A method for diagnosing spatial function coordination of a cross-border urban area based on a h3 hexagonal grid

Abstract

This invention provides a method for diagnosing the spatial functional coordination of cross-boundary urban areas based on H3 hexagonal grids, belonging to the field of spatial diagnostic methods. The method includes: acquiring multi-source geospatial data to construct a basic feature layer; constructing a three-level nested H3 grid system (micro, meso, and macro); integrating and calculating the share vectors of production, living, and ecological components at the micro-level; aggregating and extracting multi-scale spatial features of each level of grid unit along the scale chain; calculating a set of cross-scale emergent indicators characterizing the structural deviation of the macro-level relative to the meso-level, including synergy, constraint, amplification, and structural integration indices; finally, extracting judgment thresholds to perform logical rights confirmation on macro-level units, identifying various governance configuration types, and outputting spatial distribution maps. This invention overcomes the statistical identification bias caused by traditional administrative boundaries, achieving accurate quantitative diagnosis of cross-boundary implicit functional spatial configurations.

Description

Technical Field

[0001] This invention relates to the field of spatial diagnostic methods, and in particular to a method for diagnosing the spatial functional coordination of cross-border urban areas based on H3 hexagonal grids. Background Technology

[0002] The governance of large urban areas faces a structural contradiction between fluid elements and rigid administrative boundaries. Currently, spatial diagnosis for such areas mainly relies on administrative jurisdictions as physical containers for statistics and evaluation. Traditional "three-life space" identification technology usually conducts land use ratio calculations at the district and county level, and uses areal administrative boundaries to conduct local balance assessments of production, living and ecological spaces. Although this system can complete the static resource survey within the jurisdiction, it often produces systematic statistical mismatches due to the data silo effect when analyzing commuter belts, logistics corridors and continuous ecological bases that cross the city boundaries. Related studies have pointed out that assessments based on administrative units will artificially sever naturally connected functional areas, leading to a serious underestimation of regional synergy effects. (Reference: Li Guangdong, Fang Chuanglin, Quantitative Identification and Analysis of Urban Ecological-Production-Living Space Functions [J]. Acta Geographica Sinica, 2016, 71(01):49-65.)

[0003] With the application of complex adaptive systems theory in urban science, spatial planning research is gradually shifting towards the quantitative exploration of spatial emergent characteristics and cross-scale organizational mechanisms. Technological evolution trends indicate that utilizing topologically consistent discrete global grid systems such as the H3 hexagonal grid to construct spatial infrastructure that transcends administrative boundaries has become a key path to address the challenges of spatial autocorrelation directional bias and cross-boundary identification. Current research focuses on integrating multi-source micro-geographic data and, through a multi-scale nested analysis framework, tracking how functional heterogeneity at the micro-scale is filtered through meso-level organization and ultimately evolves into structural configuration at the macro-scale, thereby achieving dynamic monitoring of regional spatial resilience.

[0004] Although grid-based analysis has become more widespread, existing diagnostic models still have significant technical limitations. First, mainstream methods are mostly limited to descriptive characterization on a single plane, lacking a cross-scale diagnostic logic that connects micro-functional organization with macro-spatial configuration, making it difficult to determine whether local spatial disorder will lead to systemic structural fragility. Second, identification bias caused by the Variable Area Unit Problem (MAUP) persists, resulting in implicit functional corridors at administrative boundaries remaining "invisible" in planning views. Furthermore, for cross-border areas with extreme institutional heterogeneity, existing collaborative measurement tools cannot effectively isolate the interaction effects of institutional friction and physical spatial coupling, making it difficult to provide differentiated governance decision-making basis. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, the purpose of this invention is to provide a cross-boundary urban area spatial function coordination diagnosis method based on H3 hexagonal grid. This invention solves the problems of statistical identification bias caused by administrative boundaries and lack of cross-scale functional organization connection paths in existing technologies, which limit the accurate identification and quantification of cross-boundary implicit functional spaces.

[0006] To achieve the above objectives, the present invention provides the following solution: a method for diagnosing spatial function coordination in cross-boundary urban areas based on H3 hexagonal grids, comprising: Acquire multi-source geospatial data of the study area and map it to a raster grid of preset resolution to construct a basic feature layer; Based on the aforementioned basic feature layer, a three-level nested H3 hexagonal mesh system comprising micro-level L1, meso-level L2, and macro-level L3 is constructed, and sub-unit coverage thresholds are set for the meso-level L2 and the macro-level L3 to perform boundary expansion control. Within the micro-level L1 grid cell, activity indicators and biophysical variables from the multi-source geospatial data are integrated to calculate the intensity of production, living and ecological components, and component normalization is performed to obtain the component share vector. Along the scale chain from the micro level L1 to the meso level L2 to the macro level L3, feature aggregation is performed on the component share vector, and the functional balance features, spatial stability features, and centrality distribution features of each grid cell are extracted based on the aggregation results to establish a multi-scale spatial feature database. Based on the multi-scale spatial feature database, a set of cross-scale emergence indicators is calculated to characterize the deviation of the macro-level L3 from the meso-level L2. The set of cross-scale emergence indicators includes: a synergy index calculated based on the sub-unit quartile deviation, a constraint index calculated based on the ratio of macro-level balance to meso-level heterogeneity, an amplification index calculated based on the centrality Gini coefficient, and a structural integration index calculated based on the information entropy gain factor. The empirical distribution quantiles of the cross-scale emergence index set are extracted to obtain the judgment threshold. The judgment threshold is then used to perform logical weighting on each macro-level L3 grid cell to identify the governance configuration type of each cell and output a spatial distribution map.

