Method for constructing a multi-dimensional indicator system for urban underlying surfaces

Abstract

The present invention discloses a method for constructing a multidimensional indicator system for urban underlying surfaces, comprising the following steps: S1. collecting data, constructing an underlying surface database with high spatiotemporal resolution, and obtaining annual LUCC data within the study period; S2. dividing the sub-basin grid based on the long-term annual LUCC data, determining the threshold of the patch area, analyzing the spatiotemporal evolution characteristics of the underlying surface within a given grid, and constructing a characterization index; S3. studying the spatiotemporal evolution characteristics of multiple dimensional indicators and constructing a candidate library of underlying surface characteristic indicators; S4. constructing an underlying surface multidimensional characterization indicator system; S5. utilizing data dimensionality reduction technology to process the data in the underlying surface multidimensional characterization indicator system and construct an underlying surface characterization index. The present invention uses a more comprehensive and accurate characterization system to fully express the attributes, geometry, and spatial distribution characteristics of complex underlying surfaces, helping researchers and managers better address issues related to integrated basin management under changing environments.

Description

Technical Field

[0001] The present invention belongs to the technical field of urban underlying surface representation, and particularly relates to a method for constructing a multi-dimensional indicator system for urban underlying surfaces. Background Art

[0002] Underlying surface change is one of the fundamental drivers of the evolution of Earth's various spheres, and its spatial pattern is primarily influenced by topography and the distribution of land use patches. In the 1990s, the LUCC study, jointly initiated by the IGBP and the IHDP, analyzed the changing patterns of LUCC using area as the primary characteristic indicator and employing field experiments and statistical analysis.

[0003] Entering the 21st century, with the intensification of human activities, the spatial pattern characteristics of the underlying surface have received increasing attention. Researchers have proposed a variety of quantitative analysis methods, such as remote sensing technology combined with GIS spatial analysis, landscape index assessment, spatial statistics, and model simulation, to study the spatial pattern characteristics of the underlying surface and its environmental impacts, revealing the combined effects of land use change, urbanization, ecosystem services, and climate change on surface processes.

[0004] However, previous studies have often focused on a single or a few indicators, potentially overlooking the inherent connections between underlying surface characteristics and their combined effects on environmental processes. This has hindered the understanding of watershed runoff and its integrated management. Therefore, it is necessary to conduct multidimensional characterization and methodological research on complex underlying surfaces. This paper comprehensively considers underlying surface characteristics from three dimensions: attribute characteristics, geometric characteristics, and spatiotemporal distribution changes. This approach can more accurately understand and predict the potential impacts of underlying surface changes on the environment, providing a scientific basis for watershed runoff, urban planning, and environmental management. Summary of the Invention

[0005] In order to solve the above problems, the present invention proposes a method for constructing a multi-dimensional indicator system for urban underlying surfaces.

[0006] The method for constructing a multi-dimensional indicator system for urban underlying surfaces of the present invention comprises the following steps:

[0007] S1. Collect data, build a high-temporal and spatial resolution underlying surface database, and obtain annual LUCC data for the study period: Conduct research on multi-source remote sensing image data fusion algorithms for complex underlying surfaces in watersheds containing urban areas; utilize fused high-precision, long-term remote sensing images to extract and analyze base-year land use coverage / type (LUCC) data based on deep learning; collect DEM, precipitation, road distribution, population distribution, and other data to establish a natural-social environment auxiliary dataset, and study methods for constructing a dynamic development matrix of the underlying surface spatial pattern; based on the base-year LUCC data and the dynamic development matrix, study interpolation and reconstruction algorithms for missing year land use data to obtain annual LUCC data for the study period;

[0008] S2. Based on long-term annual LUCC data, sub-watershed grids are divided and patch area thresholds are determined. The spatiotemporal evolution characteristics of the underlying surface within a given grid are analyzed and characterization indicators are constructed. Research is conducted on sub-watershed grid division and patch area threshold determination methods by combining high-precision long-term annual LUCC data with DEM data. The spatiotemporal transformation trajectories of land use patches within a given grid are analyzed to study the spatiotemporal evolution characteristics of the underlying surface. Comprehensive and accurate characterization methods for complex underlying surface spatial patterns are developed from multiple dimensions, including the "attribute characteristics," "geometric properties," and "spatial distribution" of underlying surface patches.

