A Cross-Model, Cross-Region, and Cross-Time Evaluation Method for Urban Expansion Simulation and Deduction

Abstract

The present invention relates to a cross-model, cross-region and cross-time evaluation method for urban expansion simulation and deduction, and the method includes: extracting an urban land use classification map and a driving factor map; constructing a CA model based on multiple CA modeling methods to determine a land conversion probability map; simulating the land use change conditions of each research region during the calibration period and the verification period based on the CA model to obtain a calibration simulation result and a verification simulation result; conducting an overall evaluation on the calibration simulation result and the verification simulation result; extracting the equal-area regions such as the urban-rural fringe in the real land pattern of each research region as a mask, and cropping the calibration simulation result and the verification simulation result to obtain an equivalent region simulation result; conducting a unified evaluation of the equivalent region simulation result across models, regions and time to obtain a unified evaluation result, and comparing it with the overall evaluation result. Compared with the prior art, the present invention has the advantages that the evaluation accuracy can better reflect the actual performance of the model, etc.

Description

Technical Field

[0001] The present invention relates to an evaluation method for urban expansion simulation, and more particularly to a cross-model, cross-region, and cross-time evaluation method for urban expansion simulation and deduction. Background Art

[0002] The reliability of the Cellular Automata (CA) model is the core of whether the model can be used for historical pattern simulation and future scenario prediction. Although the CA model is constantly being improved, there are still many challenges in the accuracy comparison across models, regions, and time. Different CA models have differences in running efficiency, transition rules, and parameter sensitivity. Even when simulating the same study area, the CA model will produce different CA parameters, resulting in significant differences in the final simulation results. Therefore, it is necessary to conduct a cross-model simulation accuracy comparison to select the best CA model based on the simulation accuracy. In addition, many cross-time accuracy comparisons have been carried out in the early CA work because after the model is constructed, urban expansion in different time periods is required to calibrate and validate the CA model, and the accuracy and error usually vary in different periods. Using the same CA model to simulate urban expansion in different periods of the same study area, the simulation accuracy value does not directly represent the performance of the CA model. Currently, the cross-model and cross-time accuracy comparisons have limitations, and the accuracy is related to the urban expansion experienced by the study area, indicating that the cross-region accuracy comparison is also very important. Some studies have shown that whether it is a non-spatial evaluation method or a spatial evaluation method, the comparison of the accuracy and error between the simulation results and the actual pattern is not only closely related to the CA model but also to the study area. The same CA model applied in different study areas will produce different accuracies and errors. Therefore, in order to compare the simulation accuracy between different study areas, the key is to analyze the simulation accuracy of the urban expansion experienced by the area. The accuracy evaluation should focus on the areas with significant urban expansion, and it is necessary to eliminate the influence of non-urban areas where the cell state remains unchanged before and after the simulation.

[0003] Aiming at the limitations of the comparability of simulation accuracy across models, time, and study regions, an important problem needs to be solved: how to establish a general accuracy evaluation method that can be used to compare the simulation accuracies between different CA models, different time stages, and different study regions. Summary of the Invention

[0004] The purpose of the present invention is to provide a cross-model, cross-region, and cross-time evaluation method for urban expansion simulation and deduction, which can realize the comparison of simulation results across models, regions, and time, has wide generality, and helps to select the best CA model from multiple CA models.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] A cross - model, cross - region and cross - time evaluation method for urban expansion simulation and deduction, comprising the following steps:

[0007] Step 1) Extract the urban land use classification maps and driving factor maps of multiple study areas based on Landsat images, vector datasets and raster data;

[0008] Step 2) Construct different CA models for each study area based on multiple CA modeling methods, urban land use classification maps and driving factor maps, and determine the land conversion probability maps;

[0009] Step 3) Input the urban land use classification maps and land conversion probability maps into the CA model, and simulate the land use change situations of each study area during the calibration period and the validation period by adjusting other parameters of the CA model to obtain the calibration simulation results and the validation simulation results;

