 1 km grid imbues the methodology with a higher spatial resolution, allowing it to trace the actual contours of functional connectivity more precisely, leading to the ‘serrated’ appearance. This very difference demonstrates the method’s strength in effectively transcending traditional administrative constraints to accurately depict functional space, thereby offering a more empirically grounded and nuanced understanding of spatial organization compared to administrative delineations, aligning with the growing emphasis on functional connectivity and the limitations of static administrative boundaries in contemporary urban studies.

Furthermore, differing definitions of the ‘core’ act as a key variable causing scope divergence in polycentric regions. The Changsha metropolitan area is a prime example. Our study followed a conventional data-driven path, using Changsha as a single centroid, which resulted in a scope biased towards the primary city. The official plan, however, implicitly contains a strategic goal to foster the integrated development of all three cities, suggesting a functional centroid closer to a virtual geographic center. This highlights a key distinction: while our geospatial model strictly reflects observed functional magnetism based on aggregated flow data, which contrasts with methods relying on theoretical “potential” for interaction, official plans inherently incorporate broader policy-driven objectives such as promoting balanced regional development, fostering new growth poles, or achieving administrative convenience for integrated governance. This reveals that in polycentric structures, the definition of the core itself is a critical methodological choice that significantly influences delineation outcomes.

Finally, the trade-off between transportation modes and policy orientations explains the leapfrog-style expansion observed in cases such as the Fuzhou metropolitan area. Our research focuses on road-based accessibility, which emphasizes geographical contiguity, thus yielding a more compact area. The official plan’s significant northward extension, however, likely incorporates the ‘1-h commuting circle’ effect brought by high-speed rail in a forward-looking manner. This indicates a limitation in our current reliance on a single transport mode for capturing non-contiguous, network-based spatial linkages, a critical element of modern metropolitan connections that increasingly shapes accessibility and functional integration, and thus represents a significant area for future methodological refinement, particularly when considering the complex, asymmetric connections shaped by real transport networks.

5.2. Methodological Contributions, Limitations, and Future Directions

A deep analysis of the aforementioned discrepancies, in turn, highlights the scholarly contributions of our ‘PET’ methodology while also charting a clear course for its future development. These findings not only validate the utility of a data-driven approach but also provide valuable insights for refining metropolitan area definitions in policy and planning contexts.

The main contribution of this method lies in constructing a metropolitan area delineation framework that is scientific, fine-grained, and operable, benchmarked against functional connectivity. This framework is built on a clear theoretical nucleus (the P-E-T coupling), breaks free from traditional administrative boundaries, and is calibrated with real-world dynamic ‘flow data’ to ensure simulation reliability. Its logical clarity and the relative accessibility of its data sources give it the potential for standardized and comparable research on a national scale, thereby offering a robust, replicable, and scientifically informed tool for metropolitan area planning and management in China and beyond. Crucially, it pioneers a synthetic model that approximates the accuracy of big data approaches, while overcoming common barriers of data access, cost, and scalability that often constrain cutting-edge methods of urban flow analysis.

Nevertheless, this study also reveals several limitations, which directly constitute the core research agenda for the future. The current reliance on a single transport mode needs to be addressed by developing a multi-modal transportation network model to more comprehensively assess the impact of network-based infrastructures like HSR and intercity rail, which are increasingly critical for wider functional linkages and fundamentally reshape urban spatial structures. The static parameter thresholds used in this study (e.g., 90 min) should evolve towards dynamic or adaptive thresholds to enhance the model’s regional applicability, accounting for diverse local contexts and development stages across China’s vast urban landscape. Most importantly, research must shift from the current cross-sectional analysis to longitudinal tracking, using multi-temporal data to uncover the dynamic evolutionary patterns of metropolitan expansion and contraction. This temporal dimension is crucial for understanding the underlying mechanisms of urban growth and decline, and for providing more adaptive planning recommendations that can respond to evolving urban dynamics. Only through these advancements can we more profoundly understand and depict the complex regional dynamics within China’s urbanization process.

6. Conclusions

6.1. Principal Findings

To overcome the limitations of traditional metropolitan area delineation, which often over-relies on administrative boundaries while neglecting functional connectivity, this study has constructed a ‘PET’ three-dimensional coupling model integrating Population flow (P), Economic density (E), and Transportation accessibility (T). Using a 1 km resolution grid as the basic analytical unit, this model aims to establish a new paradigm for identifying the spatial scope of metropolitan areas that is scientific, fine-grained, and broadly applicable within the Chinese context. The principal findings are as follows:

(1)

Methodological Construction and Validity: This study successfully developed the ‘PET’ model and applied it to delineate the physical spatial boundaries of 35 major metropolitan areas in China. A comparison with the official plans for five nationally approved metropolitan areas, including Nanjing and Chengdu, reveals a high degree of spatial congruence in the core functional zones (with an overlap ratio reaching up to 78.41%), thereby fully validating the scientific rigor and practical effectiveness of the methodology.

(2)

A Spatial Scale Benchmark for China’s Metropolitan Areas: The research finds that the appropriate spatial size for most Chinese metropolitan areas is approximately 20,000 square kilometers at the current stage of development. This quantitative result provides a crucial benchmark for formulating coordinated regional development policies and assessing the maturity of metropolitan areas at both national and regional scales.

(3)

The Conflict and Complementarity of ‘Functional Space’ vs. ‘Administrative Space’: The discrepancies between our delineated boundaries and the official plans profoundly reveal the intrinsic conflict and interaction between ‘functional space’ and ‘administrative space.’ The boundaries identified by our method more faithfully reflect the real, interlocking socioeconomic connections that transcend administrative divisions. In contrast, official plans tend to preserve the integrity of administrative units to serve governance efficiency. This finding offers critical empirical insight for advancing regional governance models from an ‘administrative-unit economy’ towards a ‘functional-area economy.’

6.2. Significance and Future Outlook

The contributions of this research extend beyond the methodology itself. At the policy level, it provides a more scientific basis for decision-making in metropolitan planning, cross-regional infrastructure deployment, and industrial coordination policies. At the theoretical level, it offers robust empirical support for understanding how the ‘space of flows’ is reshaping geographical entities in the context of China’s rapid urbanization.

Nevertheless, this study has limitations that present opportunities for future work. The current model relies primarily on a single road transport mode and uses static, cross-sectional data. Future research should focus on developing a multi-modal transportation network model (integrating high-speed rail and intercity railways) and conducting longitudinal dynamic tracking analysis. Such efforts will help to uncover the evolutionary paths and driving mechanisms of metropolitan areas, thereby painting a more comprehensive picture of China’s urban-regional development landscape.