[0009] S3. Study the spatiotemporal evolution of multiple dimensional indicators and construct a candidate library of underlying surface characteristic indicators: Based on sub-watershed LUCC data, analyze scale effects, set appropriate patch area thresholds, and use a combination of landscape pattern analysis (LSA), morphological spatial pattern analysis (MSPA), and spatial trajectory analysis to study the spatiotemporal evolution of multiple dimensional indicators, including "attribute characteristics" (ATtribute) of underlying surface patch type, topographic index, NDVI index, and NDBI index; "geometric characteristics" (GEometric) such as area and shape; and "spatial distribution" (DIstribution) such as connectivity and dispersion. A candidate library of underlying surface characteristic indicators will be constructed.

[0010] S4. Construct a multi-dimensional underlying surface characterization indicator system: Based on the completion of data collection and analysis of spatiotemporal evolution characteristics, a comprehensive multi-dimensional underlying surface characterization indicator system will be constructed. This system will cover key dimensions such as attribute characteristics, geometric properties, and spatial distribution, and will use quantitative methods to assess the complexity of underlying surface characteristics. Specific steps include identifying key indicators for each dimension, assigning appropriate weights to these indicators, and developing a comprehensive scoring system that reflects the contribution of underlying surface characteristics in different dimensions.

[0011] S5. Use data dimensionality reduction technology to process the data in the underlying surface multidimensional characterization index system and construct the underlying surface characterization index: After establishing the multidimensional characterization index system, use data dimensionality reduction techniques, such as principal component analysis (PCA) and linear discriminant analysis (LDA), to process the data in the index system; the purpose is to identify the most representative and independent key indicators from a large number of original indicators. These indicators can reflect the information of the underlying surface characteristics to the greatest extent while reducing the complexity of the data; through the evaluation of correlation and independence, the most critical indicators for the characterization of the underlying surface characteristics are selected, and finally a multidimensional characterization index system for complex underlying surfaces is constructed; at the same time, the hierarchical analysis method is used to calculate an indicator that comprehensively reflects the characteristics of the complex underlying surface to simplify the expression of the underlying surface situation.

[0012] The S1 step obtains the annual LUCC data for the study period. The specific process is to fuse multi-source remote sensing image data of the complex underlying surface of the watershed containing the urban area; extract and calculate the land use coverage / type (LUCC) data using the fused high-precision long-term remote sensing image; then establish a natural-social environment auxiliary data set to study the dynamic development matrix of the underlying surface spatial pattern, and finally obtain the annual LUCC data for the study period.

[0013] The multiple dimensional indicators in S3 include attribute features, geometric features and spatial distribution.

[0014] The steps of constructing the underlying surface multi-dimensional characterization index system in S4 are: determining the key indicators of each dimensional indicator, assigning appropriate weights to these key indicators, and developing a comprehensive scoring system.

[0015] The key characteristic indicators of each dimension in S4 are: attribute characteristics include terrain attributes, soil attributes, vegetation attributes, physical attributes and surface cover attributes; geometric characteristics include the area of ​​various land use types, the number of patches, the perimeter of patches and the complexity of patch shapes; spatial distribution includes connectivity, dispersion, aggregation and diversity.

[0016] In the S5, data dimensionality reduction technology is used to process the data in the multi-dimensional characterization index system of the underlying surface. The purpose is to identify the most representative and independent key indicators from a large number of original indicators through the evaluation of correlation and independence, so as to provide a solid data foundation for the final constructed characterization index.

[0017] The steps of S5 include:

[0018] S501. Data collection and preprocessing;

[0019] S502. Data standardization;

[0020] S503. Correlation analysis;

[0021] S504. Data dimensionality reduction processing;

[0022] S505. Feature index dimensionality reduction screening and analysis.

[0023] The indicators in the multi-dimensional characterization index system of the underlying surface are divided into primary indicators, secondary indicators and tertiary indicators. The primary indicators refer to attribute characteristics, geometric properties and spatial distribution. Each primary indicator has corresponding multiple secondary indicators, and each secondary indicator also has corresponding multiple tertiary indicators.

[0024] The underlying surface characterization index includes the primary index, the secondary index and the underlying surface comprehensive index.

