Method for evaluating recoverability of vegetation in engineering disturbance area

Abstract

The invention discloses a method for evaluating the recoverability of vegetation in an engineering disturbance area. The current vegetation restoration engineering has many problems in practice. Eight key environmental indexes including monthly precipitation, monthly average temperature, soil utilization type, soil moisture content, soil freeze-thaw days, altitude, gradient and vegetation coverage are selected to assess regional ecological conditions, standardized processing and multi-factor overlay analysis are adopted, grid algebraic operation is combined, processed data are substituted into a vegetation recoverability assessment model, and a vegetation recoverability assessment model is established. Results are visualized through a GIS spatial analysis technology, an evaluation chart is generated, and comprehensive evaluation of vegetation restorability is achieved; and a geographic detector model is further utilized to detect and analyze key factors influencing the vegetation restorability and the interaction of the key factors. According to the method, the problem of low vegetation restoration efficiency or failure caused by lack of scientific evaluation in the existing vegetation restoration project is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of ecological restoration and environmental protection, and in particular relates to a method for evaluating the recoverability of vegetation in an engineering disturbance area. Background Art

[0002] The topography and climate conditions of the Qinghai-Tibet Plateau are extremely complex. Affected by harsh natural conditions such as high altitude and extremely low temperatures, the local plant community structure is single, vegetation grows slowly, the ecological environment is fragile, and the life carrying capacity is weak. Once it is damaged, it is difficult to repair. During engineering construction, the original fragile ecological environment is often disturbed and damaged to varying degrees, resulting in problems such as decreased vegetation coverage and soil erosion. In addition, the number of seeds required for local slope protection vegetation is insufficient, and the seeds have poor tolerance and a single species. They are easy to die after planting, and the results of ecological restoration are often unsatisfactory. The protection and utilization of native vegetation is particularly important. However, there are many problems in the current vegetation restoration project in practice:

[0003] 1) The cost of governance is high, and huge financial resources are needed to maintain and restore the local natural ecology;

[0004] 2) During the maintenance and restoration process, the lack of professional supervision and guidance has exacerbated the damage to the native vegetation environment;

[0005] 3) Insufficient financial support leads to the death of artificial vegetation used for planting, ineffective resource investment, and insufficient vegetation ecological recovery, which in turn leads to serious consequences such as soil erosion and road damage.

[0006] In view of this, it is particularly important to conduct vegetation restorer evaluation and ecological quality factor evaluation during engineering construction, build an ecological environment evaluation system, and obtain vegetation restorer evaluation values ​​to provide a scientific basis and decision-making support for the restoration and management of sensitive and fragile ecosystems affected by engineering construction, effectively reduce the negative ecological impacts of engineering construction, and provide reference for ecological restoration work in engineering disturbance areas. Summary of the invention

[0007] In order to make up for the shortcomings of the existing technology, the present invention provides a method for evaluating the recoverability of vegetation in engineering disturbance areas. It utilizes multi-source data and adopts spatial analysis methods to construct a vegetation recoverability evaluation model to evaluate the vegetation recovery potential and provide a scientific basis for ecological restoration projects. It is particularly suitable for the restoration and management of sensitive and fragile ecosystems affected by engineering construction.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is:

[0009] A method for evaluating the recoverability of vegetation in an engineering disturbance area is characterized by: using ArcGIS software, multi-source data and spatial analysis methods to scientifically evaluate the vegetation recoverability in the engineering disturbance area; selecting eight key environmental indicators, namely monthly precipitation, average monthly temperature, soil use type, soil moisture content, soil freeze-thaw days, altitude, slope and vegetation coverage, and grading them by natural breakpoint method or national standards, exploring the structure of the regional ecological evaluation system, influencing factors and the grade distribution of the ecological environment, evaluating the regional ecological status, using standardized processing and multi-factor overlay analysis, combined with raster algebraic operations, substituting the processed data into a vegetation recoverability evaluation model, visualizing the results through GIS spatial analysis technology, generating an evaluation map, and realizing a comprehensive evaluation of vegetation recoverability; and further using a geographic detector model to detect and analyze the key factors affecting vegetation recoverability and their interactions, exploring the degree of influence of each factor on vegetation recoverability and their interactions.

