CN114611271A - Snow water equivalent grid data modeling and analyzing method considering spatial heterogeneity - Google Patents
Snow water equivalent grid data modeling and analyzing method considering spatial heterogeneity Download PDFInfo
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Abstract
Aiming at the problems that the influence of a spatial effect is not considered in the snow water equivalent modeling of the traditional regression model, and the spatial regression model faces serious calculation bottleneck in the grid data, the snow water equivalent grid data modeling and analyzing method considering spatial heterogeneity is provided, and the global and regional spatial effects are considered. When the remote sensing image is subjected to spatial modeling, data are divided into a plurality of sub-regions with the same size, and each sub-region is modeled, so that the purpose of modeling and calculating the whole remote sensing image is achieved; and fitting the residual error by using the characteristic vector of the spatial adjacency matrix by using a spatial filtering method, and adding the fitting result as a spatial influence into the previous global model to obtain a final spatial regression model. The invention can obtain an accurate model of the equivalent of the snow water and the related factors thereof for subsequent research and analysis.
Description
Technical Field
The invention relates to the technical field of spatial statistic analysis service application, in particular to a snow water equivalent grid data modeling and analyzing method considering spatial heterogeneity.
Background
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 after the Snow is completely melted, and the common unit is mm. Because the response of snow to temperature change is very sensitive, the monitoring of snow water equivalent has important significance for researching climate change trend, water resource management, agricultural production planning and the like. Global accumulated snow areas are mainly located in high and medium latitude areas, the south and north poles and high mountain areas, and the observation results of the accumulated snow amount are different along with different geographic positions, for example, the slope orientation determines the duration of sunlight and the received radiation intensity, less solar radiation on a negative slope helps to keep soil moisture, the evaporation capacity of air is reduced, and accumulation of accumulated snow is facilitated compared with a positive slope, namely the spatial heterogeneity of accumulated snow is stronger. Therefore, a small number of stations are difficult to fully display the space-time variation characteristics of snow on a large space scale, and great limitation exists. The remote sensing technology is used as a new means for monitoring the earth surface in a large scale, overcomes the defects of the traditional site monitoring, provides long-lasting and large-range snow monitoring data, and is an important data source of snow water equivalent. The microwave sensor mainly receives the radiation energy from the accumulated snow and the underlying surface thereof, the sensor represents the received energy by a brightness temperature value, the attribute information (such as snow water equivalent) of the accumulated snow and the brightness temperature present a certain functional relationship, and the snow water equivalent can be inverted through the relationship.
The change in snow water equivalent is influenced by environmental factors such as: air Temperature (AT), surface heat flux (GFLUX), cloud water Content (CLDWP), Precipitation (PREC), vegetation cover (NDVI), Wind Speed (WS), etc. The spatial regression model is a modeling method considering a spatial effect, and can be used for researching the relation between the snow water equivalent and the correlation factor. The least square linear regression model is simple in structure and modeling process, and can carry out correlation inference under statistical significance. The conventional regression model assumes that the (residuals) are independently and identically distributed, but actually depend on each other and are associated with each other, and spatial autocorrelation exists, so that the conventional model is not suitable for spatial data. The variables of the spatial statistical analysis all have the property of being dependent and correlated in space, which is also called spatial autocorrelation, and the spatial autocorrelation of the variables affects the accuracy of the regression modeling, so that the influence of the spatial autocorrelation needs to be eliminated. The spatial regression model considers the influence of spatial autocorrelation, so that an accurate model can be established. Griffith proposes a spatial filtering method to solve the problem of spatial autocorrelation in spatial regression analysis, and the core idea is to extract the feature vectors of spatial adjacency matrices as spatial influence factors, add the spatial influence factors into a regression model, i.e., incorporate the feature vectors representing the spatial effect into the final regression model. The spatial filtering method has a large calculation amount, usually calculates in an area with a small data amount, and has not been well applied to modeling calculation of the whole remote sensing image.
Therefore, the technical problem that the modeling effect is poor in the conventional method is solved.
Disclosure of Invention
The invention provides a snow water equivalent grid data modeling and analyzing method considering spatial heterogeneity, which is used for solving or at least partially solving the technical problem of poor modeling effect of the existing method. And performing spatial regression modeling on the snow water equivalent based on the related influence factor data of the snow water equivalent, exploring the influence factor of the snow water equivalent, and analyzing the change of the snow water equivalent through a regression model. The invention aims to simultaneously consider global scale characteristics and spatial heterogeneity, reduce the influence of spatial effect, further improve the snow water equivalent modeling precision and estimation effect, and achieve the purpose of large-scale remote sensing image modeling calculation through a blocking method.
