CN114611271A - Snow water equivalent grid data modeling and analyzing method considering spatial heterogeneity - Google Patents

Abstract

Aiming at the problem that the traditional regression model does not consider the influence of spatial effects in the snow water equivalent modeling, and the spatial regression model faces a serious computational bottleneck in grid data, a snow water equivalent grid considering spatial heterogeneity is proposed. Lattice data modeling and analysis methods, taking into account both global and regional spatial effects. In the spatial modeling of remote sensing images, the data is divided into several sub-regions of the same size, and each sub-region is modeled to achieve the purpose of modeling and computing the entire remote sensing image; using the spatial filtering method, using spatial adjacency The eigenvectors of the matrix fit the residuals, and the fitting results are added to the previous global model as spatial influences to obtain the final spatial regression model. The present invention can obtain an accurate model of the snow water equivalent and its related factors for subsequent research and analysis.

Description

Modeling and Analysis Method of Snow Water Equivalent Raster Data Considering Spatial Heterogeneity

technical field

The invention relates to the technical field of spatial statistical analysis service application, in particular to a snow water equivalent grid data modeling and analysis method taking into account spatial heterogeneity.

Background technique

Snow water equivalent (SWE) is one of the important snow parameters, which refers to the vertical depth of the water layer formed by the obtained water when the snow is completely melted, and the commonly used unit is mm. Since snow is very sensitive to temperature changes, the monitoring of snow water equivalent is of great significance for the study of climate change trends, water resources management and agricultural production planning. The global snow cover area is mainly located in the middle and high latitudes, the north and south poles, and the high mountains. With different geographical locations, the observed results of snow cover are also different. For example, the slope orientation determines the duration of sunshine and the received radiation intensity. Less solar radiation on shady slopes helps to retain soil moisture and reduce the evaporation capacity of air, which is more conducive to the accumulation of snow than on sunny slopes, that is, the spatial heterogeneity of snow is stronger. This makes it difficult for a small number of stations to fully display the spatiotemporal variation characteristics of snow cover on a large spatial scale, which has great limitations. Remote sensing technology, as a new method for large-scale monitoring of the earth's surface, overcomes the shortcomings of traditional site monitoring, provides long-term, large-scale snow monitoring data, and is an important data source for snow water equivalent. The microwave sensor mainly receives the radiation energy from the snow and its underlying surface. The sensor represents the received energy by the brightness temperature value, and the attribute information of the snow (such as the snow water equivalent) has a certain functional relationship with the brightness temperature. This relationship can be reversed for the snow water equivalent.

The change of snow water equivalent is affected by environmental factors, such as: air temperature (AT), surface heat flux (GFLUX), cloud layer water content (CLDWP), precipitation (PREC), vegetation cover (NDVI), wind speed (WS), etc. . Spatial regression model is a modeling method that considers spatial effects, and can be used to explore the relationship between snow water equivalent and related factors. The least squares linear regression model is simple in structure and modeling process, and can infer the correlation in statistical significance. The premise of the traditional regression model is that (residuals) are independent and identically distributed, but in fact they are interdependent and related, and there is spatial autocorrelation, so the traditional model is not suitable for spatial data. The variables of spatial statistical analysis are spatially interdependent and interrelated, also known as spatial autocorrelation. The spatial autocorrelation of variables will affect the accuracy of regression modeling, so it is necessary to eliminate the influence of spatial autocorrelation. The spatial regression model considers the influence of spatial autocorrelation, so that an accurate model can be established. Griffith proposed the spatial filtering method to solve the spatial autocorrelation problem in spatial regression analysis. incorporated into the final regression model. The spatial filtering method has a large amount of calculation, and is usually calculated in an area with a small amount of data, and has not yet been fully applied in the modeling calculation of the entire remote sensing image.

It can be seen that the existing method has the technical problem of poor modeling effect.

SUMMARY OF THE INVENTION

The present invention proposes a snow water equivalent grid data modeling and analysis method considering spatial heterogeneity, which is used to solve or at least partially solve the technical problem that the existing methods have poor modeling effect. Based on the relevant influencing factor data of snow water equivalent, the spatial regression modeling of snow water equivalent was carried out, the influencing factors of snow water equivalent were explored, and the change of snow water equivalent was analyzed through the regression model. The invention aims to simultaneously consider global scale characteristics and spatial heterogeneity, reduce the influence of spatial effects, further improve the modeling accuracy and estimation effect of snow water equivalent, and achieve the purpose of modeling and calculation of large-scale remote sensing images through a block method.