[0025] The three first-level indicator indices are expressed as follows:

[0026] Underlying surface properties:

[0027] Among them, A T Indicates the overall score of the underlying surface attribute characteristics, n T is the number of secondary indicators under the attribute characteristics, w Ti is the weight of the secondary index i in the attribute feature, S Ti is the standardized value of the secondary indicator i;

[0028] Geometric characteristics of the underlying surface:

[0029] Among them, A G Indicates the overall score of the underlying surface geometric characteristics, n G is the number of secondary indicators under geometric characteristics, w Gj is the weight of the secondary index j in the geometric characteristics, S Gj is the standardized value of the secondary indicator j;

[0030] Spatial distribution of underlying surface:

[0031] Among them, A D Indicates the overall score of the underlying surface geometric characteristics, n D is the number of secondary indicators under spatial distribution, w Dk is the weight of the secondary index k in the spatial distribution, S Dk is the standardized value of the secondary indicator k.

[0032] The scores of the three first-level indicators are integrated to obtain a comprehensive underlying surface index:

[0033] CIS=ω A ×AT+ω G ×GE+ωD ×DI

[0034] Among them, CIS represents the comprehensive index of the underlying surface of the study area, which comprehensively reflects the characteristics of the attribute characteristics, geometric characteristics, and spatial distribution of the basin; AT, GE, and DI are the values ​​of the three first-level indicators of underlying surface attribute characteristics, geometric characteristics, and spatial distribution, respectively. A 、ω G and ω D They are the weights of underlying surface attribute characteristics, geometric properties and spatial distribution.

[0035] The beneficial effects of the present invention are:

[0036] The present invention starts with analyzing the spatiotemporal evolution characteristics of the complex underlying surface in the watershed, and characterizes the characteristics of the complex underlying surface through three dimensions: "attribute characteristics", "geometric characteristics" and "spatial distribution". It is not limited to the traditional area representation and the representation of relative spatial relationships. The present invention will fully express the attributes, geometry and spatial distribution characteristics of the complex underlying surface through a more comprehensive and accurate representation system, which will help researchers and managers better cope with the integrated management of watersheds under a changing environment. DETAILED DESCRIPTION

[0037] This application targets complex underlying surfaces in watersheds containing urban areas, conducts research on multi-source remote sensing image data fusion algorithms, and constructs an underlying surface database with high spatiotemporal resolution; analyzes the spatiotemporal evolution characteristics of the underlying surface, comprehensively and accurately classifies the spatial pattern of the underlying surface according to different dimensions, and constructs characterization indicators; analyzes the correlation between variables and screens out relatively independent underlying surface characteristic indicators.

[0038] S1. Fuse multi-source remote sensing image data of complex underlying watersheds containing urban areas; extract and calculate land use coverage / type (LUCC) data using the fused high-precision long-term remote sensing images.

[0039] Based on high-precision long-term LUCC data, combined with DEM data, precipitation, road distribution, population distribution and other data in the study area, a natural-social environment auxiliary dataset was established. In particular, due to the diversity of data sources, there are inconsistencies in the format, spatiotemporal resolution (accuracy) and other aspects of different data. Therefore, when conducting analysis, it is necessary to first determine the basic unit of research (including time and space) and unify the multi-source data into the determined basic unit. Specifically:

[0040] (1) Remote sensing image data

[0041] High-resolution satellite data (GF1-GF4) from the study area were collected and calibrated and fused with long-term remote sensing images (LandSat and MODIS) collected using the Pixel Information Expert Engine (PIE-Engine) or Google Earth Engine (GEE) platforms. Land use and land cover data that met the requirements were extracted using algorithms such as Classification and Regression Tree (CART) and Random Forest (RF) to obtain a land use and land cover (LUCC) dataset.

[0042] We collected long-term, high-resolution precipitation and evaporation datasets (such as ERA-5 and GPM), road datasets (OpenGMS), digital elevation data (DEM), and social and environmental auxiliary datasets, including population datasets, from the study area. Based on the obtained baseline LUCC dataset, we used the Ordinary Least Squares Residuals-based Moving SUM (OLS-MOSUM) algorithm to identify inter-pixel changes and construct a dynamic development matrix of LUCC suitability for each baseline year. Based on this dynamic development matrix, we used linear regression (LR) and convolutional neural network (CNN) algorithms to develop an interpolation and reconstruction algorithm for land use data in missing years, obtaining annual LUCC data for the study period.

[0043] (2) Precipitation and runoff data

[0044] The data in the collected precipitation raster dataset are calibrated using the daily precipitation data from the measured sites, and the precipitation data in NC format are organized into binary array format data that is consistent with the runoff data.