The technical scheme of the invention is as follows:
a first aspect provides a method for modeling snow water equivalent grid data that accounts for spatial heterogeneity, comprising:
s1: acquiring raster data of snow water equivalent, and preprocessing the acquired raster data;
s2: based on the preprocessed data, a global least square linear regression model is established by taking the equivalent of snow water as a dependent variable and taking an environment factor related to the equivalent of snow water as an independent variable:
yg＝β0+β1x1+β2x2+…+βkxk+ε
in the formula, ygRepresents an observed value of snow water equivalent, x1、x2、…xkThe 1 st, 2 nd and k th correlation influence factors, beta, representing the snow water equivalent respectively0、β1、…βkAre each x1、x2、…xkEpsilon is the difference between the fitting value and the observed value of the global least square linear regression model, namely a residual error;
s3: extracting the residual error of the global least square linear regression model, and dividing the residual error into a plurality of sub-region modeling units with the size of NxN;
s4: for each sub-region modeling unit after division, judging whether residual errors have spatial autocorrelation, if so, executing a step S5, otherwise, taking parameters of the global least square linear regression model in the step S2 as final model parameters of the corresponding sub-region;
s5: modeling the sub-regions by adopting a spatial filtering method, specifically fitting residual errors by adopting the characteristic vectors of a spatial adjacency matrix to obtain a fitting result;
s6: and adding the fitting result serving as a spatial influence into the global least square linear regression model constructed in the step S2 to obtain a final spatial regression model.
In one embodiment, in step S1, the acquired grid data is preprocessed, including projection transformation, mask extraction, outlier processing, near missing grid filling, and data normalization processing.
In one embodiment, in step S4, determining whether the residual has a spatial autocorrelation by calculating a morn index, where the morn index is represented by a probability p value, specifically includes: if p is less than the threshold, indicating spatial autocorrelation, then proceed to step S5; otherwise, it indicates that there is no spatial autocorrelation, the parameters of the global least squares linear regression model in step S2 are used as the final model parameters of the corresponding sub-regions.
In one embodiment, step S5 includes:
s5.1: constructing a spatial adjacency matrix W according to the grid unit adjacency relation of the subregions;
s5.2: centralizing the constructed spatial adjacency matrix to obtain a matrix C,
s5.3: calculating the eigenvalue and the eigenvector of the matrix C, and performing primary screening to obtain the space eigenvector which meets the conditions;
s5.4: gradually screening out target feature vectors by adopting a forward selection method based on the spatial feature vectors meeting the conditions;
s5.5: based on the screened target feature vectors, a region feature function space filtering value regression model is constructed for each subregion, and the formula is as follows:
εi＝Eiαi+∈i(i＝1,2,…m)
wherein epsiloniIs the residual of the global model of the ith sub-region, αiAs a vector of regression coefficients for the ith sub-region, matrix EiComprises j target characteristic vectors selected by the ith sub-region, epsiloniAnd m is the total number of the sub-regions into which the research region is divided.
In one embodiment, step S6 includes:
the fitting values of the region models constructed by modeling the sub-regions are spliced and then added with the fitting values of the global least square linear regression model to obtain a final spatial regression model, wherein the formula is as follows:
wherein,
to the snow water equivalent fit value of the final spatial regression model,
is the snow water equivalent fit value of the global least squares linear regression model,
fitting values of the spliced sub-region residual errors are obtained;
the final spatial regression model expression is:
in the formula, x1、x2、…xkIs a relevant influence factor of the snow water equivalent, beta0、β1、…βkIs with x1、x2、…xkAnd E is a selected feature vector set, alpha is a regression coefficient vector of the sub-region, and epsilon is an error vector.
In one embodiment, the method further includes step S7, evaluating and analyzing the final spatial regression model.
Based on the same inventive concept, the second aspect of the present invention provides a method for analyzing the equivalent of snow water, which is implemented based on the final spatial regression model constructed in the first aspect.