[0010] Step 4) Conduct an overall evaluation of the calibration simulation results and the validation simulation results obtained by simulating each CA model in different study areas based on the pixel - by - pixel comparison method, and output and save the overall evaluation results;

[0011] Step 5) Extract the equal - area areas such as the urban - rural fringe in the real land pattern of each study area;

[0012] Step 6) Use the extracted equal - area areas such as the urban - rural fringe as masks to respectively crop the calibration simulation results and the validation simulation results, and use the cropped results as the equivalent area simulation results;

[0013] Step 7) Conduct a unified cross - model, cross - region and cross - time evaluation of the equivalent area simulation results based on the pixel - by - pixel comparison method;

[0014] Step 8) Output and save the unified evaluation results, and compare them with the overall evaluation results.

[0015] The said Step 1) includes the following steps:

[0016] Step 1 - 1) Obtain Landsat images of different study areas, and use the supervised classification method in ENVI software to determine the urban land use classification maps;

[0017] Step 1 - 2) Obtain vector datasets and raster data, and extract the driving factor maps affecting urban expansion in each study area. Among them, the vector datasets include administrative division maps and road network maps, and the raster data include population maps, economic maps and topographic maps.

[0018] The said Step 2) includes the following steps:

[0019] Step 2-1): Based on the land use classification map and driving factor map, sampling is carried out to obtain effective sample points within the study area for the training of CA conversion rules;

[0020] Step 2-2): Using the CA model, the global land conversion probability is determined based on driving factors, the interaction between adjacent cells, local and global constraints, and random perturbation factors. Among them, the cell state in the next period is determined according to the cell state in the current period and the land conversion rule:

[0021] Cellsta next = LandConRule(Cellsta cur ,Pro df ,NeIn,LGres,RnD)

[0022] In the formula, Cellsta next and Cellsta cur represent the cell states in the next period and the current period respectively; LandConRule represents the land conversion rule; NeIn represents the influence parameter of the interaction between adjacent cells; LGres represents local and global constraints; RnD represents the influence parameter of the random perturbation factor on the cell state conversion; Pro df represents the land conversion probability based on driving factors:

[0023]

[0024] In the formula, a0 is the intercept, a1 - a n are the CA parameters of the dependent variables x1 - x n , b is the weight of the independent variable y, and γ is the modeling error;

[0025] The global land conversion probability is:

[0026]

[0027] In the formula, Scal TIP is the scaling parameter to compensate for the conversion probability decay effect, Scal LAP is the scaling parameter to offset the neighborhood effect, and t is the current time step;

[0028] Step 2-3): Obtain the land conversion probability map under the influence of urban expansion driving factors.

[0029] The CA modeling method includes CEO, SAR, and GWR.

[0030] Step 3) includes the following steps:

[0031] Step 3-1): Input the urban land use classification map and the land conversion probability map into the CA model. Under the GIS modeling and simulation environment, use the urban land use distribution map of the first initial year as the initial state, adjust other parameters of the CA model, and run the CA model M times to obtain the corrected simulation results of urban land use change. Output and save the corrected simulation results, where M represents the year difference between the first initial year and the end year of the correction period;

[0032] Step 3-2): Input the urban land use classification map and the land conversion probability map into the CA model. Under the GIS modeling and simulation environment, use the urban land use distribution map of the second initial year as the initial state, adjust other parameters of the CA model, and run the CA model N times to obtain the verification simulation results of urban land use change. Output and save the verification simulation results, where N represents the year difference between the second initial year and the end year of the verification period.

[0033] The specific content of step 4) is as follows: Based on the pixel-by-pixel comparison method, conduct an overall evaluation of the corrected simulation results and the verification simulation results to obtain various state - static and state - change evaluation indicators for evaluating the accuracy and error of the simulation results. The evaluation indicators include OA, Kappa, FOM, precision, and recall:

[0034]

[0035] In the formula, OA measures the percentage of correctly simulated cells in the total cells, CSC represents the number of correctly simulated cells, and AC represents the total number of cells; Kappa measures the overall consistency between the simulated and actual land use patterns; NAMQ represents the percentage of cells with no allocation consistency and medium quantity consistency; UR hit represents the urban expansion cells correctly captured by the CA model; FOM measures the ability of the CA model to capture urban expansion; precision measures the percentage of correctly simulated urban cells among all simulated urban cells; recall measures the percentage of correctly simulated urban cells among all real urban cells; UR miss represents the urban expansion cells missed by the CA model; UR false represents the urban expansion cells wrongly captured by the CA model.