[0045] (3) DEM elevation data

[0046] The collected DEM data were combined with measured topography and river network data to delineate sub-basins using PyFlwDir. Taking into account factors such as the area and socioeconomic status of each sub-basin, sub-basins were appropriately merged to form basic research units, ensuring that the division of basic units took into account both ecological significance and statistical rationality.

[0047] (4) Social Factors Dataset

[0048] The collected transportation network data such as railways and roads are processed into raster data using the Euclidean distance tool; the population density data are processed using the raster calculator to remove null values.

[0049] S2. Combine high-precision, long-term, annual LUCC data with DEM data to study sub-watershed gridding and patch area threshold determination methods; analyze the spatiotemporal transformation trajectories of each land use patch within a given grid and study the spatiotemporal evolution characteristics of the underlying surface; and study comprehensive and accurate characterization methods for the spatial pattern of complex underlying surfaces from multiple dimensions such as the "attribute characteristics," "geometric properties," and "spatial distribution" of underlying surface patches.

[0050] S3. Based on the LUCC data of the sub-watershed, we analyzed the scale effect and set an appropriate patch area threshold. Using a combination of landscape pattern analysis, morphological spatial pattern analysis, and spatial trajectory analysis, we studied the spatiotemporal evolution of multi-dimensional indicators such as underlying surface patch type, topographic index, NDVI index, and NDBI index, as well as geometric characteristics such as area and shape, and spatial distribution such as connectivity and dispersion. We also constructed a library of candidate underlying surface characteristic indicators.

[0051] S4. Based on the completion of data collection and analysis of spatiotemporal evolution characteristics, a comprehensive multi-dimensional underlying surface characterization index system will be constructed. This system will cover key dimensions such as attribute characteristics, geometric properties, and spatial distribution, and will use quantitative methods to assess the complexity of underlying surface characteristics. Specific operations include: determining key indicators for each dimension, assigning appropriate weights to these indicators, and developing a comprehensive scoring system that can reflect the contribution of underlying surface characteristics in different dimensions. The specific calculation formula for the quantitative characterization index is as follows:

[0052] 1. Attribute characteristics

[0053] (1) Terrain attributes

[0054] 1) Ruggedness: The standard deviation of terrain elevation changes, reflecting the severity of terrain changes.

[0055]

[0056] 2) Slope:

[0057]

[0058] (2) Soil properties

[0059] 1) Soil fertility: Soil fertility, pH value, organic matter content, etc. can be determined through laboratory testing of soil samples.

[0060] 2) Soil Moisture Content:

[0061]

[0062] 3) Soil permeability (Infiltration Rate):

[0063] f=K×(P-Suction)

[0064] Where K is the saturated hydraulic conductivity of the soil, P is the applied pressure, and Suction is the soil suction.

[0065] (3) Vegetation attributes

[0066] 1) Vegetation Cover:

[0067]

[0068] 2) Leaf Area Index (LAI):

[0069]

[0070] 3) Vegetation index (such as Normalized Difference Vegetation Index, NDVI):

[0071]

[0072] Among them, NIR is the reflectivity of the near-infrared band, and R is the reflectivity of the visible light red band.

[0073] (4) Physical properties

[0074] 1) Terrain Roughness Index (TRI): A commonly used method to quantify surface roughness, which can be calculated using the following formula:

[0075]

[0076] Among them, the standard deviation (SD) is the standard deviation of the deviation between the elevation value of each point on the DEM and its average elevation value, which can be used to measure the roughness of the surface.

[0077] 2) Heat capacity refers to the amount of heat absorbed or released per unit mass of a substance within a unit temperature range. In some cases, empirical models or formulas can be used to estimate the surface heat capacity. For example, the following simplified formula can be used to estimate the heat capacity of soil:

[0078] C=(1-ω)C solid +ωC water

[0079] Where C is the heat capacity of the soil, ω is the moisture content of the soil, and C solidis the heat capacity of the soil solid phase, C water is the heat capacity of water.

[0080] (5) Surface cover properties

[0081] The relationship between artificial and natural surfaces in a watershed can be expressed by the Impervious Surface Area Ratio:

[0082]

[0083] 2. Geometric features

[0084] (1) Area, number of patches, and perimeter of patches of various land use types.

[0085] Spatial analysis tools of GIS software can be used to calculate the number, area, perimeter, etc. of patches.