One or more technical solutions in the embodiments of the present application at least have one or more of the following technical effects:
the invention provides a snow water equivalent grid data modeling method considering spatial heterogeneity, and simultaneously considers global and regional spatial effects, aiming at the problems that the influence of the spatial effect is not considered in the snow water equivalent modeling of the traditional regression model, and the spatial regression model faces serious calculation bottleneck in grid data. When the remote sensing image is subjected to spatial modeling, data are divided into a plurality of sub-regions with the same size, and each sub-region is modeled, so that the purpose of modeling and calculating the whole remote sensing image is achieved; and fitting the residual error by using the characteristic vector of the spatial adjacency matrix by using a spatial filtering method, and adding the fitting result as a spatial influence into the previous global model to obtain a final spatial regression model. An accurate model of the equivalent of the snow water and relevant factors thereof can be obtained, and the modeling precision and the estimation effect of the equivalent of the snow water are further improved for subsequent research and analysis.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of a snow water equivalent grid data modeling method accounting for spatial heterogeneity according to an embodiment of the present invention;
FIG. 2 is a block statistical diagram illustrating data preprocessing according to an embodiment of the present invention;
FIG. 3 is a schematic diagram illustrating region partitioning of extracted global model residuals according to an embodiment of the present invention;
FIG. 4 is a flow chart of region modeling with consideration of spatial heterogeneity in an embodiment of the present invention.
Detailed Description
The core problem to be solved by the invention is as follows: the distribution of the snow water equivalent is influenced by a spatial effect, the traditional regression model only considers the global influence of environmental factors, and the spatial effect of a local area is not taken into consideration due to the existence of spatial heterogeneity; meanwhile, for the snow water equivalent grid data, a severe calculation bottleneck is faced when a specific spatial regression method is adopted for modeling. Aiming at the problems, the invention provides a snow water equivalent grid data modeling method considering spatial heterogeneity, a global-regional spatial regression model of snow water equivalent and environmental factors is constructed, and then the relation between the snow water equivalent and an influence factor can be accurately explored.
In order to make the objects, 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 drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
Example one
The embodiment provides a snow water equivalent grid data modeling method considering spatial heterogeneity, which includes:
s1: acquiring raster data of snow water equivalent, and preprocessing the acquired raster data;
s2: based on the preprocessed data, a global least square linear regression model is established by taking the equivalent of snow water as a dependent variable and taking an environment factor related to the equivalent of snow water as an independent variable:
yg＝β0+β1x1+β2x2+…+βkxk+ε
in the formula, ygRepresenting observed value of snow water equivalent, x1、x2、…xkThe 1 st, 2 nd and k th correlation influence factors, beta, representing the snow water equivalent, respectively0、β1、…βkAre respectively x1、x2、…xkEpsilon is the difference between the fitting value and the observed value of the global least square linear regression model, namely a residual error;
s3: extracting residual errors of the global least square linear regression model, and dividing the residual errors into a plurality of sub-region modeling units with the size of NxN;
s4: for each sub-region modeling unit after being divided, judging whether residual errors have significant spatial autocorrelation, if so, executing a step S5, otherwise, taking parameters of the global least square linear regression model in the step S2 as final model parameters of the corresponding sub-region;
s5: modeling the sub-regions by adopting a spatial filtering method, specifically fitting residual errors by adopting the characteristic vectors of a spatial adjacency matrix to obtain a fitting result;
s6: and adding the fitting result serving as a spatial influence into the global least square linear regression model constructed in the step S2 to obtain a final spatial regression model.
The main concept of the invention is as follows:
in order to take spatial heterogeneity into consideration, local features in spatial regression modeling are considered, and spatial autocorrelation is eliminated, the invention provides a snow water equivalent grid data modeling method taking spatial heterogeneity into consideration. According to the method, a global least square linear regression model can be used on a global scale to obtain global characteristics in large-scale snow water equivalent grid data space regression modeling; aiming at the problem that the residual error in the established global least square linear regression model has higher spatial autocorrelation, a spatial filtering method is adopted, a spatial feature vector is used for fitting the residual error, and the fitting result of the residual error is used as a spatial influence to be added into the previous global model (global least square linear regression model) to form a final spatial regression model; when the residual error is modeled by the spatial filtering method, the data is divided into a plurality of small sub-regions, the residual error of each sub-region is modeled, and finally the results of the whole modeling and the sub-region modeling are integrated, so that the purpose of modeling and calculating the whole remote sensing image is achieved.
It should be noted that the global feature refers to the response feature of the snow water equivalent to the relevant influence factor in the whole research range, such as, for example: the factor "Air Temperature (AT)" has the strongest negative correlation effect on all snow water equivalents in the region, compared to other factors, which is a global feature.
Referring to fig. 1, a flow chart of a snow water equivalent grid data modeling method considering spatial heterogeneity according to an embodiment of the present invention is provided.
Step S1 is data acquisition and processing, step S2 is global least square linear regression modeling, step S3 is global least square linear regression residual partitioning, step S4 is determination of spatial autocorrelation of the residual, step S5 is modeling of the residual by using a spatial filtering method, and step S6 is construction of a snow water equivalent global-region model taking spatial heterogeneity into account.
