Assessing county-level high-quality development and spatial adaptation paths under the space of flows perspective: a coupling detrended fluctuation analysis approach

Abstract

Given the limited research on high-quality development (HQD) at the county level, especially in major agricultural provinces such as Henan, this study constructs a multidimensional evaluation system tailored to local heterogeneity. Guided by the Five Development Concepts and incorporating the space of flows perspective to reveal inter-county spatial linkages, we introduce a coupling detrended fluctuation analysis (CDFA)-based assessment method to develop a temporally informed county-specific weighting mechanism. This enables the calculation of county-specific indicator weights and overcomes the limitation of traditional methods that assign fixed and uniform weights. Using panel data on 19 indicators for 102 counties in Henan Province from 2010 to 2021, we examine the spatiotemporal trends and structural heterogeneity of county-level HQD. Results indicate broad-based improvement in county-level HQD, while high- and medium-high-quality counties became more concentrated around core urban areas and the remaining weaker counties were mainly located in peripheral areas, demonstrating a clearer core-periphery spatial pattern under overall upgrading. The CDFA-based weighting results reveal significant county-level differences in the relative structural roles of economic vitality, green development, social welfare, and inter-county association, highlighting substantial heterogeneity in county-level indicator-weight profiles rather than a uniform indicator structure across the province. Comparative analysis shows that the proposed method is broadly consistent with a conventional objective weighting approach in overall classification patterns, while offering additional insight into county-level heterogeneity. The optimal parameters-based geographical detector further indicates that locational conditions, industrial foundations, and topographic constraints are important explanatory factors for the spatial differentiation of county-level HQD, and that factor interactions generally produce stronger explanatory power than single factors. Based on these findings, this study proposes differentiated development strategies for core counties, transitional counties, agricultural counties, and peripheral ecologically constrained areas, thereby providing a methodological reference for HQD assessment in spatially heterogeneous regions and supporting regional spatial governance.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1038/s41598-026-59014-8.

County-level development has become a key arena for implementing high-quality development (HQD) under China’s ongoing regional integration and rural revitalization strategies^1–3. Counties connect urban centers with townships and villages, and therefore play a pivotal role in coordinating industrial upgrading, public service provision, ecological protection, and urban-rural integration. This issue is particularly important in Henan Province, a major agricultural and population province where county economies are closely related to food security, characteristic industries, rural revitalization, and common prosperity⁴. Assessing county-level HQD in Henan is thus not only a question of measuring development performance, but also a basis for identifying spatially differentiated governance pathways.

Existing studies have advanced the conceptualization and measurement of HQD from several perspectives. One strand constructs indicator systems around the Five Development Concepts of innovation, coordination, green development, openness, and sharing^5–8. Another emphasizes the need to respond to unbalanced and inadequate development and to meet people’s aspirations for a better life^9–11. A further group of studies links HQD to common prosperity by incorporating income equity, consumption balance, and urban-rural integration^12–15. More recently, the space of flows perspective has drawn attention to interregional factor circulation, spatial networks, and cross-boundary interactions^16–19. These studies provide an important foundation, but their frameworks are often developed for larger spatial units and do not fully capture the structural specificity and linkage dependence of counties.

Methodologically, HQD assessment usually involves indicator standardization and weight assignment. The extreme value method and fixed-base efficacy coefficient method are commonly used for standardization²⁰, while weighting methods include both subjective and objective approaches. Subjective methods such as the Analytic Hierarchy Process may be affected by expert judgment²¹, and equal weighting cannot reflect differences in the actual role of each indicator²². Objective methods such as the entropy weight method, TOPSIS-based approaches, Principal Component Analysis, and the Longitudinal-Transversal Discrepancy Maximization (LTDM) method reduce subjective interference and improve comparability^23–27. However, these methods generally produce a common set of weights for all evaluation units. As a result, they are less able to reveal how the same indicator may play different structural roles across counties with distinct development foundations, ecological constraints, and linkage conditions.

Three gaps therefore remain in the literature on regional HQD. First, most studies focus on national^28–30, urban-agglomeration^31,32, river-basin^9,33–37, regional³⁸, or provincial^39,40 scales, whereas county-level evidence remains limited^41,42, especially for major agricultural provinces such as Henan. Second, existing county-level indicator systems seldom incorporate inter-county linkages and factor-flow mechanisms, even though county development increasingly depends on transport connectivity, market access, public service spillovers, and regional production networks^30,43–45. Third, conventional objective weighting methods mainly reflect overall spatiotemporal dispersion and rarely estimate county-specific indicator structures from each county’s own time-series information⁴⁶. This limits their capacity to support differentiated and spatially adaptive policy diagnosis.

In this study, county-level HQD is understood as a multidimensional development state in which economic performance, ecological sustainability, social well-being, and inter-county connectivity improve in a coordinated manner^47,48. Guided by the Five Development Concepts and the space of flows perspective, we construct an evaluation framework covering four dimensions: economic development, green development, shared development, and interconnected development. The interconnected development dimension is introduced to capture counties’ capacity to participate in and benefit from flows of population, goods, services, information, and regional cooperation. This framework allows county-level HQD to be examined not only as an internal development outcome, but also as a relational process embedded in broader spatial networks.

To address the limitation of uniform fixed weights, this study introduces coupling detrended fluctuation analysis (CDFA) into county-level HQD assessment⁴⁹. CDFA was originally developed to identify long-range coupling and scale-related relationships among non-stationary time series, and has been applied in complex-system research in fields such as finance^50,51, environment^52,53, transportation⁵⁴, and meteorology^55,56. County-level HQD can also be regarded as a complex system in which multiple indicators co-evolve over time. CDFA is therefore used here to extract the temporal coupling structure among indicators and to derive county-specific weights that reflect the internal structural sensitivity of each county^57,58. This does not treat CDFA as a replacement for all established weighting methods; rather, it provides a complementary way to identify local heterogeneity that fixed-weight approaches may overlook.

Empirically, we examine 102 counties in Henan Province from 2010 to 2021. The fixed-base efficacy coefficient method is used to standardize 19 indicators, and CDFA is then applied to each county’s annual indicator series to generate county-specific weights and HQD scores. LTDM is introduced as a comparative reference method, rather than as a ground-truth benchmark, to assess whether the broad classification patterns obtained from CDFA are consistent with those derived from an established objective weighting approach. On this basis, we analyze the spatiotemporal evolution, clustering characteristics, structural heterogeneity, and spatially adaptive pathways of county-level HQD in Henan. Moran’s I, local spatial association analysis, and the geographical detector are further used to examine spatial dependence and potential explanatory factors.

This paper makes three contributions. First, it develops a county-level HQD evaluation framework that integrates the Five Development Concepts with the space of flows perspective, thereby extending HQD assessment from internal development performance to both internal structure and external linkage capacity. Second, it introduces CDFA into county-level HQD measurement and derives county-specific weights from indicator time-series relationships, offering a way to identify structural heterogeneity that is difficult to capture with uniform fixed weights. Third, using panel data for 102 counties in Henan Province, it reveals the spatiotemporal pattern, typological differentiation, and potential driving mechanisms of county-level HQD, and provides empirical support for differentiated county development policies.

Materials and methods

Connotation of county-level HQD and indicator system construction

Defining the connotation of county-level HQD in Henan

At the county level, HQD does not simply refer to the expansion of aggregate economic output or a faster growth rate. Rather, it denotes a comprehensive development process in which counties, under the constraints of resources and the environment, rely on their own industrial base, public service capacity, and regional linkage networks to achieve more efficient economic performance, a more eco-friendly environment, fairer sharing of development outcomes, and smoother regional coordination. Since the 19th National Congress of the Communist Party of China identified the transition of China’s economy from a stage of high-speed growth to one of HQD, HQD has gradually become a central theme of economic and social progress in the new era. Its core requirement no longer lies in growth speed alone, but in implementing the new development philosophy, improving the quality of development, and continuously enhancing people’s well-being. Unlike macro-level discussions, which tend to emphasize normative interpretations of the five development concepts, the study of county-level HQD requires a reconstruction at the level of observable and measurable dimensions, so that abstract development principles can be translated into analytical dimensions and an evaluation framework applicable to county-level units.

Building upon this premise, the present study conceptualizes county-level HQD through four core dimensions: economic, green, shared, and interconnected development. It is worth noting that this framework avoids a mechanical decomposition of the five development concepts. Instead, it structurally reconfigures these macro-level principles to align with county-scale characteristics and the theoretical paradigm of the space of flows. Specifically, innovation and coordination are implicitly integrated into structural economic optimization, urban-rural factor harmonization, and public service allocation. Green and shared development directly correspond to ecological thresholds and the enhancement of public well-being. Most notably, at the county scale, the traditional concept of openness is less concerned with international trade or foreign capital reliance. Rather, it manifests predominantly as the horizontal exchange of population, capital, industry, and information across regional boundaries. For this reason, we redefine this spatial dynamic as “interconnected development”. It should be clarified that reframing this dimension does not theoretically negate the role of international capital or foreign trade. However, given that Henan is an inland agricultural province where foreign trade and international investments are overwhelmingly concentrated in core urban districts rather than counties, incorporating traditional macro-level openness indicators would introduce severe data sparsity (zero-inflation). Such highly skewed data structures would compromise the mathematical stability and validity of objective quantitative evaluation models. Therefore, for these inland counties, “openness” predominantly and measurably manifests as horizontal regional interconnectedness rather than global market integration. When deconstructing the core connotations of these dimensions, economic development, characterized by growth stability, market vitality, and structural refinement, serves as the material foundation for HQD. Green development establishes the definitive environmental constraint boundaries through resource conservation. Shared development, which prioritizes inclusive public services and urban-rural integration, embodies the ultimate value orientation of HQD. Meanwhile, interconnected development captures a county’s capacity to embed itself within regional networks, integrate spatial factors, and foster synergistic linkages, thereby functioning as the crucial mechanism for optimizing resource allocation and expanding developmental potential. Fundamentally, county-level HQD emerges as a multifaceted evolutionary process: anchored by the economy, bounded by ecology, driven by spatial interconnectedness, and ultimately oriented toward shared prosperity.

