Blue-green uneven city network optimization method and system based on stepping stone system

Abstract

This application discloses a method for optimizing urban ecological networks with uneven blue-green distribution based on a stepping stone system, belonging to the field of ecological network optimization technology. The method includes acquiring ecological data of the study area, using morphological spatial pattern analysis, habitat quality assessment, and landscape connectivity techniques to identify the spatial distribution characteristics of ecological source areas and their uneven blue-green distribution, simulating multi-path ecological flows based on a circuit theory model, and using identified breakpoints that block species migration and obstacles that impede energy flow as stepping stones in areas lacking blue-green space to optimize the ecological network of cities with uneven blue-green distribution. This optimization significantly increases the number of ecological corridors and improves landscape connectivity. This application verifies the landscape connectivity optimization effect through repeated simulations, continuously repairing the breakpoints and obstacles as stepping stone systems for cities with uneven blue-green distribution, to obtain the final optimized ecological network, achieving the optimal selection of the ecological network.

Description

Technical Field

[0001] This application relates to the field of ecological network optimization technology, and more specifically, to an ecological network optimization method and system for blue-green uneven cities based on a stepping stone system. Background Technology

[0002] Rapid urbanization has led to a sharp decline and fragmentation of natural habitats, resulting in a significant degradation of ecosystem services. Blue-green spaces, as the foundation of blue-green infrastructure, refer to the spatial system composed of various open spaces such as water bodies and green areas. As an important component of urban ecosystems, they are crucial for maintaining regional biodiversity and providing ecosystem services. However, due to the influence of various factors such as regional natural geographical conditions, resource distribution characteristics, and local policies, many cities exhibit an uneven distribution of blue-green spaces, characterized by localized clustering or absence (referred to as "blue-green unevenness"). This can directly or indirectly affect landscape connectivity, thereby threatening species flow and the normal functioning of ecosystems. Therefore, optimizing the blue-green spatial pattern in such areas is of great significance for enhancing ecosystem services.

[0003] Constructing and optimizing ecological networks helps improve ecosystem service functions in areas with uneven blue-green distribution. Ecological networks consist of ecological source areas, ecological corridors, and ecological nodes. Among these, ecological source areas are crucial for maintaining ecosystem service functions and ensuring ecosystem integrity. Existing research typically considers nature reserves or natural and semi-natural habitats such as forests, grasslands, rivers, and lakes of a certain scale as ecological source areas. However, in cities with uneven blue-green distribution, the lack of suitable habitats and the difficulty in constructing new ones result in a lack of necessary foundational conditions for building ecological corridors.

[0004] The fragmented habitat patterns resulting from intensive and prolonged urban construction activities have left behind numerous small, numerous, clustered, and easily overlooked island-like habitat fragments. Among these, small-scale habitat groups with a degree of connectivity and heterogeneity can serve as stepping stones, facilitating species dispersal and gene exchange within the ecosystem. Supplementing stepping stones can effectively compensate for the loss of ecological source areas in a region, playing a crucial ecological connecting role in long-distance species dispersal, and also having practical significance in maintaining ecosystem service functions and promoting the sustainable management of natural resources. Stepping stones are a commonly used concept in ecology, referring to a series of small habitat patches or islands located between important habitat areas or source areas. Under conditions of habitat loss and fragmentation, stepping stones become important links between different habitat areas, serving as important transit points and resting places for species migrating within the region. Current research has confirmed the positive role of stepping stones in promoting species migration, protecting biodiversity, and enhancing landscape connectivity. Therefore, identifying and supplementing stepping stones is one of the effective ways to optimize ecological networks. Circuit theory models can accurately locate potential stepping stones that play a key role in the construction of long-distance ecological corridors. By simulating the current flow path of species diffusion, diffusion corridors of different widths can be identified, providing an effective prediction method for multi-path diffusion processes.

[0005] However, the existing technologies mentioned above still cannot solve the problem of the lack of local ecological source areas caused by the uneven geographical distribution of blue and green spaces in certain regions (referred to as "blue-green unevenness"), which makes it difficult to construct ecological networks. Summary of the Invention

[0006] To address at least one deficiency or improvement need in the existing technology, this invention provides an ecological network optimization method and system for cities with uneven blue-green spatial distribution based on the stepping stone system, in order to solve the problem of difficulty in constructing ecological networks in certain areas due to the lack of local ecological source areas caused by the uneven geographical distribution of blue-green space.

[0007] To achieve the above objectives, according to a first aspect of the present invention, a method for optimizing urban ecological networks with uneven blue-green distribution based on a stepping stone system is provided, the method comprising: S1, Obtain ecological data of the study area, including urban land use and cover data representing the area and distribution of blue-green space, urban boundary and ecological protection red line data, natural element datasets, and socio-economic data; S2, based on the ecological data, morphological spatial pattern analysis, habitat quality assessment, landscape connectivity evaluation and key recreation hotspot analysis are carried out in the study area, and the ecological protection red line range is used as the bottom line constraint to determine the geographical characteristics of "uneven blue-green" where the ecological source area and the blue-green space are locally enriched or missing. S3. The ecological corridor of the ecological source area is initially constructed using the corridor connection path model. The migration path of species in the ecological source area and ecological corridor is simulated by a landscape ecological network simulation tool based on circuit theory to generate a current map. The potential ecological corridors at different locations are determined based on the current intensity between the ecological source areas in the current map. S4. Based on the distribution location of the potential ecological corridors, determine the breakpoints of species migration paths, use obstacle detection tools to identify obstacles that disrupt energy flow within the ecological corridors, and use the identified breakpoints and obstacles as potential stepping stones to compensate for the lack of blue-green space, so as to initially optimize the ecological network with uneven spatial distribution. S5. Repeat the simulation process of steps S3 and S4 to continuously repair the fracture points and obstacle points as stepping stones for the missing areas of blue-green space. The optimization targets are the number of ecological corridors and the current intensity value in the current graph, to obtain the optimized ecological network.