Global least squares linear regression model of S2, beta0、β1、…βkIs a coefficient of the influence factor and can reveal the influence on the snow water equivalent. That is, the sign of the coefficient represents positive correlation or negative correlation with the equivalent of snow water, and the absolute value represents the degree of correlation.
In one embodiment, in step S1, the acquired grid data is preprocessed, including projection transformation, mask extraction, outlier processing, near missing grid filling, and data normalization processing.
In the specific implementation process, snow water equivalent and related factor data are obtained. The snow water equivalent data range is northern hemisphere, and the snow water equivalent monthly data is from the GlobSnow project of the european space agency. The formation of snow is conditioned by the accumulation of snow being greater than the ablation, so that the relevant influencing factors are selected from both the accumulation of snow and the ablation. From the viewpoint of snowfall, one of the necessary conditions is water vapor saturation, so atmospheric environmental factors such as Air Temperature (AT), cloud layer water Content (CLDPP), Wind Speed (WS) and the like influence the snowfall amount and the snowfall distribution; from the viewpoint of ablation of snow, ground environmental factors such as ground heat flux (GFLUX), precipitation amount (PREC), vegetation cover (NDVI), etc. also affect the amount of snow to some extent.
And preprocessing raster data. The method comprises the following 5 sub-steps: (1) removing abnormal values; (2) projection transformation; (3) extracting a mask; (4) carrying out block statistical processing; (5) and (6) standardizing data.
(1) And removing abnormal values. And checking the quality of the snow water equivalent and the related influence factor data, explaining the abnormal value, and removing the abnormal value according to the condition.
(2) And (5) projection transformation. The spatial resolution refers to the minimum distance between two adjacent ground objects which can be identified on the remote sensing image. Because the data sources are different, the snow water equivalent correlation factor data and the snow water equivalent data have non-uniform spatial resolution, and therefore the spatial resolution of all the data needs to be unified before modeling, and the unified projection transformation processing needs to be performed. And selecting a proper projection coordinate system according to the range of the research area, if the research area is a northern hemisphere, placing a north pole at a projection center, selecting projection as Labert polar azimuth equal-product projection, and unifying the data projection coordinate system of the snow water equivalent and the related influence factor data.
(3) And (5) extracting a mask. And taking the snow water equivalent data as an extraction reference, performing mask extraction on the related influence factor data, cutting a data range, and unifying the data size.
(4) And (5) block statistical processing. Because the data sources of the snow water equivalent and the influence factors thereof are different, the coverage of the data is also different, and in order to unify the data coverage, the data of the snow water equivalent environmental influence factors are subjected to block statistical processing. Block statistics may data-fill a grid of missing data. First, the size of the operation window is selected, and as shown in fig. 2, the operation window is divided into three neighborhood sizes, namely 3 × 3, 5 × 5 and 7 × 7. Taking a 5 × 5 neighborhood window as an example, the values of the 24 pixels around the pixel to be filled are obtained by specifying the type of statistical data, i.e., the values finally allocated to the pixel to be filled. The types of statistics that may be specified include: mean, maximum, minimum, mode, minority, median, standard deviation, sum, and the like. Where the mean is selected as the specified statistical data type.
(5) And (6) standardizing data. The Z-Score standardization method is adopted to standardize the snow water equivalent and the related influence factor data, so that the data measured on different scales can be compared and analyzed on the same scale, and the interpretability of a regression analysis coefficient can be enhanced. The formula is as follows:
in the formula, ziRefers to the value after normalization, xiIs the data that is to be normalized and,
is the arithmetic mean of the data to be normalized, S is the standard of the data to be normalizedAnd (4) tolerance.
For the global least squares linear regression model constructed in step S3. The residual magnitude can measure the accuracy of the fit, and a larger residual indicates a less accurate fit. The residuals are related to the characteristics of the data itself and the choice of regression equations. Least square method for requiring snow water equivalent observed value ygAnd fitting value
The difference of (a) is minimized, so the equation is established:
in the equation, the function Q is to be minimized. For the function Q to beta respectively0、β1、…βkThe first partial derivative is calculated and its value is made equal to 0, and the system of equations is solved to obtain model regression coefficients, thereby obtaining a global least squares linear regression model.
Step S4 extracts the global model residual and divides into N × N sub-regions. As shown in fig. 3. In the subsequent steps of calculating the Moran index and applying the spatial filtering value method to regression, a spatial adjacency matrix needs to be constructed. If a spatial adjacency matrix is integrally constructed for the whole MxM remote sensing image, the matrix size is M2×M2The excessive data amount may result in slow calculation speed and even the subsequent failure to calculate the feature vector, so the global residual is divided into N × N regions. The global residual is composed of several grids, and this step divides the global residual into several N × N square sub-regions as shown in fig. 3.