[0007] The present invention discloses the following technical effects: This invention provides a diagnostic method for spatial functional coordination in cross-border urban areas based on H3 hexagonal grids, effectively overcoming the Variable Area Unit (MAUP) problem. The H3 hexagonal grid system possesses topological consistency and directional uniformity, minimizing directional deviations in spatial autocorrelation analysis compared to traditional square grids. It also completely eliminates the artificial division of administrative boundaries, allowing cross-border functional corridors and ecological structures to be fully presented within the analytical framework, achieving quantitative diagnosis of cross-scale functional coordination. The four types of spatial emergence indices constructed in this invention transform the abstract mechanisms of complex adaptive systems into operational planning diagnostic tools, quantitatively revealing how micro-level spatial heterogeneity aggregates at the macro-scale to form systemic risks or regional resilience, thus overcoming the fundamental shortcomings of existing single-scale methods; and identifying implicit functional spatial structures across administrative boundaries. This invention can identify cross-border functional zones invisible under the traditional administrative unit analysis framework, providing empirical evidence for regional spatial planning that transcends jurisdictional boundaries, especially applicable to cross-border urban areas with high institutional heterogeneity; and providing diagnostic basis for differentiated governance. By identifying three governance configuration types with different emergence mechanisms, this invention can provide targeted planning intervention strategies for different types of spatial units, challenging the traditional homogeneous regional integration paradigm and helping to formulate more adaptive and differentiated cross-border spatial governance solutions. The spatial diagnostic framework of this invention does not depend on a specific research area. By adjusting the H3 grid resolution parameters and data input, it can be applied to different types of cross-border urban agglomerations or institutionally heterogeneous regions around the world, and has broad methodological promotion value. Attached Figure Description

[0008] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0009] Figure 1 A flowchart of a cross-boundary urban area spatial function coordination diagnosis method based on H3 hexagonal grid provided for an embodiment of the present invention. Detailed Implementation

[0010] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0011] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0012] like Figure 1 As shown, this invention provides a method for diagnosing spatial function coordination in cross-boundary urban areas based on H3 hexagonal grids, including: Step 100: Acquire multi-source geospatial data of the study area and map it to a raster grid of preset resolution to construct a basic feature layer; Step 200: Based on the basic feature layer, construct a three-level nested H3 hexagonal mesh system containing micro-level L1, meso-level L2 and macro-level L3, and set sub-unit coverage thresholds for the meso-level L2 and the macro-level L3 to perform boundary expansion control; Step 300: Within the micro-level L1 grid cell, integrate the activity indicators and biophysical variables from the multi-source geospatial data, calculate the intensity of production, living and ecological components, and perform component normalization processing to obtain the component share vector; Step 400: Along the scale chain of the micro level L1 → the meso level L2 → the macro level L3, perform feature aggregation on the component share vector, and extract the functional balance features, spatial stability features and centrality distribution features of each grid unit according to the aggregation results, so as to establish a multi-scale spatial feature database. Step 500: Based on the multi-scale spatial feature database, calculate a set of cross-scale emergence indicators that characterize the deviation of the macro level L3 from the meso level L2. The set of cross-scale emergence indicators includes: a synergy index calculated based on the sub-unit quartile deviation, a constraint index calculated based on the ratio of macro-level balance to meso-level heterogeneity, an amplification index calculated based on the centrality Gini coefficient, and a structural integration index calculated based on the information entropy gain factor. Step 600: Extract the empirical distribution quantiles of the cross-scale emergence index set to obtain the judgment threshold, and use the judgment threshold to perform logical weighting on each macro-level L3 grid cell to identify the governance configuration type of each cell and output the spatial distribution map.

[0013] Furthermore, the acquisition of multi-source geospatial data of the study area and mapping it to a raster grid of a preset resolution to construct a basic feature layer includes: Acquire the multi-source geospatial data, including point of interest data, land cover data, nighttime light remote sensing data, population spatialization data, vegetation net primary productivity data, evapotranspiration data, topographic data, and statistical data. The interest point data was filtered by category to extract the financial and business theme group, the technological innovation theme group, the life service theme group, and the residential theme group; Each of the aforementioned subject groups and the remaining multi-source geospatial data are mapped to a raster grid of the preset resolution and subjected to gridding assignment processing to construct the basic feature layer.

[0014] Specifically, in one particular embodiment, the present invention first performs the collection and standardization processing of multi-source geospatial data of the study area to construct a foundational basis for subsequent cross-scale spatial analysis. Specifically, the multi-source geospatial data acquired by the system encompasses dynamic characteristic data representing socio-economic activities, static environmental data representing the Earth's surface physical background, and macro-statistical yearbook data. The multi-source geospatial data specifically includes: Points of Interest (POI) data from map platform API snapshots, nighttime light remote sensing data (such as SRUNet-NPP-VIIRS-V2-Like annual products), population spatialization data (such as LandScan Global global population grid), land cover data (such as MODIS MCD12Q1 annual products), net primary productivity (NPP) data, actual and potential evapotranspiration data, digital elevation model (DEM) data, precipitation and soil data, and statistical data such as municipal-level industrial added value (GDP). These multi-source heterogeneous data collectively constitute the raw analytical materials covering production, living, and ecological dimensions.

[0015] After acquiring the aforementioned raw multi-source geospatial data, the system performs specialized category filtering and noise reduction processing on the massive, discrete point-of-interest (POI) data. Specifically, the system sequentially performs spatial boundary trimming, funnel-shaped category cleaning, and confidence filtering on the raw POI records to eliminate low-quality redundant data. Subsequently, based on the physical representation of each POI's role in urban spatial functions, the filtered high-confidence records are precisely extracted into four core thematic groups. Records covering banks and office buildings are categorized into the financial and business thematic group; records covering research institutes and incubators are categorized into the technological innovation thematic group—these two groups primarily represent production space characteristics; records covering supermarkets and restaurants are categorized into the life services thematic group; and records covering residential areas are categorized into the residential thematic group—these two groups primarily represent living space characteristics.

