Meteorological data fusion revision method based on geographic weighted regression

Abstract

The application relates to a meteorological data fusion revision method based on geographical weighted regression, relates to the technical field of meteorological data fusion, and is characterized in that: observation data of an observation station is taken as a true value, grid data is taken as a to-be-revised value, a revision equation of each observation station is solved through geographical weighted regression, a meteorological grid data fusion revision formula is obtained through spatial smoothing, the meteorological grid data of each grid point is revised by using the meteorological data fusion revision formula, the revised meteorological grid data has spatial differences, the problem of inaccurate revision of existing grid data is solved, and the application is suitable for meteorological grid data revision.

Description

Technical Field

[0001] This invention relates to the field of meteorological data fusion technology, and in particular to a meteorological data fusion and correction method based on geographic weighted regression; Background Technology

[0002] Currently, meteorological data is widely used in daily life. People's daily travel, disaster risk assessment of power systems, and transportation security all rely on accurate and timely meteorological data. We can obtain meteorological data of varying precision and applications, including satellite data, remote sensing data, station data, and numerical simulation data. Satellite data, remote sensing data, and numerical simulation data are commonly referred to as gridded data, which can uniformly cover every location in an area; while measured station data is generally more dispersed, making it difficult to cover every location in an area. Gridded data has a larger coverage area, higher resolution, wider application range, and is more convenient to use than station data. However, due to limitations in remote sensing technology and errors in numerical simulation, there is often a certain degree of error between gridded data and the actual values.

[0003] Taking wind resource assessment as an example, in order to assess the wind resource development potential of a certain area, it is necessary to understand the spatial distribution characteristics of wind speed and wind power density at a certain height in this area. However, wind measurement towers and meteorological observation stations are scattered in different locations within the area, and their data are not representative of the region. On the other hand, gridded meteorological data with a wide coverage has a large error compared with the real data. Therefore, it is necessary to use observation data to correct the gridded data.

[0004] Currently, the main approach to reduce the impact of such errors is to systematically correct gridded data based on the characteristics of the data source. However, the spatiotemporal distribution of these errors exhibits a degree of non-uniformity, and current correction methods, which systematically correct the data itself, struggle to estimate this non-uniformity. Therefore, obtaining high-resolution meteorological data that can represent spatial differences remains a significant challenge in current meteorological data processing. Summary of the Invention

[0005] The technical problem solved by this invention is to provide a meteorological data fusion and correction method based on geographic weighted regression, which solves the problem of inaccurate correction of existing gridded data.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a meteorological data fusion and correction method based on geographic weighted regression, comprising the following steps:

[0007] S1. Obtain observation station data and meteorological grid data within the study area, and extract observation data and meteorological grid data from the observation stations at the same time.

[0008] S2. Establish the geographically weighted regression equation for the observation stations. The geographically weighted regression equation for the observation stations is: yi =β0(u i ,v i )+β(u i v i )x i +ε i , where y i Represents the observation data of the i-th observation station, (u i v i () represents the coordinates of the i-th observation station, where i is a positive integer in [1, n], n is the total number of observation stations in the study area, and x i Let β0(u) represent the meteorological grid data of the i-th observation station. i v i ) represents the regression constant of the meteorological grid data of the i-th observation station, ε i The table shows the residual values ​​for the i-th observation station, β(u). i ,v i ) represents the linear regression parameters of the meteorological grid data of the i-th observation station;

[0009] S3. Spatial smoothing of the regression constants yields the regression constants of the regression equation for all grid points; spatial smoothing of the linear regression parameters yields the regression parameters of the regression equation for all grid points; and spatial smoothing of the residual values ​​yields the residual values ​​of the regression equation for all grid points, thus obtaining the meteorological grid data fusion correction formula.

[0010] S4. Correct the meteorological grid data of each grid point using the meteorological data fusion correction formula.