In one embodiment, in step S4, determining whether the residual has a spatial autocorrelation by calculating a morn index, where the morn index is represented by a probability p value, specifically includes: if p is less than the threshold, indicating spatial autocorrelation, then proceed to step S5; otherwise, it indicates that there is no spatial autocorrelation, the parameters of the global least squares linear regression model in step S2 are used as the final model parameters of the corresponding sub-regions.
Specifically, the spatial autocorrelation is determined by calculating the Moran's I index. The expression for the residual of the global model is:
where ε is the residual, ygAs an observed value of the snow water equivalent,
fitting values for the global model.
The Moran's I index, also called the Moran index, is an index used to measure the spatial autocorrelation and ranges from-1 to 1, [0, 1] indicating a positive correlation between geographic entities, [ -1, 0] indicating a negative correlation, and 0 indicating no correlation. The larger the absolute value of the self-correlation coefficient is, the more obvious the self-correlation coefficient is, otherwise, the reverse is true. The spatial autocorrelation of the residuals can be measured by computing the Moran's I index of the global least squares linear regression model residuals. The formula is as follows:
wherein, biIs the deviation of the property of the element i from its mean value, wi,jIs the spatial weight between elements i and j, n equals the total number of elements. Interpretation of Moran's I index needs to be determined by p-value. When the Moran's I index absolute value is larger, and the p value is smaller than 0.05 (the threshold value can be set according to the situation, and the threshold value is 0.05 as an example), that is, the confidence coefficient reaches 95%, it is indicated that the spatial autocorrelation of the residual error is sufficiently obvious, and the spatial factor in the residual error needs to be removed and added into the final model. In general, since the equivalent of snow water is a geographical element with a spatial effect, the residual error of the partitioned area after global least squares linear regression modeling on the equivalent of snow water has a more obvious spatial autocorrelation when the Moran's I index is calculated, and the Moran's I index is larger and the p value thereof is less than 0.05.
The parameter of the global least squares linear regression model in step S2 is β0、β1、…βk。
In one embodiment, step S5 includes:
s5.1: constructing a spatial adjacency matrix W according to the grid unit adjacency relation of the subregions;
s5.2: centralizing the constructed spatial adjacency matrix to obtain a matrix C,
s5.3: calculating the eigenvalue and the eigenvector of the matrix C, and performing primary screening to obtain the space eigenvector which meets the conditions;
s5.4: gradually screening out target feature vectors by adopting a forward selection method based on the spatial feature vectors meeting the conditions;
s5.5: based on the screened target feature vectors, a region feature function space filtering value regression model is constructed for each subregion, and the formula is as follows:
εi＝Eiαi+∈i(i＝1,2,…m)
wherein epsiloniIs the residual of the global model of the ith sub-region, αiAs a vector of regression coefficients for the ith sub-region, matrix EiComprises j target characteristic vectors selected by the ith sub-region, epsiloniAnd m is the total number of the sub-regions into which the research region is divided.
Specifically, step S5 models a fit to the residuals of each sub-region using a spatial filtering method. See fig. 4. This step includes 4 sub-steps: (1) constructing a spatial adjacency matrix; (2) centralizing the matrix; (3) calculating a characteristic value and a characteristic vector, and performing primary screening; (4) and the forward selection method gradually screens the target feature vectors.
In a specific implementation process, the implementation method of step S5 is as follows:
step S5.1: a spatially contiguous matrix is constructed and centered. The global spatial adjacency matrix C can be constructed according to Bishop adjacency, Rook adjacency and Queen adjacency modes:
a) bishop adjacency: four pixels adjacent to four vertexes of the target pixel are adjacent positions under the adjacent rule, namely, the pixels are adjacent to each other at the same vertex;
b) rook adjacency: four pixels adjacent to four edges of the target pixel are adjacent positions under the adjacent rule, namely adjacent positions with adjacent edges;
c) queen adjacent: the four pixels adjacent to the four edges of the target pixel are adjacent positions under the adjacent rule, namely, the four pixels are adjacent to each other by common vertex and adjacent edges.