[0010] Further, the specific steps are as follows:

[0011] Step 1: Data collection and preprocessing;

[0012] Step 2: Construct an evaluation index system;

[0013] Step 3: Construct a vegetation restoration evaluation model;

[0014] Step 4: Vegetation restoration assessment;

[0015] Step 5: Geographic detector model analysis;

[0016] Step 6: Ecological restoration recommendations.

[0017] Further, step 1 is specifically as follows:

[0018] Collect multi-source environmental data related to the engineering disturbance area, digitize it, perform spatial correction, and generate 10*10m grid data.

[0019] Further, step 2 is specifically as follows:

[0020] Based on the pre-processed environmental factor data as the evaluation index of vegetation restorability, it is reclassified into five levels, and these indicators are weighted to reflect their importance in the evaluation of vegetation restorability; at the same time, the indicator data are standardized to eliminate the dimensional influence between indicators and solve the comparability between data indicators; by standardizing all data, they can be converted into dimensionless unit values ​​[0-10], and the specific conversion method is as follows:

[0021]

[0022] x' is the standardized data value, x max is the maximum value, x is the original value of the data, x min is the minimum value.

[0023] Further, step 3 is specifically as follows:

[0024] Each indicator is normalized, and then a vegetation recoverability evaluation model is constructed through spatial pattern analysis and multi-factor superposition analysis. The factor dimension analysis of each ecological quality evaluation indicator is carried out. The model formula is as follows:

[0025] X Evaluate =X DEM ×(-1.2)+X NDVI ×1+X pre2020 ×1.5+X DEM_Slope ×(-1)+X BTCH ×1.2+X tmp2020 ×1+X landuse ×1+X daynum_ave_year ×(-1)

[0026] X BTCH is the soil moisture data, X daynum_ave_year is the soil freezing and thawing days data, X DEM is the altitude data, X NDVI is the vegetation coverage data, X pre2020 is the precipitation data, X tmp2020 is the temperature data, X landuse is the land use type data, X DEM_Slope is the slope data, X Evaluate It is the vegetation recovery evaluation value.

[0027] Further, step 4 is specifically as follows:

[0028] According to the vegetation restoreability evaluation model, the Spatial Analyst function in ArcGIS software was used to input the standardized indicator values ​​into the raster calculator in turn according to the above model formula to obtain the vegetation restoreability evaluation results; then, according to the weights of the relevant indicators, the vegetation restoreability evaluation values ​​were calculated, and then the reclassify function was used to reclassify the vegetation restoreability evaluation results using the natural breakpoint method, thereby obtaining a vegetation restoreability grade evaluation map for easy result analysis.

[0029] Further, step 5 is specifically as follows:

[0030] 1) Detection factor selection

[0031] Following the principles of comprehensiveness, dominance and comparability, and based on the reference to relevant literature and the actual situation of the study area, we selected indicators closely related to vegetation resilience to conduct dominant influencing factor detection and interactive detection analysis, and quantitatively evaluated the influence of each factor on vegetation resilience and their interactions.

[0032] 2) Factor Detection Analysis

[0033] The factor detector is used to calculate the influence of each factor on vegetation coverage, and the influence of each factor on the recoverability of vegetation in the study area is quantitatively analyzed, which is expressed by q value. The formula is as follows:

[0034]

[0035] q is the influence degree of the influencing factor on vegetation recoverability; N is the number of all samples in the study area; N i is the number of stratified samples; and δ 2 are the variances of vegetation recoverability in layer i and the study area, respectively; SL is the sum of variances within the layer; SWL is the total variance of vegetation recoverability;

[0036] 3) Interaction Detection Analysis

[0037] The interaction detector is used to detect each influencing factor interactively, and further explore whether the explanatory power of the double factor on vegetation resilience is stronger or weaker than that of a single factor; identify whether the evaluation factors X1 and X2 will increase or weaken the explanatory power of the dependent variable Y when they act together, or whether the effects of these factors on Y are independent of each other. The evaluation method is to first calculate the q values ​​of the two factors X1 and X2 on Y: q(X1) and q(X2), and calculate the q value when they interact (the new polygonal distribution formed by the tangency of the two layers of superimposed variables X1 and X2): q(X1∩X2), and compare the sizes of q(X1), q(X2) and q(X1∩X2).