[0016] After initial data cleaning and feature classification, the system maps each thematic group and the remaining multi-source geospatial data to a raster grid with a preset resolution (preferably 1km resolution in this embodiment), and performs gridding assignment processing to construct a basic feature layer. During this mapping process, for the point-of-interest data extracted into the four thematic groups, the system strictly uses a direct point-to-grid mapping counting method for rasterization. This mapping process explicitly excludes the intervention of spatial smoothing algorithms such as kernel density estimation (KDE), aiming to accurately preserve the absolute economic activity intensity at the edges of administrative jurisdictions or urban boundaries, effectively avoiding the "boundary feature blurring" phenomenon caused by spatial smoothing. Simultaneously, the remaining continuous remote sensing and meteorological raster data are uniformly resampled to the same preset resolution and their coordinate systems are aligned. Through the above comprehensive processing flow, the system successfully constructs a high-fidelity basic feature layer, providing a reliable data foundation for subsequent feature extraction using nested hexagonal grids and accurate identification of cross-boundary implicit functional corridors.

[0017] Furthermore, the construction of a three-level nested H3 hexagonal mesh system based on the basic feature layer, comprising micro-level L1, meso-level L2, and macro-level L3, includes: Extract unit feature values ​​from the basic feature layer and construct the micro-level L1 using H3 resolution 7-level grid cells; The mesoscopic L2 was constructed using H3 resolution, level 5 mesh cells; The macroscopic level L3 is constructed using H3 resolution level 4 grid cells, and the microscopic level L1, the mesoscopic level L2, and the macroscopic level L3 are nested sequentially in spatial topology.

[0018] Specifically, this embodiment extracts the feature values ​​of raster cells from the basic feature layer and maps them to a three-level nested mesh system: First, a microscale L1 was constructed using H3 resolution level 7 grid cells, with a single cell area of ​​approximately 5.16 km². 2 In the application example targeting the Guangdong-Hong Kong-Macao Greater Bay Area, this level contains a total of 11,164 effective units, which are used to record the local spatial heterogeneity of production, living and ecological dimensions in a fine-grained manner.

[0019] Secondly, a mesoscopic L2 network was constructed using H3 resolution level 5 grid cells, with a single cell area of ​​approximately 252.90 km². 2 This level acts as a filter and organization layer, capturing the formation of functional corridors, balance characteristics, and the fragmentation of space. In the application example above, the L2 level contains 224 effective units.

[0020] Finally, a macroscopic-level L3 was constructed using H3 resolution level 4 mesh cells, with a single cell area of ​​approximately 1770.35 km². 2 This hierarchy comprises 30 effective units, serving as functional carriers for identifying candidate cross-boundary governance spaces. In this embodiment, the micro-level L1, meso-level L2, and macro-level L3 are nested sequentially in spatial topology, maintaining consistent parent-child hierarchical relationships and adjacency logic. The design logic of employing a 7-5-4 resolution chain is as follows: fine-grained functional distribution noise is preserved at the L1 level; corridor-like meso-level structures emerge at the L2 level; and a sufficiently large analytical scale is maintained at the L3 level to define the governance space, while avoiding compressing the regional pattern into too few units. Through this nested aggregation logic, functional heterogeneity at the micro-scale can be filtered through meso-level structures, ultimately manifesting as a coherent governance configuration at the macro-scale, effectively solving the distortion of regional spatial pattern identification caused by the Variable Area Unit Problem (MAUP).

[0021] Furthermore, within the micro-level L1 grid cell, the activity indicators and biophysical variables from the multi-source geospatial data are integrated to calculate the intensity of production, living, and ecological components, and component normalization is performed to obtain a component share vector, including: Data layers representing production and living activities are extracted from the basic feature layers as activity indicators, and data layers representing land cover and ecological functions are extracted as biophysical variables. The intensity of the production component and the intensity of the living component are calculated based on the activity indicators, and the intensity of the ecological component is calculated based on the biophysical variables; The production component intensity, living component intensity, and ecological component intensity within each micro-level L1 grid cell are subjected to minimum-maximum normalization and component closure normalization to obtain the component share vector that satisfies the condition that the sum of the proportions of each component is a preset constant.

[0022] Specifically, in one embodiment, to accurately characterize the functional structure within the microscopic space, the system performs feature decoupling and index reorganization on multi-source data in the basic feature layer within the microscopic L1 grid unit. Specifically, the system extracts two types of core feature data from the basic feature layer: one type is dynamic spatial data characterizing the intensity of human socio-economic activities, defined as the activity indicators; the other type is static or environmental physical data characterizing the natural surface substrate and ecosystem support capacity, defined as the biophysical variables. The activity indicators cover four interest point themes: finance and business, technological innovation, and living services and residence, as well as spatialized population data, regional industrial GDP statistics, and nighttime light remote sensing data; the biophysical variables are strictly limited to observational data with a physical basis, such as land cover, net primary productivity of vegetation, actual and potential evapotranspiration, digital elevation models, precipitation, and soil type. Subsequently, based on the decoupled indicators, the system calculates the initial component intensities of the three spatial dimensions of production, living, and ecology (PLE). In calculating the intensity of the production component, the system comprehensively represents it based on the extracted thematic groups of interest points in finance, business, and technological innovation, combined with downscaled industrial GDP data and nighttime light data. In calculating the intensity of the living component, the system comprehensively represents it using thematic groups of interest points in living services and residence, combined with spatialized population data and nighttime light data.