[0086] (2) Complexity of patch shape

[0087] 1) Perimeter-Area Fractal Dimension (PAFRAC):

[0088]

[0089] Where P is the perimeter of the patch and A is the area of ​​the patch.

[0090] 2) Landscape Shape Index (LSI):

[0091] LSI using a square as a reference:

[0092]

[0093] Among them, E represents the total length of all patch boundaries in the landscape, and A represents the total area of ​​the landscape. This index is used to measure the irregularity of patch shape. The larger the value, the more complex the patch shape and the more irregular it tends to be.

[0094] LSI using a circle as a reference:

[0095]

[0096] The meanings of E and A are the same as above, but a circle is used as a reference to calculate the degree of deviation of the patch shape from the circle.

[0097] 3) Area-weighted mean shape index (AWMSI), calculated as follows:

[0098]

[0099] Among them, A i is the area of ​​the ith patch, LSI i is the shape index of the ith patch (usually LSI, landscape shape index), A total is the total area of ​​the landscape.

[0100] 4) Shape Complexity Index (SCI), the calculation formula can be expressed as:

[0101]

[0102] Where E is the actual perimeter of the patch, P min is the minimum perimeter of a regular shape (usually a circle or square) with the same area. For a circle, For a square, Where A is the area of ​​the patch.

[0103] 3. Spatial distribution characteristics

[0104] (1) Connectivity

[0105] 1) Integral index of connectivity (IIC):

[0106]

[0107] Where n is the total number of patches in the landscape, a i and a j are the areas of patch i and patch j respectively, nl ij is the number of connections between patch i and patch j, A L is the area of ​​the background landscape, 0≤IIC≤l, IIC of 0 means there is no connection between habitat patches, and IIC of 1 means the entire landscape is a habitat patch.

[0108] 2) Probability of connectivity (PC):

[0109]

[0110] Among them, P ij * is the maximum probability of species spreading directly between patches i and j, 0<PC<1.

[0111] 4) Importance Value of Patches (dPC): This measures the importance of patches in maintaining landscape connectivity by calculating the impact of patch removal on the overall connectivity index.

[0112] dPC=(PC-PC remove ) / PC×100%

[0113] Among them, PC remove It is the overall index value of the remaining patches after removing a single patch. dPC refers to the change in PC after a patch is removed to measure the importance of the patch in maintaining landscape connectivity.

[0114] 5) Connectivity (CONNECT):

[0115]

[0116] Among them, c ijk is the connection status of patches j and k related to patch type i within the critical distance, n i is the number of patches of type i in the landscape, and connectivity is equal to the number of nodes between all patches of a certain type (when patches j and k are connected, c ijk =1; otherwise, c ijk =0) divided by the number of all possible nodes, the range of the connectivity index is [0, 100]. The higher the connectivity of the patch, the larger the connectivity index.

[0117] 6) CONTAG is an important landscape ecology indicator used to measure the aggregation or extension trend of different patch types in the landscape.

[0118]

[0119] Where Pi is the percentage of area occupied by type i patches; gik is the number of adjacent type i patches and type k patches; and m is the total number of patch types in the landscape.

[0120] 7) Spatial Autocorrelation Index: This index measures the degree of spatial connectivity between similar values ​​in spatial data and can indirectly reflect spatial diversity. In global correlation analysis, the most commonly used statistic is Global Moran's Index, which is mainly used to describe the average degree of correlation between all spatial units in the entire region and the surrounding areas. The calculation formula is as follows:

[0121]

[0122] in, n is the total number of spatial units, y i and y j Represent the attribute values ​​of the i-th spatial unit and the j-th spatial unit respectively, is the mean of all spatial unit attribute values, w ij is the spatial weight value.

[0123] (2) Discreteness

[0124] 1) Patch density (PD): The number of patches per unit area, reflecting the degree of landscape fragmentation.

[0125] 2) Edge density is an indicator used to measure the ratio of the total length of patch edges in a landscape to the total area of ​​the landscape. It reflects the frequency of contact between different patch types in the landscape. Edge density can be expressed as follows:

[0126]

[0127] Here, “total edge length” refers to the cumulative length of all patch edges in the landscape, while “total landscape area” refers to the total area of ​​the study area.

[0128] 3) Landscape Separation Index (Si): This index is used to measure the degree of separation between patches of the same type in the landscape. The larger the value, the higher the degree of separation between patches. The calculation formula is:

[0129]

[0130] Where A is the total area of ​​the study area, A i is the patch area of ​​landscape type i.