[0038] Beneficial effects of the present invention:

[0039] The present invention comprehensively considers ecological quality evaluation indicators such as terrain, climatic conditions, vegetation coverage and soil characteristics, constructs a vegetation restoreability evaluation model, and grades the evaluation results to generate a vegetation restoreability grade evaluation map to adapt to the ecological environment of the special area of ​​the engineering disturbance zone; through the geographic detector model, the key factors affecting the vegetation restoreability are detected and analyzed, which solves the problem of low efficiency or failure of vegetation restoration due to lack of scientific evaluation in existing vegetation restoration projects. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of the method for evaluating the recoverability of vegetation in engineering disturbance areas;

[0041] Figure 2 This is the result of the altitude evaluation of Bangda Grassland in eastern Tibet;

[0042] Figure 3 It is the result of slope evaluation of Bangda grassland in eastern Tibet;

[0043] Figure 4 This is a map of land use types in the Bangda grassland in eastern Tibet;

[0044] Figure 5 It is the result of the precipitation evaluation in Bangda grassland in eastern Tibet;

[0045] Figure 6 This is the result of temperature evaluation in Bangda grassland in eastern Tibet;

[0046] Figure 7 It is the evaluation result of vegetation coverage of Bangda grassland in eastern Tibet;

[0047] Figure 8 It is the result of soil moisture content evaluation in Bangda grassland in eastern Tibet;

[0048] Fig. 9 It is the evaluation result of soil freeze-thaw days in Bangda grassland in eastern Tibet;

[0049] Fig.10 It is the result of the vegetation restoration assessment of Bangda grassland in eastern Tibet;

[0050] Fig.11 It is the result of interactive detection of vegetation recoverability in Bangda grassland in eastern Tibet;

[0051] Fig.12 It is the method and process of interactive detection;

[0052] Fig.13 It is the type of interaction between two independent variables on the dependent variable. DETAILED DESCRIPTION

[0053] The present invention is described in detail below in conjunction with specific implementation modes.

[0054] The present invention selects the Bonda grassland in eastern Tibet as an experimental area for case study. This area is located in the eastern part of the Tibet Autonomous Region of China. It is an important part of the Sichuan-Tibet Railway. It has unique plateau ecological conditions and environmental characteristics and belongs to the plateau semi-arid monsoon climate. The region not only has abundant water resources and diverse vegetation types, but also has complex geological structures, dense fault zones, and the stratum lithology is significantly affected by internal dynamic geological effects. As one of the areas with highly concentrated biodiversity in Tibet, the Bonda grassland plays a vital role in maintaining water security and ecological security. The railway network structure in the study area is complex, including bridges, tunnels, and turnouts. Railway construction inevitably has an adverse impact on the ecological environment of the area, and ecological restoration work is particularly important. At present, there are relatively few studies on the ecological quality evaluation of the Bonda grassland in eastern Tibet. Therefore, it is urgent to conduct an in-depth analysis of the ecological situation of the grassland to support the ecological restoration work along the railway. In December 2021, the railway construction of the Bonda grassland section was officially launched. This study will be based on the ecological quality data of the study area in 2020, and remote sensing technology will be used to comprehensively evaluate the ecological environment quality and vegetation recoverability in the region.

[0055] like Figure 1 As shown, the specific steps of the present invention are as follows:

[0056] Step 1: Data collection and preprocessing

[0057] Multi-source environmental data related to the engineering disturbance area were collected, mainly including DEM data, land use type, monthly precipitation, average monthly temperature, vegetation coverage, soil moisture content and soil freeze-thaw data, and digitized and spatially corrected to generate 10*10m raster data; the above data were clipped according to the boundary line of Bangda grassland in eastern Tibet under the spatial analyst module of ArcGIS 10.2; the slope data was generated by using the DeriveSlope tool of the Surface module in ArcView software using DEM data. The altitude index was directly derived from the DEM data, and the vegetation coverage index was inverted using NDVI data based on pixel dichotomy.