[0036] The described step 5) includes the following steps:

[0037] Step 5-1): Extract urban patches from the real land use distribution map of the study area;

[0038] Step 5-2): Adopt the buffer analysis method to establish equal - area non - urban buffers for the urban patches to determine the equal - area areas on the outskirts of cities in the real land use patterns of each study area.

[0039] In step 7), the evaluation indicators for the unified evaluation are the same as those for the overall evaluation, including OA, Kappa, FOM, precision, and recall;

[0040] The cross-model unified evaluation refers to evaluating and comparing the accuracy and error of urban expansion simulated by different CA models in the same study area during the same time period;

[0041] The cross-region unified evaluation refers to evaluating and comparing the accuracy and error of urban expansion simulated by the same CA model in different study areas during the same time period;

[0042] The cross-time evaluation unity refers to evaluating and comparing the accuracy and error of urban expansion simulated by the same CA model in the same study area during the calibration period and the validation period.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] (1) The present invention uses the buffer analysis method to establish a buffer with the same area as the urban patch to achieve the equal-area division of the urban-rural fringe in the simulation results. The divided equivalent area not only retains the most significant part of urban expansion but also excludes the correctly rejected areas that have a significant impact on the state-stationary indicators, and excludes the influence of non-urban areas where the cell state remains unchanged before and after simulation on the model accuracy. The evaluation result can better reflect the performance of the CA model.

[0045] (2) The method proposed by the present invention can achieve the comparability of accuracy and error between different CA models, different time periods, and different study areas, and has strong generality and practicability.

[0046] (3) The present invention can evaluate different CA models, which is conducive to screening CA models, laying a solid foundation for model optimization and better application, and thus supporting land resource management and policies. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is the flowchart of the method of the present invention;

[0048] Figure 2 is the mechanism comparison between the overall evaluation and the unified evaluation;

[0049] Figure 3 is the case area map of an embodiment;

[0050] Figure 4 is the land conversion probability map generated based on different CA modeling methods;

[0051] Figure 5 The simulation results of each research area based on different CA models;

[0052] Figure 6 The evaluation and comparison results of simulation accuracy across models;

[0053] Figure 7 The evaluation and comparison results of simulation accuracy across regions;

[0054] Figure 8 The evaluation and comparison results of simulation accuracy across time. Specific implementation manners

[0055] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and gives detailed implementation manners and specific operation processes, but the protection scope of the present invention is not limited to the following embodiments.

[0056] This embodiment provides a cross-model, cross-region and cross-time evaluation method for urban expansion simulation and deduction, as Figure 1 shown, including the following steps:

[0057] Step 1) Extract the urban land use classification map and driving factor map of multiple research areas based on Landsat images, vector datasets and raster data;

[0058] Step 1-1) Select different cities with different natural environment and economic development conditions as research areas, obtain Landsat images of different research areas, and use the supervised classification method in ENVI software to determine the urban land use classification map for CA model calibration and verification.

[0059] In this embodiment, Ningbo, Taizhou and Wenzhou in Zhejiang Province are used as research areas, Landsat remote sensing images of the three cities in 1995, 2005 and 2015 are collected, and the supervised classification method is used in ENVI software to classify the Landsat remote sensing images of Ningbo, Taizhou and Wenzhou for land use, generating the real urban spatial patterns in 1995, 2005 and 2015, as Figure 3 shown.

[0060] Step 1-2) Obtain vector datasets and raster data, and extract the driving factor map affecting urban expansion in each research area. Among them, the vector datasets include administrative division maps and road network maps, and the raster data includes population maps, economic maps and topographic maps. The driving factors affecting urban development include urban infrastructure, topographic conditions, educational conditions, etc.

