A multi-scale correlation analysis method for analyzing spatial variability of soil organic carbon and a method for predicting soil organic carbon

Abstract

The application discloses a multi-scale correlation analysis method for analyzing spatial variability of soil organic carbon and a prediction method for soil organic carbon, and comprises the following steps: collecting soil samples, determining soil organic carbon content and obtaining environmental variables; determining the Spearman correlation coefficient of soil organic carbon content and environmental variables and performing significance analysis on global correlation; determining a geographical weighted correlation coefficient according to geographical weights of the soil samples to analyze local correlation; deleting environmental variables with multiple collinearity; performing multi-scale geographical weighted regression fitting on soil organic carbon content and environmental variables based on spatial weights of the soil samples and effective bandwidths of the environmental variables, and calculating local standardized regression coefficients of the environmental variables; determining local correlation environmental variables, and combining global correlation and local correlation to analyze spatial heterogeneity of soil organic carbon content and reveal complex relationships between soil organic carbon and environmental variables at different spatial scales.

Description

TECHNICAL FIELD

[0001] The present application relates to a multi-scale correlation analysis method for analyzing spatial variability of soil organic carbon and a prediction method for soil organic carbon, and belongs to the technical field of soil science. BACKGROUND

[0002] Soil organic carbon (SOC) is one of the largest carbon pools in terrestrial ecosystems, and has important impacts on global carbon cycle and climate change. Therefore, accurately understanding the spatial distribution characteristics of soil organic carbon (SOC) is of great significance for agricultural management, ecological protection and climate change research. However, the spatial distribution of soil organic carbon (SOC) is complex and heterogeneous, and due to the diversity of soil formation processes, geographical conditions and management practices, it shows significant spatial variability at different scales. This variability makes the prediction and mapping of soil organic carbon (SOC) a great challenge, and there is an urgent need for more advanced analysis methods to reveal the complex relationship between soil organic carbon (SOC) and environmental variables.

[0003] In existing research, global analysis methods such as Pearson correlation analysis and traditional regression models are often used to analyze the spatial variability of soil organic carbon (SOC) and its relationship with environmental variables. These methods, although to some extent, reveal the correlation between soil organic carbon (SOC) and environmental variables, often ignore spatial heterogeneity. They assume that the influence of environmental variables on soil organic carbon (SOC) is uniform within the study area, and fail to capture significant correlations or influencing factors that may exist in local areas, which may mask the complex dynamics of soil organic carbon (SOC) at small scales or in specific regions. For example, factors such as topographic changes, microclimate differences and land management practices may have a significant impact on soil organic carbon (SOC) in local areas, but these influences are often ignored in global scale analysis. Therefore, it is necessary to develop a multi-scale analysis framework that combines global and local analysis to better reveal the role of environmental variables in the interpretation of soil organic carbon (SOC) variability and provide an effective variable selection method for soil organic carbon (SOC) mapping.

[0004] Therefore, existing research has failed to fully reveal the spatial distribution patterns and driving mechanisms of soil organic carbon (SOC), limiting the in-depth understanding of soil carbon cycle processes.

[0005] The information disclosed in this BACKGROUND section is only intended to increase an understanding of the general context in which the present application can be practiced. It should not be taken as an acknowledgement or any form of suggestion that this information forms part of the prior art that is already known to those skilled in the practice of the application. SUMMARY

[0006] The technical problem to be solved by the present application is how to systematically reveal the complex relationship between soil organic carbon SOC and environmental variables at different spatial scales, while effectively identifying and capturing environmental variables that may not show significant correlation in the global range, but have strong correlation in local areas or under specific conditions.

[0007] To solve the above technical problems, the present application is implemented by using the following technical solutions:

[0008] In a first aspect, the present application provides a multi-scale correlation analysis method for analyzing spatial variability of soil organic carbon, comprising:

[0009] Collecting a plurality of soil samples in a study area, and determining the content of soil organic carbon SOC in the soil samples;

[0010] Obtaining multi-source data in the study area, and extracting environmental variables from the multi-source data; the multi-source data includes basic geographic data, terrain data, and remote sensing data, and the environmental variables include terrain factors, location conditions, landscape patterns, and remote sensing spectral indices;

[0011] Determining the correlation coefficient and significance between the content of soil organic carbon SOC and each environmental variable, analyzing the global correlation between the content of soil organic carbon SOC and each environmental variable, and obtaining globally correlated environmental variables and globally uncorrelated environmental variables;

[0012] Determining a geographically weighted correlation coefficient according to the globally correlated environmental variables, the globally uncorrelated environmental variables, and the geographic weight of each soil sample, analyzing the local correlation between the content of soil organic carbon SOC and each environmental variable, and obtaining locally correlated environmental variables;

[0013] Judging the multicollinearity of the locally correlated environmental variables according to the variance inflation factor and the tolerance of the locally correlated environmental variables, deleting the locally correlated environmental variables with multicollinearity, and obtaining environmental variables without multicollinearity;

[0014] Based on the spatial weight of each soil sample point and the effective bandwidth of the environmental variables without multicollinearity, fitting the content of soil organic carbon SOC and the environmental variables without multicollinearity by using a multi-scale geographically weighted regression model MGWR, and obtaining the local standardized regression coefficients of the environmental variables without multicollinearity;

[0015] Determining environmental variables with significant local influence on soil organic carbon SOC according to the local standardized regression coefficients of the environmental variables without multicollinearity;

[0016] According to the global correlation environment variable, the global irrelevant environment variable, the local correlation environment variable and the environment variable with the significant local standardized regression coefficient, the comprehensive analysis of the environmental variable influence scale is carried out, and the spatial heterogeneity of the soil organic carbon SOC content is analyzed.