[0058] Step 2: Build an evaluation index system

[0059] The environmental factor data of precipitation, temperature, land use type, soil moisture content, soil freeze-thaw days, altitude, slope, and vegetation coverage of Dongbangda grassland in Tibet were extracted based on pre-processing as evaluation indicators of vegetation recoverability, and the vegetation recoverability level was graded and reclassified into five levels; then, these indicators were weighted to reflect their importance in the evaluation of vegetation recoverability; at the same time, the indicator data were standardized to eliminate the dimensional influence between indicators and solve the comparability between data indicators; by standardizing all data, they can be converted into dimensionless unit values ​​[0-10], and the specific conversion method is as follows:

[0060]

[0061] x' is the standardized data value, x max is the maximum value, x is the original value of the data, x min is the minimum value;

[0062] Step 3: Construct vegetation restoration assessment model

[0063] Each indicator is normalized, and then a vegetation recoverability evaluation model is constructed through spatial pattern analysis and multi-factor superposition analysis. The factor dimension analysis of each ecological quality evaluation indicator is carried out. The model formula is as follows:

[0064] X Evaluate =X DEM ×(-1.2)+X NDVI ×1+X pre2020 ×1.5+X DEM_Slope ×(-1)+X BTCH ×1.2+X tmp2020 ×1+X landuse ×1+X daynum_ave_year ×(-1)

[0065] X BTCH is the soil moisture data, X daynum_ave_year is the soil freezing and thawing days data, X DEM is the altitude data, X NDVI is the vegetation coverage data, X pre2020 is the precipitation data, X tmp2020 is the temperature data, X landuse is the land use type data, X DEM_Slope is the slope data, X Evaluate is the vegetation restorability evaluation value;

[0066] Step 4: Vegetation Restorability Assessment

[0067] According to the vegetation restoration evaluation model, by using the Spatial Analyst function in ArcGIS software, the standardized altitude, slope, land use type, soil moisture content, precipitation, temperature, vegetation coverage, and soil freeze-thaw days are input into the grid calculator in turn according to the above model formula to obtain the vegetation restoration evaluation results. Then, according to the weights of the relevant indicators, the vegetation restoration evaluation value is calculated as follows: Figure 2-9 As shown; reclassify function is used to reclassify, and the vegetation recoverability evaluation results are divided into five levels by natural breakpoint method: difficult to recover, relatively difficult to recover, general recovery, relatively easy to recover, and easy to recover. The vegetation recoverability evaluation level of Bangda grassland in eastern Tibet is obtained as shown in Fig.10 The area proportion of each level of vegetation recoverability is shown in Table 1.

[0068] Table 1. Table of the percentage of each level of vegetation recovery index in Bangda grassland in eastern Tibet

[0069]

[0070] The altitude classification adopts Li Bingyuan's classification method, which is divided into three levels: medium-high altitude (2000m-4000m), high altitude (4000m-6000m), and extremely high altitude (above 6000m); the slope is divided into six levels according to the standards of "GB / T 38360-2019 Technical Specification for Vegetation Restoration of Exposed Slopes" and "LYT 2771-2016", namely light slope (5°), flat slope (15°), slope (25°), steep slope (35°), steep slope (45°), and dangerous slope (≧45°); the land use type indicators are divided into 10 categories: forest vegetation, shrub land, grassland, cultivated land, built-up area, bare land / sparse vegetation area, snow and glacier, permanent water body, herbaceous wetland, and other land uses; the monthly precipitation is divided into low precipitation ( The monthly average temperature is divided into slightly cold (0℃~4.9℃), slightly cold (-4.9℃~0℃), slightly cold (-5℃~-9.9℃), severely cold (10~-14.9℃), deeply cold (-15℃~-19.9℃), and severely cold (-20℃~-29.9℃) according to GB / T6529.

[0071] Vegetation coverage is divided into five levels using the unified classification method of national grassland survey:

[0072] Level Ⅰ (dense): 75% to 100%;

[0073] Level II (dense): 50% to 75%;

[0074] Grade III (general): 25% to 50%;

[0075] Grade IV (sparse): 10% to 25%;

[0076] Level V (sparse): 0-10%.

[0077] The soil moisture content is divided into five levels using the natural breakpoint method: small amount, less, general, more, and a lot; the soil freeze-thaw days are divided into small (80 days), less (100 days), general (150 days), more (200 days), much (250 days), and extremely much (300 days) according to the "Progress Made by Northwest Institute and Others in the Study of Seasonal Frozen Soil Freeze-thaw Changes on the Qinghai-Tibet Plateau".