[0061] In this embodiment, data such as administrative division maps, road network maps, economic maps, population maps, topographic maps, and POIs are collected. The Euclidean distance is used to calculate the distances from each cell to the city center, district center, main roads, coastline, and infrastructure, generating a proximity factor map. Raster maps of terrain, population, economy, etc. are obtained and jointly used as driving factors affecting urban expansion.

[0062] Step 2) Based on multiple CA modeling methods, urban land use classification maps, and driving factor maps, different CA models for each study area are constructed to determine the land conversion probability map;

[0063] Step 2-1) Sampling is performed based on the land use classification map and driving factor map to obtain valid sample points within the study area for training the CA conversion rules;

[0064] Step 2-2) Using the CA model, the global land conversion probability is determined based on driving factors, the interaction between adjacent cells, local and global constraints, and random perturbation factors. Among them, the cell state in the next period is determined according to the cell state in the current period and the land conversion rule:

[0065] Cellsta next =LandConRule(Cellsta cur ,Pro df ,NeIn,LGres,RnD)

[0066] In the formula, Cellsta next and Cellsta cur represent the cell states in the next period and the current period respectively; LandConRule represents the land conversion rule; NeIn represents the influence parameter of the interaction between adjacent cells; LGres represents local and global constraints; RnD represents the influence parameter of the random perturbation factor on the cell state conversion; Pro df represents the land conversion probability based on the driving factor.

[0067] In CA modeling, defining the influence of driving factors on cell state changes is the most crucial. Early CA work used different statistical methods and heuristic algorithms to establish CA models. The land conversion probability based on driving factors is expressed as:

[0068]

[0069] In the formula, a0 is the intercept, a1 - a n are the CA parameters of the dependent variables x1 - x n , b is the weight of the independent variable y, and γ is the modeling error.

[0070] Considering that when using different methods for CA modeling, the land conversion probability based on driving factors contains a random error term, the influence of random perturbation on the global probability is no longer included when running the CA model. The global land conversion probability is:

[0071]

[0072] In the formula, Scal TIP is a scaling parameter to compensate for the attenuation effect of the conversion probability, generally taking values from 0.0 to 0.1; Scal LAP is a scaling parameter to offset the neighborhood effect, generally taking values from 0.5 to 1.0; t is the current time step;

[0073] Step 2-3) Obtain the land conversion probability map under the influence of urban expansion driving factors.

[0074] In this embodiment, three CA modeling methods, namely CEO, SAR, and GWR, are adopted to construct the CEO-CA, SAR-CA, and GWR-CA models.

[0075] When using the CEO method, the urban expansion modeling problem needs to be projected into the CEO space. The approximate optimal CA parameters are found by fitting the selected sampling points by minimizing the root mean square error (RMSE). The constructed objective function can be expressed as:

[0076]

[0077] In the formula, Actual is the actual urban expansion, and m is the number of sample points. In this embodiment, the objective function is used to guide the automatic parameterization of the CEO-CA model, and through iterative calculation, the final CA parameters corresponding to the minimum objective function are found. The CA model obtained based on the CEO modeling method is the CEO-CA model.

[0078] When constructing the land conversion rules, SAR can exclude spatial similarity, while GWR can incorporate spatial heterogeneity into the CA model. Both land use patterns and driving factors have spatial autocorrelation. The SAR method can explicitly consider spatial autocorrelation. For the SAR-CA model established based on the SAR method, its modeling residuals are randomly distributed. GWR can generate location-based CA parameters in the CA model to explicitly express the spatial heterogeneity of urban expansion. The most important feature of the GWR-CA model established based on the GWR method is that each driving factor promotes urban expansion at a certain location, while it may inhibit urban expansion at another location.

[0079] The land probability distribution maps obtained by using the above three CA modeling methods are as Figure 4 shown.

