Research on the Priority of County-Level Territorial Space Consolidation: Form–Flow Synthesis Analysis Based on Principal Component Analysis

Abstract

The scientific identification of the priority of territorial space consolidation in counties is a key prerequisite for clarifying the direction of regional improvement and implementing differentiated spatial governance strategies. This paper breaks through the traditional evaluation paradigm of separating “form” and “flow”, and for the first time innovatively integrates the theory of “form–flow synthesis” with the method of principal component analysis. This paper takes Deqing County as the empirical study area. Through principal component analysis, 19 initial indicators were dimensionally reduced into a “flow–form” two-dimensional space with clear geographical significance. Then, the natural discontinuity method was used to classify it into nine types of “flow–form” combination types, and the 13 towns of Deqing County were projected onto the “flow–form” two-dimensional coordinates, thereby objectively revealing the matching/mismatch relationship between the “flow” and “form” in space. The results show that the current territorial space of Deqing County presents characteristics of “overall balance but local imbalance”. This paper also discusses the consolidation priority strategy based on the “flow–form” matching results.

1. Introduction

The accelerated global urbanization process has led to unprecedented multi-dimensional conflict for territorial space resources. It is predicted that the urban population will continue to grow, and by 2030 the world’s urban population will reach 6.29 billion, accounting for 69% of the world’s total population [1]. This trend will profoundly change the pattern of global territorial space development and utilization [2,3], triggering intense competition between land expansion for urban construction, ecological conservation space [4], and agricultural production space. The structural contradictions within urban space utilization [5] have also made the problem of space governance under tight resource and environmental constraints increasingly prominent. In this global context, spatial conflicts and governance responses have become important issues in fields such as urban and rural planning and land science. A large number of international studies have focused on spatial mismatches in rapid growth, such as ecological fragmentation, land use conflicts, lagging infrastructure, social spatial differentiation, etc. However, traditional rectification models that focus on a single goal, local areas, or static evaluation cannot easily meet spatial governance demands, where systematicness and dynamics coexist. The territorial space itself (“form”) is relatively static and material, while the economic and social activities behind it (“flow”) are dynamic and essential. In contrast to “form”, “flow” is a dynamic process that occurs when spatial elements change. This process can be divided into changes in spatial position and changes in activity intensity. From the perspective of constituent elements, flow elements include physical flows such as population migration, logistics, and biological flows, as well as virtual flows such as information flow, capital flow, and technological flow [6,7,8]. Against this backdrop, exploring governance paths that can coordinate the “form” and “flow” of territorial space has become a cutting-edge research area of international focus.

Especially in developing regions, rapid urbanization is often accompanied by drastic reorganization of the territorial spatial structure. China, as a typical example of rapid urbanization, has seen its urbanization rate rise from 17.92% in 1978 to 66.16% in 2023, an increase of nearly 50 percentage points over 45 years, with an increase of nearly 10 million people each year, most of whom are migrants from rural areas [9]. The unprecedented speed and scale of urbanization have made the aforementioned resource constraints and spatial conflicts particularly concentrated and acute, leading to governance predicaments such as inefficient agricultural space, unbalanced urban–rural space, fragmented ecological space, and blocked factor mobility [10,11,12]. For instance, the fragmentation of cultivated land has reduced productivity by 23% to 30% compared to areas of large-scale operations, while the country’s cultivated land is threatened by “non-agriculturalization”, “non-grainization” and “marginalization”, leading to a double decline in food security and ecological functions; the hollowing out of the rural population has led to a homestead vacancy rate of over 15% (up to 40–60% in some remote areas), while 21.2% of newly added urban construction land is inefficient due to the disconnection between industry and city, creating a scissors gap of “rural idleness—urban overload”. These mismatches are essentially a structural contradiction between the rigid control of spatial form and the dynamic demand of factor flow, highlighting the limitations of the traditional “fragmentation” and “homogenization” governance model.

In this context, counties, as key carriers of integrated urban–rural development and important spatial units of new urbanization [13], the optimal allocation of territorial space and the improvement of governance efficiency have become crucial. County-level territorial space consolidation is essentially an upgrade of the paradigm of traditional land consolidation. It differs from the original fragmented implementation model based on villages and towns and traditional comprehensive land consolidation in that that county-level territorial space consolidation takes the county as the coordinating unit and towns as the basic implementation unit to moderately reshape the three living Spaces of the entire administrative jurisdiction [14,15]. Therefore, promoting the comprehensive improvement of territorial space at the county level has become a key path to breaking tight resource constraints, coordinating multi-dimensional spatial conflicts, and supporting high-quality development. The scientific identification of the priority of county-level territorial space improvement is a key prerequisite for clarifying the direction of regional improvement and implementing differentiated spatial governance strategies, which can maximize the role of resource allocation [16]. However, there are bottlenecks in the current practice, such as the disconnection between the evaluation indicators of “form” and “flow”, as well as methodological limitations.

To fill this research gap and explore the collaborative path for the optimization of the morphological structure and functional flow of territorial space, this paper is based on the county scale and innovatively combines the theoretical framework of “form–flow synthesis” with principal component analysis (PCA). We establish a quantitative discrimination system applicable to the priority of territorial space rectification. Specifically, this paper employs the PCA method to reduce the dimension of multi-source evaluation indicators, extracting the “form” and “flow” factors with clear geographical significance, thereby objectively revealing the spatial matching/mismatch relationship between the two. Through this analytical approach, this paper aims to achieve the following goals: (1) Spatial Diagnosis: Identify coupled obstacle areas in counties where morphology restricts flow or flow lags behind morphology; (2) Priority Determination: Based on the degree of “form–flow” matching, scientifically classify and define the key directions for rectification; (3) Strategy Generation: Propose a set of differentiated and operational spatial intervention plans based on the actual situation of the region. This article breaks through the evaluation paradigm of the separation of “form” and “flow” in traditional consolidation, and explores the technical chain of “diagnosis—zoning—policy implementation”, which can provide theoretical support and practical tools for promoting the comprehensive consolidation of county-level territorial space in a refined manner.