The technical scheme of the present invention is:

The first aspect provides a snow water equivalent raster data modeling method that considers spatial heterogeneity, including:

S1: Obtain raster data of snow water equivalent, and preprocess the obtained raster data;

S2: Based on the preprocessed data, with the snow water equivalent as the dependent variable and the environmental factors related to the snow water equivalent as the independent variables, establish a global least squares linear regression model:

y _g =β ₀ +β ₁ x ₁ +β ₂ x ₂ +…+β _k x _k +ε

In the formula, y _g represents the observed value of snow water equivalent, x ₁ , x ₂ , … x _k represent the first, second and k related influencing factors of snow water equivalent, respectively, β ₀ , β ₁ , … β _k are the coefficients of x ₁ , x ₂ , ... x _k respectively, and ε is the difference between the fitted value and the observed value of the global least squares linear regression model, that is, the residual;

S3: Extract the residual of the global least squares linear regression model and divide it into several sub-region modeling units with a size of N×N;

S4: For each sub-region modeling unit after division, determine whether the residual has spatial autocorrelation, if it has spatial autocorrelation, execute step S5, otherwise, use the parameters of the global least squares linear regression model in step S2 as the final model parameters of the corresponding sub-region;

S5: Use the spatial filtering method to model the sub-region, which specifically includes using the eigenvector of the spatial adjacency matrix to fit the residual to obtain the fitting result;

S6: The fitting result is added to the global least squares linear regression model constructed in step S2 as a spatial influence to obtain a final spatial regression model.

In one embodiment, in step S1, preprocessing is performed on the acquired grid data, including projection transformation, mask extraction, outlier processing, nearby missing grid filling, and data standardization processing.

In one embodiment, in step S4, it is determined whether the residual has spatial autocorrelation by calculating the Moran index. The Moran index is represented by the probability p value, which specifically includes: if p is less than the threshold, it indicates that there is a spatial autocorrelation. If there is autocorrelation, then go to step S5; otherwise, it indicates that there is no spatial autocorrelation, and the parameters of the global least squares linear regression model in step S2 are used as the final model parameters of the corresponding sub-region.

In one embodiment, step S5 includes:

S5.1: Construct a spatial adjacency matrix W according to the grid cell adjacency relationship of the sub-region;

S5.2: Centralize the constructed spatial adjacency matrix to obtain matrix C,

S5.3: Calculate the eigenvalues and eigenvectors of matrix C, and perform preliminary screening to obtain qualified spatial eigenvectors;

S5.4: Based on the qualified spatial eigenvectors, the forward selection method is used to gradually screen out the target eigenvectors;

S5.5: Based on the filtered target feature vector, construct a regional feature function space filtering value regression model for each sub-region, the formula is:

ε _i =E _i α _i +∈ _i (i=1,2,...m)

Among them, ε _i is the residual of the global model of the ith subregion, α _i is the regression coefficient vector of the ith subregion, matrix E _i includes the j target feature vectors selected from the ith subregion, ∈ _i is the ith subregion The regional model error vector of the region, m is the total number of sub-regions divided into several sub-regions.

In one embodiment, step S6 includes:

The fitting values of the regional models constructed by modeling the sub-regions are combined, and then added to the fitting values of the global least squares linear regression model to obtain the final spatial regression model. The formula is as follows:

为最终的空间回归模型的雪水当量拟合值，

为全局最小二乘线性回归模型的雪水当量拟合值，

为拼合后的子区域残差的拟合值；in,

is the fitted value of the snow water equivalent for the final spatial regression model,

is the fitted value of the snow water equivalent of the global least squares linear regression model,

is the fitted value of the residuals of the subregions after flattening;

The final spatial regression model expression is:

In the formula, x ₁ , x ₂ , ... x _k are the relevant influencing factors of snow water equivalent, β ₀ , β ₁ , ... β _k are the global least squares linear regression coefficients independent of x ₁ , x ₂ , ... x _k , E is the selected feature vector set, α is the regression coefficient vector of the sub-region, ∈ is the error vector.

In one embodiment, the method further includes step S7 of evaluating and analyzing the final spatial regression model.

Based on the same inventive concept, the second aspect of the present invention provides an analysis method for snow water equivalent, and the analysis method is implemented based on the final spatial regression model constructed in the first aspect.

The above-mentioned one or more technical solutions in the embodiments of the present application have at least one or more of the following technical effects:

Aiming at the problem that the traditional regression model does not consider the influence of the spatial effect in the snow water equivalent modeling, and the spatial regression model faces a serious computational bottleneck in the grid data, the invention proposes a snow water taking into account spatial heterogeneity. Equivalent raster data modeling method that considers both global and regional spatial effects. In the spatial modeling of remote sensing images, the data is divided into several sub-regions of the same size, and each sub-region is modeled to achieve the purpose of modeling and computing the entire remote sensing image; using the spatial filtering method, using spatial adjacency The eigenvectors of the matrix fit the residuals, and the fitting results are added to the previous global model as spatial influences to obtain the final spatial regression model. Accurate models of snow water equivalent and its related factors can be obtained, which further improves the modeling accuracy and estimation effect of snow water equivalent for subsequent research and analysis.