With Ci,jAnd the adjacency corresponding to the grids i and j in the N multiplied by N subareas is expressed, and the value is 0 or 1. If grids i and j are adjacent, C i,j1 is ═ 1; if grids i and j are not contiguous, Ci,j0; if i is j, then Ci,j0; resulting in a spatial adjacency matrix C of corresponding N × N subregions. As shown in the following formula:
step S5.2: and (5) centralizing the matrix. Centralizing the spatial adjacency matrix C obtained in the previous step, wherein the formula is as follows:
and performing centralized conversion on the spatial adjacency matrix C to obtain a matrix MCM. Where I is an identity matrix of n × n, 1 is an n × 1 vector with all elements 1, n is the number of rows or columns of the spatially adjacent matrix, and T is a matrix transpose operator.
Step S5.3: and calculating a characteristic value and a characteristic vector, and performing primary screening. Performing mathematical decomposition on the matrix MCM:
MCM＝EΛET
the decomposition result is called a feature function and comprises n feature vectors and n corresponding feature values. The n feature vectors can be represented as E0＝(EV1,EV2,…,EVn) Wherein each feature vector is an n x 1 vector. Λ is an n × n diagonal matrix with n diagonal elementsThe characteristic value can be expressed as (lambda) in descending order1,λ2,…,λn)。
Then, the feature vectors are primarily screened, and two conditions are provided: one is its eigenvalue λi>0; secondly, the following conditions are met according to the requirements of an empirical model:
wherein λiFor the characteristic value to be screened, lambdamaxIs the largest eigenvalue. And preliminarily screening to obtain the space characteristic vector meeting the condition.
Step S5.4: and the forward selection method gradually screens the target feature vectors. The method comprises the following specific steps:
step S5.4.1: spatial feature vector ordering. The initially screened space feature vectors are arranged in a descending order according to the corresponding feature values to obtain a space feature vector set Et。
Step S5.4.2: in each N multiplied by N sub-region, the residual error of the snow water equivalent global model is used as a dependent variable, and a space feature vector set EtAs independent variables, a common least squares regression model is established and a regression equation Y is calculatediThe AIC value of (a). The Akaike Information Criterion (AIC) calculation formula is as follows:
AIC＝-2ln(L)+2k
where L is the likelihood function and k is the number of variables of the model.
Step S5.4.3: the regression equation with the smallest AIC value is selected from step S5.4.2, corresponding to the vector set E of the spatial featurestAdding a certain selected spatial feature vector into the selected feature vector set E. Then from the set of spatial feature vectors EtAnd sequentially adding the feature vectors except the feature vector in the E into a regression equation.
Step S5.4.4: judging whether the AIC value is reduced, if so, repeating the step S5.4.3; if the AIC value is not reduced, the addition of the feature vectors to the regression equation is stopped, and a number of feature vectors that have been added to the regression equation are recorded. The feature vectors are j feature vector sets E for screening to optimize the evaluation criterion AIC, namely a residual error space filtering value model of the ith sub-region is obtained:
εi＝Eiαi+∈i(i＝1,2,…m)
wherein epsiloniIs the ith sub-region residual, αiIs the regression coefficient vector of the ith sub-region. Matrix EiComprises j feature vectors selected by the ith sub-region, epsiloniAnd m is the total number of the sub-regions into which the research region is divided.
In one embodiment, step S6 includes:
the fitting values of the area model constructed by modeling the sub-areas are spliced and added with the fitting value of the global least square linear regression model to obtain a final spatial regression model, wherein the formula is as follows:
wherein,
to the snow water equivalent fit value of the final spatial regression model,
is the snow water equivalent fit value of the global least squares linear regression model,
fitting values of the spliced sub-region residual errors are obtained;
the final spatial regression model expression is:
in the formula, x1、x2、…xkIs a relevant influence factor of the snow water equivalent, beta0、β1、…βkIs with x1、x2、…xkAnd E is a selected feature vector set, alpha is a regression coefficient vector of the sub-region, and epsilon is an error vector.
Through the steps, each N multiplied by N sub-area has a corresponding area model, and the residual error of the area model is fitted to the result
Splicing, which is the reverse process of fig. 3. After splicing, fitting result y with global snow water equivalentgAnd adding to obtain the final snow water equivalent grid data model taking spatial heterogeneity into account.
In one embodiment, the method further includes step S7, evaluating and analyzing the final spatial regression model.
Specifically, the component includes evaluating a regression model and analyzing the regression model, wherein,
in the evaluation regression model, several evaluation indexes of the model are calculated: goodness of fit (R) of model2) And goodness of fit (adj.r) after adjustment2) Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percent Error (MAPE), and the Moran index of the residual (Moran's I). The formula is as follows:
(1) goodness of fit (R) of model2)
R2Is a statistic for measuring goodness of fit, which gives the change ratio of the regression model-interpreted target variable:
wherein y isiIs an observed value of the equivalent of snow water,
is the average of the observed values of the equivalent of snow water,
is the snow water equivalent fitting value of the model, and n is the number of the grids. R2The value range of (1) is 0-1, and the larger the value is, the higher the model precision is.