Construction of the indicator system for county-level HQD in Henan

The indicator system developed in this study is grounded in a core conceptual architecture defined by four pillars: the economic foundation, green constraints, shared objectives, and interconnected mechanisms. This framework delineates the logical positioning and functional interrelationships among the four dimensions. Specifically, economic development functions as the foundation, generating the requisite material capital and fiscal capacity to facilitate environmental governance, public service enhancement, and regional integration. Meanwhile, green development acts as a constraint by establishing non-negotiable thresholds for resource consumption and environmental degradation; it serves as a structural lever to compel a transition in growth patterns while validating long-term sustainability. As the overarching objective, shared development embodies a human-centric philosophy, representing the teleological end of high-quality growth where development dividends are translated into enhanced urban-rural welfare and collective well-being. Finally, interconnected development operates as the mechanism within the context of an open “space of flows”. By leveraging cross-county factor mobility and functional synergy, this dimension provides the necessary impetus and operational efficiency for the synchronized progress of the economic, green, and shared dimensions.

Crucially, the rationale for introducing “interconnected development” as a standalone dimension within our evaluation framework is anchored in the “Space of Flows” paradigm. Articulated by sociologist Manuel Castells, this theory posits that the trans-regional circulation of critical assets, specifically capital, data, technology, and human expertise, operates as the fundamental organizing mechanism of modern information societies. Applied to the county level, this implies that the caliber of high-quality growth is no longer dictated solely by static inventories of local resources. Rather, it increasingly hinges on a jurisdiction’s dynamic capacity to interface with, assimilate, synthesize, and disseminate external elements across broader regional networks. Because spatial linkages forged within the space of flows dramatically shape both economic trajectories and performance, positioning “interconnected development” as a vital metric offers a necessary corrective to traditional indicator systems, which have historically remained overly fixated on localized, internal attributes.

Grounded in the conceptual boundaries and theoretical framework outlined above, this study formulates a four-dimensional evaluation index to measure high-quality county development (Table 1). The architecture of this system strictly adheres to the tenets of systemic coherence, representativeness, measurability, and data accessibility. Furthermore, the operationalization of specific metrics within each dimension is far from arbitrary. Instead, indicator selection is fundamentally dictated by the core logic of its respective dimension. To ensure empirical validity, these theoretical metrics were subsequently tailored to the specific developmental landscape of Henan’s counties, while also being pragmatically constrained by actual data availability.

Serving as the material cornerstone of high-quality county development, the economic development dimension primarily captures the stability, dynamism, and structural upgrading of local growth. Rather than manifesting merely as an expansion in gross economic volume, true HQD prioritizes resilience, endogenous momentum, and structural evolution during the growth trajectory. Consequently, we delineate this dimension through three distinct sub-domains: economic momentum, developmental vitality, and structural optimization. First, within the “economic momentum” sub-domain, indicator selection is driven by the need to gauge growth robustness and risk-mitigation capabilities. The loan-to-deposit ratio of financial institutions serves as a crucial financial proxy for local economic vigor, representing both capital utilization efficiency and the extent to which the financial sector supports the real economy. Additionally, the ratio of public fiscal revenue to expenditure evaluates the health and self-sufficiency of local government finances, establishing the fiscal bedrock required for public service provision and infrastructure investment. Furthermore, the growth rate of agricultural yields is incorporated to deliberately account for Henan’s foundational status as a major agricultural province, illustrating the stability of baseline production capacities and the region’s contribution to national food security. In this context, sustained agricultural growth serves as a vital proxy for endogenous economic resilience, reflecting cumulative improvements in rural infrastructure, agricultural technology, and disaster management, rather than merely reflecting exogenous natural fluctuations. Second, the “developmental vitality” sub-domain aims to map market dynamism and consumption support mechanisms. As an objective spatial proxy for economic activity, mean nighttime light remote sensing data effectively bypasses the methodological adjustments and reporting lags often associated with traditional statistical metrics. Consequently, this specific indicator has recently gained widespread traction for evaluating economic intensity at the county scale. Concurrently, the consumption rate (calculated as the ratio of total retail sales of consumer goods to regional GDP) and per capita retail sales of consumer goods capture residents’ purchasing power and overall market prosperity from the demand side. In the context of China’s transition to HQD, a rising consumption rate indicates a crucial structural shift from traditional debt-fueled, investment-driven expansion toward sustainable, consumption-driven endogenous growth. Therefore, these metrics operate as vital positive manifestations of market vitality and structural optimization. Finally, under the “structural optimization” sub-domain, the industrial structure advancement index functions as a pivotal metric for tracking economic progression toward higher value-added segments. This index reveals the extent of structural upgrading as county industries transition away from resource dependency and low-end processing, moving progressively toward technology-intensive and service-oriented paradigms.

The green development dimension primarily evaluates how county-level systems adapt and respond to prevailing resource and environmental constraints. Within the context of Henan Province, counties are tasked with a dual mandate: fostering industrial growth while simultaneously safeguarding grain production and ecological stability. Consequently, green development manifests not only through the regulation of industrial pollutants but also via the ecological transition of agricultural practices.To measure these dynamics, this study prioritizes two specific analytical lenses: air quality and green agriculture. Regarding the former, both the PM_2.5 index and total CO₂ emissions are utilized to capture the most pressing public health concerns and the atmospheric pressures tied to national “Double Carbon” objectives, respectively. Collectively, these metrics delineate the environmental footprint generated by accelerating industrialization and urbanization. Regarding the latter, we incorporate the intensity of chemical fertilizer and pesticide application per unit of cultivated land. This choice is calibrated to Henan’s reality as a primary grain-producing hub, aiming to isolate agricultural non-point source pollution, a decisive factor in the county-level ecological landscape. These indicators reflect the environmental friendliness of local farming and the overall trajectory of its green transition. Ultimately, the selection of these metrics ensures a balanced consideration of both industrial and agricultural environmental pressures while maintaining rigorous data accessibility.

The dimension of “Shared Development” evaluates the extent to which the dividends of economic growth are equitably distributed and accessible across the urban-rural dichotomy and among diverse social cohorts. Given that the ultimate benchmark of HQD resides in the tangible improvement of public livelihoods and the realization of collective benefits, this study operationalizes this dimension through three primary lenses: urban-rural integration, healthcare services, and social security provisions. Regarding “urban-rural integration”, the urbanization rate is employed to capture the structural transition of population concentration within urban centers. Meanwhile, the urban-rural income coordination index (calculated as |1-(Urban Income/Rural Income)|⁻¹) ) serves as a direct proxy for measuring developmental synergy and the trajectory of narrowing wealth disparities. Higher values of this index indicate a smaller income gap, reflecting a higher degree of shared development. In the realm of “healthcare sharing”, the number of physicians and hospital beds per thousand residents are utilized as standardized global metrics to gauge the supply density and the actual accessibility of essential medical services. Finally, under the “social sharing” sub-dimension, the volume of various social welfare entities per 10,000 people and welfare beds per thousand inhabitants are adopted to characterize the robustness and the “bottom-line” support capacity of the social safety net.

The “Interconnected Development” dimension is engineered to quantify the robustness of spatial linkages and reciprocal interactions among counties. As regional integration deepens, a county’s trajectory toward HQD is no longer dictated solely by its endogenous resource endowments. Instead, it is increasingly contingent upon its operational capacity to connect, assimilate, integrate, and diffuse assets within expansive cross-county networks. To operationalize this, the metric of economic linkage intensity captures the interactive flux of economic elements across boundaries–typically modeled via gravity equations. This reflects the depth of a county’s integration into regional collaborative frameworks and the broader division of labor. Concurrently, the comprehensive county linkage intensity acts as an overarching index. It benchmarks a jurisdiction’s overall structural embeddedness and nodal prominence within a wider web of regional exchanges, explicitly incorporating dimensions such as information flow, transit grids, and demographic mobility. Due to space constraints, Supplementary Text S1 fully details the specific mathematical formulations for both indicators, which encompass the modified spatial gravity models, unstandardized constituent metrics, distance decay parameters, and the subsequent degree centrality analysis. Synthesizing these aspects, the dual metrics effectively illustrate a local system’s proficiency in optimizing factor allocation and unlocking functional synergies via trans-regional engagement.

Table 1.

HQD indicator system.