Description of drawings

In order to illustrate the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the drawings in the following description are For some embodiments of the present invention, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative efforts.

FIG. 1 is a flowchart of a method for modeling snow water equivalent grid data in consideration of spatial heterogeneity provided by an embodiment of the present invention;

2 is a schematic diagram of block statistics of data preprocessing in an embodiment of the present invention;

3 is a schematic diagram of regional division of the extracted global model residual in an embodiment of the present invention;

FIG. 4 is a flow chart of region modeling considering spatial heterogeneity in an embodiment of the present invention.

Detailed ways

The core problem to be solved by the present invention is: the distribution of snow water equivalent is affected by spatial effects, the traditional regression model only considers the global influence of environmental factors, and does not take into account the spatial effects of local areas due to the existence of spatial heterogeneity; At the same time, for the snow water equivalent raster data, there is a serious computational bottleneck when using a specific spatial regression method to model. In view of these problems, the present invention proposes a snow water equivalent grid data modeling method considering spatial heterogeneity, constructs a global-regional spatial regression model of snow water equivalent and environmental factors, and then can accurately explore the relationship between snow water equivalent and environmental factors. relationship with impact factors.

In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments These are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Example 1

This embodiment provides a snow water equivalent raster data modeling method considering spatial heterogeneity, including:

S1: Obtain raster data of snow water equivalent, and preprocess the obtained raster data;

S2: Based on the preprocessed data, with the snow water equivalent as the dependent variable and the environmental factors related to the snow water equivalent as the independent variables, establish a global least squares linear regression model:

y _g =β ₀ +β ₁ x ₁ +β ₂ x ₂ +…+β _k x _k +ε

In the formula, y _g represents the observed value of snow water equivalent, x ₁ , x ₂ , … x _k represent the first, second and k related influencing factors of snow water equivalent, respectively, β ₀ , β ₁ , … β _k are the coefficients of x ₁ , x ₂ , ... x _k respectively, and ε is the difference between the fitted value and the observed value of the global least squares linear regression model, that is, the residual;

S3: Extract the residual of the global least squares linear regression model and divide it into several sub-region modeling units with a size of N×N;

S4: For each sub-region modeling unit after division, determine whether the residual has significant spatial autocorrelation, and if it has significant spatial autocorrelation, perform step S5, otherwise use the global least squares linear regression model in step S2 The parameters of are used as the final model parameters of the corresponding sub-region;

S5: Use the spatial filtering method to model the sub-region, which specifically includes using the eigenvector of the spatial adjacency matrix to fit the residual to obtain the fitting result;

S6: The fitting result is added to the global least squares linear regression model constructed in step S2 as a spatial influence to obtain a final spatial regression model.

The main idea of the present invention is as follows:

In order to take into account the spatial heterogeneity, consider the local features in the spatial regression modeling, and eliminate the spatial autocorrelation, the invention proposes a snow water equivalent grid data modeling method that takes into account the spatial heterogeneity. The present invention considers that the spatial regression modeling of large-scale snow water equivalent grid data can first use the global least squares linear regression model on the global scale to obtain global features; for the existence of residuals in the established global least squares linear regression model For the problem of high spatial autocorrelation, the spatial filtering method is used to fit the residuals using spatial feature vectors, and the residual fitting results are added to the previous global model (global least squares linear regression model) as spatial influences. Go to, become the final spatial regression model; in the aforementioned spatial filtering method to model the residual, divide the data into several small sub-regions, model the residual of each sub-region, and finally model the overall It is integrated with the results of sub-region modeling, so as to achieve the purpose of modeling and computing the entire remote sensing image.

It should be noted that global characteristics refer to the response characteristics of snow water equivalent to relevant influencing factors in the overall research range. For example, compared with other factors, the factor "air temperature (AT)" has a Water equivalent has the strongest negative correlation, which is a global feature.

Referring to FIG. 1 , it is a flowchart of a method for modeling snow water equivalent grid data in consideration of spatial heterogeneity according to an embodiment of the present invention.

Among them, step S1 is the data acquisition and processing, S2 is the global least squares linear regression modeling, S3 is the global least squares linear regression residual difference block, S4 is the determination of the spatial autocorrelation of the residuals, and S5 is the use of spatial filtering. The value method models the residuals, and S6 is the construction of a global-regional model of snow water equivalent that takes into account spatial heterogeneity.

In the global least squares linear regression model of S2, β ₀ , β ₁ , ... β _k are the coefficients of the influencing factors, which can reveal the influence on the snow water equivalent. That is, the positive or negative sign of the coefficient represents a positive or negative correlation with the snow water equivalent, and the absolute value represents the degree of correlation.