[0011] Furthermore, the formula for solving the linear regression parameters of the meteorological grid data of the i-th observation station is: β(u i ,v i ) = [X T W(u i ,v i )] -1 X T W(u i ,v i Let X = (x1, x2, x3, ..., xn), where -1 represents the inverse of the matrix, T represents the transpose of the matrix, and X = (x1, x2, x3, ..., xn) represent the meteorological grid data of n observation stations. Let Y = (y1, y2, y3, ..., yn) n Y represents the observation data from n observation stations, and W(u i v i ) represents the spatial weight matrix, Among them, w ij The parameter represents the spatial weighting of the location of the i-th observation station and the location of the j-th observation station within the study area, where j is a positive integer in [1, n].

[0012] Furthermore, the formula for calculating the spatial weighting parameter is: or Where, d ij Let represent the distance between the i-th and j-th observation stations, and b represent the bandwidth of the weighting function.

[0013] Furthermore, cross-validation is used to find the bandwidth of the optimal weighting function. This cross-validation method includes: given a bandwidth *b* of a weighting function, removing the observation data and grid data from the *i*th observation station, using the observation data and grid data from the remaining *n-1* observation stations to fit a geographic weighted regression equation within the given bandwidth *b*, and then substituting the grid data from the *i*th observation station to obtain the optimal bandwidth. Let represent all the observation stations remaining after removing the i-th observation station from a set of n observation stations. The bandwidth corresponding to the minimum CV is the bandwidth of the optimal weighting function.

[0014] Furthermore, in S3, the spatial smoothing is either a single spatial smoothing or a double spatial smoothing.

[0015] Furthermore, the formula for fusion correction of meteorological gridded data obtained by spatial smoothing is: y k =β0(u k v k )+β(u k v k )x k +ε k The formula for calculating the regression constant of the regression equation for all grid points, obtained by performing spatial smoothing on the regression constant once, is as follows: The formula for calculating the regression parameters of the regression equation for all grid points is obtained by performing a first spatial smoothing on the linear regression parameters: The formula for calculating the residual value of the regression equation for all grid points by performing spatial smoothing on the residual values ​​is as follows: H k H represents the center coordinates of the k-th grid point within the study area. i Let |i| represent the coordinates of the i-th observation station within the study area, ||·|| represent the Euclidean norm, and K(·) represent the Gaussian kernel function. σ1 represents the standard deviation of the observation data of the observation station.

[0016] Furthermore, the formula for fusion and correction of meteorological gridded data obtained from the two spatial smoothing processes is: y f =β0(u f v f )+β(u f v f )x f +εf The formula for calculating the regression constant of the regression equation for all grid points, obtained by performing two spatial smoothing operations on the regression constant, is as follows: The formula for calculating the regression parameters of the regression equation for all grid points is obtained by performing two spatial smoothing operations on the linear regression parameters: The formula for calculating the residual value of the regression equation for all grid points by performing two spatial smoothing operations on the residual values ​​is as follows: Among them, H k H represents the center coordinates of the k-th grid point within the study area. i Let |i| represent the coordinates of the i-th observation station within the study area, ||·|| represent the Euclidean norm, and K(·) represent the Gaussian kernel function. σ1 represents the standard deviation of the observation data from the observation station. σ² represents the standard deviation of the grid data within the study area.

[0017] Furthermore, the meteorological grid data mentioned in S1 is determined according to the research object, and the meteorological grid data includes wind speed grid data, precipitation grid data or temperature grid data.

[0018] The beneficial effects of this invention are as follows: This invention is based on a meteorological data fusion and correction method using geographic weighted regression. It takes the observation data of observation stations as the true values ​​and the grid data as the values ​​to be corrected. It solves the correction equation for each observation station through geographic weighted regression, and then obtains the meteorological grid data fusion and correction formula through spatial smoothing. The meteorological grid data of each grid point is corrected using the meteorological data fusion and correction formula, so that the corrected meteorological grid data has spatial differences, thus solving the problem of inaccurate grid data correction in existing methods. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the meteorological data fusion and correction method based on geographic weighted regression of this invention. Detailed Implementation

[0020] This invention relates to a meteorological data fusion and correction method based on geographic weighted regression, such as... Figure 1 As shown, it includes the following steps:

[0021] S1. Obtain observation station data and meteorological grid data within the study area, and extract observation data and meteorological grid data from the observation stations at the same time.

[0022] Specifically, the meteorological grid data is determined according to the research object, and the meteorological grid data includes wind speed grid data, precipitation grid data or temperature grid data. For example, if the research object is wind resources, then the meteorological grid data is wind speed grid data.