Sub-index	Basic indicators	Specific indicators	Indicator Symbol	Properties
Economic Development	Economic Dynamism	Financial Institutions’ Deposit-Loan Ratio	X1	+
		Public Finance Revenue-Expenditure Ratio	X2	+
		Agricultural Output Growth	X3	+
	Development Vitality	Mean Nighttime Light Intensity	X4	+
		Consumption Rate	X5	+
		Per Capita Retail Sales of Consumer Goods	X6	+
	Structural Optimization	Industrial Structure Advancement Index	X7	+
Green Development	Air Quality	PM₂.₅ Index	X8	−
		CO₂ Emissions	X9	−
	Green Agriculture	Chemical Fertilizer Usage per Unit of Cultivated Area	X10	−
		Pesticide Usage per Unit of Cultivated Area	X11	−
Shared Development	Urban-Rural Integration	Urbanization Rate	X12	+
		Urban-Rural Income Coordination Index	X13	+
	Medical Sharing	Physicians per 1,000 People	X14	+
		Hospital beds per 1,000 People	X15	+
	Social Sharing	Social Welfare Recipients per 10,000 People	X16	+
		Social Welfare Beds per 1,000 People	X17	+
Associated Development	Economic Association	Economic Association Intensity	X18	+
	Regional Association	County Association Intensity	X19	+

Study area and data sources

This work focuses on 102 counties in Henan Province as the research subjects (Fig. 1), with the study period spanning from 2010 to 2021. The data required for the study are primarily derived from the Henan Statistical Yearbook, statistical bulletins on national economic and social development from various cities in Henan Province, PM2.5 mass concentration monitoring data released by the Socioeconomic Data and Applications Center (SEDAC) under the Center for International Earth Science Information Network (CIESIN) at Columbia University (https://www.earthdata.nasa.gov), as well as inter-county transportation distance data obtained through the Amap API. The fundamental geographic information boundaries are derived from the National Geomatics Center database (https://www.ngcc.cn/). Regarding the nighttime light data, the DMSP/VIIRS remote sensing data (DN values) were derived from an extended, cross-sensor calibrated, and harmonized continuous time-series dataset. We employed zonal statistics based on the county boundaries to extract the mean raster value as the regional nighttime light intensity. Similarly, the county-level CO₂ emission data were sourced from the Emissions Database for Global Atmospheric Research (EDGAR). We aggregated the gridded emission data to the county level utilizing spatial zonal statistics. To ensure sample completeness, linear interpolation was applied to impute individual missing values. Notably, the raw panel data exhibited exceptionally high completeness, with only 21 missing observations out of 23,256 total data points (comprising 19 indicators for 102 counties over 12 years), representing a negligible 0.09%. These sparse gaps mainly occurred in early years (e.g., 2010–2011) for specific socio-economic indicators in peripheral counties. Given this extremely low missing rate, linear interpolation smoothly maintains time-series integrity without impacting the overall data distribution or evaluation results. Finally, to eliminate the influence of different dimensions, all indicator data were uniformly standardized prior to subsequent measurements.

Fig. 1.

Spatial Distribution of the 102 Sample Counties in Henan Province, China. Based on the data resource sharing platform of the National Platform for Common Geo Spatial Information Services (https:/www.tianditu.gov.cn/) with the approval number GS(2024)0650, and the boundary of the base map has not been modified.

Methods

Coupling detrended fluctuation analysis (CDFA) method

HQD is not merely a linear summation of independent indicators, but a complex, dynamic system characterized by multidimensional synergy and continuous evolution. Traditional weighting methods, such as the standard Entropy Weight Method, often focus solely on the static statistical dispersion of cross-sectional data²³. In contrast, the LTDM method integrates the time dimension to maximize overall discrepancy but still yields a single set of fixed weights for all units¹¹. To address the need for capturing individual evolutionary paths, this study introduces the CDFA method⁴⁹ for the first time to evaluate regional HQD. The core rationale of CDFA lies in its ability to reveal the structural role of specific indicators in the long-range coupling relationships of the overall system. By evaluating the fluctuation persistence of indicator sequences and performing shuffling-based tests, CDFA estimates the structural sensitivity of each indicator on the system’s coupling dynamics and then converts these estimates into standardized weights. The specific evaluation framework proceeds through the following logical steps:

Step 1: Data homogenization and spatio-temporal alignment.

To ensure the comparability of the HQD index across different years and eliminate the influence of varying dimensions, the fixed-base efficacy coefficient method is employed for indicator standardization. The formula is as follows:

1

where and represent the original value and the standardized value, respectively, of the j-th indicator for the i-th county in the k-th year; and represent the maximum and minimum values, respectively, of the j-th indicator across all counties in the base period. The symbols “+” and “-” represent positive and negative indicators respectively.

Step 2: Quantifying systemic coupling features.

To capture the fluctuations of the original sequences relative to their mean values (), n new time profiles are constructed based on the standardized sequences. CDFA calculates the detrended multi-covariance by eliminating local trends through least-squares fitting. To explicitly adapt the algorithm to the annual panel data spanning 12 years (N = 12) in this study, we mathematically constrained the scale parameter bounds to s∈[3,12] (with s = 3 selected as the operational baseline to maximize statistical degrees of freedom) and set the detrending polynomial order to m = 1 (utilizing linear detrending to strictly avoid over-fitting in localized, short-term windows). Instead of detailing the fundamental arithmetic segmentation (which is comprehensively described in Reference⁴⁹, the crucial conceptual output here is the qth-order fluctuation function. The multifractal index, known as the generalized Hurst exponent h(q), indicates the presence of long-term persistence in the coupling correlation among the n indicator sequences, effectively representing the dynamic synergy of the HQD system.

Step 3: Sensitivity analysis via the “Shuffling” strategy.

To examine the structural influence of each indicator on regional HQD, a counterfactual sensitivity test is conducted by shuffling the indicator sequences. We randomly shuffle one specific indicator sequence, denoted as Y, while keeping the other n-1 sequences unchanged. Conceptually, this shuffling process artificially destroys the temporal auto-correlations and non-linear coupling correlations between Y and the rest of the system. Consequently, the CDFA outcome deviates from the original systemic result. This deviation is quantified using a chi-square-type discrepancy measure, as shown in Eqs. (2)–(4) following Hedayatifar et al. (2011)⁴⁹. In this study, this statistic is used to compare the original and shuffled CDFA results and to evaluate the extent to which the coupled system structure changes when the temporal ordering of indicator Y is disrupted, rather than as a strict parametric chi-square hypothesis test. A larger deviation indicates that altering the temporal structure of indicator Y leads to a greater change in the coupling pattern of the system. This suggests that indicator Y has stronger structural sensitivity within the evolution of regional HQD, and is therefore assigned a higher weight. In addition to the shuffled test, we further compared the CDFA results obtained from surrogate sequences as a supplementary robustness check, following the original CDFA literature. In our data, the q ~ h(q) curves of the surrogate sequences consistently remained closer to those of the original sequences, whereas the shuffled sequences produced larger deviations from the original coupled structure (see Supplementary Text S2, Figure S2; Supplementary Text S3, Figure S4). This indicates that the coupling characteristics of the HQD indicator system are more sensitive to shuffled perturbation than to surrogate perturbation. Accordingly, the shuffled-based discrepancy is used as the main weighting basis in this study, while the surrogate-based results are provided in the Supplementary Material.

2

3

4

where and denotes the generalized Hurst exponent and the extension of generalized standard deviation respectively of CDFA for the n original time series in different q moments, while and correspond to those respectively after shuffling one indicator Y.

Step 4: Indicator weight determination and index synthesis.

Building on the conceptual logic and computational results derived in Step 3, the weighting formulation in Eq. (5) is developed on the basis of Eq. (2). This formulation systematically assigns weights to the regional HQD evaluation indicators according to their structural sensitivity within the coupled system. Let represent the M regions to be evaluated. Based on this weighting system, the comprehensive HQD index for the i-th region () can be derived as provided in Eq. (6).

5

6

Longitudinal-transversal discrepancy maximization(LTDM) method

Let there be M evaluated objects , corresponding to n evaluation indicators . The original data {x_ij(t_k)} are obtained in chronological order . Let {x_ij^*(t_k)} denote the data normalized via the min-max method. The indicator weight vector is defined as . For each time point , the comprehensive evaluation function is defined as . The degree of variation among the evaluated objects is then characterized by the total sum of squares of y_i(t_k). Given that the standardized data has a mean of zero =0, the total sum of squares can be expressed as , where is an n-order symmetric matrix. Under the constraint , the maximum value of is achieved when W is the eigenvector corresponding to the largest eigenvalue of H. To ensure all weights are positive, the additional constraint w>0 is imposed. Thus, the weight vector W is determined by solving Eq. (7)¹¹.

7

Finally, the HQD Index for the i-th region in year is calculated by Eq. (6). Note that the LTDM method also utilizes the standardized indicators processed by Eq. (1).

Global and local Moran’s/method

To examine the spatial distribution characteristics of the HQD index derived from the CDFA method, spatial autocorrelation analysis was conducted. Global Moran’s I was used to test whether the HQD index showed spatial clustering, dispersion, or randomness across the study area, and is calculated as follows:

8

where I∈[-1, 1], and I > 0 indicates positive spatial autocorrelation. To further identify the specific locations of spatial clusters and outliers, Local Indicators of Spatial Association (LISA) were calculated⁵⁹. The local Moran’s I_i is expressed as:

9

Based on permutation significance tests, the spatial linkage patterns were classified into High–High (HH) and Low–Low (LL) clusters, as well as High–Low (HL) and Low–High (LH) outliers.

Geographical detector method

Geodetector is a spatial statistical method used to identify spatial differentiation and its explanatory factors⁶⁰. To further examine the external mechanisms underlying the spatial differentiation of county-level HQD, this study employed the optimal parameters-based geographical detector (OPGD). Compared with a conventional geographical detector, OPGD improves the treatment of continuous explanatory variables by optimizing the discretization scheme and classification parameters before calculating explanatory power. The factor detector and interaction detector were used to evaluate the independent and joint effects of selected influencing factors on the county-level HQD index. The explanatory power of each factor was measured using the q-statistic:

10

where q ∈ [0,1], and a larger q value indicates stronger explanatory power for the spatial differentiation of the HQD index.