(2) Adjusted goodness of fit (adj.R)2)
Adjusting R2The number of independent variables used to fit the target variable is considered. I.e. at R2On the basis of (1), the number of samples to R is offset2The penalty is given to the added insignificant variable. Adjusting R2Is a statistic that measures goodness of fit. The formula is as follows:
where p is the number of arguments. Adj. R2Is the same as R2Similarly, the value range is 0-1, and the larger the value is, the higher the model precision is.
(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 values from the true values to the number of observations n. The deviation between the fitted value and the true value is measured and is sensitive to outliers in the data:
wherein the parameters are as defined above. Smaller values indicate higher model accuracy.
(4) Mean Absolute Error (MAE)
The mean absolute error is the average value of the absolute error, and the dispersion is converted into an absolute value, so that the situation that positive and negative are mutually cancelled does not occur, and the actual situation of the fitting value error can be better reflected by the mean absolute error. The formula is as follows:
wherein the parameters are as defined above. Smaller values indicate higher model accuracy.
(5) Mean Absolute Percent Error (MAPE)
The average absolute percentage error is a statistical index for measuring the fitting accuracy, and is a percentage value, generally, when MAPE is less than 10, the fitting accuracy is higher, and is used for measuring the accuracy of the fitting model, and the formula is as follows:
wherein the parameters are as defined above. Smaller values indicate higher model accuracy.
(6) Mulan index (Moran's I)
The Moran's I index, also known as the Molan index, is an index used to measure spatial autocorrelation. The value range is between-1 and 1, [0, 1] indicates that positive correlation exists between geographic entities, the value range of [ -1, 0] indicates that negative correlation exists, and the value of 0 indicates that no correlation exists. The larger the absolute value of the self-correlation coefficient is, the more obvious the self-correlation coefficient is, otherwise, the reverse is true. The formula is as follows:
wherein, biIs the deviation of the property of the element i from its mean value, wi,jIs the spatial weight between elements i and j, n equals the total number of elements. The closer its value is to 0, the weaker the residual spatial autocorrelation and the more reliable the model.
The regression model is analyzed. The final model obtained by the above steps is shown as the following formula:
in the formula,
snow water equivalent grid number accounting for spatial heterogeneityAccording to the model fitting value, x1、x2、…xkIs a relevant influence factor of the snow water equivalent, beta0、β1、…βkThe method is characterized in that the method is a regression coefficient, a feature vector set E comprises j selected feature vectors, alpha is a regression coefficient vector of a subregion, and epsilon is an error vector.
Beta in the model0、β1、…βkNamely, the regression coefficient corresponds to the relevant influence factor of each snow water equivalent, and the positive and negative signs of the regression coefficient represent the positive and negative correlation relationship with the snow water equivalent: if the sign is positive, the factor plays a positive role in the accumulation of the equivalent of the snow water, the larger the factor is, the larger the equivalent of the snow water is, otherwise, the reverse is true. The absolute value of which represents the magnitude of the influence on the snow water equivalent. The spatial visualization analysis is carried out on different E alpha terms of each region, so that the change rule of the spatial influence in the whole research region can be obtained, and further analysis can be carried out by combining with relevant scientific knowledge
Example two
Based on the same inventive concept as the first embodiment, the present embodiment provides an analysis method of snow water equivalent, which is implemented based on the final spatial regression model constructed in the first embodiment.
The specific role of the constructed global-regional model of the snow water equivalent, which takes spatial heterogeneity into consideration, is to explore the influence of the influence factors related to the snow water equivalent, and simultaneously, consider the spatial effect, namely the E alpha term in the model when exploring the influence. In the model there is a set of overall coefficients beta0、β1、…βkRespectively analyzing the positive and negative properties of the correlation and the influence degree on the snow water equivalent by the positive and negative and absolute values of different coefficients of different influence factors; and performing spatial visualization analysis on different E alpha items of each region to obtain a change rule of a spatial influence in the whole research region, and providing conditions for analyzing the spatial effect by combining specific environmental factors of the region.
The embodiment is a specific application of the constructed model, and the final regression model constructed in the first embodiment can be used for analyzing the snow water equivalent change according to the relevant environmental factor change.