[0017] Further, the correlation coefficient and significance between the soil organic carbon SOC content and each environment variable are determined, the global correlation between the soil organic carbon SOC content and each environment variable is analyzed, and the method for obtaining the global correlation environment variable and the global irrelevant environment variable comprises:

[0018] The correlation coefficient between the soil organic carbon SOC content and each environment variable is calculated by using the Spearman correlation analysis method;

[0019] The significance between the soil organic carbon SOC content and each environment variable is determined according to the statistical significance test of the correlation coefficient between the soil organic carbon SOC content and each environment variable;

[0020] According to the correlation coefficient and significance between the soil organic carbon SOC content and each environment variable, the global correlation between the soil organic carbon SOC content and each environment variable is analyzed, and the global correlation environment variable and the global irrelevant environment variable are obtained.

[0021] Further, the geographical weighted correlation coefficient is determined according to the global correlation environment variable and the global irrelevant environment variable and the geographical weight of each soil sample, the local correlation between the soil organic carbon SOC content and each environment variable is analyzed, and the method for obtaining the local correlation environment variable comprises:

[0022] The geographical weight of each soil sample is determined by using the Gaussian kernel function;

[0023] According to the geographical weight of each soil sample, the geographical weighted covariance between the soil organic carbon SOC content and each environment variable at different spatial positions and the geographical weighted standard deviation of the soil organic carbon SOC content and the geographical weighted standard deviation of each environment variable at different spatial positions are calculated;

[0024] The geographical weighted correlation coefficient at different spatial positions is calculated according to the geographical weighted covariance between the soil organic carbon SOC content and each environment variable at different spatial positions and the geographical weighted standard deviation of the soil organic carbon SOC content and the geographical weighted standard deviation of each environment variable at different spatial positions;

[0025] According to the global correlation environment variable and the global irrelevant environment variable and the geographical weighted correlation coefficient, the local correlation between the soil organic carbon SOC content and each environment variable is analyzed, and the local correlation environment variable is obtained.

[0026] Further, the geographically weighted covariance between the soil organic carbon SOC content at different spatial locations and each environmental variable and the geographically weighted standard deviation of the soil organic carbon SOC content at different spatial locations and the geographically weighted standard deviation of each environmental variable are calculated.

[0027] wherein the geographically weighted covariance between the soil organic carbon SOC content at different spatial locations and each environmental variable is represented as:

[0028] ;

[0029] wherein, is the geographically weighted covariance value between the soil organic carbon SOC content at different spatial locations and each environmental variable; and are the rank of the environmental variable at location i and the rank of the soil organic carbon SOC in the soil sample at location i, respectively; and are the rank of the environmental variable at location j and the rank of the soil organic carbon SOC in the soil sample at location j, respectively; and are the geographically weighted average rank of the environmental variable at location i and the geographically weighted average rank of the soil organic carbon SOC in the soil sample at location i, respectively; is the sample at the th location, is the geographically weighted weight of the sample at the th location to the sample at the th location,

[0030] is the total number of soil samples.

[0031] ;

[0032] the geographically weighted standard deviation of the soil organic carbon SOC content is represented as:

[0033] ;

[0034] wherein, and are the geographically weighted standard deviation value of each environmental variable and the geographically weighted standard deviation value of the soil organic carbon SOC content at different spatial locations, respectively.

[0035] Further, the geographically weighted correlation coefficient at different spatial locations is calculated according to the geographically weighted covariance between the soil organic carbon SOC content at different spatial locations and each environmental variable and the geographically weighted standard deviation of the soil organic carbon SOC content at different spatial locations and the geographically weighted standard deviation of each environmental variable, and the geographically weighted correlation coefficient at different spatial locations is represented as:

[0036] ;

[0037] In the formula, is a geographical weighted correlation coefficient value of different spatial positions.

[0038] Further, according to the variance inflation factor and tolerance of the local correlation environmental variable, a multiple collinearity judgment is performed on the local correlation environmental variable, and the local correlation environmental variable with multiple collinearity is deleted to obtain an environmental variable without multiple collinearity, comprising:

[0039] The variance inflation factor and tolerance of the local correlation environmental variable are determined by a regression analysis method. When the variance inflation factor is greater than 5 and the tolerance is less than 0.2, it indicates that the local correlation environmental variable has multiple collinearity, and the local correlation environmental variable with multiple collinearity is deleted to obtain an environmental variable without multiple collinearity.

[0040] Further, based on the spatial weight of each soil sample and the effective bandwidth of the environmental variable without multiple collinearity, a multi-scale geographical weighted regression model MGWR is used to fit the soil organic carbon SOC content and the environmental variable without multiple collinearity to obtain a local standardized regression coefficient of the environmental variable without multiple collinearity, comprising:

[0041] Each soil sample is weighted using a Gaussian kernel function to obtain the spatial weight of each soil sample;

[0042] The Akaike Information Criterion AIC or the Bayesian Information Criterion BIC is used to determine the effective bandwidth of the environmental variable without multiple collinearity;

[0043] Based on the spatial weight and the effective bandwidth, a multi-scale geographical weighted regression model MGWR is used to fit the soil organic carbon SOC content and the environmental variable without multiple collinearity, and according to the fitting result of the multi-scale geographical weighted regression model MGWR, a local standardized regression coefficient of the environmental variable without multiple collinearity is calculated.

[0044] Further, the multi-scale geographical weighted regression model MGWR is expressed as:

[0045] ;

[0046] In the formula, is a dependent variable of a soil sample ; is the i-th environmental variable of a soil sample ; is the i-th environmental variable of a soil sample ; a regression equation of the environmental variables; is the total number of variables; is the spatial location coordinates where the soil sample is located; is the intercept term, which varies with the spatial location ; is the spatial location coordinates where the soil sample is located; is the regression coefficient of the first variable at the spatial location coordinates where the soil sample is located; is the random error term.

[0047] Further, according to the fitting result of the multi-scale geographically weighted regression model MGWR, the method for calculating the local standardized regression coefficient of the environmental variable without multicollinearity comprises:

[0048] estimating the local standardized regression coefficient of the environmental variable without multicollinearity by weighted least squares method ;

[0049] performing statistical significance test on the local standardized regression coefficient of the environmental variable without multicollinearity, and performing spatial visualization to determine the environmental variable having significant local influence on the soil organic carbon SOC.