2. Literature Review

Many theories and practices have been developed with regard to territorial space consolidation worldwide, as an important means of optimizing territorial space resource allocation [17]. At the international level, land consolidation practices rooted in specific social, economic, and historical transformation contexts have been established from European transitional countries (such as Poland, Slovakia, Latvia, and Croatia) to southern Europe (such as Spain, Greece, and Turkey) and Asia (such as Uzbekistan and South Korea) [18,19,20,21,22,23,24,25,26,27,28,29]. These practices are generally aimed at addressing long-accumulated spatial development problems. It is notable that existing international research is mostly confined to a single agricultural dimension and lacks systematic and coordinated governance of the “production–living–ecology” space, which to some extent reflects the research challenges brought about by the complexity of territorial space consolidation itself.

In contrast to international research, the practice of territorial space consolidation in the Chinese context presents a unique paradigm transformation path. This transformation not only placed emphasis on spatial functional zoning based on international experience, but also, under the dual pressure of China’s rapid urbanization and ecological protection demands, promoted theoretical innovation and methodological upgrading. Focusing on the Chinese context, the theoretical and practical paradigms of territorial space improvement have undergone a significant leap. The goal has shifted from the early “regulation of development order” to an equal emphasis on “optimization of protection pattern” and “improvement of spatial quality”. The methodology shifted from administrative control dominance to emphasis on differentiated governance by zones; the core logic has deepened from a mere “quantity balance” to the comprehensive optimization of “quality–function–structure” [30,31]. Before 2010, territorial space management was centered on the “quantity control” paradigm, and its theoretical basis was mainly derived from the land supply theory and location theory of the classical school of economics. During this period, the total amount of cultivated land was forcibly balanced through administration-led engineering (such as the “balance of occupation and compensation” policy established in the revision of the Land Administration Law in 1998). This model simplifies land to a rigid and replaceable quantifiable indicator, essentially a mechanical control. In the rapid urbanization process, its drawbacks have become increasingly prominent, concentratedly manifested as the triple contradiction of declining cultivated land quality, unbalanced spatial structure, and restricted ecological space. These contradictions profoundly reveal the unsustainability of the simple quantitative balance model and lay the foundation for the subsequent paradigm shift. Since 2010, driven by the concept of sustainable development, systems theory and landscape ecology theory have been widely introduced into the field of territorial space improvement, promoting a paradigm shift towards a “quality–ecological-function” integration. The theory of “rural reconstruction” proposed by domestic scholars such as Long Hualou [32] and the reconstruction path of production–living–ecological Spaces under its guidance have become important practical directions. The research focus has also shifted according to the assessment of spatial pattern stability [33] and the improvement of ecosystem service functions. Although there is a significant increase in attention to spatial functional coordination at this stage, in-depth systematic deconstruction of the interaction mechanism between spatial form and element flow is still insufficient.

In recent years, with the expansion of the influence of the theory of “the space of flows” [34], territorial space has been re-recognized as a dialectical unity of “static carriers (form)” and “dynamic processes (flow)”. Based on theoretical and practical accumulation, the team led by academician Wu Zhiqiang innovatively proposed the planning concept of “form–flow synthesis”. Based on this, Zhang Yingnan and Long Hualou proposed the “form–flow synthesis” analytical framework [35]. The framework advocates optimizing spatial efficiency through a cyclic iterative process of structuring “form” by referencing “flow”—guiding “flow” through optimizing “form”—coupling “form” and “flow”. The core insight is that priority areas for territorial space consolidation should be confined to spatial units where “flow” obstructions (such as population loss and insufficient industrial momentum) and “form” defects (such as fragmented farmland and scattered construction land) are highly coupled. This theoretical breakthrough provides a new, more dynamic analytical perspective for accurately identifying the priorities of remediation.

However, despite the significant innovative value of the “form–flow synthesis” theory, it still faces prominent challenges in promoting the quantitative evaluation of the priority of county-level territorial space consolidation and the application of the results: (1) At the methodological level, a collaborative diagnostic tool that can simultaneously capture the dual dimensions of “form” and “flow” has not yet been formed. Traditional methods cannot easily integrate the static stability of spatial structure and the dynamic intensity of functional flow, and they lack precise quantification of the coupling relationship between the two. (2) In terms of scale adaptation, as key units for urban–rural integration and spatial governance, counties have unique characteristics, such as the intensity of element flow, spatial heterogeneity, and functional mixing, which require the evaluation framework to have corresponding scale-sensing capabilities. However, the existing systematic county-level empirical evidence based on the “form–flow synthesis” theory is still insufficient. (3) At the integration level, there is a lack of a universal indicator system that organically integrates the specific representations of agriculture, towns, and ecological Spaces in terms of “form” and “flow”, and researchers have also failed to effectively construct core indicators for evaluating the coupling/decoupling state of “form–flow”, resulting in limited accuracy in the identification of priority areas and restricting the formulation of differentiated rectification strategies.

In response to the above research gaps, this study achieves the following innovations: (1) Innovation in method integration: By combining the “form–flow synthesis” theoretical framework with the principal component analysis (PCA) method, a comprehensive evaluation model capable of simultaneously handling the stability of spatial form and the intensity of element flow is constructed, solving the problem of collaborative dimensionality reduction and classification of the “form” and “flow” systems. (2) Innovation in scale application: Focusing on the county as the core scale for urban–rural integration and spatial governance, we establish an evaluation framework that conforms to the spatial heterogeneity and flow characteristics of counties, and fill the research gap in the “form–flow synthesis” theory from the empirical aspect of counties. (3) Innovation in the indicator system: We construct a universal indicator system that integrates the three major spatial “form” and “flow” representation factors—agriculture, urban areas, and ecology—to effectively identify the coupled areas of “form defect—flow obstruction”, providing a scientific basis for the formulation of differentiated spatial governance strategies.