[0023] In this stage, nighttime light data serves as a shared proxy variable for activities in the built-up area, simultaneously supporting the calculation of production and living components. In calculating the intensity of ecological components, the system strictly adheres to the biophysical variables for feature fusion, excluding human activity data such as points of interest to ensure the objectivity and accuracy of ecological space indicators at the biophysical definition level. After obtaining the initial component intensities for each dimension, the system performs a two-stage normalization process on the production component intensity, living component intensity, and ecological component intensity within each micro-level L1 grid cell. In the first stage, the system performs a min-max normalization operation on each underlying indicator layer involved in the calculation to eliminate dimensional differences between multi-source heterogeneous data.

[0024] In the second stage, after fusing the comprehensive functional intensity values ​​of production, living, and ecology within a single grid cell, the system further performs component closure normalization on these three intensity values. The essence of this closure process is to transform the absolute functional intensity physical quantity into a relative spatial composition ratio, ensuring that the sum of the proportions of the three components—production, living, and ecology—within the same micro-level L1 grid cell is strictly equal to a preset constant (in this embodiment, this preset constant is set to 1). Through the aforementioned rigorous index extraction and normalization process, the system ultimately outputs the component share vector characterizing the relative spatial composition logic, laying a unified metric foundation for the subsequent construction of a cross-scale spatial emergence diagnostic model.

[0025] Furthermore, the step of extracting the functional balance characteristics, spatial stability characteristics, and centrality distribution characteristics of grid cells at each level based on the aggregation results to establish a multi-scale spatial feature database includes: Based on the aggregation result of the component share vector at the mesoscopic level L2, the functional balance index and spatial fragmentation index are calculated to obtain the functional balance characteristics. Based on the aggregation result of the component share vector at the macroscopic level L3, the structural stability field is extracted to obtain the spatial stability feature, and the gravitational centrality distribution feature is extracted to obtain the centrality distribution feature, so as to integrate and establish the multi-scale spatial feature database.

[0026] Specifically, in one particular embodiment, the system performs cross-scale aggregation on the component share vectors to extract feature indicators that reflect the organizational logic at different levels, thereby constructing the multi-scale spatial feature database and providing structured data support for subsequent spatial emergence diagnosis.

[0027] Specifically, at the meso-level L2, the system first calculates the functional balance index and spatial fragmentation index based on the aggregation results of the component share vectors within the meso-level L2 grid cells to extract the functional balance characteristics. In this process, the functional balance index quantifies the relative equilibrium of the three components—production, living, and ecology—within a single meso-level cell, and its value range reflects the evolutionary state of spatial function from extreme imbalance to high equilibrium. The spatial fragmentation index measures the spatial discontinuity of micro-functional patches as they aggregate towards the meso-level. In applications targeting specific regions, the average balance level and fragmentation degree at the meso-level are used as key parameters for filtering micro-noise, capturing the initial formation of corridors or functional zoning.

[0028] At the macroscopic L3 level, the system obtains the spatial stability features and the centrality distribution features based on the aggregation results of the component share vectors within the macroscopic L3 grid cells using a structure extraction algorithm. The spatial stability features are characterized by the extracted structural stability field, used to describe the stability of the macroscopic spatial pattern at the structural level. The centrality distribution features are obtained by extracting gravitational centrality distribution features. Specifically, the system uses a gravity model to estimate the interaction strength between the mesoscopic L2 cells and aggregates it into the macroscopic L3 cells to characterize the polarization trend of network weights and the core-periphery organizational morphology. During this calculation process, the system effectively avoids the signal duplication counting problem in the gravity model by performing deduplication and union calculations on the built-up activity proxy variables, ensuring the physical accuracy of the centrality distribution features.

[0029] Finally, the system performs correlation mapping on the extracted functional balance features, spatial stability features, and centrality distribution features to integrate and establish the multi-scale spatial feature database. This multi-scale spatial feature database uses the macro-level L3 unit as the top-level index, and correlates downwards with the corresponding meso-level L2 sub-unit features and the micro-level L1 component shares, forming a feature matrix with a tightly nested topological relationship. Through this database, analysts can quantitatively trace how functional heterogeneity at the micro-scale is reorganized across different scale chains and ultimately manifests as specific macro-level governance configurations.

[0030] Furthermore, the calculation process of the synergy index based on the sub-unit quartile deviation includes: For each of the macroscopic-level L3 grid cells, the coupling values ​​of the production-living dimension, production-ecology dimension, and living-ecology dimension in the multi-scale spatial feature database are extracted respectively. The distribution quartiles and interquartile ranges of the corresponding meso-level L2 grid cells within each macro-level L3 grid cell are obtained as the sub-cell quartile deviations. The coupling values ​​of each dimension are compared with the corresponding quartiles and interquartile ranges of the distribution, and the maximum score after the comparison is extracted as the synergy index.

[0031] Furthermore, the calculation process of the constraint index based on the ratio of macroscopic equilibrium degree to mesoscopic heterogeneity includes: The macroscopic balance is calculated based on the average component share of each of the corresponding mesoscopic L2 grid units within each of the macroscopic L3 grid units. The mesoscopic heterogeneity is calculated based on the standard deviation of the component proportions of each corresponding mesoscopic L2 grid cell; When the macro-level balance is greater than the average level of the corresponding sub-unit group, the ratio of the macro-level balance to the meso-level heterogeneity is calculated to obtain the constraint index.