[0050] In the second aspect, the application further provides a prediction method of soil organic carbon, which comprises the following steps: selecting environmental variables according to the analysis result of the multi-scale correlation analysis method for analyzing spatial variability of soil organic carbon according to the first aspect, and predicting the soil organic carbon.

[0051] Compared with the prior art, the application has the following beneficial effects:

[0052] The application provides an innovative multi-scale correlation analysis method for analyzing spatial variability of soil organic carbon SOC. The method combines Spearman correlation analysis, geographically weighted correlation analysis and multi-scale geographically weighted regression model MGWR, aims to capture the distribution characteristics of soil organic carbon SOC at different spatial scales, and optimize the selection of environmental variables, so as to improve the generalization ability of the soil organic carbon SOC mapping model. Through Spearman correlation analysis, the application firstly reveals the global relationship between the environmental variables and SOC. Secondly, through geographically weighted correlation analysis, the local correlation between soil organic carbon SOC and environmental variables at different spatial locations is further explored, and the unique influence of environmental variables in different regions is revealed. Subsequently, the introduction of the multi-scale geographically weighted regression model MGWR fully considers the spatial heterogeneity and the influence difference of different environmental variables at different scales, and effectively solves the problem of insufficient explanation of local spatial relationship in the traditional method.

[0053] The present application systematically discloses the complex relationship between soil organic carbon SOC and environmental variables at different spatial scales, and effectively identifies and captures environmental variables that may not show significant correlation in the global range, but have strong correlation in local areas or specific conditions. BRIEF DESCRIPTION OF DRAWINGS

[0054] Figure 1 is a whole process schematic diagram of a multi-scale correlation analysis method for soil organic carbon spatial variability analysis provided by an embodiment of the present application;

[0055] Figure 2 is a schematic diagram of soil sample distribution in a study area provided by an embodiment of the present application;

[0056] Figure 3 is a schematic diagram of part of environmental variables in a study area provided by an embodiment of the present application;

[0057] Figure 4 is a schematic diagram of geographical weighted local correlation formed in the analysis process provided by an embodiment of the present application;

[0058] Figure 5 is a schematic diagram of significant local standardized regression coefficients of a multi-scale geographical weighted regression model MGWR formed in the analysis process provided by an embodiment of the present application. DETAILED DESCRIPTION

[0059] The technical solutions of the present application will be described in detail below with the aid of the accompanying drawings and specific embodiments. It should be understood that the specific features in the embodiments and the specific embodiments are detailed descriptions of the technical solutions of the present application, and are not limitations of the technical solutions of the present application. In the case of no conflict, the technical features in the embodiments and the specific embodiments can be combined with each other.

[0060] According to the correlation coefficient and significance between the soil organic carbon SOC content and each environmental variable, the global correlation between the soil organic carbon SOC content and each environmental variable is analyzed to obtain the globally correlated environmental variables and the globally uncorrelated environmental variables. According to the globally correlated environmental variables and the globally uncorrelated environmental variables and the geographical weighted correlation coefficient, the local correlation between the soil organic carbon SOC content and each environmental variable is analyzed to obtain the locally correlated environmental variables, etc. All of the above are prior art, and the undisclosed part of the present specification is the known technology available to those skilled in the art.

[0061] Embodiment 1

[0062] As shown in Figure 1 , the present embodiment introduces a multi-scale correlation analysis method for soil organic carbon spatial variability analysis, characterized in that it comprises:

[0063] Multiple soil samples were collected from the study area, and the soil organic carbon (SOC) content in the soil samples was determined through laboratory analysis, providing a data basis for the spatial distribution and variability of soil SOC in the study area.

[0064] Multi-source data within the study area were acquired, and environmental variables were extracted from the multi-source data. The multi-source data included basic geographic data, topographic data, and remote sensing data. The environmental variables included topographic factors, location conditions, landscape patterns, and remote sensing spectral indices. Data on various environmental factors that may affect soil organic carbon (SOC) content were collected to comprehensively consider the influencing factors of soil SOC distribution, which helps to reveal the causes of spatial heterogeneity of soil SOC.

[0065] The correlation coefficients and significance between soil organic carbon (SOC) content and each environmental variable were determined. The global correlation between soil organic carbon (SOC) content and each environmental variable was analyzed to obtain globally correlated and globally uncorrelated environmental variables.

[0066] A preliminary analysis of the global correlation between soil organic carbon (SOC) content and environmental variables was conducted to identify environmental factors that may have a significant impact.

[0067] By determining the geographically weighted correlation coefficient based on globally relevant and globally irrelevant environmental variables and the geographical weight of each soil sample, the local correlation between soil organic carbon (SOC) content and each environmental variable is analyzed, and the locally relevant environmental variables are obtained. This can reveal the spatial variability of the relationship between soil organic carbon (SOC) content and environmental variables, and help to understand the causes of spatial heterogeneity of soil organic carbon (SOC) more accurately.

[0068] Based on the variance inflation factor and tolerance of locally correlated environmental variables, multicollinearity is assessed for these variables. Variables exhibiting multicollinearity are then removed to obtain environmental variables free from multicollinearity. Removing multicollinearity avoids its impact on the results, making the analysis more reliable.

[0069] Based on the spatial weight of each soil sample point and the effective bandwidth of environmental variables without multicollinearity, the multiscale geographically weighted regression model MGWR is used to fit the soil organic carbon (SOC) content with environmental variables without multicollinearity to obtain the local standardized regression coefficients of environmental variables without multicollinearity. Based on the local standardized regression coefficients of environmental variables without multicollinearity, environmental variables with significant local impact on soil organic carbon (SOC) are identified.