[0008] Furthermore, step S1 of the above-mentioned ecological network optimization method also includes: The natural element dataset includes: digital height model data from geospatial data cloud, and normalized vegetation index; The socioeconomic data includes: urban points of interest data, road network data, nighttime light data, and population density data.

[0009] Furthermore, step S2 of the above-mentioned ecological network optimization method also includes: S201, using a morphological spatial pattern analysis model to identify the urban landscape pattern and extract the ecological core area; S202, Use the habitat quality assessment module to characterize the habitat type and habitat quality of the ecological function of the ecological core area; S203, based on the area effect, small ecological patches are screened and removed from the high habitat quality area of ​​the ecological core area, and landscape connectivity screening is performed on the ecological core area, and ecological protection red line areas are superimposed on the landscape connectivity screening. S204, taking into account the distribution, accessibility and future development potential of eco-recreation resources, conducts a key recreation hotspot analysis based on POI, and forms a comprehensive eco-recreation service potential spatial distribution map based on the calculation results of threat factors affecting the eco-recreation function of the ecological core area; S205, based on the selected spatial distribution map of landscape connectivity and comprehensive ecological recreation service potential, determines the ecological source areas and the uneven distribution of blue-green spaces in the core area.

[0010] Furthermore, step S202 of the above-mentioned ecological network optimization method also includes: The habitat type is used to characterize the ecological function of the ecological core area using the habitat quality assessment module; The habitat quality of rasters in the land use and cover data of the current habitat type is calculated based on the degree of habitat degradation of raster cells and the habitat suitability of the current habitat type.

[0011] Furthermore, step S202 of the above-mentioned ecological network optimization method also includes: The habitat quality of rasters in the land use and cover data of the current habitat type is calculated based on the degree of habitat degradation of raster cells and the habitat suitability of the current habitat type.

[0012] Furthermore, step S3 of the above-mentioned ecological network optimization method also includes: The optimal ecological corridor is simulated using a minimum cost path model, and the optimal routes for species migration and diffusion are determined based on the landscape resistance of grid units between ecological source areas. Considering both natural and social factors, the natural breakpoint method was used to classify land use and cover data, and values ​​and weights were assigned to them. The grid calculator tool was used to calculate the edge effect of land due to human modification as a threat factor to obtain the initial resistance surface of the core area. The initial ecological resistance surface was corrected using nighttime light data, and the ecological resistance surface was constructed based on the optimal routes of ecological corridors and species migration and diffusion.

[0013] Furthermore, step S4 of the above-mentioned ecological network optimization method also includes: Obstacle detection tools are used to identify obstacles that disrupt energy flow within ecological corridors. Obstacle removal is performed using a moving window search method, and the improvement in connectivity after obstacle removal is characterized by the minimum cost distance improvement value per unit.

[0014] Furthermore, step S5 of the above-mentioned ecological network optimization method also includes: Iterative calculations are performed using a preset radius, and the calculation results are classified into levels using the natural breakpoint method, with the highest level obstacle points being transformed into stepping stones. By identifying patches around fracture points that can serve as potential stepping stones through current mapping, and by repairing fracture points and obstacle points as regional ecological stepping stones, the uneven ecological network of blue and green can be optimized. Using the number of ecological corridors and the current intensity value in the current graph as optimization targets, the effect of landscape connectivity optimization is verified, and the final optimized ecological network is obtained.

[0015] According to a second aspect of the present invention, a blue-green uneven urban ecological network optimization system based on a stepping stone system is also provided, the system comprising the following modules: An ecological data acquisition module is configured to acquire ecological data of the study area, including urban land use and cover data representing the area and distribution of blue-green space, urban boundary and ecological protection red line data, natural element datasets, and socio-economic data. The ecological source area determination module is configured to perform morphological spatial pattern analysis, habitat quality assessment, landscape connectivity evaluation, and key recreation hotspot analysis on the study area based on the ecological data, and to use the ecological protection red line range as a bottom-line constraint to determine the state of uneven distribution of ecological source areas and blue-green space. The ecological corridor determination module is configured to initially construct the ecological corridor of the ecological source area using a corridor connection path model, simulate the migration path of species in the ecological source area and ecological corridor using a landscape ecological network simulation tool based on circuit theory to generate a current map, and determine the potential ecological corridors at different locations based on the current intensity between ecological source areas in the current map. An ecological network generation module is configured to determine the breakpoints of species migration paths based on the distribution location of the potential ecological corridors, use an obstacle detection tool to identify obstacles that disrupt energy flow within the ecological corridors, and use the identified breakpoints and obstacles as potential supplementary stepping stone locations for areas lacking green space and blue space in order to initially optimize the ecological network of uneven distribution of blue space in the study area. The ecological network optimization module is configured to repeat the simulation process of the ecological corridor determination module and the ecological network generation module, continuously repair the breakpoints and obstacle points as ecological stepping stones for green and blue-deficient areas in the blue-green space, and use the number of ecological corridors and the current intensity value in the current graph as optimization targets to obtain the final optimized ecological network with uniform blue-green space distribution in the study area.

[0016] According to a third aspect of the present invention, a computer program product is also provided, comprising a computer program / instructions, characterized in that, when executed by a processor, the computer program / instructions implement the steps of any of the methods described above.