In one embodiment, in step S1, preprocessing is performed on the acquired grid data, including projection transformation, mask extraction, outlier processing, nearby missing grid filling, and data standardization processing.

In the specific implementation process, the snow water equivalent and related factor data are obtained. The snow water equivalent data range is in the northern hemisphere, from the monthly snow water equivalent data in the European Space Agency's GlobSnow project. The formation condition of snow is that the accumulation of snow is greater than the ablation, so the relevant influencing factors are selected from the two aspects of snow accumulation and ablation. From the perspective of snowfall, one of the necessary conditions is water vapor saturation, so atmospheric environmental factors such as air temperature (AT), cloud water content (CLDWP), wind speed (WS), etc. affect the amount of snowfall and the distribution of snow cover; from snow cover From the perspective of ablation, ground environmental factors such as surface heat flux (GFLUX), precipitation (PREC), and vegetation cover (NDVI) also affect snow cover to a certain extent.

Raster data preprocessing. It includes the following five sub-steps: (1) outlier removal; (2) projection transformation; (3) mask extraction; (4) block statistical processing; (5) data standardization.

(1) Outliers are eliminated. Check the quality of snow water equivalent and related impact factor data, interpret outliers, and eliminate outliers according to the situation.

(2) Projection transformation. Spatial resolution refers to the minimum distance between two adjacent objects that can be identified on remote sensing images. Due to different data sources, snow water equivalent-related factor data and snow water equivalent data have different spatial resolutions. Therefore, the spatial resolution of all data needs to be unified before modeling, and unified projection transformation processing is required. Select the appropriate projection coordinate system according to the scope of the study area. If the study area is the northern hemisphere, place the North Pole in the projection center, and select the projection as the Lambert polar position equal-area projection. Unification of data projection coordinate systems.

(3) Mask extraction. Taking the snow water equivalent data as the extraction benchmark, the relevant influence factor data is extracted by mask, the data range is cut, and the data size is unified.

(4) Block statistics processing. Due to the different data sources of snow water equivalent and its influencing factors, the coverage of the data is also different. In order to unify the data coverage, block statistical processing is performed on the data of the environmental impact factors of snow water equivalent. Block statistics can fill in rasters with missing data. First select the size of the operation window, as shown in Figure 2, which is divided into three neighborhood sizes: 3×3, 5×5, and 7×7. Taking the 5×5 neighborhood window as an example, the values of the 24 pixels around the pixel to be filled are obtained by specifying the statistical data type, which is the value finally assigned to the pixel to be filled. The types of statistics that can be specified include: mean, maximum, minimum, mode, minority, median, standard deviation, sum, etc. Here select Average as the specified statistic type.

(5) Data standardization. The Z-Score standardization method is used to standardize the data of snow water equivalent and related influencing factors, so that the data measured on different scales can be compared and analyzed on the same scale, and the interpretability of the regression analysis coefficients can also be enhanced. The formula is as follows:

是待标准化数据的算数平均值，S是待标准化数据的标准差。In the formula, _zi refers to the value after standardization, x _i is the data to be standardized,

is the arithmetic mean of the data to be normalized, and S is the standard deviation of the data to be normalized.

的差值达到最小，因此建立方程：For the global least squares linear regression model constructed in step S3. The size of the residual can measure the accuracy of the fitting. The larger the residual, the less accurate the fitting. Residuals are related to the characteristics of the data itself and the choice of regression equation. The least squares method requires the observed value of snow water equivalent y _g and the fitted value

The difference is minimized, so the equation is established:

In the equation, the function Q should be minimized. For the function Q, obtain the first-order partial derivatives for β ₀ , β ₁ , ... β _k respectively, and make its value equal to 0, solve the equation system to obtain the model regression coefficient, and thus obtain the global least squares linear regression model.

Step S4 extracts the global model residual and divides it into N×N sub-regions. As shown in Figure 3. In the subsequent steps to calculate the Moran index and to use the spatial filter method for regression, it is necessary to construct a spatial adjacency matrix. If a spatial adjacency matrix is constructed for the entire M×M remote sensing image, the size of the matrix is M ² ×M ² . Excessive amount of data will lead to slow calculation speed or even failure to calculate eigenvectors later. The residuals are N×N regions. The global residual is composed of several grids. In this step, the global residual is divided into several N×N square sub-regions as shown in FIG. 3 .

In one embodiment, in step S4, it is determined whether the residual has spatial autocorrelation by calculating the Moran index. The Moran index is represented by the probability p value, which specifically includes: if p is less than the threshold, it indicates that there is a spatial autocorrelation. If there is autocorrelation, then go to step S5; otherwise, it indicates that there is no spatial autocorrelation, and the parameters of the global least squares linear regression model in step S2 are used as the final model parameters of the corresponding sub-region.