[0032] Furthermore, the calculation process of the magnification index based on the centrality Gini coefficient includes: Network centrality is calculated based on the comprehensive functional strength and spatial connectivity of each meso-level L2 grid cell. The centrality Gini coefficient is calculated based on the network centrality of each corresponding meso-level L2 grid cell within the macro-level L3 grid cell; The amplification index is obtained by multiplying the centrality Gini coefficient with the average network centrality relative deviation of the preset high-resolution sub-unit.

[0033] Furthermore, the calculation process of the structural integration index based on the information entropy gain factor includes: The spatial stability characteristics of the macroscopic L3 grid cell are obtained, as well as the information entropy gain factor calculated based on the discretized mesoscopic configuration state; Calculate the cross-scale parent-child consistency term for the degree of alignment between the macroscopic-level L3 mesh cell and its internal dominant sub-state contour; The structural integration index is obtained by performing a product aggregation operation on the spatial stability feature, the information entropy gain factor, and the cross-scale parent-child consistency term.

[0034] Specifically, in this embodiment, the specific calculation logic and data processing of four types of cross-scale emergence indicators are described in detail. For each macro-level grid unit, this embodiment extracts the coupling values ​​of the production and living dimensions, production and ecology dimensions, and living and ecology dimensions from the multi-scale spatial feature database. The function of the coupling value is to characterize the interaction and synergy efficiency of two heterogeneous spatial functions within the same geographical unit. The specific mathematical extraction source is: performing a direct product operation on the proportions of two components to be measured within the same grid unit after component closure normalization (e.g., the product of production share and living share). To establish a benchmark for cross-boundary spatial comparison, the system obtains the distribution quartiles and interquartile ranges of all corresponding meso-level grid units within each macro-level grid unit in the corresponding dimensions. The distribution quartiles explicitly include the first quartile and the third quartile, and the interquartile range is defined as the difference between the third quartile and the first quartile. The two together constitute the sub-unit quartile deviation, used to characterize the normal fluctuation range of functional coupling at the meso-scale. In the specific comparison calculation, the system subtracts the corresponding third quartile of the meso-level from the coupling value of the macro-level dimension, and divides the resulting difference by the sum of the interquartile range and a minimum constant, which is fixed at 0.0001 to prevent division by zero overflow. The system extracts the maximum score generated after the comparison calculation among the above three functional dimensions as the synergy index. In the quantitative implementation, when the production and living shares of a macro-level unit are 0.60 and 0.40 respectively, its macro-level coupling value is 0.24; if the third quartile of the coupling value of its subordinate meso-level units is 0.15 and the interquartile range is 0.05, this embodiment calculates its synergy index to be 1.80, clearly indicating that the macro-level functional coordination strength has significantly exceeded the preset distribution limit of the meso-level.

[0035] To extract the macro-level regulatory baseline characteristics, the system calculates the macro-level balance degree based on the average component share of all corresponding meso-level grid units within each macro-level grid unit. The macro-level balance degree is essentially the quotient of the minimum and maximum values ​​among the average share characteristics of production, living, and ecology within the macro-level unit, used to determine the equilibrium state of the overall functional structure. Simultaneously, the system calculates the meso-level heterogeneity based on the standard deviation characteristics of each corresponding meso-level grid unit across different component shares. The value of the meso-level heterogeneity is absolutely quantified by calculating the arithmetic mean of the ratios of the standard deviations of each component to their corresponding average shares. In the operational logic, the system performs gating judgment on the macro-level balance degree and the average balance degree level of the corresponding sub-unit group. Only when the macro-level balance degree is strictly greater than the average level of the corresponding sub-unit group, the system obtains the constraint index by calculating the quotient of the macro-level balance degree and the meso-level heterogeneity. Through quantitative anchoring calculations, if the extracted macro-balance degree is 0.85 and the meso-heterogeneity derived from the standard deviation of the underlying share reaches 0.20, this embodiment directly calculates and confirms that its constraint degree index is 4.25, thereby accurately diagnosing the system's ability to maintain macro-ecological and functional order under conditions of high heterogeneous fluctuations at the underlying level.

[0036] In the computational stage of diagnosing network polarization characteristics, the system estimates network centrality based on the comprehensive functional strength and spatial connectivity of each meso-level grid cell. The comprehensive functional strength is derived from the total number of deduplicated unions of active layers built within the cell. The calculation logic for spatial connectivity is as follows: extract the geographic centroids of the target meso-level cell and all other meso-level cells, calculate the Euclidean distance between each pair of centroids, and take the reciprocal of the square of this distance as a decay weight. This weight is then combined with the comprehensive functional strength to generate a gravity model mass term, thereby obtaining the network centrality of a single node. Subsequently, the system calculates the centrality Gini coefficient based on the network centrality scores of each meso-level grid cell within the macro-level grid cell. The effective value boundary of the centrality Gini coefficient is strictly limited to the interval between 0 and 1, used to characterize the degree of absolute inequality in the distribution of functional weights. Following this, the system calculates the average relative deviation of network centrality for sub-cells with preset high scores. The preset high-resolution sub-units specifically refer to the core meso-level unit group ranking in the top 10% of network centrality values. Their relative deviation is the dimensionless ratio obtained by dividing their average network centrality by the average network centrality of all sub-units. The system multiplies the centrality Gini coefficient with the relative deviation to obtain the amplification index. In the implementation test, when the Gini coefficient of a certain cross-boundary macro-level unit is measured to be 0.72, and the relative deviation of the top 10% of core units reaches 5.00, this embodiment determines its amplification index to be 3.60, accurately mapping the asymmetric amplification mechanism of network function clustering towards core polarization.