[0080] Step 3) Input the urban land use classification map and the land conversion probability map into the CA model. By adjusting other parameters of the CA model, simulate the land use changes in each study area during the calibration period and the validation period to obtain the calibration simulation results and the validation simulation results;

[0081] Step 3-1) Input the urban land use classification map and the land conversion probability map into the CA model. Under the GIS modeling and simulation environment, based on the actual urban expansion from 1995 to 2005, calibrate the CEO-CA, SAR-CA, and GWR-CA models. Use the urban land use distribution map in 1995 as the initial state, adjust other parameters of the CA model, run the CA model 10 times, obtain the calibration simulation results of urban land use changes, and output and save the calibration simulation results;

[0082] Step 3-2) Input the urban land use classification map and the land conversion probability map into the CA model. Under the GIS modeling and simulation environment, based on the actual urban expansion from 2005 to 2015, validate the CEO-CA, SAR-CA, and GWR-CA models. Use the urban land use distribution map in 2005 as the initial state, adjust other parameters of the CA model, run the CA model 10 times, obtain the validation simulation results of urban land use changes, and output and save the validation simulation results.

[0083] The simulation results obtained based on the above method are as Figure 5 shown.

[0084] Step 4) Based on the pixel-by-pixel comparison method, conduct an overall evaluation of the calibration simulation results and the validation simulation results obtained by simulating each CA model in different study areas to obtain various state-static and state-changing evaluation indicators for evaluating the accuracy and error of the simulation results, and output and save the overall evaluation results;

[0085] The evaluation indicators include OA, Kappa, FOM, precision, and recall:

[0086]

[0087] In the formula, OA measures the percentage of correctly simulated cells in the total cells, CSC represents the number of correctly simulated cells, and AC represents the total number of cells; Kappa measures the overall consistency between the simulated and actual land use patterns; NAMQ represents the percentage of cells with no allocation consistency and medium quantity consistency; UR hitCells representing the correct capture of urban expansion by the CA model; FOM measures the ability of the CA model to capture urban expansion; precision measures the percentage of correctly simulated urban cells among all simulated urban cells; recall measures the percentage of correctly simulated urban cells among all real urban cells; UR miss Cells representing the missed urban expansion cells by the CA model; UR false Cells representing the wrongly captured urban expansion cells by the CA model.

[0088] Among them, OA and Kappa belong to the state-stationary evaluation indicators, and FOM, precision, and recall belong to the state-change evaluation indicators, as shown in Table 1 specifically.

[0089] Table 1 Evaluation indicators for evaluating simulation results

[0090]

[0091] Step 5) Extract the equal-area suburban areas in the real land pattern of each study area;

[0092] Since there are significant differences in the urban scale and urban expansion rate in regions at different economic development stages, a general evaluation method needs to be established to achieve the comparability of simulation accuracy and error among different models, regions, and time periods.

[0093] Step 5-1) Extract urban patches from the real land use distribution map of the study area;

[0094] Step 5-2) Adopt the buffer analysis method to establish equal-area non-urban buffers for urban patches, and determine the equal-area suburban areas in the real land pattern of each study area.

[0095] Step 6) Use the extracted equal-area suburban areas as masks to crop the corrected simulation results and the verification simulation results respectively, and take the cropped results as the equivalent area simulation results;

[0096] This masking process specifically belongs to the conventional settings in this field. To avoid obscuring the purpose of this application, it will not be elaborated here.

[0097] Step 7) Conduct a unified evaluation across models, regions, and time for the equivalent area simulation results based on the pixel-by-pixel comparison method;

[0098] The mechanism comparison diagram of the overall evaluation and the unified evaluation is as Figure 2 shown.

[0099] The evaluation indicators of the said unified evaluation are the same as those of the overall evaluation, as shown in Table 1.

[0100] The simulation accuracies and errors of the three CA model calibration and validation periods are shown in Table 2.