3. Research Methods and Cases

3.1. Principal Component Analysis

Principal component analysis (PCA) is a multivariate statistical method that converts high-dimensional correlated variables into low-dimensional independent variables through orthogonal transformation [36,37,38]. Evaluation indicators can be regarded as indicator variables, each of which reflects the information of that type of indicator to varying degrees, and there are inevitably overlapping and correlation relationships among the variables. When studying multivariable problems using modern multivariate statistical methods, too many variables will increase the computational load and complexity of the problem. It is naturally hoped that in the process of quantitative analysis, the number of variables involved should be as few as possible and the amount of information as much as possible. Principal component analysis is an ideal tool to solve this problem. The mathematical model of the principal component analysis method assumes there are n indicators X₁, X₂, …, X_n. If there are N objects, X_n can be represented by an N × n matrix; that is,

$$X_{N\times n}=\left[\begin{array}{ccc}{x}_{11}& \dots & x_{1n}\\ ⋮& ⋮& ⋮\\ x_{N1}& \dots & x_{Nn}\end{array}\right]$$

(1)

First, perform central normalization to generate the standard matrix Y; that is,

$$y_{ij}={\displaystyle \frac{x_{ij}-{\overline{x}}_j}{s_j}},(i=1,2,\dots ,N;j=1,2,\dots ,n)$$

(2)

where ${\overline{x}}_j$ and $s_j$ are the mean and variance of the metric variable x_ij, respectively.

After a linear change, the following is obtained:

$$\left\{\begin{array}{c}{Z}_1=w_{11}{Y}_1+w_{12}{Y}_2+\dots +w_{1n}{Y}_n,\\ Z_2=w_{21}{Y}_1+w_{22}{Y}_2+\dots +w_{2n}{Y}_n,\\ ⋮\\ Z_n=w_{n1}{Y}_1+w_{n2}{Y}_2+\dots +w_{nn}{Y}_n,\end{array}\right.$$

(3)

Take n standard indicator variables Y₁, Y₂, …, Y_n and transform them into N new variables Z₁, Z₂, …, Z_n, with the linear transformation satisfying three conditions: (1) Z_i and Z_j are independent, i ≠ j, i, j = 1, 2, …, n; (2) var (Z₁) ≥ var (Z₂) ≥ … ≥ var (Z_n); (3) w_i1² + w_i2² + … + w_in² = 1. Then they are denoted by Z₁, Z₂, …; Z_n is Y₁, Y₂, …, Y_n, where n is the principal component of Y; and Z_j is the jth principal component.

The principal components are calculated by first calculating the autocorrelation matrix R = E(YY^T) of the standard variable, and then calculating the eigenvalues λ₁, λ₂, …, λ_N of the autocorrelation matrix and the corresponding eigenvectors q₁, q₂, …, q_N. Principal component values are equivalent to projecting the standard variable Y onto the random vector q; that is, A = Y^Tq. The larger the eigenvalue, the more important the corresponding eigenvector. The maximum eigenvector is extracted based on the cumulative contribution rate or the number of specified principal features [39].

In the analysis of “form–flow synthesis” in territorial space, there are numerous factors influencing “form” (spatial morphological structure) and “flow” (functional flow intensity) (such as land fragmentation, population density, ecological connectivity, economic agglomeration, etc.), and there are often significant correlations among the indicators (such as the high correlation between urbanization rate and construction land scale). Traditional methods are prone to multicollinearity interference, while PCA can effectively overcome indicator redundancy and correlation by extracting independent comprehensive factors, and precisely quantify the complex coupling characteristics of the “flow–form” system. Further, based on the scores of the principal components, objective classification or prioritization can be performed. Based on this, this paper uses the principal component analysis method.

3.2. Researching the Technical Route

This paper assigns the county as the research object of the priority of territorial space consolidation, and each township as an evaluation unit. The technical route is shown in Figure 1, mainly including three stages: (1) Selection of evaluation indicators and data preprocessing: Based on the theory of “form–flow synthesis”, combined with the literature, the actual situation of the study area, and principles such as data accessibility, an indicator evaluation system is initially selected and constructed; then, the collected raw data is standardized to eliminate the influence of dimensions. (2) Diagnosis and classification: The principal component analysis method is used to reduce the dimension of the standardized data and extract the top two principal component factors with the maximum interpretability, and we name them “flow” and “form”; we calculate the scores of each township unit for the “flow” and “shape” factors, and project them onto the “flow–form” two-dimensional coordinate system, and reveal the spatial matching/mismatch relationship between the two. (3) Classification, evaluation of consolidation priorities, and generation of differentiated strategies: We comprehensively evaluate the core contradictions revealed by the “flow–form” combination types of each township unit, determine their consolidation priorities based on this, identify the key consolidation directions, and propose differentiated consolidation strategies.

3.3. Case Studies

This paper selects Deqing County in the northern part of Zhejiang Province as the empirical research subject (Figure 2). This county is located in Huzhou City, in the western part of the Hangzhou–Jiaxing–Huzhou Plain of the Yangtze River Delta. It covers a total area of 936 square kilometers and governs 8 towns and 4 sub-districts. It is an important node of the Hangzhou Metropolitan Area and has a significant geographical advantage.

This paper selects Deqing County as the study case, mainly based on its outstanding typicality, representativeness, and research value. Our reasons for choosing Deqing County are as follows: (1) Its geographical location and development stage are typical. Deqing County is located in the core area of the Yangtze River Delta. It has undergone rapid industrialization, urbanization, and agricultural modernization processes, and faces prominent problems of resource constraints and unbalanced spatial structure. Research on Deqing county can provide a reference for counties in developed regions to break through spatial bottlenecks. (2) Its spatial composition and element complexity are strong. Within the county, towns, agriculture, ecology, and comprehensive Spaces coexist, covering the central urban area, agricultural production areas, ecological barriers, historical and cultural clusters, etc. It is an ideal sample area for studying the multi-functional integration and synergy of territorial space. (3) The feature of “form–flow synthesis” is prominent in this area. During the process of urbanization, the coupling relationship between spatial form and functional flow is obvious. There are problems such as the occupation of cultivated land by urban expansion and the blocking of ecological corridors. It is suitable to apply the “form–flow synthesis” framework to conduct research on the priority of rectification. (4) It is at the forefront of reforming practices. As a pioneering area for spatial improvement in Zhejiang Province, Deqing has conducted much exploration into the construction of beautiful villages and comprehensive land improvement. Studying the priority of its improvement can provide a scientific basis for county-level spatial governance and address the demand for refined and intelligent governance.