[0037] To measure the compression state of spatial complexity, the system acquires the spatial stability characteristics of the macro-level grid cells and the information entropy gain factor calculated based on the discretized meso-level configuration state. The specific data processing source for the spatial stability characteristics is: principal component eigenvalue decomposition is performed on the multidimensional feature matrix of all meso-level sub-cells within the macro-level cell; the variance contribution rate of the first principal component is extracted as the structural stability score of the macro-level cell, used to characterize the explanatory power of the main spatial pattern on the overall variance. The information entropy gain factor is calculated by: calculating the normalized Shannon information entropy of the discretized meso-level configuration characteristics and summing it with a constant 1; its core function is to quantify the initial heterogeneous divergence of the underlying configuration. Simultaneously, the system calculates the cross-scale parent-child consistency term of the alignment degree between the macro-level grid cell and its internal dominant sub-state contours. The quantification process of the cross-scale parent-child consistency term is: extracting the macro-level feature vector and the dominant feature vector in the sub-cell; calculating the standardized vector dot product result (i.e., cosine similarity score) of the two as the alignment degree value. The system jointly extracts the spatial stability features, the information entropy gain factor, and the cross-scale parent-child consistency term, and performs a direct multiplication and aggregation operation to generate the final structural integration index. Based on the quantitative benchmark in the embodiment, even if the gain factor derived from the underlying normalized information entropy is as high as 1.45, as long as the variance contribution rate (spatial stability) of the first principal component reaches 0.88 and the parent-child cosine similarity (consistency) is confirmed to be 0.92, the system outputs a structural integration index as high as 1.17, fully demonstrating that the underlying fragmented features are effectively integrated into a coherent macroscopic order field.

[0038] By integrating the aforementioned four progressive index calculation steps, the system ultimately constructs a complete emergent index feature library reflecting boundless cross-scale functions. This feature library deconstructs traditional urban spatial models influenced by administrative boundaries through four absolutely orthogonal technical dimensions: synergy, constraint, amplification, and structural integration. In the overall data output stage, the system directly inputs the four index feature matrices of 30 macro-level grid units into the structured top-level index. The system extracts the third quartile of the empirical distribution of these four indices as the high-value judgment threshold. Through rule-driven comparison, it finally outputs a spatial topology distribution atlas containing four polarization core judgment records and seven highly synergistic corridor judgment records. All feature mapping and multiplication / division aggregation operations are performed within a closed H3 geographic coordinate framework, free from the interference of administrative division surface elements. This ensures that the entire data processing chain, from basic data input to the output of the cross-scale emergent index set, is free from any surface-source statistical distortion, thus providing a completely reliable and quantitatively transparent technical implementation path for the logical confirmation of rights in cross-boundary functional areas at all levels.

[0039] Specifically, the formula for calculating the synergy index is: ; in, S represents the synergy index; d represents the functional coupling dimension, including the production-living dimension (PL) and the production-ecology dimension. PE and the life-ecology dimension (LE); For macroscopic L3 mesh cells in dimensional d The coupling value on; For all meso-level L2 sub-units within the macro-level L3 grid cell, in dimensional... d The 75th percentile of the upper coupled distribution; For each of the aforementioned meso-level L2 subunits in dimensional d Interquartile range of the upper coupling distribution; To prevent the denominator from being zero, a preset minimum constant is used.

[0040] The mathematical expression for the constraint index is: ; Where C is the constraint index; The macroscopic balance of the L3 grid cells at the macroscopic level; It is the mesoscopic heterogeneity coefficient representing the component proportions of each mesoscopic L2 sub-unit within the macroscopic L3 grid cell.

[0041] The mathematical expression for the magnification index is: ; Where A is the magnification index; The network centrality Gini coefficient of each meso-level L2 sub-unit within the macro-level L3 grid unit; The average network centrality of the top 10% of meso-level L2 sub-units within the macro-level L3 grid cell; This represents the average network centrality of all meso-level L2 sub-units within the macro-level L3 grid cell.

[0042] The mathematical expression for the structural integration index is: ; Where R is the structural integration index; Scoring of spatial stability characteristics for macroscopic-level L3 grid cells; The normalized information entropy for the meso-level L2 grid cell; The score is given for the cross-scale parent-child consistency term of the macroscopic L3 grid cell and its internal dominant sub-state.

[0043] Furthermore, the step of using the determination threshold to perform logical weighting on each of the macro-level L3 mesh cells to identify the governance configuration type of each cell includes: When the magnification index and the structural integration index of a certain macroscopic L3 grid cell both exceed the corresponding judgment threshold, the cell is identified as a polarization core type. When the synergy index exceeds the corresponding judgment threshold, it is identified as a synergy corridor type; When the constraint index exceeds the corresponding judgment threshold and the synergy index is lower than the empirical median judgment benchmark, it is identified as a constrained ecological barrier type. The macroscopic-level L3 mesh cells that do not fall under any of the above rule conditions are identified as transitional. The governance configuration types include: the polarization core type, the collaborative corridor type, the constrained ecological barrier type, and the transition type.

[0044] Specifically, in this embodiment, the implementation process of using the judgment threshold to perform logical confirmation of each macro-level grid unit to identify the governance configuration type is described in detail. This embodiment first performs statistical distribution analysis on the cross-scale emergent index set of the entire macro-level grid units, extracting the empirical distribution quantiles of each index as the judgment threshold. In terms of specific parameter settings, this embodiment preferably uses the 75th percentile (Q75) as the criterion for identifying dominant features, and simultaneously uses the 50th percentile (median, Q50) as the empirical median criterion for determining the background noise of the function. The logical confirmation refers to this embodiment performing conditional retrieval on the numerical combinations of each macro-level grid unit in four orthogonal dimensions according to preset nested logical rules, thereby assigning it a unique spatial functional identity, i.e., the governance configuration type.