[0101] Table 2 Simulation accuracies and errors of the three CA model calibration and validation periods

[0102]

[0103]

[0104] The unified cross-model evaluation refers to evaluating and comparing the accuracies and errors of urban expansion simulated by different CA models in the same study area during the same time period. In this embodiment, the unified cross-model evaluation results are shown in Table 3, and a comparison diagram of one simulation result is as Figure 6 shown, representing the comparison of the simulation results of Ningbo in 2005 based on three CA models, showing two enlarged areas located in the center of Ningbo and Cixi City.

[0105] Table 3 Cross-model comparison of simulation accuracies and errors in three study areas (2005)

[0106]

[0107] The unified cross-region evaluation refers to evaluating and comparing the accuracies and errors of urban expansion simulated by the same CA model in different study areas during the same time period. In this embodiment, the unified cross-region evaluation results are shown in Table 4, and among them, the simulation results of different study areas of the CEO-CA model in 2015 are as Figure 7 shown.

[0108] Table 4 Cross-region comparison of simulation accuracies and errors of three CA models (2015)

[0109]

[0110]

[0111] The unified cross-time evaluation refers to evaluating and comparing the accuracies and errors of urban expansion simulated by the same CA model in the calibration period and the validation period of the same study area. In this embodiment, the unified cross-time evaluation results are shown in Table 5, and among them, the urban dynamic changes of three study areas simulated by the GWR-CA model from 1995 to 2015 are as Figure 8 shown.

[0112] Table 5 Simulation accuracy differences between the calibration and validation periods of three CA models (2015 minus 2005)

[0113]

[0114] Step 8) Output and save the unified evaluation result, and compare it with the overall evaluation result.

[0115] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative efforts. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art should fall within the protection scope determined by the claims.

Claims

1. A cross-model, cross-region, and cross-time evaluation method for urban expansion simulation and deduction, characterized in that It includes the following steps: Step 1) Extract the urban land use classification maps and driving factor maps of multiple study areas based on Landsat images, vector datasets, and raster data; Step 2) Based on multiple CA modeling methods, urban land use classification maps, and driving factor maps, construct different CA models for each study area to determine the land conversion probability maps; Step 3) Input the urban land use classification maps and land conversion probability maps into the CA model, and simulate the land use changes in each study area during the calibration period and validation period by adjusting other parameters of the CA model to obtain the calibration simulation results and validation simulation results; Step 4) Based on the pixel-by-pixel comparison method, conduct an overall evaluation of the calibration simulation results and validation simulation results obtained by simulating each CA model in different study areas, and output and save the overall evaluation results; Step 5) Extract the equal-area suburban areas in the real land pattern of each study area; Step 6) Use the extracted equal-area suburban areas as masks to respectively crop the calibration simulation results and validation simulation results, and take the cropped results as the equivalent area simulation results; Step 7) Based on the pixel-by-pixel comparison method, conduct a unified evaluation of the equivalent area simulation results across models, regions, and time; Step 8) Output and save the unified evaluation results, and compare them with the overall evaluation results.

2. The cross-model, cross-region, and cross-time evaluation method for urban expansion simulation and deduction according to claim 1, wherein The said Step 1) includes the following steps: Step 1-1) Obtain Landsat images of different study areas, and use the supervised classification method in ENVI software to determine the urban land use classification maps; Step 1-2) Obtain vector datasets and raster data, and extract the driving factor maps affecting urban expansion in each study area. Among them, the vector datasets include administrative division maps and road network maps, and the raster data includes population maps, economic maps, and topographic maps.