3.4. Indicator Selection and Data Processing

3.4.1. Indicator Selection

In order to determine the assessment indicators, the author first proposes four fundamental principles that the selection of diagnostic indicators should follow, namely systematicness (covering the three functional Spaces of agriculture, urban areas, and ecology), “form–flow” coordination (taking into account both spatial form and functional activities), operability (data should be accessible and reflect regional differences), and policy relevance (aligning with national strategies such as food security and ecological red lines). Then, during the process of indicator selection, the content analysis method [40,41] is adopted to systematically sort the evaluation indicators used in the existing literature (

Table 1. Evaluation indicators of the priority of territorial space consolidation selected in previous studies.

Functional Space	Dimensions	Perspective	Criteria and Indicators	Related Literature
Agricultural	Form	Rationality of permanent basic farmland protected area	Cultivated land quality grade, spatial form (spatial continuity, plot regularity), conditional location (distance from residential areas, distance from river systems), consistency of territorial spatial planning	[42]
Agricultural	Form	Cultivated land	Farmland fragmentation index, average plot size, farmland continuity, degree of concentration in basic farmland protection areas, farmland slope grade, irrigation guarantee rate, soil quality grade, farmland forest network density, etc.	[43]
Agricultural	Form	Applicability of agricultural machinery	Road accessibility, elevation difference, minimum transportation cost distance, shape index, flatness level, area index	[44]
Agricultural	Form–Flow	The relationship between farmland regulations, agricultural productivity, and trade efficiency	Yield trends, irrigation coverage, land use efficiency, trade performance	[45]
Urban	Form	Urban residents’ satisfaction	Construction land development intensity, building density, floor area ratio, per capita construction land area, industrial land proportion, public service facility land proportion, green space ratio, road network density, land use mix, proportion of idle/inefficient land, etc.	[46]
Ecological	Form	Ecological sensitivity	Elevation, slope, road, land use type, water area, vegetation coverage index	[47]
Ecological	Form	Risk of ecological degradation	Ecological land ratio, forest/grassland/wetland coverage, core ecological source area, ecological land fragmentation index, landscape diversity/evenness index, length/width of important ecological corridors, proportion of nature reserve area, area with of land with slope > 25 degrees, etc.	[48]
Ecological	Form	Ecological security pattern	Natural features (landscape type, elevation, slope, spatial pattern type), human development (distance from road, landscape fragmentation), environmental response (NDVI)	[49]
Ecological	Form–Flow	Rural tourism sustainability	Ecological standards (biodiversity), social culture (local community engagement), economy (livelihood diversification)	[50]
Agricultural–Urban	Form–Flow	Potential constraints—probabilistic choices	Economic factors (rural residents’ income level, per capita fiscal expenditure), social factors (rural population retention rate, village type positioning, degree of rural population concentration), distance from the town center to dense road network, land use factors (average residential area size, average homestead area per household, per capita cultivated land area), improvement efficiency (degree of contiguous improvement), degree of contiguous cultivated land that is easy to reclaim), village layout (whether within the layout range of the central village), current status of residential areas (degree of hollowing out of residential areas; residents’ concerns about degree of decay, degree of sporadic settlements, and degree of road connectivity in settlements), house quality grade, road convenience, location advantage (degree of commercial service accessibility, degree of educational facility accessibility, degree of medical facility accessibility)	[51]
Agricultural–Ecological	Form	Farmland protection, ecological protection of territorial space	Topographic conditions (slope, elevation, topographic undulation), soil conditions (topsoil texture, soil organic carbon, soil PH, soil), tillage conditions (distance from road, distance from irrigation water source), climatic conditions (annual average precipitation, dryness)	[52]
Urban–Ecological	Form–Flow	Pattern–process–effect	Landscape pattern (diffusion, agglomeration, proximity), development process (level of spatial decline, proportion of inefficient land use, population change trend), ecological effect (change in vegetation, change in carbon sequestration)	[53]

). Finally, based on on-site sampling surveys and consultation with experts, 19 indicators with “form” and “flow” characteristics are established from four dimensions, comprehensive, agricultural, urban, and ecological, which are used as indicators for evaluating the priority of county-level territorial space improvement (

Table 2. Indicator system for territorial space diagnosis in Deqing County.

Functional Space	“Form” or “Flow” Characteristics	Indicators (Representative Symbols)	Units	Indicator Direction
Comprehensive	Form	Area of land for transportation (C1)	Hectares	+
	Form/Flow	Number of POIs (C2)	Pieces	+
	Form/Flow	Permanent resident population (C3)	Ten thousand	+
	Flow	Population growth rate (C4)	%	+
	Flow	Total water usage (C5)	Ten thousand cubic meters	+
	Flow	GDP (C6)	Billion yuan	+
Agricultural space	Form	Proportion of cultivated land in agricultural land (A1)	%	+
	Form	Permanent basic farmland area (A2)	Hectares	+
	Form	Average patch area of permanent basic farmland (A3)	Hectares	+
	Flow	Grain yield per unit area (A4)	Kilograms per mu	+
	Flow	Per capita agricultural income in rural areas (A5)	Yuan	+
Urban space	Form	Industrial land area (U1)	Hectares	+
	Form	Commercial and residential land area (U2)	Hectares	+
	Flow	Combined energy consumption (U3)	10,000 tons of standard coal	+
	Flow	Taxes (U4)	100 million yuan	+
Ecological space	Form	Proportion of ecological conservation red-line area (E1)	%	+
	Form/Flow	Mean NDVI (E2)	Hectares	+
	Flow	Rate of change in NDVI (E3)	%	+
	Flow	Annual average concentration of PM2.5 (E4)	(μg/m3)	−

).