[0131] (3) Aggregation

[0132] 1) Cohesion Index is an indicator used in landscape ecology to measure landscape connectivity. It helps to understand the degree of connection between different landscape segments. The formula for calculating the cohesion index is as follows:

[0133]

[0134] Among them, a ij represents the area of ​​the jth patch in the i-th type of landscape, P ij represents the perimeter of the jth patch in the i-th type of landscape, A is the area of ​​the entire landscape, and n is the number of patches in landscape type i.

[0135] 2) LandscapeAggregation Index (AI): The aggregation index is measured by calculating the degree of connectivity within the patch type, which takes into account the compactness of the distribution of patches within the same landscape type.

[0136]

[0137] Where n is the total number of patches of a certain type in the landscape, N i It is the number of patches of the same type that share a common boundary with the i-th patch. The AI ​​value usually ranges from -1 to 1. Positive values ​​indicate that patches tend to be clustered, negative values ​​indicate that patches are more dispersed, and values ​​close to 0 indicate that patches are randomly distributed.

[0138] (4) Diversity

[0139] 1) Shannon's Diversity Index (SHDI):

[0140]

[0141] Among them, Pi is the proportion of the area of ​​the i-th type of patch in the landscape to the total area, n is the total number of patch types, and the value of the Shannon diversity index ranges from 0 to infinity. The larger the value, the higher the diversity of the system. When all types in the landscape appear in the same proportion, the diversity index reaches its maximum value. If a certain type dominates the landscape and other types are rare or absent, then the diversity index will decrease.

[0142] 2) Shannon's Evenness Index (SHEI):

[0143]

[0144] Where SHEI is the Shannon Evenness Index, SHDI is the Shannon Diversity Index, and S is the total number of different patch types in the landscape. The Shannon Evenness Index ranges from 0 to 1, with values ​​closer to 1 indicating a more even distribution of patch types in the landscape, and values ​​closer to 0 indicating a more uneven distribution. If all patch types are evenly distributed, meaning that each type occupies an equal proportion of the area, the SHEI will reach its maximum value of 1. If one patch type dominates, while other types are rare or absent, the SHEI will be close to 0.

[0145] S5. After establishing a database of candidate multidimensional characterization indicators, data within the indicator system is processed using data dimensionality reduction techniques, such as principal component analysis (PCA) and linear discriminant analysis (LDA). The goal is to identify the most representative and independent key indicators from the large number of raw indicators. These indicators can best reflect the underlying surface characteristics while reducing data complexity. By evaluating correlation and independence, the indicators that are most critical to characterizing the underlying surface characteristics are selected, providing a solid data foundation for the final constructed characterization index.

[0146] Specifically, you can follow the steps below:

[0147] (1) Data collection and preprocessing: Data cleaning is performed on the collected data of all underlying surface characteristic indicators, and missing values ​​and outliers are processed.

[0148] (2) Data standardization: Since methods such as PCA are affected by the data scale, the data needs to be standardized so that each indicator has a standard normal distribution with a mean of 0 and a standard deviation of 1.

[0149] (3) Correlation analysis: Before dimensionality reduction, correlation analysis is performed, such as calculating the Pearson correlation coefficient matrix to identify highly correlated variable pairs.

[0150] (4) Data dimensionality reduction processing:

[0151] 1) Principal Component Analysis (PCA): Apply PCA to reduce the dimensionality of a dataset while preserving most of the variability in the dataset. Interpret the principal components to see which original variables are highly correlated with the principal components.

[0152] 2) Linear Discriminant Analysis (LDA): If your dataset has multiple classes, you can use LDA to find the best dimensionality reduction directions that preserve the variability of the data while also considering class separability. LDA generates discriminant coefficients, which can be used to select the most discriminative features.

[0153] 3) Local Linear Embedding (LLE): LLE is a nonlinear dimensionality reduction method based on local preservation of neighboring points. LLE is applied to discover the intrinsic structure of data and identify relatively independent variables in low-dimensional space.

[0154] (5) Feature index dimensionality reduction screening and analysis: Analyze the dimensionality reduction results of methods such as PCA, LDA, and LLE to see which original variables maintain a high degree of independence in the space after dimensionality reduction.

[0155] 1) Feature Screening: Based on the results of the dimensionality reduction method, select variables that contribute significantly to the reduced dimensionality space and are independent of each other. Consider the variables’ explanatory power, stability, and relevance to the research objective.