[0017] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: This invention presents an ecological network optimization method for cities with uneven blue-green spatial distribution based on a stepping stone system. This method utilizes morphological spatial pattern analysis, habitat quality assessment, and landscape connectivity techniques to identify the spatial distribution characteristics of ecological source areas and their uneven blue-green spatial distribution. By repairing fault points and ecological barrier points as ecological stepping stones in areas lacking blue-green space, the ecological network of cities with uneven blue-green spatial distribution is optimized, resulting in a significant increase in the number of ecological corridors after optimization. Multi-path ecological flow simulations based on circuit theory models were conducted, and stepping stones could be identified and supplemented, significantly improving landscape connectivity in the study area. Repeated simulations were used to verify the landscape connectivity optimization effect, continuously repairing the fault points and barrier points as ecological stepping stones in areas lacking blue-green space, to obtain the final optimized ecological network, achieving the optimal selection of the ecological network. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A flowchart illustrating the ecological network optimization method for blue-green uneven cities based on the stepping stone system provided in this application embodiment; Figure 2 A schematic diagram of ecological corridor construction is provided for the embodiments of this application; Figure 3 A current simulation diagram is provided for the embodiments of this application; Figure 4 A schematic diagram of an ecological network optimization system for uneven blue-green urban development based on a stepping stone system, provided in an embodiment of this application. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0021] The terms "first," "second," "third," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or apparatuses.

[0022] This invention aims to provide innovative ideas and solutions for optimizing the ecological network of cities with uneven blue-green development. Taking a central urban area of ​​a certain city as an example, it uses a combination of methods such as morphological spatial pattern analysis (MSPA), habitat quality assessment (HQ), landscape connectivity evaluation, and key recreation hotspot analysis to identify ecological source areas. It also uses circuit theory models to identify potential stepping stone locations to achieve and verify the effectiveness of ecological network optimization, in order to provide scientific basis and practical guidance for blue-green space planning and ecological restoration practices in similar areas. The main contents include the following: (1) evaluating the ecological source areas of cities with uneven blue-green development and exploring their distribution characteristics; (2) constructing the current ecological network and diagnosing its weak areas; (3) identifying and supplementing stepping stones to optimize the ecological network of areas with uneven blue-green development and verifying its effectiveness.

[0023] The exemplary research area of ​​this invention is a certain city, which has a subtropical monsoon climate with four distinct seasons, simultaneous rainfall and heat, an average annual temperature of 15℃ to 16℃, and an annual rainfall of 820-1100mm. The terrain is diverse, sloping from west to east, with elevations ranging from 44m to 1929m, divided into western mountainous areas, central hilly plains, and eastern low hills, forming a landscape pattern of "western screen and eastern wedge, separated by three rivers." Green spaces are concentrated in a national forest park in the southwest, a national forest park in the southeast, a central ecological park in the center, and three rivers; while the northern and northeastern areas are mainly construction land, with green spaces scattered and highly unsystematic.

[0024] According to the first aspect of the present invention, and in conjunction with the above-mentioned research area, a method for optimizing the ecological network of cities with uneven blue-green distribution based on a stepping stone system is provided, such as... Figure 1 As shown, the method includes: S1, acquire ecological data for the study area. This ecological data includes urban land use and cover data characterizing the area and distribution of blue-green spaces, urban boundary and ecological protection red line data, natural element datasets, and socioeconomic data. Further, step S1 of the above ecological network optimization method also includes: the natural element dataset includes: digital height model data and normalized vegetation index (DVI) data from a geospatial data cloud; the socioeconomic data includes: urban points of interest data, road network data, nighttime light data, and population density data. It should be noted that the present invention requires the following data (see Table 1): (1) Land Use and Land Cover (LULC) data of the central urban area of ​​a certain city, which is from the database of the Third National Land Survey provided by the Natural Resources Bureau of a certain city. It is divided into 48 land use types, including various green spaces, water areas, wetlands and other blue-green spaces within the urban development boundary; (2) The boundary of the central urban area and the ecological protection red line are from the Natural Resources Bureau of a certain city; (3) The natural element dataset includes: ① Digital height model (DEM) from the geospatial data cloud, ② Normalized Difference Vegetation Index (NDVI) data from the United States Geological Survey; (4) Socioeconomic data are used to analyze the distribution of recreational resources in the central urban area and assess the cultural ecosystem service functions, including: ① Points of Interest (POI) data: obtained by crawling through the map API using Python, which includes information such as name, type, latitude and longitude coordinates, etc. After manual cleaning and coordinate correction, scenic spots, parks, squares, bus stations and other POIs are selected; ② Road network data: from Open StreetMap is an open street map platform that includes 10 road categories such as urban arterial roads, urban secondary arterial roads, and urban expressways; ③ Nighttime light data: Based on the nighttime light remote sensing image of "Luojia-1", the nighttime light data of the central urban area was obtained through radiometric conversion on the ArcGIS 10.8 platform; ④ Population density data: Sourced from the WorldPop platform, it was obtained by "extracting by mask"; (5) The relevant parameters used for model simulation are derived from the references and the official model manual. All spatial data were reprojected and clipped on the ArcGIS 10.8 platform, with a unified spatial resolution of 5m×5m and the coordinate system being the 2000 National Geodetic Coordinate System (CGCS2000).

[0025]

[0026] Table 1 Data and Sources Against the backdrop of uneven blue-green landscape in a central urban area of ​​a certain city, this study proposes an innovative approach for identifying ecological restoration points. First, morphological spatial pattern analysis (MSPA), habitat quality assessment (HQ), landscape connectivity evaluation, and key recreational hotspot analysis were conducted on the study area, using the ecological protection red line as a baseline constraint to determine the ecological source areas. Then, the Linkage pathway model in the Linkage mapper toolbox was used to initially construct ecological corridors. Current maps were generated by simulating species migration paths using Circuitscape 4.0. After determining the breakpoints based on the potential distribution of ecological corridors, stepping stones were added using barrier points identified by Barrier Mapper, thereby optimizing the ecological network. The above simulation process was repeated to verify the results before and after optimization. Figure 2 As shown, the left side (a) shows the optimal ecological corridor and ecological obstacle points before optimization, and the right side (b) shows the optimal ecological corridor and supplementary stepping stones after optimization. The specific research methods are shown in the following steps.