[0078] Step 5: GeoDetector Model Analysis

[0079] 1) Detection factor selection

[0080] Following the principles of comprehensiveness, dominance and comparability, based on reference to relevant literature and combined with the actual situation of the study area, indicators closely related to vegetation recoverability were selected to conduct dominant influencing factor detection and interactive detection analysis, and quantitatively evaluate the influence of each factor on vegetation recoverability and their interactions.

[0081] 2) Factor Detection Analysis

[0082] The factor detector is used to calculate the influence of each factor on vegetation coverage, and the influence of each factor on the recoverability of vegetation in the study area is quantitatively analyzed, which is expressed by q value. The formula is as follows:

[0083]

[0084] q is the influence degree of the influencing factor on vegetation recoverability; N is the number of all samples in the study area; N i is the number of stratified samples; and δ 2 are the variances of vegetation resilience in layer i and the study area, respectively; SL is the sum of variances within the layer; SWL is the total variance of vegetation resilience. The q value is between 0 and 1. The larger the q value, the greater the influence of the factor on vegetation resilience; the closer it is to 1, the stronger the explanatory effect of the dependent variable on the independent variable, and vice versa.

[0085] The vegetation recoverability evaluation value of Bangda grassland in eastern Tibet in 2020 was taken as the dependent variable. The natural breakpoint method of ArcGIS10.2 software was first used to preliminarily classify the data of the eight dependent variables, and then the classified data were substituted into the geographic detector for factor detection. The results are shown in Table 2.

[0086] Table 2 Q value ranking table of eight indicators of Bangda grassland in eastern Tibet

[0087]

[0088]

[0089] 3) Interaction Detection Analysis

[0090] The interactive detector was used to interactively detect each influencing factor to further explore whether the explanatory power of the double factor on vegetation resilience is stronger or weaker than that of a single factor. Fig.11 shown.

[0091] Then compare the interaction intensity value with the q value obtained from the single factor detection. Interaction detection is used to identify whether the evaluation factors X1 and X2 will increase or weaken the explanatory power of the dependent variable Y when they act together, or whether the effects of these factors on Y are independent of each other. The evaluation method is to first calculate the q values ​​of the two factors X1 and X2 on Y respectively: q(X1) and q(X2), and calculate the q value when they interact (the new polygonal distribution formed by the tangency of the two layers of superimposed variables X1 and X2): q(X1∩X2), and compare the sizes of q(X1), q(X2) and q(X1∩X2). The method and process of two-factor interaction detection are as follows: Fig.12 As shown, the types of interactions are Fig.13 shown.

[0092] Step 6: Ecological Restoration Recommendations

[0093] Based on the vegetation restoreability assessment results, assessment maps, and detection analysis of the geographic detector model, formulate vegetation restoration strategies and measures, determine the priorities and key areas for vegetation restoration, and select appropriate vegetation restoration technologies and species in combination with local climate, soil conditions, and vegetation characteristics; monitor the effects of vegetation restoration to provide a scientific basis and decision-making support for ecological restoration projects.

[0094] The content of the present invention is not limited to the embodiments listed, and any equivalent changes made to the technical solution of the present invention by ordinary technicians in this field after reading the description of the present invention are covered by the claims of the present invention.

Claims

1. A method for evaluating the recoverability of vegetation in an engineering disturbance area, characterized in that: Using ArcGIS software, multi-source data and spatial analysis methods, a scientific assessment of vegetation restoration in the engineering disturbance area was conducted; eight key environmental indicators, including monthly precipitation, average monthly temperature, soil use type, soil moisture content, soil freeze-thaw days, altitude, slope, and vegetation coverage, were selected and graded using the natural breakpoint method or national standards to explore the structure of the regional ecological evaluation system, influencing factors, and the grade distribution of the ecological environment, evaluate the regional ecological status, and use standardized processing and multi-factor overlay analysis combined with raster algebraic operations to substitute the processed data into the vegetation restoreability assessment model. The results were visualized using GIS spatial analysis technology to generate an evaluation map to achieve a comprehensive assessment of vegetation restoreability; and the geographic detector model was further used to detect and analyze the key factors affecting vegetation restoreability and their interactions, to explore the degree of influence of each factor on vegetation restoreability and their interactions.

2. The method for evaluating the recoverability of vegetation in an engineering disturbance area according to claim 1, characterized in that: The specific steps are as follows: Step 1: Data collection and preprocessing; Step 2: Construct an evaluation index system; Step 3: Construct a vegetation restoration evaluation model; Step 4: Vegetation restoration assessment; Step 5: Geographic detector model analysis; Step 6: Ecological restoration recommendations.