[0070] By considering the spatial heterogeneity of different environmental variables, the relationship between soil organic carbon (SOC) content and environmental variables is fitted using a multi-scale geographic weighted regression model (MGWR), which can more accurately reflect the multi-scale effects of environmental variables on soil organic carbon (SOC) and improve the explanation of the spatial heterogeneity of soil organic carbon (SOC).

[0071] Based on the global correlation environmental variables, global irrelevant environmental variables, local correlation environmental variables and environmental variables with significant local standardized regression coefficients, the comprehensive analysis of environmental variable influence scale is carried out to analyze the spatial heterogeneity of soil organic carbon (SOC) content.

[0072] The environmental factors with significant local influence on soil organic carbon (SOC) content are identified, which provides key information for understanding the causes of spatial heterogeneity of soil organic carbon (SOC), helps to develop targeted soil management measures and improve soil quality. Comprehensive global correlation and local correlation analysis and multi-scale geographic weighted regression model (MGWR) results are used to comprehensively analyze the spatial heterogeneity of soil organic carbon (SOC) content. It provides a scientific basis for the rational use of soil resources and environmental protection, and helps to achieve sustainable land use and management.

[0073] Embodiment 2

[0074] Based on the same inventive concept as embodiment 1, this embodiment provides a multi-scale correlation analysis method for analyzing the spatial variability of soil organic carbon, which includes the following steps:

[0075] Step 1: Collect multiple soil samples in the study area and measure the soil organic carbon (SOC) content in the soil samples.

[0076] The expansion of human activities in plateau areas has led to the loss of ecological land and exacerbated habitat fragmentation. Qi'ulu Lake is one of the nine plateau lakes in Yunnan Province, China, with a watershed area of 354 square kilometers. The watershed is located in the Yungui Plateau, and due to market-oriented and industrialized agricultural management, Qi'ulu Lake is surrounded by highly dispersed farmland, with high landscape heterogeneity, making it an interesting case study area.

[0077] The complexity of soil in this area, characterized by land management heterogeneity, makes the distribution pattern of soil organic carbon (SOC) and its relationship with soil forming factors complex.

[0078] Therefore, from November 16 to 20, 2018, 216 surface soil samples were collected in the study area, and the global positioning system GPS position and surrounding environment information of each soil sample were recorded. In the above process, the local landscape pattern is mainly considered. In the area where the land is relatively broken, the density of the sampling points is relatively high. The collected soil samples are put into sealed bags, labeled, and then quickly transported to the laboratory for analysis. The specific distribution of multiple soil points in the study area is shown in Figure 2 .

[0079] Step 2: Obtain multi-source data in the study area, and extract environmental variables from the multi-source data, wherein the multi-source data includes basic geographic data, terrain data, remote sensing data, and the environmental variables include terrain factors, location conditions, landscape patterns, and remote sensing spectral indexes.

[0080] After analysis and demonstration, it is considered that the factors affecting the soil organic carbon SOC in the study area should be considered from the aspects of terrain conditions, location conditions, landscape patterns, vegetation, and water conditions. Based on this, the present application collects and arranges different categories of environmental variables of the Qiluhu Basin as shown in Table 1, and the spatial distribution of part of the environmental variables is shown in Figure 3 .

[0081]

[0082] Step 3: Determine the correlation coefficient and significance between the soil organic carbon SOC content and each environmental variable, analyze the global correlation between the soil organic carbon SOC content and each environmental variable, and obtain the global correlation environmental variable and the global non-correlation environmental variable, including:

[0083] Using the Spearman correlation analysis method, the correlation coefficient between the soil organic carbon SOC content and each environmental variable is calculated , and the value range is-1 to 1; through the Spearman correlation analysis, the global relationship between the soil organic carbon SOC and each environmental variable can be comprehensively understood, which lays a foundation for in-depth study of the spatial variability of SOC and its influencing factors.

[0084] Among them, the Spearman correlation analysis method is represented as:

[0085] ;

[0086] In the formula, is the difference between the rank of the environmental variable and the soil organic carbon SOC of the ith sample, is the total number of soil samples.

[0087] The statistical significance test is performed according to the correlation coefficient between the soil organic carbon SOC content and each environmental variable to determine the significance between the soil organic carbon SOC content and each environmental variable.

[0088] The statistical significance test is usually performed by using the p value, and when the p value is less than a set significance level, such as 0.05, the correlation coefficient is considered to be statistically significant, as shown in Table 2.

[0089]

[0090] According to the Spearman correlation coefficient and significance between the soil organic carbon SOC content and each environmental variable, the global correlation between the soil organic carbon SOC content and each environmental variable is analyzed to obtain the globally correlated environmental variables and the globally uncorrelated environmental variables.

[0091] Step 4: According to the globally correlated environmental variables and the globally uncorrelated environmental variables and the geographical weight of each soil sample, the geographical weighted correlation coefficient is determined to analyze the local correlation between the soil organic carbon SOC content and each environmental variable, and the locally correlated environmental variables are obtained, including:

[0092] The geographical weight of each soil sample is determined using a Gaussian kernel function;

[0093] According to the geographical weight of each soil sample, the geographical weighted covariance between the soil organic carbon SOC content and each environmental variable at different spatial positions, and the geographical weighted standard deviation of the soil organic carbon SOC content and the geographical weighted standard deviation of each environmental variable at different spatial positions are calculated;

[0094] The geographical weighted correlation coefficient at different spatial positions is calculated according to the geographical weighted covariance between the soil organic carbon SOC content and each environmental variable at different spatial positions, and the geographical weighted standard deviation of the soil organic carbon SOC content and the geographical weighted standard deviation of each environmental variable at different spatial positions;

[0095] According to the globally correlated environmental variables and the globally uncorrelated environmental variables and the geographical weighted correlation coefficient, the local correlation between the soil organic carbon SOC content and each environmental variable is analyzed to obtain the locally correlated environmental variables, and the local correlation is visually displayed in space to reveal the local correlation between the soil organic carbon SOC content and each environmental variable at different spatial positions. Some environmental variables and the geographical weighted correlation results of the soil organic carbon SOC are shown in FIG. 1. Figure 4

[0096] wherein the geographical weighted covariance between the soil organic carbon SOC content and each environmental variable at different spatial positions is represented as:

[0097] ;​

[0098] wherein, is the geographically weighted covariance value between the soil organic carbon SOC content and each environmental variable at different spatial locations; and are the rank of the environmental variable at location i and the rank of the soil organic carbon SOC in the soil sample at location i, respectively; and are the rank of the environmental variable at location j and the rank of the soil organic carbon SOC in the soil sample at location j, respectively; and are the geographically weighted average rank of the environmental variable at location i and the geographically weighted average rank of the soil organic carbon SOC in the soil sample at location i, respectively; n is the total number of soil samples.