Specifically, the spatial autocorrelation is judged by calculating Moran's I index. The expression for the residuals of the global model is:

为全局模型拟合值。Among them, ε is the residual error, y _g is the observed value of the snow water equivalent,

Fit values for the global model.

Moran's I index, also known as Moran's index, is an index used to measure spatial autocorrelation, its value ranges from -1 to 1, [0, 1] indicates that there is a positive correlation between geographic entities, [ -1, 0] indicates that there is a negative correlation, while a value of 0 indicates no correlation. The larger the absolute value, the more obvious the spatial autocorrelation, otherwise the opposite. The spatial autocorrelation of the residuals can be measured by calculating Moran’s I index of the residuals of the global least squares linear regression model. The formula is as follows:

where bi is the deviation of the attribute of feature _i from its mean, wi _,j is the spatial weight between features i and j, and n is equal to the total number of features. Interpretation of Moran's I index requires a p-value to determine. When the absolute value of Moran's I index is large, and the p value is less than 0.05 (the threshold value can be set according to the situation, the threshold value is 0.05 as an example), that is, when the confidence level reaches 95%, it means that the spatial autocorrelation of the residual is obvious enough, it is necessary to The spatial factors in the residuals are removed and added to the final model. Generally speaking, because the snow water equivalent is a geographical element with spatial effects, the regional residuals after the global least squares linear regression modeling for the snow water equivalent are calculated when Moran's I index is larger and the higher the Moran's I index is. When the p-value is less than 0.05, the residuals have obvious spatial autocorrelation.

The parameters of the global least squares linear regression model in step S2 are β ₀ , β ₁ , . . . β _k .

In one embodiment, step S5 includes:

S5.1: Construct a spatial adjacency matrix W according to the grid cell adjacency relationship of the sub-region;

S5.2: Centralize the constructed spatial adjacency matrix to obtain matrix C,

S5.3: Calculate the eigenvalues and eigenvectors of matrix C, and perform preliminary screening to obtain qualified spatial eigenvectors;

S5.4: Based on the qualified spatial eigenvectors, the forward selection method is used to gradually screen out the target eigenvectors;

S5.5: Based on the filtered target feature vector, construct a regional feature function space filtering value regression model for each sub-region, the formula is:

ε _i =E _i α _i +∈ _i (i=1,2,...m)

Among them, ε _i is the residual of the global model of the ith subregion, α _i is the regression coefficient vector of the ith subregion, matrix E _i includes the j target feature vectors selected from the ith subregion, ∈ _i is the ith subregion The regional model error vector of the region, m is the total number of sub-regions divided into several sub-regions.

Specifically, step S5 uses the spatial filtering method to model and fit the residuals of each sub-region. See Figure 4. This step includes 4 sub-steps: (1) constructing a spatial adjacency matrix; (2) centralizing the matrix; (3) calculating eigenvalues and eigenvectors, and performing preliminary screening; (4) progressively screening target eigenvectors by forward selection.

In the specific implementation process, the implementation method of step S5 is as follows:

Step S5.1: Construct a spatial adjacency matrix and center it. The global space adjacency matrix C can be constructed according to Bishop adjacency, Rook adjacency and Queen adjacency:

a) Bishop adjacency: the four pixels adjacent to the four vertices of the target pixel are adjacent positions under the adjacency rule, that is, common vertex adjacency;

b) Rook adjacency: the four pixels adjacent to the four sides of the target pixel are adjacent positions under the adjacency rule, that is, the common adjacent edges are adjacent;

c) Queen adjacency: The four pixels adjacent to the four sides of the target pixel are adjacent positions under the adjacency rule, that is, both common vertex adjacency and common edge adjacency.

Use C _i,j to represent the adjacency corresponding to grids i and j in the N×N sub-region, and take the value 0 or 1. If grid i and j are adjacent, then C _i,j =1; if grid i and j are not adjacent, then C _i,j =0; if i=j, then C _i,j =0; The spatial adjacency matrix C of the corresponding N×N subregions. As shown in the following formula:

Step S5.2: Matrix centralization. Centralize the spatial adjacency matrix C obtained in the previous step, and the formula is as follows:

The matrix MCM is obtained by centralizing the spatial adjacency matrix C. where I is an n*n identity matrix, 1 is an n×1 vector with all elements 1, n is the number of rows or columns of the spatial adjacency matrix, and T is the matrix transpose operator.

Step S5.3: Calculate eigenvalues and eigenvectors, and perform preliminary screening. Mathematically decompose the matrix MCM:

MCM=EΛE ^T

The decomposition result is called an eigenfunction, which includes n eigenvectors and n corresponding eigenvalues. The n eigenvectors can be represented as E ₀ =(EV ₁ , EV ₂ , . . . , EV _n ), where each eigenvector is an n×1 vector. Λ is an n×n diagonal matrix whose diagonal elements are n eigenvalues, which can be expressed as λ=(λ ₁ ,λ ₂ ,...,λ _n ) in descending order.