• The functional space of comprehensive land: This refers to transitional or composite areas in the national spatial system that possess two or more functional attributes. It is not a fourth type of “functional space” on par with agriculture, towns, and ecological Spaces, but rather a “vein” and “skeleton” that provides support, connection, and services for the three. For example, transportation land (C1) connects urban nodes (urban functions), crosses farmland or ecological reserves (agricultural/ecological functions), and at the same time constitutes a linear infrastructure space by itself; the number of POIs (C2), the permanent resident population (C3), the population growth rate (C4), the total water consumption (C5), and the GDP (C6) represent the “flow” and “aggregation” nodes of human activities and economic and social functions in the entire region.
• The functional space of agricultural land: This focuses on food security and sustainable rural development, and includes five indicators: the proportion of cultivated land in agricultural land (A1), the area of permanent basic farmland (A2), the average patch area of permanent basic farmland (A3), the per-unit yield of grain (A4), and the per capita agricultural income in rural areas (A5). The first three “shape” indicators lock in the foundation of cultivated land resources (structure, red line, and degree of contiguity), while the last two “flow” indicators verify production benefits (per unit yield) and people’s livelihood and well-being (income). This combination is conducive to systematically assessing the comprehensive performance of agricultural space in “protecting cultivated land, increasing production capacity and enriching farmers”, identifying prominent problems such as the “non-grain use” of cultivated land, fragmentation, low production efficiency, or insufficient economic benefits, and providing a basis for implementing differentiated rectification strategies.
• The functional space of urban land: This focuses on economic agglomeration and efficient operation, and includes four indicators: industrial land area (U1), commercial and residential land area (U2), comprehensive energy consumption (U3), and tax revenue (U4). The first two, which are “form” indicators, depict the scale of industrial and residential carriers, while the last two, which are “flow” indicators, reveal energy efficiency (energy consumption) and economic vitality (tax revenue). The area of industrial land should be combined with tax evaluation to assess the degree of intensification, the area of commercial and residential land reflects the functional structure, comprehensive energy consumption is related to low-carbon development, and tax reflects the quality of the industry. Together, they support decisions such as “industrial map drawing” and “priority determination of land renewal”.
• The functional space of ecological land: This focuses on ecological security and service functions, and includes four indicators: the proportion of ecological protection red-line area, the average value of NDVI, the change rate of NDVI, and the annual average concentration of PM2.5. The “form” indicators (red-line ratio, average NDVI value) define the bottom line of protection and the basis of green-space volume, while the “flow” indicators (NDVI change rate, PM2.5) monitor ecological dynamics and environmental quality, forming a complete diagnostic chain of “holding the bottom line—enhancing functions—benefiting people’s livelihood”.

3.4.2. Data Processing

• Data source

The territorial space utilization data for Deqing County and its townships were sourced from the Natural Resources and Planning Bureau of Deqing County, including the latest change survey data from the third national land survey 2022 (including land use status classification and patches), land use master plan map, permanent basic farmland protection area map, ecological conservation red-line map, urban development boundary map, etc. Socio-economic statistics were derived from the statistical yearbook and bulletin of Deqing County, including population data (permanent residents, registered population), GDP, industrial structure, fixed asset investment, per capita income of farmers in Deqing County and its towns and sub-districts. Ecological and environmental data were derived from ecological and environmental departments and remote sensing image interpretation, including the vegetation coverage index (NDVI), surface water quality monitoring data, air quality data, biodiversity distribution information, etc. Other relevant environmental, economic, and social data were derived from statistical yearbooks, policy documents, relevant planning texts, historical improvement project data, and public data. The time span of the data was mainly from 2018 to 2024 to ensure the relevance and accuracy of the analysis.

2.

Data preprocessing

Based on the relevant statistical data from departments such as the Bureau of Natural Resources and Planning and the Bureau of Statistics, the relevant indicators were further calculated to obtain the evaluation indicator data for the territorial space diagnosis of each township in Deqing County, as shown in

Table 3. Indicator data for territorial space diagnosis of townships in Deqing County.

Administrative Unit	C1	C2	C3	C4	C5	C6	A1	A2	A3	A4	A5	U1	U2	U3	U4	E1	E2	E3	E4
Wukang Sub-district	3296	7475	11.90	0.80	3980	287	12.13	42	0.74	520	2943	963	860	93	15.82	15.13	0.57	5.56	29
Wuyang Sub-district	9606	1706	4.71	4.90	1208	93	21.55	1071	1.44	508	9350	222	300	29	6.89	4.45	0.73	12.31	27
Fuxi Sub-district	33,634	1846	4.75	6.60	4150	298	49.27	531	1.42	532	33,336	743	352	105	25.16	2.60	0.56	1.82	34
Xiazhuhu Sub-district	55,880	458	1.93	3.30	1150	78	47.11	1204	1.21	495	55,543	328	165	24	4.05	8.00	0.75	10.29	24
Kangqian Sub-district	15,695	296	2.43	8.60	1635	125	3.76	89	2.77	518	15,579	23	97	38	12.05	2.93	0.71	14.52	27
Qianyuan Town	27,559	2053	3.90	3.90	2840	196	36.13	1371	1.78	528	27,273	486	270	61	18.93	0.24	0.66	4.76	31
Xinshi Town	37,060	2746	6.45	9.00	6580	468	2.39	3450	2.40	612	36,783	53	262	187	27.58	0.00	0.52	0.00	36
Loshe Town	48,821	832	1.87	2.30	1780	121	18.31	1342	2.81	585	48,613	94	41	38	7.41	0.00	0.70	4.48	31
Zhongguan Town	49,336	1316	3.82	3.00	3720	259	30.52	1934	2.63	598	49,096	79	95	90	16.74	0.00	0.62	3.33	33
Leidian Town	39,926	1720	4.34	4.20	3420	244	58.14	1138	2.01	568	39,574	321	213	76	11.68	0.00	0.62	6.90	34
Yuyue Town	81,973	1415	3.55	2.80	2670	179	62.40	814	1.21	553	81,740	715	45	64	9.27	0.00	0.64	4.92	33
Xin’an Town	50,787	1028	3.00	2.10	1890	126	43.03	1819	2.13	540	50,551	295	47	39	5.16	0.00	0.61	3.39	29
Moganshan Town	57,501	2455	2.21	1.60	1062	77	42.45	592	0.81	472	57,222	579	146	25	3.92	66.64	0.89	8.54	22

.