[0099] The geographically weighted standard deviation of each environmental variable at different spatial locations is represented as:

[0100]

[0101] The geographically weighted standard deviation of the soil organic carbon SOC content is represented as:

[0102]

[0103] wherein, and are the geographically weighted standard deviation value of each environmental variable and the geographically weighted standard deviation value of the soil organic carbon SOC content at different spatial locations, respectively.

[0104] wherein, the geographically weighted average rank of the i-th environmental variable and the geographically weighted average rank of the soil organic carbon SOC in the i-th soil sample are represented as:

[0105]

[0106]

[0107] The geographically weighted correlation coefficient at different spatial locations is represented as:

[0108]

[0109] wherein, is the geographically weighted correlation coefficient value at different spatial locations.

[0110] Step 5: According to the variance inflation factor and the tolerance of the locally correlated environmental variables, the multicollinearity of the locally correlated environmental variables is judged, and the locally correlated environmental variables with multicollinearity are deleted to obtain environmental variables without multicollinearity, including:​​​​​

[0111] Before performing the multi-scale geographically weighted regression modeling, the multiple collinearity diagnosis of the variables needs to be performed to ensure the stability and reliability of the multi-scale geographically weighted regression model.

[0112] The variance inflation factor and tolerance of the local correlation environment variables are determined by the regression analysis method. When the variance inflation factor is greater than 5 and the tolerance is less than 0.2, it indicates that the local correlation environment variables have multiple collinearity. The local correlation environment variables with multiple collinearity are deleted, and the variance inflation factor VIF and the tolerance Tolerance of each local correlation environment variable are calculated again. When the variance inflation factor is less than 5 and the tolerance is greater than 0.2, the environment variables without multiple collinearity are obtained, and then the multi-scale geographically weighted regression model MGWR modeling is performed. The multiple collinearity diagnosis results are shown in Table 3.

[0113]

[0114] wherein the tolerance and the variance inflation factor of the local correlation environment variables are represented as:

[0115]

[0116]

[0117] wherein, is the variance inflation factor of the local correlation environment variables, Tolerance is the tolerance of the local correlation environment variables, R 2 is the determination coefficient of the regression analysis method.

[0118] wherein the determination coefficient of the regression analysis method is represented as:

[0119]

[0120] wherein, is the actual measured value of the soil organic carbon SOC in the soil sample at the i-th position, is the predicted value of the soil organic carbon SOC in the soil sample at the i-th position, is the mean value of the actual measured value of the soil organic carbon SOC, is the total number of soil samples.

[0121] Step 6: Based on the spatial weight of each soil sample and the effective bandwidth of the environment variables without multiple collinearity, the multi-scale geographically weighted regression model MGWR is used to fit the soil organic carbon SOC content and the environment variables without multiple collinearity, and the local standardized regression coefficients of the environment variables without multiple collinearity are obtained, including: ​​​​

[0122] The spatial weights of each soil sample are obtained by using a Gaussian kernel function to perform spatial weighting on each soil sample.

[0123] The effective bandwidth for each environment variable is determined using the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC).

[0124] Based on the spatial weights and effective bandwidth, the multi-scale geographically weighted regression model MGWR was used to fit the soil organic carbon (SOC) content with each environmental variable that does not have multicollinearity, and the local standardized regression coefficients of the environmental variables that do not have multicollinearity were obtained, revealing the complex relationship between soil organic carbon (SOC) and environmental variables at different spatial scales. The standardized regression coefficients and bandwidth statistics of each environmental variable are shown in Table 4.

[0125]

[0126] The spatial weight of each soil sample was calculated using methods such as the Gaussian kernel function or the biquadratic kernel function, reflecting the spatial weight of the first soil sample. Soil samples from the locations in the first... The degree of influence in the estimation of regression coefficients at each position.

[0127] Taking the Gaussian kernel function as an example, the specific formula for the spatial weight of each soil sample is as follows:

[0128] ;

[0129] In the formula, , It is the first Position and number The distance between each location It is the first Spatial bandwidth of each environment variable .

[0130] The multi-scale geographically weighted regression model MGWR is represented as:

[0131] ;

[0132] In the formula, Soil sample The dependent variable; Soil sample The One environment variable; For the first Regression equations for environmental variables; differential bandwidth of environmental variables; The total number of variables; Soil sample The spatial coordinates of its location; Intercept term, varying with spatial location change; Soil sample Spatial coordinates The first The regression coefficients of each variable; This is the random error term.

[0133] Step 7: Based on the fitting results of the multiscale geographically weighted regression model MGWR, calculate the local standardized regression coefficients of environmental variables that do not exhibit multicollinearity.

[0134] Local standardized regression coefficients of environmental variables without multicollinearity were estimated using weighted least squares method. ;

[0135] The statistical significance of the locally standardized regression coefficients of environmental variables that do not exhibit multicollinearity was tested, and spatial visualization was performed to identify environmental variables that have a significant local impact on soil organic carbon (SOC).