Results

Reliability and validity test of the indicator system

To verify whether the constructed indicator system possesses a reasonable structural foundation, this study performed the Kaiser-Meyer-Olkin (KMO) test and Bartlett’s test of sphericity on the 19 indicators. The results show that the overall KMO value is 0.729. This suggests a sufficient degree of shared variance among the variables, validating the dataset’s appropriateness for subsequent comprehensive assessment. Furthermore, Bartlett’s test of sphericity yielded a highly significant result (=10682.604, df=171, p < 0.001). Achieving significance at the 1% level verifies that the correlation matrix departs significantly from an identity matrix, confirming robust inter-indicator correlations. These findings collectively demonstrate that our indicator system is far from an arbitrary assembly; rather, it possesses a sound structural fit and statistical grounding, reliably supporting the subsequent measurement of HQD at the county level. To further explore the internal traits of these metrics, we conducted a reliability check. The overall Cronbach’s alpha sits at 0.565, pointing to a pronounced multidimensional heterogeneity across the system. It is important to recognize that we constructed a formative, multi-dimensional evaluation framework instead of a conventional unidimensional reflective scale. Because our objective is to measure a structurally diverse composite index rather than a single latent variable, the overall internal consistency is naturally lower. Therefore, the Cronbach’s alpha serves purely as an auxiliary diagnostic of the data’s multidimensional architecture. A more detailed methodological discussion regarding the validation logic and the specific indicator correlations is provided in Applicability of the CDFA method to regional HQD assessment Section.

Comparative analysis of spatial distributions and weight structures

To evaluate the relative consistency and robustness of the CDFA assessment and examine its methodological divergence from established approaches, this section conducts a comparative analysis between CDFA and the LTDM. This comparison is grounded in methodological consistency: both approaches are designed to integrate longitudinal and transversal information to derive a unified weight set from panel data. For the sake of comparability, this study utilizes Steps 1–4 of the CDFA framework to calculate a provincial baseline weight set. Specifically, weights are first extracted from the annual cross-sectional data of all 102 counties to capture the spatial coupling among the 19 indicators, and are then averaged over the 12-year period to obtain the baseline weights. (Note: For the calculation and validation of the provincial baseline weight set, see Text S2 and Figure S1)

Based on these two sets of unified weights (Table 2), the HQD index of each county in 2011, 2016, and 2021 was calculated, and the K-medians clustering method was employed to classify counties into four types (low quality, medium low quality, medium high quality, and high quality), as shown in Figs. 2 and 3. It is worth noting that the number of clusters in this study (such as 4 types here, and 5 types in subsequent structural analysis) was predetermined based on the actual regional development gradients of Henan Province and established empirical precedents in spatial HQD evaluation⁶¹. This approach was chosen to maximize the geographic and economic interpretability of the spatial patterns, rather than relying solely on data-driven algorithmic optimization (e.g., the elbow method). The spatial distributions generated by both methods exhibit a high degree of macroscopic resemblance. Beyond the crude spatial coincidence rates of 74%, 68%, and 79% in 2011, 2016, and 2021, respectively, we calculated kappa statistics to rigorously evaluate the classification agreement. The overall Cohen’s kappa coefficient was 0.6508, while the linear and quadratic weighted kappa coefficients were 0.7678 and 0.8580, respectively. These results indicate substantial to almost perfect consistency, especially considering the ordinal nature of the classification levels. This robust statistical agreement indicates that the CDFA method does not deviate from the fundamental macro-level patterns of regional development; rather, it effectively captures the baseline spatial structure identified by established longitudinal-transversal variance maximization techniques. As presented in Table 2, the CDFA approach assigns higher systemic importance to county association intensity (X₁₉), economic association intensity (X₁₈), and pesticide usage per unit of cultivated area (X₁₁), whereas the LTDM method places greater emphasis on basic provision indicators such as hospital beds per 1,000 people (X₁₅) and social welfare beds per 1,000 people (X₁₇).

Table 2.

Indicator weight values and their rankings calculated by the CDFA and LTDM.

Specific indicators	indicator	LTDM weight	CDFA weight
Financial Institutions’ Deposit-Loan Ratio	X1	0.1468(14)	0.0644(5)
Public Finance Revenue-Expenditure Ratio	X2	0.1648(9)	0.0401(12)
Agricultural Output Growth	X3	0.1905(7)	0.0287(16)
Mean Nighttime Light Intensity	X4	0.1223(16)	0.0318(15)
Consumption Rate	X5	0.2111(5)	0.0477(8)
Per Capita Retail Sales of Consumer Goods	X6	0.2595(4)	0.0717(4)
Industrial Structure Advancement Index	X7	0.1602(10)	0.0255(18)
PM₂.₅ Index	X8	0.1599(11)	0.0438(10)
CO₂ Emissions	X9	0.1526(13)	0.0353(14)
Chemical Fertilizer Usage per Unit of Cultivated Area	X10	0.1577(12)	0.0412(11)
Pesticide Usage per Unit of Cultivated Area	X11	0.1014(19)	0.0729(3)
Urbanization Rate	X12	0.1781(8)	0.0482(7)
Urban-Rural Income Coordination Index	X13	0.1289(15)	0.0286(17)
Physicians per 1000 People	X14	0.195(6)	0.0458(9)
Hospital beds per 1000 People	X15	0.5106(1)	0.0381(13)
Social Welfare Recipients per 10,000 People	X16	0.3609(3)	0.021(19)
Social Welfare Beds per 1000 People	X17	0.4192(2)	0.0634(6)
Economic Association Intensity	X18	0.1211(17)	0.1145(2)
County Association Intensity	X19	0.1039(18)	0.1371(1)

The numbers in parentheses indicate the descending rank order of each indicator’s weight value in the corresponding method. Unlike conventional methods constrained by a linear sum of 1 (∑w_i=1), the LTDM weights represent an eigenvector governed by the Euclidean norm constraint (); therefore, their simple mathematical sum naturally exceeds 1.

Fig. 2.

Spatial distribution of classification levels of HQD in Henan counties based on the LTDM method.

Fig. 3.

Spatial distribution of classification levels of HQD in Henan counties based on the CDFA method.

Spatiotemporal heterogeneity analysis based on county-specific weights

Spatial differentiation of indicator weights and comparison of representative counties

Moving beyond the initial baseline validation, the analysis now transitions from a spatial cross-sectional view to a temporal one to fully utilize the CDFA framework. Instead of calculating a unified weight set shared across all counties, the CDFA method is now applied to the time-series data of each individual county, generating 102 sets of county-specific weights that reflect the unique structural coupling dynamics of local development systems. Specifically, the CDFA method is applied to analyze the multifractal coupling relationships among the 19 indicators within each county using 12 years of time-series data from 2010 to 2021, thereby quantifying the structural sensitivity of each indicator within the coupled system and achieving county-specific weighting. The HQD level of each county is then evaluated based on its exclusive weight set, and the spatiotemporal heterogeneity of HQD across counties in Henan Province is analyzed.

Next, we quantify the structural sensitivity of each indicator sequence within the coupled system in each county; details of the calculation and validation are provided in Text S3 and Figure S3. The resulting indicator weights for all 102 counties are shown in Fig. 4, with a statistical summary presented in Table 3. Figure 4 visually and systematically illustrates the differences in the structural sensitivity of various indicators among the counties. It can be seen from Fig. 4 that some indicators such as X₄, X₉, X₁₀, X₁₁, X₁₂, X₁₇, and X₁₈ exhibit pronounced peaks in weight concentration, with the highest values approaching or exceeding 0.20, while most indicators have weights concentrated in the 0.01–0.15 interval. Overall, the distribution displays a pattern of multi-peak dispersion, with the counties showing marked variation in their indicator-weight profiles. The interlaced lines and multiple distribution points reflect that different counties exhibit varying degrees of structural dependence on economic, social, and ecological dimensions, with each county’s development system shaped by a distinct combination of driving indicators. Each county has certain indicators that play a dominant structural role, while others contribute less to the system’s coupling dynamics, and no single indicator-weight profile dominates across all counties.

Fig. 4.

Distribution of indicator weights.

Table 3.

Statistical analysis table of indicator weights.

Indicator	Max	Min	SD	Mean
X1	0.1925(Yuanyang)	0.0065(Mengzhou)	0.0389	0.0496
X2	0.1715(Xixia)	0.0033(Yima)	0.0292	0.0396
X3	0.1434(Weishi)	0.0065(Wugang)	0.0279	0.0624
X4	0.2367(Wuzhi)	0.0063(Tongbai)	0.0415	0.0591
X5	0.1586(Linzhou)	0.0053(Gongyi)	0.0329	0.0454
X6	0.092(Xiangcheng)	0.0015(Puyang)	0.0167	0.023
X7	0.1784(Zhecheng)	0.0064(Ye)	0.0327	0.0685
X8	0.1131(Yima)	0.0057(Huixian)	0.0269	0.0494
X9	0.1945(Yichuan)	0.008(Anyang)	0.0371	0.0696
X10	0.2165(Zhenping)	0.0076(Linzhou)	0.0375	0.0667
X11	0.1912(Changyuan)	0.0031(Xincai)	0.0442	0.0568
X12	0.2458(Xinmi)	0.0034(Baofeng)	0.0504	0.0624
X13	0.0836(Nanzhao)	0.0049(Lushan)	0.0197	0.0372
X14	0.1149(Luoning)	0.0195(Xiayi)	0.0213	0.0563
X15	0.1576(Huojia)	0.0015(Xincai)	0.0348	0.0441
X16	0.1744(Fan)	0.0058(Nanle)	0.0436	0.0584
X17	0.2283(Tongxu)	0.0061(Xinxiang)	0.0419	0.067
X18	0.2164(Xingyang)	0.0042(Dancheng)	0.0347	0.0456
X19	0.1667(Yanjin)	0.0037(Neixiang)	0.037	0.0523

The parentheses in the max and min columns indicate the names of the counties to which the maximum and minimum indicator weights belong.