[0027] S2, based on the aforementioned ecological data, morphological spatial pattern analysis, habitat quality assessment, landscape connectivity evaluation, and key recreational hotspot analysis were conducted on the study area. The ecological protection red line was used as a baseline constraint to determine the geographical characteristics of "blue-green unevenness"—specifically, the enrichment or absence of blue-green spaces in ecological source areas. It should be noted that ecological source areas contribute to maintaining ecosystem services, and patches with high connectivity and high habitat quality are typically selected as the final ecological source areas. The ecological source area evaluation in a certain central urban area takes into account both ecological functions and residents' recreational needs to promote the sustainable development of high-density urban areas.

[0028] Furthermore, step S2 of the above-mentioned ecological network optimization method also includes: S201, using a morphological spatial pattern analysis model to identify the landscape pattern of the urban area and extracting the ecological core area; S202, using a habitat quality assessment module to characterize the habitat type and habitat quality of the ecological functions of the ecological core area. Further, step S202 of the above-mentioned ecological network optimization method also includes: using a habitat quality assessment module to characterize the habitat type of the ecological functions of the ecological core area; calculating the habitat quality of the raster in the land use and cover data of the current habitat type based on the degree of habitat degradation of the raster cells in the land use and cover data of the current habitat type and the habitat suitability of the current habitat type. Specifically, firstly, the MSPA model is used to identify the landscape pattern of a central urban area of ​​a certain city and extract the core area. Then, the HabitatQuality (HQ) module of the InVEST model is used to characterize ecological functions (see Tables 2 and 3 for details). Habitat type is the basis for the HQ module to assess habitat quality, and the calculated HQ value is between 0 and 1. The closer the value is to 1, the greater the potential of the habitat type to support biodiversity. Furthermore, step S202 of the above-mentioned ecological network optimization method further includes: calculating the habitat quality of the raster in the land use and cover data of the current habitat type based on the degree of habitat degradation of the raster cells in the land use and cover data of the current habitat type and the habitat suitability of the current habitat type. Specifically, Q xj The habitat quality of grid x in LULC class j is calculated using the following formula (threat factors and weights are detailed in Tables 2 and 3):

[0029] Where z and k are scaling parameters; H j Let D be the habitat suitability of the j-th type of LULC. xj This refers to the degree of habitat degradation of raster cell x in the j-th type of LULC.

[0030]

[0031] Table 2 Threat factors and maximum impact distance in the habitat quality model.

[0032] Table 3 Habitat suitability and sensitivity to threat factors in various land types

[0033] In the formula, y is the number of grid cells for the r-th type of threat factor, Y rThis represents the total number of raster cells representing the threat factor (r). Since modified LULCs can lead to edge effects, such land uses are generally considered threat factors (r). This study, considering practical circumstances and research needs, uses paddy fields, irrigated land, dry land, industrial land, mining land, urban residential land, rural homesteads, railway land, and highway land as threat factors. r The weight of threat factor r ranges from 0 to 1. The reachability of each threat factor to grid x is represented by β. x (β x ∈[0,1]), 1 represents complete reachability; the sensitivity of the j-th LULC type to the r-th threat factor is S. jr (S jr ∈[0,1]). The stress value ry of the raster y obtained by linear decay has a stress degree on the raster x as i. rxy The formula is as follows:

[0034]

[0035] S203, based on the area effect, smaller ecological patches are removed from the high-habitat-quality areas of the ecological core area. Landscape connectivity is then screened within the ecological core area, and ecological protection red line areas are overlaid on top of this screening. Specifically, by combining the ecological core area and the high-habitat-quality area, ecological patches smaller than 1 km² are removed based on the area effect, leaving 27 patches. Conefor connectivity screening is then performed to calculate dPC. The formula is as follows:

[0036] In the formula, the PC value is greater than or equal to 0 and less than or equal to 1. As the PC value increases, the connectivity of the patch is also optimized. PCremove represents the potential connectivity index after removing the patch. Since there is currently no unified standard for threshold settings in the Conefor software, different thresholds need to be repeatedly tried to determine the value. Threshold measurements were performed at 5km intervals. Test results showed that when the threshold reached 30km, the dPC value basically stabilized; therefore, 30km was set as the threshold parameter for simulation. The top 25 ecological patches with the highest dPC values ​​were retained for further calculations, and ecological protection red line areas were superimposed on the patches identified by the model.

[0037] S204, taking into account the distribution, accessibility, and future development potential of eco-recreation resources, conducts a point-of-interest (POI)-based critical recreation hotspot analysis. Based on the calculation results of threat factors affecting the eco-recreation function of the ecological core area, a comprehensive spatial distribution map of eco-recreation service potential is generated. Specifically, the POI-based critical recreation hotspot analysis comprehensively considers the distribution, accessibility, and future development potential of eco-recreation resources. Eco-recreation resource distribution selects scenic spots, leisure and entertainment parks, historical and cultural squares, and bus stops. Their service areas are determined using the "Buffer" function in ArcGIS 10.8 software, and then classified and assigned values ​​(as shown in Table 4). Accessibility analysis selects road network density, calculating it using Open Street Map vector files and the "fishing net" tool, and dividing it into high, medium, and low distribution areas using the natural breakpoint method. Future development potential analysis selects population density and nighttime light characteristics, which can effectively reveal the distribution of potential eco-recreation resource users and the level of regional economic activity, used to assess critical recreation sources in the central urban area.

[0038] S205, based on the selected spatial distribution map of landscape connectivity and comprehensive ecological recreation service potential, determines the ecological source areas and the uneven distribution of blue-green spaces in the core area. Specifically, it calculates various factors affecting the ecological recreation function of the central urban area to form a spatial distribution map of comprehensive ecological recreation service potential. Combining the above results and... Figure 2 As shown, the uneven distribution of ecological sources and blue-green spaces in the central urban area of ​​a certain city was finally identified.