Compared with the prior art, the invention has the advantages that:
a snow water equivalent grid data modeling method considering spatial heterogeneity is provided, and the global and regional spatial effects are considered. When the remote sensing image is subjected to spatial modeling, data are divided into a plurality of sub-regions with the same size, and each sub-region is modeled, so that the purpose of modeling and calculating the whole remote sensing image is achieved; and fitting the residual error by using the characteristic vector of the spatial adjacency matrix by using a spatial filtering method, and adding the fitting result as a spatial influence into the previous global model to obtain a final spatial regression model. The invention can obtain an accurate model of the equivalent of the snow water and the related factors thereof for subsequent research and analysis.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (7)
1. The snow water equivalent grid data modeling method considering spatial heterogeneity is characterized by comprising the following steps:
s1: acquiring raster data of snow water equivalent, and preprocessing the acquired raster data;
s2: based on the preprocessed data, a global least square linear regression model is established by taking the equivalent of snow water as a dependent variable and taking an environment factor related to the equivalent of snow water as an independent variable:
yg＝β0+β1x1+β2x2+…+βkxk+ε
in the formula, ygRepresenting observed value of snow water equivalent, x1、x2、…xk1 st one representing snow water equivalent respectively2 nd and k th correlation influence factor, beta0、β1、…βkAre respectively x1、x2、…xkEpsilon is the difference between the fitting value and the observed value of the global least square linear regression model, namely a residual error;
s3: extracting the residual error of the global least square linear regression model, and dividing the residual error into a plurality of sub-region modeling units with the size of NxN;
s4: for each sub-region modeling unit after division, judging whether residual errors have spatial autocorrelation, if so, executing a step S5, otherwise, taking parameters of the global least square linear regression model in the step S2 as final model parameters of the corresponding sub-region;
s5: modeling the sub-regions by adopting a spatial filtering method, specifically fitting residual errors by adopting the characteristic vectors of a spatial adjacency matrix to obtain a fitting result;
s6: and adding the fitting result serving as a spatial influence into the global least square linear regression model constructed in the step S2 to obtain a final spatial regression model.
2. The method for modeling snow water equivalent grid data according to claim 1, wherein in step S1, the acquired grid data is preprocessed, including projection transformation, mask extraction, outlier processing, nearby missing grid filling, and data normalization processing.
3. The snow water equivalent grid data modeling method of claim 1, wherein in step S4, it is determined whether the residual error has significant spatial autocorrelation by calculating a morn index, which is embodied by a probability p value, and specifically includes: if p is less than the threshold, indicating significant spatial autocorrelation, then proceed to step S5; otherwise, it indicates that there is no significant spatial autocorrelation, the parameters of the global least squares linear regression model in step S2 are taken as the final model parameters of the corresponding sub-region.
4. The snow water equivalent grid data modeling method of claim 1, wherein step S5 includes:
s5.1: constructing a spatial adjacency matrix W according to the grid unit adjacency relation of the subregions;
s5.2: centralizing the constructed spatial adjacency matrix to obtain a matrix C,
s5.3: calculating the eigenvalue and the eigenvector of the matrix C, and performing primary screening to obtain the space eigenvector which meets the conditions;
s5.4: gradually screening out target feature vectors by adopting a forward selection method based on the spatial feature vectors meeting the conditions;
s5.5: based on the screened target feature vectors, a region feature function space filtering value regression model is constructed for each subregion, and the formula is as follows:
εi＝Eiαi+∈i(i＝1,2,…m)
wherein epsiloniIs the residual of the global model of the ith sub-region, αiAs a vector of regression coefficients for the ith sub-region, matrix EiComprises j target characteristic vectors selected from ith sub-region, epsiloniAnd m is the total number of the sub-regions into which the research region is divided.
5. The snow water equivalent grid data modeling method of claim 1, wherein step S6 includes:
the fitting values of the region models constructed by modeling the sub-regions are spliced and then added with the fitting values of the global least square linear regression model to obtain a final spatial regression model, wherein the formula is as follows:
wherein,
as a final spatial regression modelThe snow water equivalent fitting value of (a),
is the snow water equivalent fit value of the global least squares linear regression model,
fitting values of the spliced sub-region residual errors are obtained;
the final spatial regression model expression is:
in the formula, x1、x2、…xkIs a relevant influence factor of the snow water equivalent, beta0、β1、…βkIs with x1、x2、…xkAnd E is a selected feature vector set, alpha is a regression coefficient vector of the sub-region, and epsilon is an error vector.
6. The method for modeling snow water equivalent grid data as claimed in claim 1, wherein said method further comprises a step S7 of evaluating and analyzing the final spatial regression model.
7. An analysis method of snow water equivalent, characterized in that the analysis method is realized based on a final spatial regression model constructed according to any one of claims 1 to 5.
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