[0023] S2. Establish the geographically weighted regression equation for the observation stations. The geographically weighted regression equation for the observation stations is: y i =β0(u i v i )+β(u i v i )x i +ε i , where y i Represents the observation data of the i-th observation station, (u i v i () represents the coordinates of the i-th observation station, where i is a positive integer in [1, n], and n is the total number of observation stations in the study area. i Let β0(u) represent the meteorological grid data of the i-th observation station. i v i ) represents the regression constant of the meteorological grid data of the i-th observation station, ε i The table shows the residual values ​​for the i-th observation station, β(u). i v i ) represents the linear regression parameters of the meteorological grid data of the i-th observation station;

[0024] Specifically, based on the principle that the closer the data is to the location of the i-th observation station, the greater its influence on the linear regression parameters of the meteorological grid data at the i-th observation station, the weighted least squares method is used to solve for the linear regression parameters of the meteorological grid data at the i-th observation station. The formula for solving the linear regression parameters of the meteorological grid data at the i-th observation station is: β(u i v i ) = [X T W(u i v i )] -1 X T W(u i ,v i Let X = (x1, x2, x3, ..., xn), where -1 denotes the inverse of the matrix, T denotes the transpose of the matrix, and X = (x1, x2, x3, ..., xn). n Let X represent the meteorological grid data from n observation stations, and Y = (y1, y2, y3, ..., y4) n Y represents the observation data from n observation stations, and W(u i ,v i ) represents the spatial weight matrix, Among them, w ij The parameter represents the spatial weighting of the location of the i-th observation station and the location of the j-th observation station within the study area, where j is a positive integer in [1, n].

[0025] Spatial weighting functions are a type of linear decay function used to represent the impact of distance on data correlation. The formula for calculating spatial weighting parameters can be any of the following: distance threshold function, inverse distance function, Bi-square function, and Gaussian function. The specific formula is as follows: or Among them, s ij Let represent the distance between the i-th and j-th observation stations, and b represent the bandwidth of the weighting function, reflecting the range of data observation points that influence the estimated value at the regression point. When using the distance threshold function, when d... ij The spatial weighting parameter w is greater than the selected bandwidth b. ij =0, meaning that explanatory variables outside the bandwidth range are considered not to affect the value of the dependent variable. ij Within the selected bandwidth range, the spatial weighting parameter w ij =1, this method is relatively simple, but may lead to spatial discontinuities in the calculation results; when using the inverse distance proportional function, the rule of "the closer the distance, the greater the weight" is followed, assigning larger weights to grid data points closer to the observation station. When a grid data point coincides with the observation station, w ij The result is infinity, so this issue needs to be considered when choosing and using this function; when using the Bi-square function, data points that have little impact on parameter estimation, i.e., distant data points, are also not calculated. This method is widely used, but spatial discontinuity issues still exist; when using the Gauss function, a continuously monotonically decreasing function is used to describe d. ij and w ij The relationship between data points increases as the distance between them increases. ij The closer the value is to 0 and the slower the decay, the more it avoids the problem of spatial discontinuity.

[0026] Cross-validation is used to find the bandwidth of the optimal weighting function. The cross-validation method includes: given a bandwidth *b* of a weighting function, removing the observation data and grid data from the *i*th observation station, using the observation data and grid data from the remaining *n-1* observation stations to fit a geographic weighted regression equation within the given bandwidth *b*, and then substituting the grid data from the *i*th observation station to obtain the optimal bandwidth. Let represent all the observation stations remaining after removing the i-th observation station from a set of n observation stations. The bandwidth corresponding to the minimum CV is the bandwidth of the optimal weighting function.

[0027] After obtaining the bandwidth b of the optimal weighting function, w can be obtained. ij Thus, the spatial weighted matrix W(u) is obtained. i ,v i ), thereby obtaining the linear regression parameter β(u)i ,v i Then, by substituting the geographical coordinates, observation data, and meteorological grid data of the observation stations, the regression constant β0(u) in the geographically weighted regression equation for each observation station can be obtained. i v i ) and residual ε i .