[0039]

[0040] Table 4. Factors influencing the identification of key eco-recreation source areas S3, using a corridor connection path model, the ecological corridors of the ecological source areas are initially constructed. A landscape ecological network simulation tool based on circuit theory is used to simulate the migration paths of species in the ecological source areas and ecological corridors to generate a current map. Based on the current intensity between ecological source areas in the current map, potential ecological corridors at different locations are determined. Further, step S3 of the above ecological network optimization method also includes: simulating the optimal ecological corridors using a minimum cost path model; determining the optimal routes for species migration and diffusion based on the landscape resistance of grid units between ecological source areas; classifying land use and cover data using the natural discontinuity method, considering natural and social factors, and assigning values ​​and weights to them; calculating the edge effect of land use due to human modification as a threat factor using a raster calculator tool to obtain the preliminary resistance surface of the core area; correcting the preliminary ecological resistance surface using nighttime light data; and constructing the ecological resistance surface based on the ecological corridors and the optimal routes for species migration and diffusion. It should be noted that the minimum cost path (LCP) model is used to simulate the optimal ecological corridors, and the optimal routes for species migration and diffusion are determined based on the landscape resistance of grid units between ecological source areas. Landscape resistance represents the level of resistance that species must overcome to migrate from their ecological home to other locations. Given the complex development situation in the central urban area, both natural and social factors were incorporated into the construction of the ecological resistance surface. Natural factors included LULC type, height, and slope; social factors included distance from roads, distance from water sources, and intensity of human activity (as shown in Table 5). Subsequently, the natural discontinuity method was used to classify height, slope, distance from roads, distance from water sources, and intensity of human activity, and values ​​and weights were assigned based on relevant literature. The preliminary resistance surface of the central urban area was obtained by overlaying these factors using a raster calculator. Finally, nighttime light data was used to further refine the ecological resistance surface.

[0041]

[0042] Table 5 Ecological resistance surface factors and their assigned values Furthermore, step S3 of the above-mentioned ecological network optimization method also includes: simulating the migration paths of species in the ecological source areas and ecological corridors using a landscape ecological network simulation tool based on circuit theory, identifying multiple diffusion paths, displaying corridor redundancy, generating a current map, and determining the relative importance of multiple diffusion paths by the current intensity between ecological source areas; and determining potential ecological corridors for species to move between ecological source areas based on the current intensity between ecological source areas in the current map. It should be noted that, based on the LCP results, to further determine the connectivity between ecological source areas, this study uses Circuitscape 4.0 based on circuit theory to simulate current maps and identify potential ecological corridors. Circuit theory can compensate for the shortcomings of LCP results. Given that species do not always choose the optimal path, some suboptimal paths may also become potential migration corridors for species. This theory can simulate and identify multiple diffusion paths with a certain width, display corridor redundancy, and determine their relative importance by the current intensity between ecological source areas, providing potential ecological corridors at different locations. This invention uses a "pairwise" mode for calculation, and the current density values ​​in the obtained current map represent potential corridors for species to move between ecological source areas.

[0043] S4, based on the distribution location of the potential ecological corridors, determine the breakpoints in species migration paths, and use a barrier detection tool to identify barriers that disrupt energy flow within the ecological corridors. These identified breakpoints and barriers serve as potential stepping stones to compensate for areas lacking blue-green space, thus initially optimizing the spatially uneven ecological network. It should be noted that effectively repairing breakpoints and barriers as regional ecological stepping stones optimizes the "uneven blue-green" ecological network. Step S4 of the above ecological network optimization method further includes: using a barrier detection tool to identify barriers that disrupt energy flow within the ecological corridors, performing barrier removal operations based on a moving window search method, and using the minimum cost distance improvement value to characterize the improvement in connectivity after barrier removal. Specifically, firstly, the Barrier Mapper tool is used to identify key barriers that disrupt energy flow within the ecological corridors, and the moving window search method is used to perform the operation. The minimum cost distance improvement value is used to characterize the improvement in connectivity after barrier removal; areas with large values ​​are the barrier areas within the corridor.

[0044] S5, repeating the simulation process of steps S3 and S4, continuously repairing the fracture points and obstacle points as stepping stones in areas lacking blue-green space, using the number of ecological corridors and the current intensity value in the current graph as optimization targets to obtain the optimized ecological network. Step S5 of the above ecological network optimization method also includes: performing iterative calculations using a preset radius, and classifying the calculation results into levels using the natural breakpoint method, transforming the highest-level obstacle points into stepping stones; identifying patches around fracture points that can serve as potential stepping stones through the current graph, and optimizing the uneven blue-green ecological network by repairing fracture points and obstacle points as regional ecological stepping stones; verifying the landscape connectivity optimization effect using the number of ecological corridors and the current intensity value in the current graph as optimization targets, and obtaining the final optimized ecological network. It should be noted that this invention uses a 200m radius for iterative calculations and uses the natural breakpoint method to divide the results into five levels, transforming the highest-level obstacle points into stepping stones. Subsequently, patches around fracture points that can serve as potential stepping stones are identified through the current graph. The simulation is repeated based on the above results to verify the landscape connectivity optimization effect, and the top 10% of the main corridors are extracted for comparison.

[0045] For example, according to the method of the present invention, firstly, the distribution characteristics of ecological source areas are obtained. Specifically, 20 ecological source areas were identified in the central urban area of ​​a certain city, with a total area of ​​126.19 km². 2 This area, accounting for 13.24% of the central urban area, exhibits an uneven pattern similar to its "uneven distribution of blue and green spaces." First, the MSPA results show that the core area is 101.52 km², accounting for 10.66% of the central urban area, mainly distributed along major rivers. Second, the highest HQ value is 0.9964; areas with high HQ values ​​are selected as high habitat quality areas. Third, through Conefor connectivity filtering, the maximum dPC value is found to be 30.22. Finally, based on the analysis of key recreation hotspots of POIs, a recreation service potential distribution map is obtained, showing that recreation service potential generally decreases from the central urban area outwards. The final ecological source areas are obtained by overlaying these results and taking their intersection.