In order for indicators to be eligible for calculation, it is necessary to use functions to map the values to the interval [0, 1] and to make the dimensional expressions dimensionless [54]. Here, this paper uses the indicator standard method to normalize the indicator data for territorial space diagnosis in each township of Deqing County.

$$Z_{ij}={\displaystyle \frac{X_{ij}-Min\left\{X_{ij}\right\}}{Max\left\{X_{ij}\right\}-Min\left\{X_{ij}\right\}}}$$

(4)

$$Z_{ij}={\displaystyle \frac{Max\left\{X_{ij}\right\}-X_{ij}}{Max\left\{X_{ij}\right\}-Min\left\{X_{ij}\right\}}}$$

(5)

In Formula (4), we observe that the evaluation indicators are directly proportional to their standard values, meaning that as the values of these indicators increase, so do their positive effects. In Formula (5), we can see an inverse relationship between each evaluation indicator and its corresponding actual measurement result. In other words, if the value of a certain indicator increases, its negative impact will also increase accordingly. In this equation, Z_ij represents the normalized value of the j-th evaluation criterion within the i-th evaluation unit; X_ij is the specific value of the j-th assessment indicator within that assessment unit; and finally, Max{X_ij} and Min{X_ij}, respectively, refer to the best and worst values of a particular indicator in all evaluation units.

All the indicators for diagnosing territorial space in each township of Deqing County were normalized according to the above two formulas. The maximum value after normalization was 1, the minimum value was 0, and the rest of the data were between 0 and 1. (See

Table 4. Standardized diagnostic indicator values for territorial space in each township of Deqing County.

Administrative Unit	C1	C2	C3	C4	C5	C6	A1	A2	A3	A4	A5	U1	U2	U3	U4	E1	E2	E3	E4
Wukang Sub-district	0.00	1.00	1.00	0.00	0.53	0.54	0.16	0.00	0.00	0.34	0.00	1.00	1.00	0.42	0.50	0.23	0.14	0.38	0.52
Wuyang Sub-district	0.08	0.20	0.28	0.50	0.03	0.04	0.32	0.30	0.34	0.26	0.08	0.21	0.32	0.03	0.13	0.07	0.57	0.85	0.68
Fuxi Sub-district	0.39	0.22	0.29	0.71	0.56	0.57	0.78	0.14	0.33	0.43	0.39	0.77	0.38	0.49	0.90	0.04	0.11	0.13	0.14
Xiazhuhu Sub-district	0.67	0.02	0.01	0.30	0.02	0.00	0.75	0.34	0.22	0.16	0.67	0.32	0.15	0.00	0.01	0.12	0.62	0.71	0.84
Kangqian Sub-district	0.16	0.00	0.06	0.95	0.10	0.12	0.02	0.01	0.98	0.33	0.16	0.00	0.07	0.09	0.34	0.04	0.51	1.00	0.63
Qianyuan Town	0.31	0.24	0.20	0.38	0.32	0.31	0.56	0.39	0.50	0.40	0.31	0.49	0.28	0.22	0.63	0.00	0.38	0.33	0.32
Xinshi Town	0.43	0.34	0.46	1.00	1.00	1.00	0.00	1.00	0.80	1.00	0.43	0.03	0.27	1.00	1.00	0.00	0.00	0.00	0.00
Loshe Town	0.58	0.07	0.00	0.18	0.13	0.11	0.27	0.38	1.00	0.81	0.58	0.08	0.00	0.08	0.15	0.00	0.49	0.31	0.36
Zhongguan Town	0.59	0.14	0.19	0.27	0.48	0.47	0.47	0.56	0.91	0.90	0.59	0.06	0.07	0.40	0.54	0.00	0.27	0.23	0.23
Leidian Town	0.47	0.20	0.25	0.41	0.43	0.43	0.93	0.32	0.61	0.69	0.46	0.32	0.21	0.32	0.33	0.00	0.27	0.48	0.12
Yuyue Town	1.00	0.16	0.17	0.24	0.29	0.26	1.00	0.23	0.22	0.58	1.00	0.74	0.00	0.24	0.23	0.00	0.32	0.34	0.20
Xin’an Town	0.60	0.10	0.11	0.16	0.15	0.13	0.68	0.52	0.67	0.49	0.60	0.29	0.01	0.09	0.05	0.00	0.24	0.23	0.47
Moganshan Town	0.69	0.30	0.03	0.10	0.00	0.00	0.67	0.16	0.03	0.00	0.69	0.59	0.13	0.00	0.00	1.00	1.00	0.59	1.00

).

4. Results

4.1. Extraction of Principal Components

We used SPSS 26.0 software to process the standardized table (Table 4) and employed the Principal Components and Classification Analysis function to obtain the eigenroots and contribution rates of the synthetic factors. As shown in

Table 5. Characteristic root values and Contribution rates of factors.

	Initial Eigenvalues			Extraction of the Sum of Squares of the Loads			Rotation of the Sum of the Load Squares
Factors	Characteristic Root Values	Contribution Rates	Cumulative %	Total	Percentage of Variance	Cumulative %	Total	Percentage of Variance	Cumulative %
1	7.89	41.54	41.54	7.89	41.54	41.54	7.86	41.37	41.37
2	5.06	26.61	68.15	5.06	26.61	68.15	5.09	26.78	68.15
3	2.51	13.19	81.35
4	1.12	5.90	87.24
5	1.05	5.54	92.78
6	0.63	3.30	96.08
7	0.37	1.94	98.02
8	0.19	1.02	99.04
9	0.09	0.47	99.52
10	0.04	0.21	99.72
11	0.04	0.19	99.92
12	0.02	0.08	100.00

, the cumulative contribution rates of factor 1 and factor 2 were close to 70%, which means that factor 1 and factor 2 combined most of the information of the original evaluation indicator. Therefore, factor 1 and factor 2 were selected as principal components for analysis. The selection of the first two principal components (with a cumulative contribution rate of approximately 70%) is based on the goal orientation of our research. This study focuses on “form–flow synthesis” analysis, with the first two principal components precisely corresponding to the core dimensions (“flow” and “form”) of this research framework. Although the third principal component may increase the cumulative contribution rate to 80%, it was not included in order to maintain the simplicity of the analytical framework, because it is difficult to achieve clear theoretical significance, and the increment of the contribution rate is relatively small.