[0045] For regions exhibiting high-intensity polarization characteristics, this embodiment employs a first determination rule. When the amplification index and structural integration index of a macroscopic grid unit simultaneously exceed the corresponding determination threshold (Q75), this embodiment identifies the unit as a polarization core. The function of a polarization core is defined as a functional hub within the region where network power is highly concentrated and spatial structure is extremely stable. In stress tests targeting the Guangdong-Hong Kong-Macao Greater Bay Area, if a macroscopic unit located near the Shenzhen-Hong Kong interface has an amplification index of 3.60 and a structural integration index of 1.17, and both indicators are higher than the corresponding determination thresholds of 0.85 and 0.95, it is directly identified as a polarization core. This identification result quantitatively proves that the functional core of this region is not an isolated unit restricted by administrative boundaries, but rather an emerging center that transcends boundaries and possesses extremely high system weight.

[0046] For corridor areas representing cross-boundary functional flows, this embodiment implements a second determination rule. When the synergy index of the macro-level grid unit exceeds the corresponding determination threshold (Q75), this embodiment identifies it as a synergy corridor type. The essential function of the synergy corridor type is to capture those strip-shaped spaces that still maintain high-intensity functional coupling and element exchange at the administrative boundaries. In specific calculations, if the synergy index of a cross-boundary macro-unit reaches 3.18, significantly exceeding the overall Q75 determination threshold of 2.45, it is confirmed as a synergy corridor type. The spatial distribution map output by this diagnostic result shows that synergy corridor type units are distributed in a continuous strip along the administrative boundaries, breaking the statistical obscuring of the regional integration pattern by traditional administrative containers.

[0047] For regions primarily serving ecological security and baseline regulation functions, this embodiment employs a third judgment rule. When the constraint index exceeds the corresponding judgment threshold (Q75) and the synergy index is lower than the empirical median judgment benchmark (Q50), this embodiment identifies the unit as a constrained ecological barrier type. The technical connotation of the constrained ecological barrier type refers to a region that mainly maintains system order through macro-constraint mechanisms, lacking explicit cross-dimensional functional synergy. In quantitative implementation, if a macro-unit located in the western part of the region has a constraint index of 4.25 (higher than the Q75 threshold of 2.10), while its synergy index is only 1.20 (lower than the Q50 median of 1.50), then the classification label of constrained ecological barrier type is output. Subsequently, this embodiment identifies the remaining macro-level grid units that do not fall under any of the above rule conditions as transitional types, used to characterize background spaces whose functional characteristics are not yet clear or are in a dynamic evolution process.

[0048] After completing the above logical rights confirmation, this embodiment uses a GIS topology mapping engine to overlay the identified governance configuration types with their corresponding geographic coordinates and administrative boundary vector layers, outputting the final spatial distribution map of cross-boundary governance configurations. To ensure the rigor of the rights confirmation results, this embodiment simultaneously performs robustness checks, including performing 1000 Bootstrap resampling operations on the synergy benchmark value and fine-tuning the judgment threshold within the empirical distribution range of 70% to 80% (Q70-Q80). Test data shows that even within the threshold fluctuation range, the consistency rate of the identification results remains as high as 96.7%. The spatial distribution map finally output by this embodiment contains 4 polarization core judgment records and 7 synergy corridor judgment records, providing a complete and verifiable chain of evidence for accurately identifying implicit functional spaces that cross administrative boundaries and their differentiated governance configurations.

[0049] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0050] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for diagnosing the spatial function coordination of a cross-border urban area based on a H3 hexagonal grid, characterized in that, include: Acquire multi-source geospatial data of the study area and map it to a raster grid of preset resolution to construct a basic feature layer; Based on the aforementioned basic feature layer, a three-level nested H3 hexagonal mesh system comprising micro-level L1, meso-level L2, and macro-level L3 is constructed, and sub-unit coverage thresholds are set for the meso-level L2 and the macro-level L3 to perform boundary expansion control. Within the micro-level L1 grid cell, activity indicators and biophysical variables from the multi-source geospatial data are integrated to calculate the intensity of production, living and ecological components, and component normalization is performed to obtain the component share vector. Along the scale chain from the micro level L1 to the meso level L2 to the macro level L3, feature aggregation is performed on the component share vector, and the functional balance features, spatial stability features, and centrality distribution features of each grid cell are extracted based on the aggregation results to establish a multi-scale spatial feature database. Based on the multi-scale spatial feature database, a set of cross-scale emergence indicators is calculated to characterize the deviation of the macro-level L3 from the meso-level L2. The set of cross-scale emergence indicators includes: a synergy index calculated based on the sub-unit quartile deviation, a constraint index calculated based on the ratio of macro-level balance to meso-level heterogeneity, an amplification index calculated based on the centrality Gini coefficient, and a structural integration index calculated based on the information entropy gain factor. The empirical distribution quantiles of the cross-scale emergence index set are extracted to obtain the judgment threshold. The judgment threshold is then used to perform logical weighting on each macro-level L3 grid cell to identify the governance configuration type of each cell and output a spatial distribution map.

2. The H3 hexagonal grid-based cross-border urban area spatial function coordination diagnostic method according to claim 1, characterized in that, The process of acquiring multi-source geospatial data of the study area and mapping it to a raster grid of a preset resolution to construct a basic feature layer includes: Acquire the multi-source geospatial data, including point of interest data, land cover data, nighttime light remote sensing data, population spatialization data, vegetation net primary productivity data, evapotranspiration data, topographic data, and statistical data. The interest point data was filtered by category to extract the financial and business theme group, the technological innovation theme group, the life service theme group, and the residential theme group; Each of the aforementioned subject groups and the remaining multi-source geospatial data are mapped to a raster grid of the preset resolution and subjected to gridding assignment processing to construct the basic feature layer.