[0046] Then, the existing ecological network was constructed. Specifically, 31 ecological corridors were constructed in the central urban area of ​​a certain city, with a total length of 89.31 km, the longest being 17.82 km and the shortest being 0.012 km. First, the preliminary resistance surface of the central urban area was obtained by overlaying resistance factors using a grid calculator tool. The southwest and southeast of the study area had lower resistance values, while high-resistance areas were mainly distributed in the northern construction area. Overall, the resistance showed a trend of high in the northwest and low in the southeast, hindering the function of species migration and exchange across the north and south. The ecological corridors were mainly concentrated between a certain location in the southwest and another in the east, with the longest connecting a river and a reservoir, and the shortest connecting the northern part of a mountain. There were fewer ecological corridors in the north, because the ecological space was blocked by the densely built urban areas, making it difficult to form high-quality ecological sources and connections between them.

[0047] Next, ecological stepping stones were identified and supplemented. Specifically, based on current maps and Barrier Mapper simulation results, key ecological stepping stones were identified and supplemented to optimize the ecological network. Among these, there are 10 ecological barrier points in the central urban area, see [link to relevant documentation]. Figure 2 As shown in the left side (a), the total area is 4.24 km². 2 The maximum area is 2.39 km². 2 The first site is located between a park and a river, while the second is situated in the eastern part of Wuwan Village, Xiangjing Village, and the intersection with Provincial Highway S63, as well as their surrounding areas. The primary land use types are cultivated land and construction land. Given the lack of ecological corridors in the north and south, eight ecological corridor breakpoints were identified as potential supplementary sites, primarily consisting of lakes, reservoirs, and woodlands. In summary, a total of 18 supplementary sites were identified and added. (See [link to relevant documentation]). Figure 3 As shown in the right side (b), the total area is 10.35 km². 2 (See Table 6).

[0048]

[0049] Table 6 Distribution of stepping stones in the central urban area Finally, ecological network optimization was validated. Specifically, after optimization based on stepping stone restoration, 77 ecological corridors were identified, with a total length of 240.53 km, representing a 1.48-fold increase in the number of corridors and a 1.69-fold increase in length compared to the initial 31 corridors. Current values ​​before and after restoration also showed that adding stepping stones effectively improved landscape connectivity in the study area. Stepping stone addition increased the maximum current value in the study area from 0.50 A to 2.17 A, and the average current value from 0.03 A to 0.11 A. (See [link to relevant documentation]). Figure 3 As shown. Meanwhile, the longest optimized ecological corridor is 8.93 km, the shortest is 0.01 km, and the average length is 3.12 km. The newly added ecological corridors are mainly distributed between a certain area in the east and a certain area in the north, see [reference needed]. Figure 3As shown in the right side (b), it makes up for the lack of ecological corridors in the east and north.

[0050] It is evident that maintaining a stable regional ecological security pattern has garnered widespread attention from cities worldwide, as demonstrated by the solutions outlined in this invention. Similar goals and effects can be achieved by constructing ecological networks, greenways, and ecological corridors. This study focuses on the issue of "blue-green disparity," using a central urban area of ​​a city as an example. It employs diverse technological methods to identify ecological source areas, optimize the ecological network, and enhance regional network efficiency by adding stepping stones. The results reveal that in cities with "blue-green disparity," identifying and adding stepping stones significantly improves the ecological network. This invention not only provides a pathway for optimizing the blue-green spatial system in a city's central urban area but also offers a scientific basis for formulating ecological restoration strategies in other similar regions.

[0051] First, the area and distribution of blue-green spaces significantly influence the selection of ecological source areas. Due to urban development and agricultural expansion, the blue-green spaces in the central urban area of ​​a certain city are mainly concentrated in the southwest, while the blue-green spaces in the north and east are more fragmented and smaller in area. This invention preferably uses Conefor 2.6 software to select the top 25 patches with the highest dPC values, finding that ecological source areas are concentrated in the southwest of the central urban area, and the patch with the highest connectivity is located in a national forest park. The causes of the "uneven blue-green" pattern usually include limitations imposed by natural geographical conditions, resource distribution characteristics, and local policies. First, the city is located between the Qinling-Bashan and Dabie Mountains in China, encompassing topographic units such as western mountainous areas, central hilly plains, and eastern low hills. Due to topographical limitations, rapid urban construction and agriculture are mainly concentrated in the plains, resulting in limitations on the development of blue-green spaces. Second, as an important agricultural center, the city prioritizes agricultural development to meet regional needs. Simultaneously, during the period of rapid urbanization, many Chinese cities, including this one, focused on economic growth without incorporating environmental sustainability into their short- and long-term planning strategies. Insufficient attention to and protection of blue and green spaces has exacerbated the uneven distribution of these spaces.

[0052] Secondly, protecting stepping stones plays a crucial role in maintaining the ecological security pattern of areas with uneven blue-green distribution. Ecological networks are essential for maintaining biodiversity and enhancing ecological security, and their construction is heavily dependent on the number and distribution of ecological source areas. In a certain city's central urban area, the lack of large ecological source areas in some areas with uneven blue-green distribution poses a challenge to maintaining long-distance ecological corridors. The 31 optimal ecological corridors identified by the LCP model are mainly concentrated in the southwest region, while significant gaps exist in the north and east. After adding 18 stepping stones, the number of ecological corridors increased to 77, significantly improving regional landscape connectivity. Therefore, it is evident that restoring and supplementing stepping stones can effectively optimize ecological networks in areas with uneven blue-green distribution.