4.2. Naming of Principal Components

The load plots of the evaluation indicators (variables) projected onto factor 1 and factor 2 are shown in Figure 3. The magnitude of the load values reflects the correlation between the evaluation indicators (variables) and the principal components. The range of load values is typically between −1 and 1. The closer the value is to 1 or −1, the stronger the relationship between the variable and the principal component; the closer the value is to 0, the weaker the relationship between the variable and the principal component.

As shown in Figure 3, factor 1 is closely positively correlated with indicators such as GDP (C6), tax revenue (U4), comprehensive energy consumption (U3), total water use (C5), grain yield per unit area (B4), and population growth rate (C4), and negatively correlated with ecological conservation red-line area (E1), mean NDVI (E2), proportion of cultivated land in agricultural land (A1), industrial land (U1), etc. Therefore, factor 1 is named the “flow” element.

Factor 2 is closely positively correlated with indicators such as industrial land (U1), transportation land (C1), commercial-residential land (U2), and POI (C2), and negatively correlated with rural per capita agricultural income (A5), population growth rate (C4), grain yield per unit area (A4), and NDVI change rate (E3). Therefore, factor 2 is named the “form” factor.

4.3. Priority Classification

SPSS 26.0 software was employed to calculate the scores of the “flow” and “form” factors for each evaluation unit in every township. Subsequently, Origin 2025 software was utilized to plot a scatter matrix diagram of the two factors (Figure 4). Partitioning was carried out using the tercile method: units with scores greater than 1 were defined as high-value areas (H), those with scores less than −1 were defined as low-value areas (L), and units with scores within the range of [−1, 1] were defined as medium-value areas (M). Based on this, the evaluation units were classified into a total of nine types of characteristic partitions, which were combinations of “flow” (factor 1) and “form” (factor 2), forming a 3 × 3 matrix. Figure 4 visually depicts the distribution of each unit in the “flow–form” two-dimensional coordinates. For instance, units located in the M-H area have a medium score for the “flow” factor (M) and a high score for the “form” factor (H), indicating that these units possess good spatial form but average functional flow. Different partition types reveal distinct core contradictions and bottlenecks, reflecting the matching or mismatching states of “flow–form”: the high “flow” and low “form” (H-L) situation may imply high carrying pressure but weak background support; the low “flow” and high “form” (L-H) situation may suggest well-developed infrastructure (“form”) but insufficient functional vitality (“flow”).

Based on the diagnostic results in Figure 4, the current territorial space of Deqing County exhibits characteristic of “overall balance but local imbalance”. The specific manifestations are as follows: (1) There are no extreme types (H-H/L-L/L-H/H-L are absent). (2) The proportion of stable main-body units is 53.8% (7 out of 13 townships are of the M-M type). (3) The proportion of significantly mismatched units is 46.2% (6 out of 13 townships), which can be further divided into two types of contradictions: morphological constraint type (M-L/H-M) and functional lag type (L-M/M-H). Among them, the morphological constraint type includes Kangqian Sub-district and Luoshe Town (M-L), where the flow potential is restricted by the spatial form, and Xinshi Town (H-M), where there is a misalignment between high flow demand and inefficient space; the functional lag type includes Xiazhuhu Sub-district and Moganshan Town (L-M), where the functional flow of these areas’ excellent ecological background has not been fully activated, and Wukang Sub-district (M-H), where the high-quality built environment does not match the flow level.

5. Findings and Discussions

The results of this study indicate that the “form–flow synthesis” framework can go beyond the traditional static, spatial, functional zoning and dynamically reveal the internal operational logic of territorial space from the interactive relationship between “form” and “flow”. The analysis of the four mismatch types (M-L, H-M, L-M, M-H) identified accurately captured the heterogeneous contradictions faced by different towns and townships in the processes of urbanization, industrialization, and ecologicalization. For instance, the “high flow–medium form” (H-M) characteristics of the new town reveal the tension between high-intensity socio-economic activities and the relatively lagging spatial carrying capacity, making it a typical “growth pressure-type” area. The “low flow–medium form” (L-M) feature of Moganshan Town reflects the “value transformation bottleneck” between its high-quality ecological background and its failure to fully transform this ecological background into economic and social benefits.

The results of this study have clear policy implications for the precise governance of territorial space in Deqing County and other counties in similar developed regions. The “one-size-fits-all” rectification model is no longer applicable here. Decision-makers must implement targeted “one town, one policy” intervention based on the “flow–form” matching types of different districts. Based on this, this paper maps a distribution map of the leading strategies for territorial space consolidation in Deqing County (Figure 5) and constructs the following three-level priority action framework.

• Prioritize Urban Renewal (Three towns with strong “flow” but weak “form”)

This type of area faces the prominent contradiction that the functional flow is restricted by the lagging spatial form. The goal of spatial consolidation is to reshape the “form” to adapt to high “flow” demands. Through the renewal of construction land and structural optimization, it aims to alleviate spatial pressure and improve development capacity.

• Kangqian Sub-district and Luoshe Town (M-L, Flow > Form): The medium-level functional flows (in terms of industries and population) are restricted by the shortcomings in terms of spatial form (fragmented farmland and lagging infrastructure). We will focus on phasing out and reusing inefficient industrial land, improving regional transportation connections (such as increasing the frequency of expressways with the Second Ring Road of Hangzhou), carrying out concentrated and continuous farmland improvement, and enhancing spatial carrying capacity efficiency.
• Xinshi Town (H-M, Flow > Form): There is a mismatch between the high-intensity flow demand (as a hub of the Hangzhou–Deqing Intercity railway) and the inefficient spatial form (sprawling built-up areas and scattered arable land). With Xinshi Town’s reliance on the Hangzhou–Dezhou Intercity railway hub stations, TOD comprehensive development should be implemented to enhance the functional mixing and development intensity of the land use around the stations. We will simultaneously promote the construction of “ten thousand mu” of permanent basic farmland to prevent urban sprawl and coordinate efforts to address the contradiction between supply and demand.