It can be seen from Table 3 that the indicators related to HQD of counties in Henan Province generally exhibit the characteristic of coexistence of foundational improvement and differentiation. In terms of mean values, CO₂ emissions (X₉), the industrial structure advancement index (X₇), social welfare beds per 1,000 people (X₁₇), chemical fertilizer usage per unit of cultivated area (X₁₀), agricultural output growth (X₃), and urbanization rate (X₁₂) are all relatively high. However, the average structural weights of indicators related to people’s livelihood and income structure, such as per capita retail sales of consumer goods (X₆) and the urban-rural income coordination index (X₁₃), are relatively low. From the perspective of standard deviation, several indicators, including urbanization rate (X₁₂), pesticide usage per unit of cultivated area (X₁₁), and social welfare recipients (X₁₆), not only have high mean structural weights (or significant impact) but also exhibit large standard deviations (all exceeding 0.04). There is also a clear contrast between the maximum and minimum values, such as the structural weight of urbanization rate (X₁₂) in Xinmi (0.2458) and Baofeng (0.0034), and the significant disparity in the structural sensitivity of economic association intensity (X₁₈) between Xingyang (0.2164) and Dancheng (0.0042). Similarly, the weight of social welfare recipients (X16) reaches 0.1744 in Fan County but is only 0.0058 in Nanle County (a roughly 30-fold difference). It is crucial to clarify that CDFA-derived weights do not represent conventional static contribution rates or literal policy importance. Rather, they denote “temporal structural sensitivity”, which refers to the degree to which an indicator’s fluctuations are tightly coupled with the long-term evolution of the local HQD system. For instance, diagnostic checks reveal that the temporal correlation between the standardized X16 sequence and the overall HQD trajectory is extremely strong in Fan County (-0.875), whereas it is minimal in Nanle County (0.112). This explains the extreme weight disparity: X16 profoundly couples with the developmental trajectory in Fan County, but acts as a highly decoupled, structurally insensitive variable in Nanle County.

To further characterize the developmental features of individual counties, Text S4 and Table S1 in the Supplementary Material presents the indicator weight values for selected representative counties. The structural weight profiles of each county essentially align with their actual socioeconomic conditions, demonstrating that the CDFA-based county-specific weighting approach can effectively capture the distinctive structural characteristics of local development systems. It should be noted that these structural weights reflect the internal coupling sensitivity of each county’s development system over time, rather than the spatial explanatory power of each dimension across counties. This distinction is important when interpreting the macro-level driving factors examined in Spatial correlation and driving mechanisms Section.

Cluster identification and spatial patterns of indicator structural heterogeneity

In order to investigate the structural heterogeneity of HQD indicators in 102 counties of Henan Province, we conducted Euclidean distance calculations and K-medians cluster analysis on the sets of indicator weights from these counties. First, we averaged the weights of 19 indicators across the 102 counties to obtain a 19-dimensional mean weight vector, which serves as the provincial benchmark for HQD. Secondly, for each county, the Euclidean distance between its 19-dimensional weight vector and the provincial mean vector was calculated to measure the degree of deviation from the province’s average structure. A smaller distance value indicates that the development structure of the county is more balanced and closer to the provincial average level, while a larger distance value reveals a greater divergence, which may reflect either distinctive local structural configurations or dimensions with pronounced coupling sensitivity that deviate markedly from the provincial norm. Finally, based on the 102 Euclidean distance values, K-medians cluster analysis was performed, classifying the counties into five categories according to the degree of deviation, from lowest to highest: Core balanced type (minimum distance), Robust convergent type, Moderate distinctive type, Locally divergent type, and Highly differentiated type (maximum distance). This classification comprehensively demonstrates the balance and diversity of indicator structures among the counties. The specific spatial distribution is shown in Fig. 5.

Fig. 5.

Spatial distribution of structural heterogeneity types of HQD indicators.

Moreover, Fig. 5 also displays that the highly differentiated type (red) counties in Henan Province are mainly concentrated in the core areas of Zhengzhou and adjacent industrial nodes within the Central Plains urban agglomeration. The degree of deviation between these areas and the provincial average index structure is the largest, indicating that their HQD structure shows notable local characteristics and pronounced structural coupling heterogeneity. This is often due to the more complex industrial structures, higher levels of economic development, and more diverse social demands in core cities and their surroundings. In contrast, the core balanced type (dark blue) counties are mostly located in fringe regions and some traditional agricultural areas, suggesting that their HQD structures are closer to the provincial average, and thus exhibit greater structural balance and development stability. Robust convergent type (light green) and moderate distinctive type (yellow) counties are more widely distributed and constitute the main body supporting HQD across the province. They display a pattern characterized by both convergence and some unique features to a moderate extent. The locally divergent type (orange) counties are primarily found in parts of northern, western, and southern Henan, forming a roughly right-opening “U”-shaped spatial pattern. This indicates distinct deviations from the average structure in certain aspects of these counties, which may be influenced by natural conditions, industrial development paths, and other factors.

Spatiotemporal evolution of the comprehensive HQD level

Finally, based on the county-specific weights assigned to each county, the HQD index was calculated using Eq. (6), and the K-medians clustering method was applied to classify the counties into four types according to their respective indices: “Low”, “Medium low”, “Medium high” and “High”, as shown in Fig. 6.

Fig. 6.

Spatial distribution of HQD classification levels in Henan counties based on the county-specific CDFA method.

Throughout the 2011–2021 period, the types of HQD among counties in Henan Province exhibited a trend of increasing spatial agglomeration, forming a clearer “core-periphery” spatial pattern under overall upgrading. Specifically, the proportion of “High” quality and “Medium high” quality counties increased from 33.3% in 2011 to 64.7% in 2021, Correspondingly, the share of “Medium low” and “Low” quality counties dropped significantly, with low-quality counties decreasing from 32.4% to 5.9%. It should be clarified that this sharp reduction in low-quality counties reflects a broad-based absolute improvement in development levels across the province. However, the “core-periphery” pattern persists because the relative regional gradient has become more spatially clustered. Geographically, “High” quality counties are progressively concentrated around Zhengzhou, Luoyang, and other core cities of the Central Plains urban agglomeration, with their influence expanding outward to surrounding areas. Furthermore, counties classified as “Medium high” quality are mainly distributed in regions with convenient transportation and strong industrial bases, such as central and northern Henan, gradually forming agglomeration zones along urban clusters and major transportation hubs. Meanwhile, “Low” quality counties have gradually contracted from a widespread distribution to a few less developed areas, primarily located in northeastern Henan and marginal mountainous regions, thereby manifesting an “island-like” pattern. Ultimately, The spillover and driving effect of “High” quality development in core regions has become increasingly pronounced.

Spatial correlation and driving mechanisms

Spatial autocorrelation of county-level HQD

To verify whether the HQD indices calculated via the CDFA method exhibit non-random spatial distribution patterns, we applied spatial autocorrelation methods to examine their spatial connection characteristics. Spatial autocorrelation analysis was implemented in GeoDa software, and the spatial weight matrix was constructed based on the classic Queen contiguity matrix. The global Moran’s I values for Henan’s county HQD index in 2011, 2016, and 2021 were 0.106, 0.123, and 0.100, respectively. All these statistics passed the significance test (p < 0.05), which confirms a notable positive spatial correlation across the province throughout the study period. However, the Moran’s I index followed a trajectory of an initial increase followed by a subsequent decline. Specifically, the peak in spatial agglomeration in 2016 was largely driven by strong polarization effects during the rapid construction phase of the Central Plains Urban Agglomeration. During this period, capital and resources were heavily concentrated in core areas like Zhengzhou, intensifying spatial disparities. The subsequent decline by 2021 reflects a transition from polarization to spatial spillover and balanced development. This shift was primarily facilitated by the completion of targeted poverty alleviation, the implementation of rural revitalization strategies, and the expansion of transportation networks, which collectively lifted the developmental baseline of peripheral counties. Consequently, this pattern suggests that the clustering intensity of extreme high-value or low-value areas has generally weakened, leading to an overall improvement in the equilibrium of regional spatial development.

Local LISA analysis, illustrated in Fig. 7 and evaluated at the p < 0.05 significance level, further clarifies the evolution of these spatial clustering patterns. Results indicate that high-high hotspots gradually shifted and expanded from the central region toward the west (e.g., Luoyang and Sanmenxia areas), whereas low-low cold spots remained concentrated in the northern and northeastern regions as continuous patches. Notably, the 2021 spatial layout featured new low-high and high-low clusters in the north-central periphery, which suggests that the radiation effects from high-value regions have encountered structural barriers in specific areas. Consequently, regional spatial heterogeneity has become more prominent, even as most counties in the province continue to exhibit non significant spatial clustering. These findings verify that the HQD indices calculated via CDFA possess significant spatial dependency and clustering characteristics, rather than being randomly distributed.

Fig. 7.

Spatial patterns of LISA clusters for county-level HQD in Henan Province (2011, 2016, 2021).

External driving mechanisms of spatial differentiation

To identify the external driving sources underlying the spatial differentiation of county-level high-quality development (HQD), this study selects eight observable variables across natural, social, and economic dimensions based on existing literature and data availability (Table 4).

Table 4.

Indicator system of influencing factors for county-level economic HQD.