[0053] Finally, the protection and restoration of small habitat patches should be incorporated into the formulation of ecological restoration planning strategies. Although small in area, stepping stone systems can supplement large patches and serve as habitat extensions for species. Their optimal distribution should be effectively integrated between source areas and along important species migration routes. Current conservation policies often focus on large habitat patches such as nature reserves, neglecting the ecosystem role of small patches. Furthermore, compared to large source areas, stepping stones are typically smaller, easily overlooked, and face the risk of continuous erosion from development and agricultural activities. Stepping stones not only enhance the resilience of local ecological networks but also provide important corridors for species migration; once damaged, they are difficult to restore. Therefore, they should be valued and protected, and relevant restoration measures should be implemented. For example, for ecological barriers in cities where land use is difficult to change, green infrastructure such as ecological bridges or underground biochannels can be constructed to ensure the smooth flow of ecological resources.

[0054] It is evident that this invention addresses the challenges of constructing ecological networks in cities with uneven blue-green environments. Taking a central urban area of ​​a certain city as an example, it optimizes the ecological network of cities with uneven blue-green environments by identifying and repairing potential stepping stone locations. Using multiple technologies such as morphological spatial pattern analysis (MSPA), habitat quality assessment (HQ), and landscape connectivity, the research results show that: (1) a total of 20 ecological source areas were identified, exhibiting a spatial distribution characteristic of western agglomeration and northern absence; (2) by repairing 8 fault points and 10 ecological barrier points as ecological stepping stones for the region, the number of ecological corridors increased from 31 to 77 after optimization, and the maximum value (2.17 A) and average value (0.11 A) of the current map significantly exceeded the 0.50 A and 0.03 A before optimization, respectively. The results emphasize the importance of protecting and repairing small habitat patches and provide scientific basis and practical guidance for blue-green space planning and ecological restoration in similar areas. After identifying and supplementing 18 stepping stones based on circuit theory models, it was confirmed that the landscape connectivity of this area was significantly improved, emphasizing the importance of paying attention to and protecting small habitat patches. The Circuitscape model, based on circuit theory, simulates multipath ecological flows.

[0055] According to a second aspect of the present invention, a blue-green uneven urban ecological network optimization system based on a stepping stone system is also provided, such as... Figure 4 As shown, the system includes the following modules: An ecological data acquisition module is configured to acquire ecological data of the study area, including urban land use and cover data representing the area and distribution of blue-green space, urban boundary and ecological protection red line data, natural element datasets, and socio-economic data. The ecological source area determination module is configured to perform morphological spatial pattern analysis, habitat quality assessment, landscape connectivity evaluation, and key recreation hotspot analysis on the study area based on the ecological data, and to use the ecological protection red line range as the bottom line constraint to determine the geographical characteristics of "uneven blue-green space" where the ecological source area and the blue-green space are locally enriched or missing. The ecological corridor determination module is configured to initially construct the ecological corridor of the ecological source area using a corridor connection path model, simulate the migration path of species in the ecological source area and ecological corridor using a landscape ecological network simulation tool based on circuit theory to generate a current map, and determine the potential ecological corridors at different locations based on the current intensity between ecological source areas in the current map. An ecological network generation module is configured to determine the breakpoints of species migration paths based on the distribution location of the potential ecological corridors, use an obstacle detection tool to identify obstacles that disrupt energy flow within the ecological corridors, and use the identified breakpoints and obstacles as potential stepping stones to compensate for the lack of blue-green space, so as to initially optimize the ecological network with uneven spatial distribution. An ecological network optimization module is configured to repeat the simulation process of the ecological corridor determination module and the ecological network generation module, continuously repair the fracture points and obstacle points as stepping stones for the missing blue-green space, and use the number of ecological corridors and the current intensity value in the current graph as optimization targets to obtain an optimized ecological network.

[0056] It should be noted that the ecological network optimization system for blue-green uneven cities based on the stepping stone system of the present invention is implemented in accordance with the steps in the aforementioned ecological network optimization method for blue-green uneven cities based on the stepping stone system, and will not be repeated here.

[0057] According to a third aspect of the present invention, a computer program product is also provided, comprising a computer program / instructions, characterized in that, when executed by a processor, the computer program / instructions implement the steps of any of the methods described above.

[0058] This application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method. The computer-readable storage medium may include, but is not limited to, any type of disk, including floppy disks, optical disks, DVDs, CD-ROMs, microdrives, as well as magneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, DRAMs, VRAMs, flash memory devices, magnetic cards or optical cards, nanosystems (including molecular memory ICs), or any type of medium or device suitable for storing instructions and / or data.

[0059] It should be noted that, for the sake of simplicity, the foregoing method embodiments are all described as a series of actions. However, those skilled in the art should understand that this application is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to this application. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to this application.

[0060] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0061] In the several embodiments provided in this application, it should be understood that the disclosed apparatus can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some service interface; the indirect coupling or communication connection between devices or units may be electrical or other forms.

[0062] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0063] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0064] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage device (CMD). Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned memory includes various media capable of storing program code, such as USB flash drives, read-only memory (ROM), random access memory (RAM), portable hard drives, magnetic disks, or optical disks.

[0065] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, which may include: a flash drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, etc.

[0066] The foregoing description is merely an exemplary embodiment of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure. Those skilled in the art will readily conceive of embodiments of this disclosure upon considering the specification and practicing the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described herein. The specification and embodiments are to be considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

[0067] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0068] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing a blue-green uneven city ecological network based on a stepping stone system, characterized in that, include: S1, Obtain ecological data of the study area, including urban land use and cover data representing the area and distribution of blue-green space, urban boundary and ecological protection red line data, natural element datasets, and socio-economic data; S2, based on the ecological data, morphological spatial pattern analysis, habitat quality assessment, landscape connectivity evaluation and key recreation hotspot analysis are carried out in the study area, and the ecological protection red line range is used as the bottom line constraint to determine the geographical characteristics of "uneven blue-green" where the ecological source area and the blue-green space are locally enriched or missing. S3. The ecological corridor of the ecological source area is initially constructed using the corridor connection path model. The migration path of species in the ecological source area and ecological corridor is simulated by a landscape ecological network simulation tool based on circuit theory to generate a current map. The potential ecological corridors at different locations are determined based on the current intensity between the ecological source areas in the current map. S4. Based on the distribution location of the potential ecological corridors, determine the breakpoints of species migration paths, use obstacle detection tools to identify obstacles that disrupt energy flow within the ecological corridors, and use the identified breakpoints and obstacles as potential stepping stones to compensate for the lack of blue-green space, so as to initially optimize the ecological network with uneven spatial distribution. S5. Repeat the simulation process of steps S3 and S4 to continuously repair the fracture points and obstacle points as stepping stones for the missing areas of blue-green space. The optimization targets are the number of ecological corridors and the current intensity value in the current graph, to obtain the optimized ecological network.