2.

Prioritize Planning Guidance (Three towns with strong “form” but weak “flow”)

The spatial background of this type of area is excellent, but the flow efficiency is insufficient. The core of spatial consolidation lies in transforming “form” advantages into “flow” development momentum through the precise introduction of functions and policy incentives.

• Xiazhuhu Sub-district and Moganshan Town (L-M, Flow < Form): There is a contradiction between these areas’ excellent ecological background (national wetland/ecological resources of Moganshan) and their low-intensity cultural and tourism flows. It is necessary to activate the flows through the transformation of ecological values. For example, Xiazhuhu has developed an integrated IP of “wetland research + ecological agriculture”, and Moganshan has optimized the layout of homestay clusters in combination with the ecological red line and introduced international cultural and creative functions.
• Wukang Sub-district (M-H, Flow < Form): The built environment of the county-level administrative and cultural center is of high quality (superior form), but the high-end service flows are insufficient. It is necessary to introduce producer services (to address the spill-over from the innovation area in western Hangzhou), optimize public service facilities (such as the layout of 3A hospitals and high-quality school districts), and strengthen the functional connection with the innovation corridor in Hangzhou.

3.

Systematic Enhancement (seven towns with balanced “flow” and “form”)

The current manifold relationships between flow and form in these areas are basically the same. Attention should be paid to the improvement of spatial quality and overall efficiency, and the risk of inefficient lock-in should be prevented.

• The seven towns of Fuxi Sub-district, Zhongguan Town, Leidian Town, Qianyuan Town, Yuyue Town, Xin’an Town, and Wuyang Sub-district (M-M, Flow ≈ Form) are distributed in a north–south band, forming an area with a dynamic balance of “flow–form” in the county. It is suggested that seven towns, including Fuxi Sub-district, be taken as pilot areas to comprehensively promote comprehensive land consolidation throughout the region, optimize the spatial layout of rural areas, explore the mechanism of the reuse of existing homesteads, strengthen the construction of digital governance platforms, and achieve the structural optimization and sustainable management of territorial space.

In conclusion, Deqing County should take the “flow–form” fit relationship as the core scientific basis to formulate a differentiated spatial governance toolkit: for the renewal area, it should (1) focus on the inclination of land use indicators and infrastructure investment and (2) focus on policy empowerment and project investment promotion for the guidance area; (3) for the improvement zone, emphasis should be placed on institutional innovation and long-term management, thereby forming a replicable and scalable model for the refined governance of county-level territorial space.

6. Conclusions

The territorial space itself (“form”) is relatively static and material, while the economic and social activities behind it (“flow”) are dynamic and essential. Based on the “form–flow synthesis” theory, this study uses principal component analysis to construct a priority diagnosis model for territorial space consolidation. Through the dynamic coupling analysis paradigm of “form” and “flow” and spatial classification technology, it has achieved systematic deconstruction of the complexity of territorial space at the county scale. Compared with traditional evaluation methods that are oriented towards the potential or goals of a single element, this study breaks through the binary thinking of the segmentation of “form” and “flow” in traditional spatial evaluation. This study takes Deqing County as the empirical study area. Through principal component analysis, 19 initial indicators are dimensionally reduced to the “form” factor and “flow” factor with clear geographical significance. The two-dimensional classification map constructed based on the factor score matrix projected the 13 township units of Deqing County onto nine “flow–form” combination types, achieving precise identification of the “spatial supply–demand” mismatch types at the county scale for the first time.

Our research results reveal the spatial pattern of “overall balance and local imbalance” in Deqing County, directly supporting the formulation of differentiated rectification strategies: (1) For units with rigid constraints on spatial form and flow potential (flow > form, such as M-L/H-M types), a priority strategy for urban renewal should be implemented, and the development bottleneck of “flow” being suppressed by “form” should be broken through hardware breakthroughs (land integration, infrastructure upgrading). (2) For units where morphological advantages do not trigger functional elastic responses (flow < form, such as L-M/M-H types), a strategy of prioritizing planning guidance should be implemented. Through software activation (functional implantation, policy intervention), morphological dividends should empower “flow”. (3) For units in the “flow–form” medium-level equilibrium trap (flow ≈ form, such as M-M type), it is necessary to initiate a system improvement strategy, promoting a coordinated leap in performance through the reorganization of spatial elements throughout the domain and governance mechanism reform. At the practical level, the three types of leading strategies proposed can provide a direct and scientific decision-making basis for the implementation of differentiated and precise territorial space consolidation in Deqing County and other similar regions, demonstrating the significant application potential of this methodology in promoting the transformation of spatial governance from a “one-size-fits-all” approach to “precise policy implementation”.

Our research has made some contributions to the literature. The complete technical chain of “diagnosis–zoning–policy implementation” that integrates the “form–flow synthesis” theory with principal component analysis has shifted decision-making for territorial space consolidation from empirical to scientific, which is of great value for enriching and developing the theory of territorial space planning. However, our research also has certain limitations, which point to directions for future studies. Firstly, although the indicators selected in this study are representative, in the future, indicators that better reflect new elements, such as population day–night mobility, carbon sink flow, and digital information flow, can be included to make the measurement of “flow” more precise and dynamic. Secondly, this study is a static cross-section analysis, revealing the spatial characteristics of the cross-section at a certain time. Future research can introduce time series data to dynamically track the evolution process of the “flow–form” relationship, thereby better predicting trends and evaluating the long-term effects of consolidation policies. Finally, the zonal diagnosis framework proposed in this study can be applied and verified in other similar counties to test its universality and further improve the theoretical model.