Then, the eigenvectors are preliminarily screened under two conditions: one is that their eigenvalues λ _i >0; the other is that the following conditions are met according to the empirical model requirements:

where λ _i is the eigenvalue to be screened, and λ _max is the largest eigenvalue. Preliminary screening to obtain qualified spatial feature vectors.

Step S5.4: The forward selection method gradually screens the target feature vector. Specific steps are as follows:

Step S5.4.1: Sorting of spatial feature vectors. Arrange the spatial eigenvectors after preliminary screening in descending order of the corresponding eigenvalues to obtain the spatial eigenvector set E _t .

Step S5.4.2: In each N×N sub-region, take the residual of the global model of snow water equivalent as the dependent variable, and the spatial feature vector set E _t as the independent variable, establish the ordinary least squares regression model and calculate the regression equation Y AIC value of _i . The calculation formula of Akaike Information Criterion (AIC) is as follows:

AIC=-2ln(L)+2k

where L is the likelihood function and k is the number of variables in the model.

Step S5.4.3: Select the regression equation with the smallest AIC value from step S5.4.2, and add a certain spatial feature vector selected from the spatial feature vector set E _t to the selected feature vector set E. Then, the eigenvectors except the eigenvectors in E are added to the regression equation in turn from the spatial eigenvector set E _t .

Step S5.4.4: judge whether the AIC value decreases, if the AIC value decreases, repeat step S5.4.3; if the AIC value does not decrease, stop adding the eigenvector to the regression equation, and record the number of parameters that have been added to the regression equation. Feature vector. These eigenvectors are the j eigenvector sets E that make the evaluation standard AIC optimal, that is, the residual spatial filtering value model of the ith sub-region is obtained:

ε _i =E _i α _i +∈ _i (i=1,2,...m)

Among them, ε _i is the residual of the ith sub-region, and α _i is the regression coefficient vector of the ith sub-region. The matrix E _i includes j eigenvectors selected from the ith sub-region, ∈ _i is the regional model error vector of the ith sub-region, and m is the total number of sub-regions divided into several sub-regions.

In one embodiment, step S6 includes:

The fitting values of the regional models constructed by modeling the sub-regions are combined, and then added to the fitting values of the global least squares linear regression model to obtain the final spatial regression model. The formula is as follows:

为最终的空间回归模型的雪水当量拟合值，

为全局最小二乘线性回归模型的雪水当量拟合值，

为拼合后的子区域残差的拟合值；in,

is the fitted value of the snow water equivalent for the final spatial regression model,

is the fitted value of the snow water equivalent of the global least squares linear regression model,

is the fitted value of the residuals of the subregions after flattening;

The final spatial regression model expression is:

In the formula, x ₁ , x ₂ , ... x _k are the relevant influencing factors of snow water equivalent, β ₀ , β ₁ , ... β _k are the global least squares linear regression coefficients independent of x ₁ , x ₂ , ... x _k , E is the selected feature vector set, α is the regression coefficient vector of the sub-region, ∈ is the error vector.

拼合，即为图3的逆过程。拼合之后再与全局雪水当量拟合结果y_g加和，即得到最终的顾及空间异质性的雪水当量栅格数据模型。Through the aforementioned steps, each N×N sub-region has its corresponding regional model, and the residual error of the regional model is fitted to the result.

Flattening is the inverse process of Figure 3. After assembling, it is added with the global snow water equivalent fitting result y _g to obtain the final snow water equivalent raster data model considering spatial heterogeneity.

In one embodiment, the method further includes step S7 of evaluating and analyzing the final spatial regression model.

Specifically, this section includes evaluating regression models and analyzing regression models, where,

In evaluating the regression model, several evaluation indicators of the model are calculated: model goodness of fit (R ² ), adjusted goodness of fit (Adj.R ² ), root mean square error (RMSE), mean absolute error (MAE) , Mean Absolute Percent Error (MAPE), and Moran's I of the residuals. Its formula is as follows:

(1) Goodness of fit of the model (R ² )

^R2 is a statistic that measures goodness of fit and gives the proportion of change in the target variable explained by the regression model:

是雪水当量观测值的平均值，

是模型的雪水当量拟合值，n是栅格的个数。R²的取值范围是0～1，值越大说明模型精度越高。where y _i is the observed value of the snow water equivalent,

is the mean of the snow water equivalent observations,

is the snow water equivalent fitting value of the model, and n is the number of grids. The value range of R ² is 0 to 1, and the larger the value, the higher the accuracy of the model.