[0136] Among them, the weighted sum of squared residuals (WSSR) is estimated by minimizing the first... The locally standardized regression coefficients of each location environmental variable, expressed as the minimum weighted sum of squared residuals (WSSR), are as follows:

[0137] ;

[0138] In the formula, To minimize the weighted sum of squared residuals; For position SOC content of soil samples at the location; It is the first Samples at position n, pair of n The geographic weight of each location sample depends on the spatial bandwidth. and distance decay function, It is the first Spatial bandwidth of each independent variable; Soil sample points The One independent variable; For the first The differential bandwidth of the independent variables in the regression equation for each independent variable; The total number of variables; Soil sample points The spatial coordinates of its location; The intercept term varies with spatial location. change; Soil sample points Spatial coordinates The first The regression coefficients of each variable; This represents the total number of soil samples.

[0139] The residual sum of squares (RSS) is expressed as:

[0140] ;

[0141] The Akaike Information Content Criterion (AIC) is expressed as follows:

[0142] ;

[0143] In the formula, This represents the number of all regression coefficients and intercept terms in the multi-scale geographically weighted regression model MGWR. It represents the logarithm with the constant e as the base.

[0144] The significance of the locally standardized regression coefficients for each environmental variable without multicollinearity is tested and the results are spatially visualized. This interprets the results of the multiscale geographically weighted regression model (MGWR), identifies environmental variables with significant local impacts on soil organic carbon (SOC), analyzes their spatial heterogeneity, and provides an in-depth analysis of the multiscale effects of environmental variables on SOC. Figure 5 As shown.

[0145] Step 8: Based on globally relevant environmental variables, globally irrelevant environmental variables, locally relevant environmental variables, and environmental variables with significant local standardized regression coefficients, conduct a comprehensive analysis of the scale of influence of environmental variables to analyze the spatial heterogeneity of soil organic carbon (SOC) content.

[0146] First, based on the global correlation analysis results shown in Table 2, it can be seen that soil moisture content (SMC), topographic humidity index (TWI), distance from road (Road_D), enhanced vegetation index (EVI), brightness index (BI), normalized shortwave infrared differential bare soil moisture index (NSDSI1), brightness, greenness, and wetness are positively correlated with soil organic carbon (SOC). Elevation (DEM), slope, distance from river (River_D), landscape abundance density (PRD), and color index (CI) are negatively correlated with soil organic carbon (SOC). The global correlation between soil total porosity (SP), spread index (CONTAG), and maximum patch area percentage (LPI) and soil organic carbon (SOC) is low and not significant.

[0147] Secondly, local correlation analysis revealed spatial differences in the positive and negative values ​​and magnitudes of the geographically weighted correlation coefficients between various environmental variables and soil organic carbon (SOC), reflecting the different local effects of these variables on SOC. Furthermore, the three variables with no significant global correlation to SOC—total soil porosity (SP), contagion index (CONTAG), and maximum patch area percentage (LPI)—all showed geographically weighted local correlations with SOC. Figure 4 As shown, this demonstrates that even variables that are not significant in the global analysis can still play an important role in the local analysis, revealing the complex spatial heterogeneity between soil organic carbon (SOC) and environmental variables.

[0148] Furthermore, the standardized regression coefficients of the multi-scale geographically weighted regression model MGWR further reflect the overall influence and local explanatory power of various environmental variables on soil organic carbon (SOC), as shown in Table 4. Figure 5 As shown, the multi-scale geographically weighted regression model (MGWR) analysis primarily revealed the local-scale effects of soil moisture content (SMC), total soil porosity (SP), distance from river (River_D), distance from road (Road_D), landscape abundance density (PRD), spread index (CONTAG), maximum patch area percentage (LPI), and enhanced vegetation index (EVI) on soil organic carbon (SOC), exhibiting geographical variability. Although variables such as soil moisture content (SMC), distance from river (River_D), distance from road (Road_D), landscape abundance density (PRD), and enhanced vegetation index (EVI) showed significant global correlations with SOC, their effects were primarily local, possibly due to the aggregation of local effects. However, while total soil porosity (SP), contagiousness index (CONTAG), and maximum patch area percentage (LPI) also have local effects, they are easily overlooked in global correlation analyses due to their insignificant correlation with soil organic carbon (SOC), leading to their exclusion as invalid variables in SOC prediction. In contrast, variables that are significantly correlated with SOC in global correlation analyses, such as slope, topographic moisture index (TWI), color index (CI), normalized shortwave infrared differential bare soil moisture index (NSDSI1), brightness, and greenness, do not show significant effects in the MGWR model. Their local scale effects may be masked or balanced by other variables with greater local significance.

[0149] In a global range, the global variable can be used to build a preliminary soil organic carbon SOC prediction model, and provide an overview of the distribution trend of the soil organic carbon SOC in the whole region. However, in order to apply detailed management and accurate prediction in a local range, variables that are important at a local level must be further introduced to achieve more accurate prediction results and effective management strategies. Therefore, the example results have verified that the present application can reveal the relationship between the environmental variable and the soil organic carbon SOC globally, accurately capture the overall influence of the environmental variable on the soil organic carbon SOC, and reflect more fine changes in a local area, identify and explain the local influence of the environmental variable at different spatial positions, thereby enhancing the understanding of the spatial distribution of the soil organic carbon SOC.

[0150] Embodiment 3

[0151] Based on the same inventive concept as other embodiments, the present application also provides a soil organic carbon prediction method, which selects an environmental variable according to the analysis result of the multi-scale correlation analysis method for analyzing the spatial variability of soil organic carbon according to Embodiment 1 or 2, and predicts the soil organic carbon.

[0152] In summary of the embodiments, the present application provides a multi-scale correlation analysis method for analyzing the spatial variability of soil organic carbon, which is based on Spearman correlation analysis, geographic weighted correlation analysis and multi-scale geographic weighted regression model, captures the distribution characteristics of the soil organic carbon SOC at different spatial scales, optimizes the selection of environmental variables, and improves the generalization ability of the soil organic carbon SOC mapping model.