[0156] 2) Model validation: Use leave-one-out cross-validation (LOOCV) or other validation methods to assess the robustness of the selected variable model.

[0157] 3) Interpretation and application of results: Interpret the dimensionality reduction results and determine which underlying surface characteristic indicators are relatively independent and can be used for further analysis or model construction.

[0158] In practical applications, the results of different dimensionality reduction methods can be comprehensively considered based on professional knowledge and research objectives. Furthermore, the choice of dimensionality reduction method should be based on the characteristics of the data and the analysis objectives. For example, if class distinction in the dataset is important, LDA may be a better choice; if the intrinsic structure of the data is of interest, LLE may be more appropriate; and PCA is often used for exploratory data analysis to identify the principal components in the data.

[0159] According to the provided indicator system table (such as Table 1), the indicators in the underlying surface multidimensional characterization indicator system are divided into first-level indicators, second-level indicators and third-level indicators. The first-level indicators refer to attribute characteristics, geometric properties and spatial distribution. Each first-level indicator has corresponding multiple second-level indicators, and each second-level indicator also has corresponding multiple third-level indicators.

[0160] Furthermore, the first-level indicators, their corresponding second-level indicators, and their third-level indicators are integrated, weights are assigned to the third-level indicators, and the attribute characteristics, geometric characteristics, and spatial distribution of the underlying surface are linearly expressed in sequence. Assuming that each third-level indicator has been assigned a weight through methods such as data standardization, PCA, and expert scoring, it can reasonably reflect the importance of each indicator in the comprehensive evaluation.

[0161] 1. Secondary indicators

[0162] For each secondary indicator under the primary indicator, we can calculate it according to the following formula:

[0163]

[0164] in, represents the comprehensive score of the secondary indicators under the primary indicator k, n k is the number of third-level indicators under the first-level indicator k, w ki is the weight of the third-level indicator i in the first-level indicator k, N ki is the standardized value of the third-level indicator i.

[0165] 2. Primary indicators

[0166] (1) Attribute characteristics of underlying surface (ATtribute):

[0167]

[0168] Among them, A T Indicates the overall score of the underlying surface attribute characteristics, n T is the number of secondary indicators under the attribute characteristics, w Ti is the weight of the secondary index i in the attribute feature, s Ti is the standardized value of the secondary indicator i.

[0169] (2) Geometric characteristics of the underlying surface:

[0170]

[0171] Among them, A G Indicates the overall score of the underlying surface geometric characteristics, n G is the number of secondary indicators under geometric characteristics, w Gi is the weight of the secondary index j in the geometric characteristics, s Gi is the standardized value of the secondary indicator j.

[0172] (3) Spatial distribution of underlying surface (Dlstribution):

[0173]

[0174] Among them, A D represents the overall score of the underlying surface spatial distribution, n D is the number of secondary indicators under spatial distribution, w Dk is the weight of the secondary index k in the spatial distribution, s Dk is the standardized value of the secondary indicator k.

[0175] (3) Comprehensive underlying surface index

[0176] Finally, we can combine the scores of the three first-level indicators to form a composite underlying surface index (Composite Index for Subsurface, CIS):

[0177] CIS=ω A ×AT+ω G ×GE+ω D ×DI

[0178] Among them, CIS represents the comprehensive index of the underlying surface of the study area, which comprehensively reflects the characteristics of the attribute characteristics, geometric characteristics, and spatial distribution of the basin; AT, GE, and DI are the values ​​of the three first-level indicators of underlying surface attribute characteristics, geometric characteristics, and spatial distribution, respectively. A 、ω G and ω D They are the weights of underlying surface attribute characteristics, geometric properties and spatial distribution.

[0179]

[0180]

[0181]

[0182] Although the above embodiments have been shown and described, it is understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. Changes, modifications, substitutions and variations of the above embodiments by those skilled in the art are all within the scope of protection of the present invention.