3. The H3 hexagonal grid-based cross-border urban area spatial function coordination diagnostic method according to claim 1, characterized in that, The construction of a three-level nested H3 hexagonal mesh system based on the aforementioned basic feature layer, comprising micro-level L1, meso-level L2, and macro-level L3, includes: Extract unit feature values ​​from the basic feature layer and construct the micro-level L1 using H3 resolution 7-level grid cells; The mesoscopic L2 was constructed using H3 resolution, level 5 mesh cells; The macroscopic level L3 is constructed using H3 resolution level 4 grid cells, and the microscopic level L1, the mesoscopic level L2, and the macroscopic level L3 are nested sequentially in spatial topology.

4. The H3 hexagonal grid-based cross-border urban area spatial function coordination diagnostic method according to claim 1, characterized in that, Within the micro-level L1 grid cell, activity indicators and biophysical variables from the multi-source geospatial data are integrated to calculate the intensity of production, living, and ecological components. Component normalization is then performed to obtain a component share vector, including: Data layers representing production and living activities are extracted from the basic feature layers as activity indicators, and data layers representing land cover and ecological functions are extracted as biophysical variables. The intensity of the production component and the intensity of the living component are calculated based on the activity indicators, and the intensity of the ecological component is calculated based on the biophysical variables; The production component intensity, living component intensity, and ecological component intensity within each micro-level L1 grid cell are subjected to minimum-maximum normalization and component closure normalization to obtain the component share vector that satisfies the condition that the sum of the proportions of each component is a preset constant.

5. The H3 hexagonal grid-based cross-border urban area spatial function coordination diagnostic method according to claim 1, characterized in that, The step of extracting functional balance features, spatial stability features, and centrality distribution features of grid cells at each level based on the aggregation results to establish a multi-scale spatial feature database includes: Based on the aggregation result of the component share vector at the mesoscopic level L2, the functional balance index and spatial fragmentation index are calculated to obtain the functional balance characteristics. Based on the aggregation result of the component share vector at the macroscopic level L3, the structural stability field is extracted to obtain the spatial stability feature, and the gravitational centrality distribution feature is extracted to obtain the centrality distribution feature, so as to integrate and establish the multi-scale spatial feature database.

6. The H3 hexagonal grid-based cross-border urban area spatial function coordination diagnostic method according to claim 1, characterized in that, The calculation process of the synergy index based on the sub-unit quartile deviation includes: For each of the macroscopic-level L3 grid cells, the coupling values ​​of the production-living dimension, production-ecology dimension, and living-ecology dimension in the multi-scale spatial feature database are extracted respectively. The distribution quartiles and interquartile ranges of the corresponding meso-level L2 grid cells within each macro-level L3 grid cell are obtained as the sub-cell quartile deviations. The coupling values ​​of each dimension are compared with the corresponding quartiles and interquartile ranges of the distribution, and the maximum score after the comparison is extracted as the synergy index.

7. The H3 hexagonal grid-based cross-border urban area spatial function coordination diagnostic method according to claim 1, characterized in that, The calculation process of the constraint index based on the ratio of macroscopic equilibrium to mesoscopic heterogeneity includes: The macroscopic balance is calculated based on the average component share of each of the corresponding mesoscopic L2 grid units within each of the macroscopic L3 grid units. The mesoscopic heterogeneity is calculated based on the standard deviation of the component proportions of each corresponding mesoscopic L2 grid cell; When the macro-level balance is greater than the average level of the corresponding sub-unit group, the ratio of the macro-level balance to the meso-level heterogeneity is calculated to obtain the constraint index.

8. The method for diagnosing spatial function coordination in cross-border urban areas based on H3 hexagonal grids according to claim 1, characterized in that, The calculation process of the magnification index based on the centrality Gini coefficient includes: Network centrality is calculated based on the comprehensive functional strength and spatial connectivity of each meso-level L2 grid cell. The centrality Gini coefficient is calculated based on the network centrality of each corresponding meso-level L2 grid cell within the macro-level L3 grid cell; The amplification index is obtained by multiplying the centrality Gini coefficient with the average network centrality relative deviation of the preset high-resolution sub-unit.

9. The method for diagnosing spatial function coordination in cross-border urban areas based on H3 hexagonal grids according to claim 1, characterized in that, The calculation process of the structural integration index based on the information entropy gain factor includes: The spatial stability characteristics of the macroscopic L3 grid cell are obtained, as well as the information entropy gain factor calculated based on the discretized mesoscopic configuration state; Calculate the cross-scale parent-child consistency term for the degree of alignment between the macroscopic-level L3 mesh cell and its internal dominant sub-state contour; The structural integration index is obtained by performing a product aggregation operation on the spatial stability feature, the information entropy gain factor, and the cross-scale parent-child consistency term.

10. The method for cross-border urban area spatial function coordination diagnosis based on H3 hexagonal grid according to claim 1, characterized in that, The step of using the determination threshold to perform logical weighting on each of the macro-level L3 grid cells to identify the governance configuration type of each cell includes: When the magnification index and the structural integration index of a certain macroscopic L3 grid cell both exceed the corresponding judgment threshold, the cell is identified as a polarization core type. When the synergy index exceeds the corresponding judgment threshold, it is identified as a synergy corridor type; When the constraint index exceeds the corresponding judgment threshold and the synergy index is lower than the empirical median judgment benchmark, it is identified as a constrained ecological barrier type. The macroscopic-level L3 mesh cells that do not fall under any of the above rule conditions are identified as transitional. The governance configuration types include: the polarization core type, the collaborative corridor type, the constrained ecological barrier type, and the transition type.

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