[0153] The present application firstly reveals the global relationship between the environmental variable and the SOC through the Spearman correlation analysis, secondly explores the local correlation between the soil organic carbon SOC and the environmental variable at different spatial positions by introducing the geographic weighted correlation, reveals the local influence of the environmental variable in different regions, and then introduces the multi-scale geographic weighted regression model MGWR, fully considers the heterogeneity of the spatial process and the influence degree of different environmental variables at different spatial scales, thereby solving the problem of insufficient explanation of the local spatial relationship in the prior art.

[0154] After the method of the present application is adopted, firstly, the relationship between the environmental variables and the soil organic carbon SOC is revealed globally, and the influence of the overall environmental variables on the soil organic carbon SOC is accurately captured; secondly, finer changes in the local region are reflected, the local influence of the environmental variables on different spatial positions can be identified and explained, and the understanding of the spatial distribution law of the soil organic carbon SOC is enhanced. Finally, based on the soil organic carbon SOC variability analysis result of the method of the present application, scientific basis and decision support can be provided for soil management, agricultural planning and ecological environment protection. By revealing the multi-scale relationship between the environmental variables and the soil organic carbon SOC, the present application can not only improve the accuracy and reliability of the spatial prediction of the soil organic carbon SOC, but also has certain universality and generalizability, and can provide effective tools and methods for the management and research of the soil organic carbon SOC in different regions.

[0155] Those skilled in the art will appreciate that embodiments of the present application can be supplied as methods, systems, or computer program products. Accordingly, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer-readable program code.

[0156] The present application is described in reference to flowcharts and / or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as combinations of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing apparatus produce an apparatus that implements the flow Figure 1 The functions specified in one or more flows and / or blocks Figure 1 The functions specified in one or more flows and / or blocks

[0157] These computer program instructions can also be stored in a computer-readable memory that can direct the computer or other programmable data processing apparatus to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including instruction apparatus, which implements the flow Figure 1 The functions specified in one or more flows and / or blocks Figure 1 The functions specified in one or more flows and / or blocks

[0158] These computer program instructions can also be loaded into a computer or other programmable data processing devices, so that a series of operational steps are generated to realize the computer-implemented processes, and the instructions executed on the computer or other programmable devices provide a process for implementing the functions specified in the flowchart Figure 1 one flow or multiple flows and / or the functions specified in the block Figure 1 one flow or multiple flows and / or the functions specified in the block

[0159] The embodiments of the present application are described above with reference to the accompanying drawings, but the present application is not limited to the specific embodiments described above, and the specific embodiments described above are merely illustrative, but not restrictive, and those of ordinary skill in the art can make many forms under the inspiration of the present application without departing from the purpose of the present application and the scope protected by the claims, which are all within the protection of the present application.

Claims

1. A multi-scale correlation analysis method for analyzing spatial variability of soil organic carbon, characterized in that, The method comprises the following steps: Collecting a plurality of soil samples in a study area, and measuring soil organic carbon (SOC) content in the soil samples; Obtaining multi-source data in the study area, and extracting environmental variables from the multi-source data; the multi-source data comprises basic geographic data, terrain data and remote sensing data, and the environmental variables comprise terrain factors, site conditions, landscape patterns and remote sensing spectral indexes; Determining correlation coefficients and significances between the soil organic carbon (SOC) content and each environmental variable, analyzing global correlations between the soil organic carbon (SOC) content and each environmental variable, and obtaining globally correlated environmental variables and globally uncorrelated environmental variables; Determining geographically weighted correlation coefficients according to the globally correlated environmental variables, the globally uncorrelated environmental variables and geographical weights of each soil sample, analyzing local correlations between the soil organic carbon (SOC) content and each environmental variable, and obtaining locally correlated environmental variables; Judging multiple collinearity of the locally correlated environmental variables according to variance inflation factors and tolerances of the locally correlated environmental variables, deleting the locally correlated environmental variables with multiple collinearity, and obtaining environmental variables without multiple collinearity; Fitting the soil organic carbon (SOC) content and the environmental variables without multiple collinearity by using a multi-scale geographically weighted regression model (MGWR) based on spatial weights of each soil sample point and effective bandwidths of the environmental variables without multiple collinearity, and obtaining local standardized regression coefficients of the environmental variables without multiple collinearity; Determining environmental variables with significant local influence on the soil organic carbon (SOC) according to the local standardized regression coefficients of the environmental variables without multiple collinearity; Comprehensively analyzing environmental variable influence scales according to the globally correlated environmental variables, the globally uncorrelated environmental variables, the locally correlated environmental variables and the environmental variables with significant local standardized regression coefficients, and analyzing spatial heterogeneity of the soil organic carbon (SOC) content.

2. The multi-scale correlation analysis method for resolving spatial variability of soil organic carbon according to claim 1, characterized in that, The method for determining correlation coefficients and significances between the soil organic carbon (SOC) content and each environmental variable, analyzing global correlations between the soil organic carbon (SOC) content and each environmental variable, and obtaining globally correlated environmental variables and globally uncorrelated environmental variables comprises the following steps: Using a Spearman correlation analysis method to calculate correlation coefficients between the soil organic carbon (SOC) content and each environmental variable; Determining significances between the soil organic carbon (SOC) content and each environmental variable according to statistical significance tests of the correlation coefficients between the soil organic carbon (SOC) content and each environmental variable; Analyzing global correlations between the soil organic carbon (SOC) content and each environmental variable according to the correlation coefficients and the significances between the soil organic carbon (SOC) content and each environmental variable, and obtaining globally correlated environmental variables and globally uncorrelated environmental variables.