[0028] S3. Spatial smoothing of the regression constants yields the regression constants of the regression equation for all grid points; spatial smoothing of the linear regression parameters yields the regression parameters of the regression equation for all grid points; and spatial smoothing of the residual values ​​yields the residual values ​​of the regression equation for all grid points, thus obtaining the meteorological grid data fusion correction formula.

[0029] Specifically, the regression constant β0(u) in the geographically weighted regression equation of each observation station is used. i ,v i ), linear regression parameter β(u) i ,v i ) and residual ε i To calculate the regression equation for all grid points within the region, spatial smoothing is used to obtain the regression constant, linear regression parameters, and residual values ​​of the regression equation for all grid points. Specifically, the spatial smoothing is either single-stage or double-stage.

[0030] The formula for fusion correction of meteorological grid data obtained by spatial smoothing is: y k =β0(u k ,v k )+β(u k ,v k )x k +ε k u k ,v k ) represents the coordinates of the k-th grid point in the meteorological grid, y k x represents the data correction value for the k-th grid point in the meteorological grid. k Let f represent the data for the f-th meteorological grid point. The formula for calculating the regression constant of the regression equation for all grid points, obtained by performing spatial smoothing on the regression constant once, is: The formula for calculating the regression parameters of the regression equation for all grid points is obtained by performing a first spatial smoothing on the linear regression parameters: The formula for calculating the residual value of the regression equation for all grid points by performing spatial smoothing on the residual values ​​is as follows: H k H represents the center coordinates of the k-th grid point within the study area. i Let |i| represent the coordinates of the i-th observation station within the study area, ||·|| represent the Euclidean norm, and K(·) represent the Gaussian kernel function. σ1 represents the standard deviation of the observation data of the observation station.

[0031] Since the regression equation parameters for each grid point are calculated based on the geographically weighted regression equation parameters of neighboring observation stations, spatial discontinuities may exist between the data points. Therefore, spatial smoothing is performed again on the spatial distribution of parameters at different grid points, i.e., a second spatial smoothing is performed based on the first spatial smoothing. Thus, the formula for fusing and correcting meteorological grid point data obtained from the two spatial smoothing processes is: y f =β0(u f ,v f )+β(u f ,v f )x f +ε f , (u f ,v f ) represents the coordinates of the f-th grid point in the meteorological grid, y f x represents the data correction value for the f-th grid point in the meteorological grid. f Let f represent the data for the f-th meteorological grid point. The regression constant of the regression equation for all grid points is calculated by performing two spatial smoothing operations on the regression constant. The formula for calculating the regression parameters of the regression equation for all grid points is obtained by performing two spatial smoothing operations on the linear regression parameters: The formula for calculating the residual value of the regression equation for all grid points by performing two spatial smoothing operations on the residual values ​​is as follows: Among them, H k H represents the center coordinates of the k-th grid point within the study area. i Let |i| represent the coordinates of the i-th observation station within the study area, ||·|| represent the Euclidean norm, and K(·) represent the Gaussian kernel function. β1 represents the standard deviation of the observation data from the observation station. σ² represents the standard deviation of the grid data within the study area.

[0032] Based on this, the meteorological grid data fusion correction formula obtained by spatial smoothing is: y k =β0(u k v k )+β(u k ,v k )x k +ε k And the formula for fusion and correction of meteorological grid data obtained from two spatial smoothing processes: y f =β0(u f ,v f )+β(u f ,v f (x f +εf Both can be used to correct meteorological grid data for each grid point.

[0033] S4. Correct the meteorological grid data of each grid point using the meteorological data fusion correction formula.

[0034] Specifically, the meteorological grid data fusion correction formula obtained using first-order spatial smoothing is: y k =β0(u k ,v k )+β(u k ,v k )x k +ε k Or, the formula for fusion correction of meteorological grid data obtained by two spatial smoothing processes: y f =β0(u f ,v f )+β(u f ,v f )x f +ε f The meteorological grid data for each grid point is corrected. For spatial points, spatial smoothing is a process of removing noise, presenting the trend of spatial changes, eliminating the spatial discontinuity of the data, and making the corrected meteorological grid data have spatial differences.