3. A cross-model, cross-region, and cross-time evaluation method for urban expansion simulation and deduction according to claim 1, characterized in that The said Step 2) includes the following steps: Step 2-1) Conduct sampling based on the land use classification maps and driving factor maps to obtain effective sample points within the study area for the training of CA conversion rules; Step 2-2) Use the CA model to determine the global land conversion probability based on driving factors, the interaction between adjacent cells, local and global constraints, and random perturbation factors. Among them, the cell state in the next period is determined according to the cell state in the current period and the land conversion rules: Cellsta next = LandConRule(Cellsta cur , Pro df , NeIn, LGres, RnD) In the formula, Cellsta next and Cellsta cur represent the cell states in the next period and the current period respectively; LandConRule represents the land conversion rule; NeIn represents the influence parameter of the interaction between adjacent cells; LGres represents local and global constraints; RnD represents the influence parameter of the random perturbation factor on the cell state transition; Pro df represents the land conversion probability based on the driving factors: where a0 is the intercept, a1 - a n are the CA parameters of the dependent variables x1 - x n , b is the weight of the independent variable y, and γ is the modeling error; The global land conversion probability is: where Scal TIP is the scaling parameter to compensate for the decay effect of the conversion probability, Scal LAP is the scaling parameter to offset the neighborhood effect, and t is the current time step; Step 2-3) Obtain the land conversion probability maps affected by urban expansion driving factors.

4. The cross-model, cross-region, and cross-time evaluation method for urban expansion simulation and deduction according to claim 1, characterized in that The said CA modeling methods include CEO, SAR, and GWR.

5. A cross-model, cross-region, and cross-time evaluation method for urban expansion simulation and deduction according to claim 1, characterized in that The said Step 3) includes the following steps: Step 3-1) Input the urban land use classification maps and land conversion probability maps into the CA model. In the GIS modeling and simulation environment, use the urban land use distribution map in the first initial year as the initial state, adjust other parameters of the CA model, and run the CA model M times to obtain the calibration simulation results of urban land use changes, and output and save the calibration simulation results, where M represents the year difference between the first initial year and the end year of the calibration period; Step 3-2): Input the urban land use classification map and the land conversion probability map into the CA model. Under the GIS modeling and simulation environment, use the urban land use distribution map in the second initial year as the initial state, adjust other parameters of the CA model, and run the CA model N times to obtain the verified simulation results of urban land use change. Then output and save the verified simulation results, where N represents the year difference between the second initial year and the end year of the verification period.

6. The cross-model, cross-region, and cross-time evaluation method for urban expansion simulation and deduction according to claim 1, characterized in that The specific content of step 4) is as follows: Based on the pixel-by-pixel comparison method, conduct an overall evaluation of the corrected simulation results and the verified simulation results to obtain various state-static and state-changing evaluation indicators, which are used to evaluate the accuracy and error of the simulation results. The evaluation indicators include OA, Kappa, FOM, precision, and recall. Where, OA measures the percentage of correctly simulated cells in the total cells, CSC represents the number of correctly simulated cells, and AC represents the total number of cells; Kappa measures the overall consistency between the simulated and actual land use patterns; NAMQ represents the percentage of cells with no allocation consistency and medium quantity consistency; UR hit represents the urban expansion cells correctly captured by the CA model; FOM measures the ability of the CA model to capture urban expansion; precision measures the percentage of correctly simulated urban cells among all simulated urban cells; recall measures the percentage of correctly simulated urban cells among all real urban cells; UR miss represents the urban expansion cells missed by the CA model; UR false represents the urban expansion cells wrongly captured by the CA model.

7. A cross-model, cross-region, and cross-time evaluation method for urban expansion simulation and deduction according to claim 1, characterized in that Step 5) includes the following steps: Step 5-1): Extract urban patches from the real land use distribution map of the study area. Step 5-2): Adopt the buffer analysis method to establish non-urban buffers with equal areas for the urban patches, and determine the urban-rural equal-area regions in the real land pattern of each study area.

8. A cross-model, cross-region, and cross-time evaluation method for urban expansion simulation and deduction according to claim 6, characterized in that In step 7), the evaluation indicators for the unified evaluation are the same as those for the overall evaluation, including OA, Kappa, FOM, precision, and recall. The cross-model unified evaluation refers to evaluating and comparing the accuracy and error of urban expansion simulated by different CA models for the same study area in the same time period. The cross-region unified evaluation refers to evaluating and comparing the accuracy and error of urban expansion simulated by the same CA model for different study areas in the same time period. The cross-time evaluation unified refers to evaluating and comparing the accuracy and error of urban expansion simulated by the same CA model for the same study area during the correction period and the verification period.

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