Dependent Variable (Y)	Independent Variable Category	Independent Variable (X)	Calculation / Proxy	Symbol
Regional economic HQD index	Natural factors	Topography	Terrain relief	X1
		Temperature	Average annual temperature	X2
		Locational conditions	Distance from county to provincial capital	X3
	Social factors	Public input capacity	Per capita general budget expenditure	X4
		Social security level	Per capita number of social welfare institutions	X5
	Economic factors	Innovation vitality	Per capita utility model patent applications	X6
		Non-agricultural transition level	Tertiary industry value-added / GDP	X7
		Industrial foundation	Number of industrial enterprises above designated size	X8

Natural factors primarily reflect the fundamental spatial and environmental constraints, encompassing terrain relief (X1), temperature (X2), and locational conditions (X3). Specifically, terrain relief influences transport accessibility and land development; average annual temperature indicates climatic conditions and ecological carrying capacity⁶². Furthermore, locational conditions represented by the distance to the provincial capital reflect the convenience of accessing regional central markets and absorbing administrative radiation and resource spillovers⁶³.

Social and economic factors delineate practical supporting capacities. Social factors include public input capacity (X4) and social security level (X5), representing local fiscal and public service supply. Economic factors consist of innovation vitality (X6), non-agricultural transition level (X7), and industrial foundation (X8), which characterize industrial structural upgrading and physical carrying capacity⁶⁴.

These external factors were incorporated into the Optimal Parameters-based Geographical Detector (OPGD) model to conduct a spatial attribution analysis (Variance Inflation Factors (VIF) for all variables were < 5, indicating no severe multicollinearity)⁶⁵. The results demonstrate that while the explanatory power of different factors varies significantly, the primary drivers remain relatively stable across different time cross-sections.

The factor detector results, as shown in Fig. 8, reveal that locational conditions (X3) consistently maintain high explanatory power, showing a distinct spatial gradient driven by market linkages and administrative radiation from the core city. The industrial foundation (X8) and terrain relief (X1) also exhibit strong explanatory power, suggesting that regional development is heavily anchored by industrial capacity and rigid geographic constraints. Conversely, temperature (X2), public input (X4), and social security (X5) show limited independent explanatory power in certain years, implying their impacts are rarely manifested in isolation and rely on synergies with broader spatial environments.

Fig. 8.

Factor detection forces of influencing factors on regional economic HQD. (*, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively)

The interaction detector results (Fig. 9) indicate that the explanatory power of any two interacting factors is universally higher than that of a single factor (manifesting as bivariate or nonlinear enhancement). It is important to clarify that “enhancement” in this context strictly refers to an increase in the statistical explanatory power (q-statistic) for spatial variance, rather than implying that these driving factors are necessarily synergistic or mutually reinforcing in a real-world causal sense. This confirms that HQD spatial differentiation is driven by the superposition of multiple conditions. Notably, locational conditions (X3) interact strongly with terrain relief (X1) and industrial foundation (X8), demonstrating that locational advantages are profoundly co-regulated by natural topography and industrial carrying capacity. Furthermore, the explanatory power of socio-economic factors (e.g., X4, X5, X6, X7) is significantly amplified when interacting with X1, X3, or X8. This proves that policy and economic inputs primarily shape spatial disparities through their synergistic interactions with inherent geographical and industrial endowments.

Fig. 9.

Interaction detection of influencing factors on county-level economic HQD.

Discussion

Applicability of the CDFA method to regional HQD assessment

HQD is characterized by multidimensional heterogeneity, structural coupling, and dynamic evolution, which together provide a methodological basis for the application of Coupling Detrended Fluctuation Analysis (CDFA). Using county-level units in Henan Province as an example, the overall Cronbach’s alpha of the indicator system developed in this study was 0.565, with substantial differences in Cronbach’s alpha across dimensions. Specifically, Cronbach’s alpha was 0.9724 for the linkage development dimension, whereas it was − 0.4241 for the economic development dimension.

For a formative indicator system such as that used to assess county-level HQD, these results do not indicate inappropriate indicator design. Rather, they suggest that the indicators are not intended to measure a single latent construct, but instead capture different facets of a complex development system⁶⁶. Unlike formative latent variables in Structural Equation Modeling (SEM), which assume indicators exert independent causal effects, our Composite Indicator System (CIS) defines HQD through a set of conceptually distinct and jointly constitutive components⁶⁷. Furthermore, the Coupling Detrended Fluctuation Analysis (CDFA) employed in this study evaluates non-stationary time series by extracting multi-scale dynamic covariances via local polynomial detrending. This dynamic mechanism naturally bypasses the static linear collinearity interference common in traditional econometrics, rendering conventional diagnostics like Variance Inflation Factor (VIF) conceptually and procedurally inapplicable. Internal consistency coefficients therefore should not be treated as the sole criterion for evaluating the validity of the indicator framework⁶⁸.

Specifically, a correlation matrix diagnosis reveals that the severe negative correlation observed within the economic dimension is primarily driven by inverse relationships among specific indicator pairs, notably X₁ and X₂ (-0.505), X₁ and X₇ (− 0.426), and X₂ and X₅ (− 0.412). These results indicate that the indicators within this dimension represent distinct economic functions, such as financial circulation, fiscal self-sufficiency, consumption vitality, and industrial upgrading, that do not necessarily increase synchronously at the county level. For example, the negative correlations essentially reflect a structural trade-off in county development between safeguarding the agricultural foundation and advancing industrial upgrading. Counties with stronger industrial or urban economic activity may exhibit drastically different financial and fiscal structures compared to those with distinct agricultural prominence. This interpretation demonstrates that the negative alpha does not indicate arbitrary indicator selection; instead, it objectively reflects the coexistence of multiple diverse county-level economic development pathways in Henan Province, including agriculture-oriented, industry-oriented, and core urban-adjacent development patterns. This interpretation is also consistent with previous studies on county-level HQD, economy-ecology coupling, and obstacle-factor identification^41,47.

More importantly, the supplementary materials (Figure S1 and Figure S3) show that the generalized Hurst exponent curves, q ~ h(q), are markedly nonlinear and strongly q-dependent, both in annual cross-sections and in county-level time series. This suggests that the indicator series contain evident multiscale coupling and multifractal features. Such internal heterogeneity and scale-coupling structure form an important methodological basis for applying CDFA to the assessment of county-level HQD^49–51. To provide an alternative robustness and interpretability reference for the composite assessment, the evaluation results obtained from LTDM under uniform weighting (Fig. 2) were compared with those derived from CDFA (Fig. 3). This comparison does not treat LTDM as a “gold standard” or a definitive benchmark, because LTDM itself is merely a mathematical weighting construct rather than an externally observed true value. Instead, it serves as a comparative reference method to examine whether the spatial pattern identified by CDFA is broadly consistent with that produced by a mature objective evaluation framework. In composite assessment research, this practice is methodologically reasonable, as the interpretation of results typically needs to account for the influence of methodological choices rather than rely on a unique “true” benchmark⁶⁹. As a mature objective evaluation method with a clear methodological basis, LTDM has been applied in regional and HQD-related assessment studies^14,15. The relatively high degree of agreement (supported by the kappa statistics reported in Sect. 3.2) therefore suggests that CDFA remains consistent with the basic judgments of mainstream evaluation methods in identifying the overall regional development pattern, and thus has good credibility and interpretive stability.

However, the value of CDFA is not limited to its agreement with LTDM; it is also reflected in the approximately 21%–32% spatial classification discrepancy between the two methods. This discrepancy does not imply that one method is absolutely more accurate, but rather highlights their methodological divergence. These discrepancies suggest that conventional uniform-weighting approaches may be less capable of fully capturing structural differences in county development and the latent forces underlying its evolution. Since LTDM determines weights according to cross-sectional statistical variation, it tends to assign greater importance to indicators related to basic public provision, such as hospital beds and social welfare beds, thus reflecting the baseline conditions of development. CDFA, by contrast, is more attentive to long-range coupling within the system, and accordingly gives higher weights to indicators such as economic association intensity (X₁₈), county association intensity (X₁₉), agricultural green transformation, and industrial upgrading. Compared with LTDM, which is more effective in identifying basic disparities, CDFA places greater emphasis on factor mobility, regional interdependence, and structural upgrading. This makes it more closely aligned with Henan’s development needs as it shifts from basic provision toward innovation-driven growth, green transformation, and regional coordination. It also accords with findings from the space-of-flows perspective, which emphasize the roles of regional connectivity, network embeddedness, and their contributions to improving development quality^16–18,45. Put differently, LTDM is better suited to answering where the gaps lie, whereas CDFA is more informative for identifying the structurally sensitive factors of high-quality transformation.

Moreover, LTDM is mathematically restricted to a single uniform-weighting scheme, whereas CDFA can be used not only to derive uniform weights for cross-sectional spatial comparisons, but also to identify time-specific weights along the temporal dimension. Under a time-series framework, CDFA draws on the historical trajectories of individual counties to reveal their distinctive coupling relationships, internal heterogeneity, and structural trade-offs, thereby addressing the limitations of uniform-weighting schemes in capturing local variation. In this sense, CDFA extends the methodological framework from “horizontal comparison under a unified standard” to “individualized structural diagnosis based on temporal evolutionary coupling.” This is the principal advantage that sets CDFA apart from conventional variance-based weighting methods and also constitutes the main methodological innovation of this study.

County-specific weighting based on CDFA

County-specific weighting based on CDFA can be implemented for the independent time-series analysis of each county, thus moving beyond the limitations of a uniform weighting scheme and providing a new perspective for understanding structural differences in county-level HQD. Comparing Fig. 3 (uniform-weight CDFA) with Fig. 6 (county-specific-weight CDFA) shows that the latter yields a spatial pattern more consistent with the actual development situation of counties in Henan. The agglomeration of HQD around Zhengzhou and its neighbouring core areas is more evident, while the weaknesses of peripheral areas are also brought out more clearly. This indicates that uniform weights tend to smooth over local variation, whereas county-specific weights are better able to reflect heterogeneity in development paths, system coupling, and structural constraints. This finding is in line with earlier studies suggesting that counties differ substantially from one another and should not be interpreted through an overly homogeneous development framework⁷⁰. Compared with surrogate perturbation, shuffled perturbation produced systematically larger deviations from the original q ~ h(q) curves in both the annual cross-sectional tests and the representative county-level time-series tests reported in Supplementary Text S2, Figure S2 and Supplementary Text S3, Figure S4. This suggests that, for the present dataset, shuffled perturbation has stronger discriminatory power for identifying structurally sensitive indicators within the coupled HQD system. Supplementary Table S1 further shows that the drivers of HQD vary considerably across counties and broadly correspond to their socioeconomic characteristics. Traditional agricultural counties are more strongly affected by agricultural output, green development, and resource and environmental pressures, whereas counties located at core nodes rely more on factor flows, economic association, and spatial connectivity.