3. The multi-scale associated analysis method for resolving spatial variability of soil organic carbon according to claim 1, characterized in that, The method for determining geographically weighted correlation coefficients according to the globally correlated environmental variables, the globally uncorrelated environmental variables and geographical weights of each soil sample, analyzing local correlations between the soil organic carbon (SOC) content and each environmental variable, and obtaining locally correlated environmental variables comprises the following steps: Determining geographical weights of each soil sample by using a Gaussian kernel function; According to the geographical weight of each soil sample, geographical weighted covariance between soil organic carbon SOC content at different spatial positions and each environmental variable, and geographical weighted standard deviation of soil organic carbon SOC content at different spatial positions and geographical weighted standard deviation of each environmental variable are calculated; According to the geographical weighted covariance between soil organic carbon SOC content at different spatial positions and each environmental variable, and the geographical weighted standard deviation of soil organic carbon SOC content at different spatial positions and the geographical weighted standard deviation of each environmental variable, geographical weighted correlation coefficients at different spatial positions are calculated; According to the global correlation environmental variables, the global non-correlation environmental variables and the geographical weighted correlation coefficients, local correlation between soil organic carbon SOC content and each environmental variable is analyzed to obtain local correlation environmental variables.

4. The multi-scale associated analysis method for resolving spatial variability of soil organic carbon according to claim 3, characterized in that, According to the geographical weight of each soil sample, geographical weighted covariance between soil organic carbon SOC content at different spatial positions and each environmental variable, and geographical weighted standard deviation of soil organic carbon SOC content at different spatial positions and geographical weighted standard deviation of each environmental variable are calculated; The geographical weighted covariance between soil organic carbon SOC content at different spatial positions and each environmental variable is represented as: ； wherein, GWCi,jis the geographically weighted covariance value between the soil organic carbon SOC content and each environmental variable for different spatial locations; and respectively the rank of the environmental variable at location i and the rank of the soil organic carbon SOC in the soil sample at location i; and respectively the rank of the environmental variable at location j and the rank of the soil organic carbon SOC in the soil sample at location j; and respectively the geographically weighted average rank of the environmental variable at location i and the geographically weighted average rank of the soil organic carbon SOC in the soil sample at location i; is the sample at the th location, is the geographically weight of the sample at the th location to the sample at the th location, and N is the total number of soil samples. The geographical weighted standard deviation of each environmental variable at different spatial positions is represented as: ； The geographical weighted standard deviation of soil organic carbon SOC content is represented as: ； wherein, and respectively are the geographically weighted standard deviation values of each environmental variable and the geographically weighted standard deviation values of soil organic carbon SOC content at different spatial locations.

5. The multi-scale associated analysis method for soil organic carbon spatial variability resolution according to claim 4, characterized in that, According to the geographical weighted covariance between soil organic carbon SOC content at different spatial positions and each environmental variable, and the geographical weighted standard deviation of soil organic carbon SOC content at different spatial positions and the geographical weighted standard deviation of each environmental variable, geographical weighted correlation coefficients at different spatial positions are calculated, and the geographical weighted correlation coefficients at different spatial positions are represented as: ； wherein are geographically weighted correlation coefficient values for different spatial locations.

6. The multi-scale associated analysis method for resolving spatial variability of soil organic carbon according to claim 1, wherein, According to the variance inflation factor and tolerance of the local correlation environmental variables, multiple collinearity of the local correlation environmental variables is judged, and the local correlation environmental variables with multiple collinearity are deleted to obtain environmental variables without multiple collinearity, comprising: The variance inflation factor and tolerance of the local correlation environmental variables are determined by regression analysis method, when the variance inflation factor is greater than 5 and the tolerance is less than 0.2, it indicates that the local correlation environmental variables have multiple collinearity, and the local correlation environmental variables with multiple collinearity are deleted to obtain environmental variables without multiple collinearity.

7. The multi-scale associated analysis method for resolving spatial variability of soil organic carbon according to claim 1, wherein, Based on the spatial weight of each soil sample and the effective bandwidth of the environmental variables without multiple collinearity, a multi-scale geographical weighted regression model MGWR is used to fit soil organic carbon SOC content and the environmental variables without multiple collinearity to obtain local standardized regression coefficients of the environmental variables without multiple collinearity, comprising: The spatial weight of each soil sample is weighted using a Gaussian kernel function to obtain the spatial weight of each soil sample; The effective bandwidth of each environmental variable is determined using Akaike information criterion AIC or Bayesian information criterion BIC; The effective bandwidth of each environmental variable is determined using Akaike information criterion AIC or Bayesian information criterion BIC; Based on the spatial weight and the effective bandwidth, fitting the soil organic carbon SOC content and the environmental variables without multiple collinearity using a multi-scale geographically weighted regression model MGWR, and calculating the local standardized regression coefficients of the environmental variables without multiple collinearity according to the fitting result of the multi-scale geographically weighted regression model MGWR.

8. The multi-scale associated analysis method for resolving spatial variability of soil organic carbon according to claim 7, characterized in that, The multi-scale geographically weighted regression model MGWR is expressed as: ； wherein is the dependent variable for the soil sample; is the dependent variable for the soil sample; is the dependent variable for the soil sample; is the dependent variable for the soil sample; is the dependent variable for the soil sample; is the bandwidth of differentiation for the dependent variable; is the total number of variables; is the spatial location coordinate for the soil sample; is the spatial location coordinate for the soil sample; is the spatial location coordinate for the soil sample; is the intercept term, which varies with the spatial location; is the spatial location coordinate for the soil sample; is the spatial location coordinate for the soil sample is the spatial location coordinate for the soil sample is the spatial location coordinate for the soil sample is the spatial location coordinate for the soil sample is the random error term.

9. The multi-scale associated analysis method for resolving spatial variability of soil organic carbon according to claim 7, characterized in that, The method for calculating the local standardized regression coefficients of the environmental variables without multiple collinearity according to the fitting result of the multi-scale geographically weighted regression model MGWR, comprises: Local standardized regression coefficients of the environmental variables are estimated by weighted least squares method without multicollinearity ; The local standardized regression coefficients of each environmental variable without multiple collinearity are subjected to statistical significance test and spatial visualization to determine the environmental variables having significant local influence on the soil organic carbon SOC.

10. A method of predicting soil organic carbon, characterized by, The environmental variables are selected according to the analysis result of the multi-scale correlation analysis method for analyzing the spatial variability of soil organic carbon according to claim 1, and the soil organic carbon is predicted.

Images