(2) Adjusted goodness of fit (Adj.R ² )

Adjusting R2 ^takes into account the number of independent variables used to fit the target variable. That is, on the basis of R ² , the effect of the sample size on R ² is offset, and the added non-significant variable is penalized. Adjusted ^R2 is a statistic that measures goodness of fit. Its formula is as follows:

where p is the number of independent variables. Adj.R ² is the same as R ² , and its value range is 0 to 1. The larger the value, the higher the model accuracy.

(3) Root Mean Square Error (RMSE)

The root mean square error is the square root of the ratio of the square of the deviation of the fitted value from the true value to the number of observations n. It measures the deviation between the fitted value and the true value, and is sensitive to outliers in the data:

The parameters have the same meaning as above. The smaller the value, the higher the accuracy of the model.

(4) Mean Absolute Error (MAE)

The mean absolute error is the average value of the absolute error. Since the dispersion is absolute valued, the positive and negative offsets will not occur. Therefore, the mean absolute error can better reflect the actual situation of the fitting value error. Its formula is as follows:

The parameters have the same meaning as above. The smaller the value, the higher the accuracy of the model.

(5) Mean Absolute Percentage Error (MAPE)

The mean absolute percentage error is a statistical index to measure the fitting accuracy, which is a percentage value. It is generally believed that when the MAPE is less than 10, the fitting accuracy is higher and is used to measure the accuracy of the fitted model. The formula is as follows:

The parameters have the same meaning as above. The smaller the value, the higher the accuracy of the model.

(6) Moran's I

Moran's I index, also known as Moran's index, is an index used to measure spatial autocorrelation. Its value ranges from -1 to 1, [0, 1] indicates that there is a positive correlation between geographic entities, [-1, 0] indicates that there is a negative correlation, and a value of 0 indicates no relationship. The larger the absolute value, the more obvious the spatial autocorrelation, otherwise the opposite. The formula is as follows:

where bi is the deviation of the attribute of feature _i from its mean, wi _,j is the spatial weight between features i and j, and n is equal to the total number of features. The closer its value is to 0, the weaker the residual spatial autocorrelation and the more reliable the model.

Analyze regression models. After the above steps, the final model is obtained as follows:

是顾及空间异质性的雪水当量栅格数据模型拟合值，x₁、x₂、…x_k是雪水当量的相关影响因子，β₀、β₁、…β_k是回归系数，特征向量集E包括选取的j个特征向量，α为子区域的回归系数向量，∈为误差向量。In the formula,

are the fitted values of the snow water equivalent grid data model considering the spatial heterogeneity, x ₁ , x ₂ , … x _k are the relevant influencing factors of the snow water equivalent, β ₀ , β ₁ , … β _k are the regression coefficients, and the characteristic The vector set E includes the selected j feature vectors, α is the regression coefficient vector of the sub-region, and ∈ is the error vector.

β ₀ , β ₁ , …β _k in the model, that is, the relevant influencing factors of the regression coefficient corresponding to each snow water equivalent, and the positive and negative signs represent the positive and negative correlation with the snow water equivalent: if the sign is positive, the factor It has a positive effect on the accumulation of snow water equivalent. The larger the factor is, the greater the snow water equivalent is, otherwise, the opposite is true. Its absolute value represents the degree of influence on the snow water equivalent. For the different Eα items in each area, perform spatial visualization analysis, so as to obtain the variation law of spatial influence in the entire study area, which can be further analyzed in combination with relevant geoscience knowledge

Embodiment 2

Based on the same inventive concept as the first embodiment, this embodiment provides an analysis method for snow water equivalent, and the analysis method is implemented based on the final spatial regression model constructed in the first embodiment.

Example The specific function of a constructed global-regional model of snow water equivalent that takes into account spatial heterogeneity is to explore the influence of snow water equivalent-related factors on it, and at the same time, the spatial effect is considered when exploring the impact, that is, Eα in the model item. There is a set of overall coefficients β ₀ , β ₁ , ... β _k in the model, and the positive and negative of the correlation and the degree of influence on the snow water equivalent are analyzed respectively by the positive and negative and absolute values of the different coefficients of different influencing factors. ; For the different Eα items in each area, the spatial visualization analysis is carried out, so as to obtain the variation law of the spatial influence in the whole study area, which provides conditions for analyzing the spatial effect in combination with the specific environmental factors of the area.

This embodiment is a specific application of the constructed model, and the final regression model constructed in the first embodiment can be used to analyze the change of snow water equivalent according to the change of relevant environmental factors.

Compared with the prior art, the advantages and beneficial effects of the present invention are:

A modeling method for snow water equivalent raster data is proposed that takes into account spatial heterogeneity, and considers both global and regional spatial effects. In the spatial modeling of remote sensing images, the data is divided into several sub-regions of the same size, and each sub-region is modeled to achieve the purpose of modeling and computing the entire remote sensing image; using the spatial filtering method, using spatial adjacency The eigenvectors of the matrix fit the residuals, and the fitting results are added to the previous global model as spatial influences to obtain the final spatial regression model. The present invention can obtain an accurate model of the snow water equivalent and its related factors for subsequent research and analysis.