2. The ecological network optimization method of claim 1, wherein, In step S1: The natural element dataset includes: digital height model data from geospatial data cloud, and normalized vegetation index; The socioeconomic data includes: urban points of interest data, road network data, nighttime light data, and population density data.

3. The ecological network optimization method of claim 1, wherein, The analysis of morphological spatial patterns, habitat quality, landscape connectivity, and key recreational hotspots in the study area based on the ecological data includes: S201, using a morphological spatial pattern analysis model to identify the urban landscape pattern and extract the ecological core area; S202, Use the habitat quality assessment module to characterize the habitat type and habitat quality of the ecological function of the ecological core area; S203, based on the area effect, small ecological patches are screened and removed from the high habitat quality area of ​​the ecological core area, and landscape connectivity screening is performed on the ecological core area, and ecological protection red line areas are superimposed on the landscape connectivity screening. S204, taking into account the distribution, accessibility and future development potential of eco-recreation resources, conducts a key recreation hotspot analysis based on POI, and forms a comprehensive eco-recreation service potential spatial distribution map based on the calculation results of threat factors affecting the eco-recreation function of the ecological core area; S205, based on the selected spatial distribution map of landscape connectivity and comprehensive ecological recreation service potential, determines the ecological source areas and the uneven distribution of blue-green spaces in the core area.

4. The ecological network optimization method of claim 3, wherein, Step S202 also includes: The habitat type is used to characterize the ecological function of the ecological core area using the habitat quality assessment module; The habitat quality of rasters in the land use and cover data of the current habitat type is calculated based on the degree of habitat degradation of raster cells and the habitat suitability of the current habitat type.

5. The ecological network optimization method of claim 1, wherein, Step S3 also includes: The optimal ecological corridor is simulated using a minimum cost path model, and the optimal routes for species migration and diffusion are determined based on the landscape resistance of grid units between ecological source areas. Considering both natural and social factors, the natural breakpoint method was used to classify land use and cover data, and values ​​and weights were assigned to them. The grid calculator tool was used to calculate the edge effect of land due to human modification as a threat factor to obtain the initial resistance surface of the core area. The initial ecological resistance surface was corrected using nighttime light data, and the ecological resistance surface was constructed based on the optimal routes of ecological corridors and species migration and diffusion.

6. The ecological network optimization method of claim 1, wherein, Step S3 also includes: The migration paths of species in the ecological source areas and ecological corridors are simulated using a landscape ecological network simulation tool based on circuit theory. Multiple diffusion paths are identified, corridor redundancy is displayed, and a current map is generated. The relative importance of multiple diffusion paths is determined by the current intensity between ecological source areas. Potential ecological corridors for species to move between ecological sources are determined based on the current intensity between ecological sources in the current graph.

7. The ecological network optimization method of claim 1, wherein, Step S4 also includes: Obstacle detection tools are used to identify obstacles that disrupt energy flow within ecological corridors. Obstacle removal is performed using a moving window search method, and the improvement in connectivity after obstacle removal is characterized by the minimum cost distance improvement value per unit.

8. The ecological network optimization method as described in claim 1, characterized in that, Step S5 also includes: Iterative calculations are performed using a preset radius, and the calculation results are classified into levels using the natural breakpoint method, with the highest level obstacle points being transformed into stepping stones. By identifying patches around fracture points that can serve as potential stepping stones through current mapping, and by repairing fracture points and obstacle points as regional ecological stepping stones, the uneven ecological network of blue and green can be optimized. Using the number of ecological corridors and the current intensity value in the current graph as optimization targets, the effect of landscape connectivity optimization is verified, and the final optimized ecological network is obtained.

9. A blue-green uneven urban ecological network optimization system based on a stepping stone system, characterized in that, The system includes the following modules: An ecological data acquisition module is configured to acquire ecological data of the study area, including urban land use and cover data representing the area and distribution of blue-green space, urban boundary and ecological protection red line data, natural element datasets, and socio-economic data. The ecological source area determination module is configured to perform morphological spatial pattern analysis, habitat quality assessment, landscape connectivity evaluation, and key recreation hotspot analysis on the study area based on the ecological data, and to use the ecological protection red line range as the bottom line constraint to determine the geographical characteristics of "uneven blue-green space" where the ecological source area and the blue-green space are locally enriched or missing. The ecological corridor determination module is configured to initially construct the ecological corridor of the ecological source area using a corridor connection path model, simulate the migration path of species in the ecological source area and ecological corridor using a landscape ecological network simulation tool based on circuit theory to generate a current map, and determine the potential ecological corridors at different locations based on the current intensity between ecological source areas in the current map. An ecological network generation module is configured to determine the breakpoints of species migration paths based on the distribution location of the potential ecological corridors, use an obstacle detection tool to identify obstacles that disrupt energy flow within the ecological corridors, and use the identified breakpoints and obstacles as potential stepping stones to compensate for the lack of blue-green space, so as to initially optimize the ecological network with uneven spatial distribution. An ecological network optimization module is configured to repeat the simulation process of the ecological corridor determination module and the ecological network generation module, continuously repair the fracture points and obstacle points as stepping stones for the missing blue-green space, and use the number of ecological corridors and the current intensity value in the current graph as optimization targets to obtain an optimized ecological network.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 8.

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