3. The method for evaluating the recoverability of vegetation in an engineering disturbance area according to claim 2, characterized in that: Step 1 is as follows: Collect multi-source environmental data related to the engineering disturbance area, digitize it, perform spatial correction, and generate 10*10m grid data.

4. The method for evaluating the recoverability of vegetation in an engineering disturbance area according to claim 3, characterized in that: Step 2 is as follows: Based on the pre-processed environmental factor data as the evaluation index of vegetation restorability, it is reclassified into five levels, and these indicators are weighted to reflect their importance in the evaluation of vegetation restorability; at the same time, the indicator data are standardized to eliminate the dimensional influence between indicators and solve the comparability between data indicators; by standardizing all data, they can be converted into dimensionless unit values ​​[0-10], and the specific conversion method is as follows: x' is the standardized data value, x max is the maximum value, x is the original value of the data, x min is the minimum value.

5. The method for evaluating the recoverability of vegetation in an engineering disturbance area according to claim 4, characterized in that: Step 3 is as follows: Each indicator is normalized, and then a vegetation recoverability evaluation model is constructed through spatial pattern analysis and multi-factor superposition analysis. The factor dimension analysis of each ecological quality evaluation indicator is carried out. The model formula is as follows: X Evaluate =X DEM ×(-1.2)+X NDVI ×1+X pre2020 ×1.5+X DEM_Slope ×(-1)+X BTCH ×1.2+X tmp2020 ×1+X landuse ×1+X daynum_ave_year ×(-1) X BTCH is the soil moisture data, X daynum_ave_year is the soil freezing and thawing days data, X DEM is the altitude data, X NDVI is the vegetation coverage data, X pre2020 is the precipitation data, X tmp2020 is the temperature data, X landuse is the land use type data, X DEM_Slope is the slope data, X Evaluate It is the vegetation recovery evaluation value.

6. The method for evaluating the recoverability of vegetation in an engineering disturbance area according to claim 5, characterized in that: Step 4 is as follows: According to the vegetation restoreability evaluation model, the Spatial Analyst function in ArcGIS software was used to input the standardized indicator values ​​into the raster calculator in turn according to the above model formula to obtain the vegetation restoreability evaluation results; then, according to the weights of the relevant indicators, the vegetation restoreability evaluation values ​​were calculated, and then the reclassify function was used to reclassify the vegetation restoreability evaluation results using the natural breakpoint method, thereby obtaining a vegetation restoreability grade evaluation map for easy result analysis.

7. The method for evaluating the recoverability of vegetation in an engineering disturbance area according to claim 6, characterized in that: Step 5 is as follows: 1) Detection factor selection Following the principles of comprehensiveness, dominance and comparability, and based on the reference to relevant literature and the actual situation of the study area, we selected indicators closely related to vegetation resilience to conduct dominant influencing factor detection and interactive detection analysis, and quantitatively evaluated the influence of each factor on vegetation resilience and their interactions. 2) Factor Detection Analysis The factor detector is used to calculate the influence of each factor on vegetation coverage, and the influence of each factor on the recoverability of vegetation in the study area is quantitatively analyzed, which is expressed by q value. The formula is as follows: q is the influence degree of the influencing factor on vegetation recoverability; N is the number of all samples in the study area; N i is the number of stratified samples; and δ 2 are the variances of vegetation recoverability in layer i and the study area, respectively; SL is the sum of variances within the layer; SWL is the total variance of vegetation recoverability; 3) Interaction Detection Analysis The interaction detector is used to detect each influencing factor interactively, and further explore whether the explanatory power of the double factor on vegetation resilience is stronger or weaker than that of a single factor; identify whether the evaluation factors X1 and X2 will increase or weaken the explanatory power of the dependent variable Y when they act together, or whether the effects of these factors on Y are independent of each other. The evaluation method is to first calculate the q values ​​of the two factors X1 and X2 on Y: q(X1) and q(X2), and calculate the q value when they interact (the new polygonal distribution formed by the tangency of the two layers of superimposed variables X1 and X2): q(X1∩X2), and compare the sizes of q(X1), q(X2) and q(X1∩X2).

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