It should be clarified that the weights derived from CDFA in this study do not represent the true causal contribution of each indicator to high-quality development (HQD), but rather its relative structural importance within the given indicator system and coupling-analysis framework. In fact, this interpretive boundary is not unique to CDFA, but reflects a general methodological issue in weighting research. Different weighting methods capture different meanings of “importance.” AHP reflects relative importance based on expert judgment; equal weighting embodies a normative principle of balance; the entropy method assigns weights according to indicator dispersion and thus reflects informational differentiation; PCA reflects the explanatory power of indicators with respect to overall variation through variance-covariance structures; and LTDM emphasizes the discriminatory ability of indicators in terms of spatiotemporal variation. In essence, these methods are not direct measures of the actual real-world contribution of indicators, but rather mathematical representations of relative importance under specific criteria.

It is important to note that CDFA weights do not indicate the absolute level or relative merit of an indicator. Rather, they reflect its structural sensitivity and influence within the evolution of the system. A higher weight does not mean that the indicator performs better; instead, it suggests that changes in that indicator are more strongly coupled with the overall evolution of the county-level development system over the long run. For instance, a high weight for negative indicators such as fertilizer application intensity (X₁₀) or CO₂ emissions (X₉) should not be interpreted as evidence of better ecological performance. It instead indicates that the county’s development system is highly sensitive to environmental pressure variables. More specifically, if the temporal structure of one indicator sequence is randomly disrupted and this causes a larger deviation in the system’s multifractal coupling characteristics, then that indicator can be understood as playing a stronger structural role in maintaining the overall coupling pattern of the system. In this sense, CDFA weights are better interpreted as measures of relative structural importance or coupling contribution within the HQD system, rather than as evidence of real-world causal importance. Compared with weighting methods such as the entropy method, PCA, and LTDM, which mainly rely on dispersion, variance contribution, or spatiotemporal differentiation, CDFA further considers the system response induced by perturbations to temporal structure. This gives it a particular advantage for evaluating objects such as HQD that exhibit dynamic evolution and temporal dependence, although its results should still be interpreted as structural importance rather than genuine contribution. In this sense, CDFA is designed to identify structural drivers and potential points for policy interventions in local system evolution, rather than to rank indicators in a static sense according to whether they are better or worse. At the same time, CDFA remains subject to limitations under short time-series conditions. The analysis in this study is based on 12 annual observations from 2010 to 2021.

In CDFA, statistical reliability requires a sufficient number of non-overlapping segments (Ns = int(N/s)). With an absolute length of N = 12, calculating the detrended cross-covariance requires at least 6 to 8 segments to avoid severe finite-size effects and statistical distortion. Mathematically, this rigidly constrains our feasible minimum scale s_min to either 3 (yielding 8 segments) or 4 (yielding 6 segments). Any scale s ≥ 5 would collapse the segment count to ≤ 4, causing the algorithm to fail. To alleviate concerns that our structural evaluations might be arbitrarily distorted by the chosen baseline window scale s_min=3, we conducted a rigorous parameter sensitivity test. Shifting the scale parameter constraint to s_min=4 yielded an exceptionally highly consistent structural evaluation with a Spearman rank correlation of R = 0.8731 (p < 0.0001) (detailed in Supplementary Text S6 and Figures S9 and S10), proving that the relative structural hierarchy remains highly robust against parameter perturbations. Furthermore, to explicitly verify the statistical significance of the extracted indicator weights against pure random noise, we executed 100 independent random shuffling iterations for each sequence to construct a robust null distribution. The empirical results demonstrated that the variations in the indicator weights across the majority of counties passed strict statistical significance thresholds (detailed in Supplementary Text S5 and Figures S5–S8). This robustly indicates that the algorithm captures genuine deterministic coupling rather than fragile, parameter-dependent statistical illusions. Even so, as an extended application to county-level HQD assessment, the applicability of CDFA should be further tested with longer time series, more regional samples, and richer continuous observations^49–51.

Overall, the evaluation of county-level HQD does not admit a mathematically unique “exact” solution. What matters more is the relative characterization of complex system evolution, the identification of development trends, and the comparison of structural differences. Given the current data conditions, CDFA is admittedly constrained by the short sample length, yet it still captures structural heterogeneity and evolutionary features across counties reasonably well. Unlike the entropy method and the vertical-and-horizontal differentiation method, which mainly derive a common set of weights from cross-sectional variation, CDFA brings temporal evolution into the process of weight identification and thus yields differentiated, county-specific weights. With the accumulation of longer time series, higher-frequency data, and richer multi-source observations, CDFA is likely to show even greater potential in the dynamic analysis of complex regional systems and in county-specific weighting for development evaluation.

Mechanistic interpretation of the spatial differentiation of county-level HQD and adaptive path optimization

Characteristics and formation mechanisms of the spatial differentiation of county-level HQD

Based on the evaluation results using county-specific weights, the overall level of HQD among counties in Henan improved from 2011 to 2021. The number of counties in the “high” and “upper-middle” categories increased, while those in the “low” and “lower-middle” categories decreased, indicating a shift from broad catch-up growth toward a stage characterized by both quality improvement and structural optimization. Spatially, county-level HQD in Henan shows four main features: overall improvement, stronger local agglomeration, clear advantages in core areas, and persistent weaknesses in peripheral regions. High-value clusters have gradually formed around core cities such as Zhengzhou and Luoyang and their surrounding counties, whereas peripheral areas and some mountainous counties continue to lag behind. As a result, the core-periphery structure has become more evident. This implies that, despite the overall upward trend, counties remain uneven in their development foundations, capacity for structural adjustment, and pathways to quality upgrading, and spatial imbalance remains a defining feature of this process. This pattern is broadly consistent with previous studies that describe the evolution of regional development as a process of overall improvement, intensified local clustering, and growing core–periphery differentiation⁷¹.

More importantly, inter-county differences are manifested not only in the composite development level, but also in the structural configuration of key driving factors. The county-specific weighting results show that carbon dioxide emissions, industrial structure upgrading, social welfare provision, fertilizer application intensity, agricultural output growth, and the urbanization rate carry relatively high average structural weights. This suggests that green transition pressure, industrial transformation, public service provision, adjustments in agricultural production patterns, and the urbanization process constitute the main dimensions with relatively high structural sensitivity in the county-level HQD of Henan. In particular, the relatively high weights assigned to pressure-related indicators such as CO₂ emissions and fertilizer application intensity per unit of cultivated land indicate that county-level development is highly sensitive to ecological constraints and the demands of green transition, which is consistent with previous studies emphasizing strengthened environmental constraints and obstacle factors^6,33,72. At the same time, as the overall level of development has improved, counties have not converged toward a common set of dominant drivers or factor combinations. Instead, they exhibit stronger local heterogeneity, suggesting that county-level HQD in Henan follows multiple pathways toward shared development goals.

In terms of spatial heterogeneity types, county-level HQD in Henan generally exhibits a pattern of “core divergence and peripheral convergence.” Counties located in Zhengzhou and the core area of the Central Plains urban agglomeration deviate more markedly from the provincial average in their structural composition. Their industrial structures, factor mobility, and spatial linkages are more complex, resulting in stronger local structural heterogeneity. By contrast, peripheral counties, traditional agricultural counties, and some border areas are more similar to the provincial average, showing a relatively balanced structure but limited distinctiveness. This suggests that the advantages of core areas lie not only in their higher development levels, but also in the greater diversity of dominant structurally sensitive factors and the more complex coupling among development subsystems. Peripheral areas, although exhibiting less structural fluctuation, are more likely to be constrained by a narrow industrial base, infrastructure deficiencies, and insufficient functional integration^34,73.

Spatial autocorrelation analysis further indicates a significant positive spatial dependence in county-level HQD. The results of global Moran’s I suggest that county development does not evolve in isolation, but is jointly shaped by spillover effects from neighboring areas, factor mobility, and regional linkage networks. LISA results show that high-value clusters have gradually expanded from central Henan toward the western part of the province, while low-value clusters in the north and northeast remain spatially continuous to some extent. This suggests that although the radiating influence of core areas is strengthening, its spillover effects in some regions are still constrained by industrial foundations, locational conditions, and institutional settings. Further Geodetector results reveal that locational conditions, industrial foundations, and terrain relief have consistently been the primary factors explaining the spatial differentiation of county-level HQD. Meanwhile, the explanatory power of socio-economic factors (such as public input, social security, and innovation vitality) is significantly amplified when interacting with these geographical and industrial endowments, and the interaction between any two factors is universally stronger than the effect of a single factor alone. These findings indicate that the spatial disparities in county-level HQD are not shaped by isolated economic or social inputs. Instead, they are driven by a synergistic mechanism where local development efforts are profoundly co-regulated by the rigid constraints of natural topography, the path dependence of industrial bases, and the radiation effects of regional core markets. Meanwhile, the CDFA results show that indicators such as CO₂ emissions, fertilizer application intensity, and the strength of inter-county linkages have consistently maintained relatively high weights in a large number of counties, suggesting a strong correspondence between the macro-level mechanisms of spatial differentiation and the internal structural sensitivity of individual counties.