The above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: The recorded technical solutions are modified, or some technical features thereof are equivalently replaced; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (7)

1. Taking into account the spatial heterogeneity of the snow water equivalent grid data modeling method, it is characterized in that, comprising: S1: Obtain raster data of snow water equivalent, and preprocess the obtained raster data; S2: Based on the preprocessed data, with the snow water equivalent as the dependent variable and the environmental factors related to the snow water equivalent as the independent variables, establish a global least squares linear regression model: y _g =β ₀ +β ₁ x ₁ +β ₂ x ₂ +…+β _k x _k +ε In the formula, y _g represents the observed value of snow water equivalent, x ₁ , x ₂ , … x _k represent the first, second and k related influencing factors of snow water equivalent, respectively, β ₀ , β ₁ , … β _k are the coefficients of x ₁ , x ₂ , ... x _k respectively, and ε is the difference between the fitted value and the observed value of the global least squares linear regression model, that is, the residual; S3: Extract the residual of the global least squares linear regression model and divide it into several sub-region modeling units with a size of N×N; S4: For each sub-region modeling unit after division, determine whether the residual has spatial autocorrelation, if it has spatial autocorrelation, execute step S5, otherwise, use the parameters of the global least squares linear regression model in step S2 as the final model parameters of the corresponding sub-region; S5: Use the spatial filtering method to model the sub-region, which specifically includes using the eigenvector of the spatial adjacency matrix to fit the residual to obtain the fitting result; S6: The fitting result is added to the global least squares linear regression model constructed in step S2 as a spatial influence to obtain a final spatial regression model. 2. The method for modeling snow water equivalent grid data as claimed in claim 1, wherein in step S1, preprocessing is performed on the acquired grid data, including projection transformation, mask extraction, outlier processing, nearby Missing raster fill, data normalization. 3. The method for modeling snow water equivalent grid data as claimed in claim 1, wherein in step S4, it is judged whether the residual has significant spatial autocorrelation by calculating the Moran index, and the Moran index passes through. It is represented by the probability p value, which specifically includes: if p is less than the threshold, it indicates that there is significant spatial autocorrelation, then go to step S5; otherwise, it indicates that there is no significant spatial autocorrelation, then the global least squares linear regression model in step S2 is used. The parameters of are used as the final model parameters of the corresponding sub-regions. 4. the snow water equivalent grid data modeling method as claimed in claim 1, is characterized in that, step S5 comprises: S5.1: Construct a spatial adjacency matrix W according to the grid cell adjacency relationship of the sub-region; S5.2: Centralize the constructed spatial adjacency matrix to obtain matrix C, S5.3: Calculate the eigenvalues and eigenvectors of matrix C, and perform preliminary screening to obtain qualified spatial eigenvectors; S5.4: Based on the qualified spatial eigenvectors, the forward selection method is used to gradually screen out the target eigenvectors; S5.5: Based on the filtered target feature vector, construct a regional feature function space filtering value regression model for each sub-region, the formula is: ε _i =E _i α _i +∈ _i (i=1,2,...m) Among them, ε _i is the residual of the global model of the ith subregion, α _i is the regression coefficient vector of the ith subregion, matrix E _i includes the j target feature vectors selected from the ith subregion, ∈ _i is the ith subregion The regional model error vector of the region, m is the total number of sub-regions divided into several sub-regions. 5. the snow water equivalent grid data modeling method as claimed in claim 1, is characterized in that, step S6 comprises: The fitting values of the regional models constructed by modeling the sub-regions are combined, and then added to the fitting values of the global least squares linear regression model to obtain the final spatial regression model. The formula is as follows:

in,

is the fitted value of the snow water equivalent for the final spatial regression model,

is the fitted value of the snow water equivalent of the global least squares linear regression model,

is the fitted value of the residuals of the subregions after flattening; The final spatial regression model expression is:

In the formula, x ₁ , x ₂ , ... x _k are the relevant influencing factors of snow water equivalent, β ₀ , β ₁ , ... β _k are the global least squares linear regression coefficients independent of x ₁ , x ₂ , ... x _k , E is the selected feature vector set, α is the regression coefficient vector of the sub-region, ∈ is the error vector. 6 . The method for modeling snow water equivalent grid data according to claim 1 , wherein the method further comprises step S7 , evaluating and analyzing the final spatial regression model. 7 . 7 . An analysis method for snow water equivalent, characterized in that, the analysis method is implemented based on the final spatial regression model constructed according to any one of claims 1 to 5 .

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