Claims

1. A method for constructing a multi-dimensional indicator system for urban underlying surfaces, characterized in that: The following steps are involved: S1. Collect data, build a high-temporal and spatial resolution underlying surface database, and obtain annual LUCC data for the study period; Based on the baseline year LUCC data and the dynamic development matrix, the interpolation and reconstruction algorithm of land use data in missing years was studied to obtain the annual LUCC data during the study period. S2. Based on the long-term annual LUCC data, divide the sub-basin grid and determine the threshold of patch area. Analyze the spatiotemporal evolution characteristics of the underlying surface within a given grid and construct characterization indicators. S3. Study the spatiotemporal evolution characteristics of multiple dimensional indicators and construct a candidate library of underlying surface characteristic indicators; the multiple dimensional indicators include attribute characteristics, geometric characteristics, and spatial distribution; S4. Construct a multi-dimensional characterization index system for the underlying surface. The indicators in the multi-dimensional characterization index system for the underlying surface are divided into primary, secondary and tertiary indicators. The primary indicators refer to attribute characteristics, geometric properties and spatial distribution. Each primary indicator has multiple corresponding secondary indicators, and each secondary indicator also has multiple corresponding tertiary indicators. The key characteristic indicators of the indicators of each dimension are: attribute characteristics include terrain attributes, soil attributes, vegetation attributes, physical attributes and surface cover attributes; geometric characteristics include the area of ​​various land use types, the number of patches, the perimeter of patches and the complexity of patch shapes; spatial distribution includes connectivity, dispersion, aggregation and diversity. S5. Use data dimensionality reduction technology to process the data in the underlying surface multi-dimensional characterization index system and construct an underlying surface characterization index; The steps of data dimensionality reduction technique include: S501. Data collection and preprocessing; S502. Data standardization; S503. Correlation analysis; S504. Data dimensionality reduction processing; S505. Dimensionality reduction screening and analysis of feature indicators.

2. The method for constructing a multi-dimensional indicator system for urban underlying surfaces according to claim 1 is characterized in that: The S1 obtains the annual LUCC data during the study period. The specific process is to fuse the multi-source remote sensing image data of the complex underlying surface of the watershed containing the urban area; and extract and calculate the land use cover / type (LUCC) data using the fused high-precision long-term remote sensing image. Then, a natural-social environment auxiliary data set was established to study the dynamic development matrix of the underlying surface spatial pattern, and finally obtain the annual LUCC data during the study period.

3. The method for constructing a multi-dimensional indicator system for urban underlying surfaces according to claim 1 is characterized in that: The steps of constructing the underlying surface multi-dimensional characterization index system in S4 are: determining the key indicators of each dimensional indicator, assigning appropriate weights to these key indicators, and developing a comprehensive scoring system.

4. The method for constructing a multi-dimensional indicator system for urban underlying surfaces according to claim 1 is characterized in that: In the S5, data dimensionality reduction technology is used to process the data in the multi-dimensional characterization index system of the underlying surface. The purpose is to identify the most representative and independent key indicators from a large number of original indicators through the evaluation of correlation and independence, so as to provide a solid data foundation for the final constructed characterization index.

5. The method for constructing a multi-dimensional indicator system for urban underlying surfaces according to claim 4 is characterized in that: The underlying surface characterization index includes the primary index, the secondary index and the underlying surface comprehensive index. The three first-level indicator indices are expressed as follows: Underlying surface properties: Among them, A T Indicates the overall score of the underlying surface attribute characteristics, n T is the number of secondary indicators under the attribute characteristics, w Ti is the weight of the secondary index i in the attribute feature, S Ti is the standardized value of the secondary indicator i; Geometric characteristics of the underlying surface: Among them, A G Indicates the overall score of the underlying surface geometric characteristics, n G is the number of secondary indicators under geometric characteristics, w Gj is the weight of the secondary index j in the geometric characteristics, S Gj is the standardized value of the secondary indicator j; Spatial distribution of underlying surface: Among them, A D Indicates the overall score of the underlying surface geometric characteristics, n D is the number of secondary indicators under spatial distribution, w Dk is the weight of the secondary index k in the spatial distribution, S Dk is the standardized value of the secondary indicator k.

6. The method for constructing a multi-dimensional indicator system for urban underlying surfaces according to claim 5 is characterized in that: The scores of the three first-level indexes are integrated to obtain a comprehensive underlying surface index: CIS=ω A ×AT+ω G ×GE+ω D ×DI Among them, CIS represents the comprehensive index of the underlying surface of the study area, which comprehensively reflects the characteristics of the attribute characteristics, geometric characteristics, and spatial distribution of the basin; AT, GE, and DI are the values ​​of the three first-level indicators of underlying surface attribute characteristics, geometric characteristics, and spatial distribution, respectively. A 、ω G and ω D They are the weights of underlying surface attribute characteristics, geometric properties and spatial distribution.

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