Taken together, the uniform weighting approach captures the overall pattern and average trend of county-level HQD in Henan, whereas county-specific weights further reveal the reality that different counties may pursue the same development goal through distinct structural pathways. This implies that there is no universally replicable model for county-level HQD. Instead, a differentiated analytical framework should be established on the basis of identifying local structural characteristics, diagnosing dominant structurally sensitive factors, and recognizing key constraints.

Optimizing spatially adaptive pathways and policy implications

Based on the county-specific CDFA weights calculated for Henan’s counties in this study, the following targeted policy recommendations are proposed.

First, core counties around Zhengzhou, Luoyang, and major transport corridors should shift from scale-oriented growth to network-based upgrading. These counties already show stronger development levels and more complex structural heterogeneity, so their policy focus should not be limited to local industrial expansion. Instead, they should strengthen their role as regional nodes by building cross-county industrial chains, innovation transfer platforms, logistics hubs, and producer-service networks. In particular, Zhengzhou and its surrounding counties can enhance cooperation in advanced manufacturing, digital services, logistics, and technology diffusion, while Luoyang and western Henan can further integrate equipment manufacturing, cultural tourism, ecological resources, and specialized industries. Such measures would help transform the advantages of core counties into spillover capacity for surrounding counties.

Second, counties located between core areas and peripheral regions should be strengthened as transmission belts for inter-county cooperation. The empirical results show that the spillover effects of high-value areas remain constrained in counties such as Lankao County, Yuanyang County, Yanjin County, Fengqiu County, Wuyang County, and Sheqi County, especially where transport connectivity, industrial foundations, and public service capacity are weak. For these transitional counties, policy should focus on improving road and logistics connections with core cities, developing shared industrial parks, establishing cross-county supply-chain cooperation, and improving vocational training and labor mobility mechanisms. Rather than passively receiving spillovers, these counties should be supported to participate in regional production networks, agricultural product processing chains, e-commerce distribution systems, and public service cooperation platforms.

Third, low-value clusters in northern, northeastern, and peripheral mountainous areas should receive targeted support to overcome structural constraints. These clusters are mainly concentrated in counties such as Nanle County, Qingfeng County, Neihuang County, Fanxian County, Taiqian County, and Xunxian County in northern and northeastern Henan, as well as Luoning County, Lushi County, Xixia County, Xichuan County, Xinxian County, and Shangcheng County in peripheral mountainous areas. For traditional agricultural counties such as Huaxian County, Neihuang County, Xunxian County, Taikang County, Shangcai County, and Xiping County, the relatively high structural sensitivity of fertilizer application, pesticide use, agricultural output, and ecological pressure suggests that green agricultural transformation should be a priority. Policy measures should include reducing fertilizer and pesticide intensity, promoting standardized green production, improving cold-chain logistics, and linking agricultural counties with processing, branding, and sales platforms in core urban markets. For mountainous and ecologically constrained counties such as Luanchuan County, Songxian County, Lushi County, Xixia County, Xichuan County, Tongbai County, Xinxian County, and Shangcheng County, development should rely less on extensive industrial expansion and more on ecological compensation, eco-tourism, specialty agriculture, and cross-county ecological governance. These measures can help weaker counties improve development quality without intensifying environmental pressure.

Fourth, the interaction detector results indicate that Henan should establish more concrete cooperation mechanisms across counties. Since fiscal input, public services, innovation activity, and non-agricultural transformation often show stronger explanatory power when interacting with location, terrain, and industrial foundation, policy should emphasize coordinated rather than isolated intervention. This includes joint planning of transport corridors, shared industrial parks across administrative boundaries, coordinated investment promotion, inter-county public service alliances, and mutual recognition of employment, healthcare, education, and social security services where feasible. In low-value and cold-spot areas such as Nanle County, Qingfeng County, Neihuang County, Fanxian County, Taiqian County, and Xunxian County, cooperation should focus on improving access to regional markets and public resources; in core areas such as Zhongmu County, Xinzheng City, Xinmi City, Gongyi City, Xingyang City, Changge City, and Yuzhou City, it should focus on outward diffusion of innovation, services, and industrial functions.

Finally, policy evaluation should also shift from uniform target assessment to county-specific structural diagnosis. Provincial authorities may set common goals for green development, public service equalization, industrial upgrading, and regional coordination, but county-level implementation should be adjusted according to the dominant CDFA weight structure and spatial clustering type of each county. Ecologically sensitive counties such as Luanchuan County, Songxian County, Lushi County, Xixia County, Xichuan County, and Tongbai County should be assessed more strongly on resource efficiency and pollution reduction; counties with high public-service sensitivity, such as Qingfeng County, Nanle County, Fanxian County, Taiqian County, and Xunxian County, should focus on healthcare, elderly care, and social welfare provision; counties with high linkage sensitivity, such as Zhongmu County, Xinzheng City, Changge City, Yuzhou City, Changyuan City, and Lankao County, should be evaluated by their participation in inter-county cooperation networks. In this way, Henan can move from isolated county-level improvement toward coordinated regional upgrading based on differentiated local pathways and stronger inter-county connectivity.

Conclusions

This study takes 102 counties in Henan Province as the research sample. Drawing on data for 19 indicators from 2010 to 2021, it constructs an evaluation framework for county-level HQD from the perspective of the Five Development Concepts and the Space of Flows. The coupling detrended fluctuation analysis (CDFA) method is then introduced to examine the level, spatial differentiation, and driving mechanisms of county-level HQD. The main conclusions are as follows.

1. CDFA is well suited to the assessment of regional HQD, particularly for capturing regional systems characterized by strong multidimensional heterogeneity and pronounced dynamic coupling. The indicator system for county-level HQD is formative and structurally differentiated, and the relationships among indicators cannot be reduced to simple linear aggregation. Additionally, the generalized Hurst exponent results confirm that the indicator series exhibit significant nonlinearity and multifractal characteristics, providing a solid methodological basis for the application of CDFA. Furthermore, a comparison with the LTDM reveals that CDFA, when implemented with unified weights, is highly consistent with traditional objective weighting methods in identifying broad spatial patterns. Crucially, CDFA is uniquely capable of deriving county-specific weights, thereby effectively revealing the internal coupling relationships and structural sensitivity of individual development systems.

2. The evaluation results based on the county-specific weights derived from CDFA indicate that county-level HQD in Henan improved overall between 2011 and 2021. The share of counties classified as “high” or “medium high” increased, whereas the proportion of “low” or “medium low” counties declined, suggesting that county development has gradually shifted from broad-based catch-up to a stage more strongly oriented toward quality improvement and structural optimization. Spatially, counties with higher levels of HQD became increasingly concentrated around core cities such as Zhengzhou and Luoyang, while also extending along the Central Plains urban agglomeration. At the same time, the remaining lower-performing counties were mainly located in northeastern Henan and peripheral mountainous areas. Overall, the spatial pattern evolved toward a more differentiated structure characterized by core-area agglomeration and residual peripheral weakness. Moreover, the weighting results further show that the dominant coupled indicators vary substantially across counties, indicating that there is no single structural pathway to county-level HQD.

3. County-level HQD in Henan exhibits significant spatial autocorrelation, and its spatial differentiation is jointly driven by the superposition of multiple socio-economic and natural factors. The global Moran’s I indicates a significant positive spatial clustering of county development levels. The LISA results further show that high-high clusters expanded from the central part of the province toward the west, whereas low-low clusters remained concentrated in the north and northeast. The optimal parameters-based geographical detector (OPGD) analysis reveals that locational conditions, industrial foundations, and terrain relief consistently remained the primary factors explaining this spatial differentiation. Furthermore, the interaction effects between any two factors were universally stronger than those of any single factor alone, suggesting that county-level spatial disparities are shaped by a synergistic mechanism where policy and economic inputs interact with inherent geographical endowments.

4. County-level HQD in Henan should follow differentiated and spatially adaptive pathways. Core counties should capitalize on their advantages in industrial agglomeration and regional linkages to strengthen innovation diffusion and spillover effects. Transitional counties should be empowered as transmission belts to deeply embed into regional cooperative networks. Traditional agricultural counties must prioritize green agricultural transformation, while peripheral and ecologically constrained mountainous counties should focus on overcoming structural constraints through eco-tourism and ecological compensation. Overall, county-level HQD cannot rely on a uniform policy template; rather, governance strategies must be tailored to the specific development stages, structurally sensitive factors, and locational conditions of different counties.

This study still has certain limitations. Owing to the availability of continuous county-level statistical data, the study period is relatively short, which may affect the stability of scale-relationship estimation in the CDFA framework. Future research should incorporate higher-frequency and more diversified data sources, and conduct comparative analyses across a wider range of regional samples, in order to further test the robustness and broader applicability of the CDFA approach in evaluating complex regional HQD systems.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Conceptualization: LS and WZ; Methodology: XW, ZL and ZZ; Formal analysis and investigation: ZZ, QY and SY; Writing - original draff preparation: LS, QY and SY; Writing - review and editing: WZ, XW and ZL.

Funding

The research was supported by the National Natural Science Foundation of China (41771124), Joint Fund Project of the Henan Provincial Science and Technology Research and Development Program (242103810099), National Natural Science Foundation of Jiangxi Province (20252BAC240248), Major Project of Applied Research in Philosophy and Social Sciences in Henan Provincial Higher Education Institutions (2024-YYZD-02), General Project of Humanities and Social Sciences Research in Henan Provincial Universities (2025-ZZJH-172) and Key Scientific Research Project Funding Program for Higher Education Institutions of Henan Province (23A170011).

Data availability

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.