[0035] Based on this, the meteorological data fusion and correction method based on geographic weighted regression of this invention takes into account the spatial differences of the study area, avoids the drawbacks of systematically correcting gridded data, applies geographic weighted regression to meteorological data correction, improves the accuracy of gridded meteorological data, and is easy to apply to meteorological forecasting.

Claims

1. A meteorological data fusion and correction method based on geographically weighted regression, characterized in that, Includes the following steps: S1. Obtain observation station data and meteorological grid data within the study area, and extract observation data and meteorological grid data from the observation stations at the same time. S2. Establish the geographically weighted regression equation for the observation stations. The geographically weighted regression equation for the observation stations is as follows: ,in Indicates the first Observational data from several observation stations Indicates the first The coordinates of each observation station, for Positive integers in This represents the total number of observation stations within the study area. Indicates the first Meteorological grid data from several observation stations, Indicates the first The regression constants of meteorological grid data from individual observation stations, The table shows the residual values ​​for the i-th observation station. The linear regression parameters represent the meteorological grid data of the i-th observation station; S3. Spatial smoothing of the regression constants yields the regression constants of the regression equation for all grid points; spatial smoothing of the linear regression parameters yields the regression parameters of the regression equation for all grid points; and spatial smoothing of the residual values ​​yields the residual values ​​of the regression equation for all grid points, thus obtaining the meteorological grid data fusion correction formula. The spatial smoothing can be a single spatial smoothing or a double spatial smoothing; The formula for fusion correction of meteorological grid data obtained by spatial smoothing is: The formula for calculating the regression constant of the regression equation for all grid points, obtained by performing spatial smoothing on the regression constant once, is as follows: The formula for calculating the regression parameters of the regression equation for all grid points is obtained by performing spatial smoothing on the linear regression parameters once: The formula for calculating the residual value of the regression equation for all grid points by performing spatial smoothing on the residual values ​​is as follows: ; Indicates the first within the study area The center coordinates of each grid point Indicates the first in the study area The coordinates of each observation station, Represents the Euclidean norm. Represents the Gaussian kernel function. , This represents the standard deviation of the observation data from the observation station. The formula for fusion correction of meteorological grid data obtained from two spatial smoothing processes is as follows: The formula for calculating the regression constant of the regression equation for all grid points, obtained by performing two spatial smoothing operations on the regression constant, is as follows: , The formula for calculating the regression parameters of the regression equation for all grid points is obtained by performing two spatial smoothing operations on the linear regression parameters: , The formula for calculating the residual value of the regression equation for all grid points by performing two spatial smoothing operations on the residual values ​​is as follows: , ;in, Indicates the first within the study area The center coordinates of each grid point Indicates the first in the study area The coordinates of each observation station, Represents the Euclidean norm. Represents the Gaussian kernel function. , This represents the standard deviation of the observation data from the observation station. , This indicates the standard deviation of the grid data within the study area; S4. Correct the meteorological grid data of each grid point using the meteorological grid data fusion correction formula.

2. The meteorological data fusion and correction method based on geographically weighted regression according to claim 1, characterized in that, No. The formula for solving the linear regression parameters of the meteorological grid data from a certain observation station is as follows: Where -1 represents the inverse of the matrix, and T represents the transpose of the matrix. , express Meteorological grid data from several observation stations, , express Observational data from several observation stations Represents the spatial weight matrix. ,in, Indicates the first The location of the first observation station and the first [location] within the study area Spatial weighted parameters of the locations of each observation station for Positive integers in the range.

3. The meteorological data fusion and correction method based on geographically weighted regression according to claim 2, characterized in that, The formula for calculating the spatial weighting parameter is: , , or ,in, Indicates the first The first observation station and the first The distance between the observation stations This represents the bandwidth of the weighting function.

4. The meteorological data fusion and correction method based on geographically weighted regression according to claim 3, characterized in that, Cross-validation is used to find the bandwidth of the optimal weighting function. The cross-validation method includes: given the bandwidth b of a weighting function, removing the first... Using the observation data and gridded data from the n-1 observation stations, and the observation data and gridded data from the remaining n-1 observation stations, a geographic weighted regression equation is fitted under the given bandwidth b of the weighting function. Then, the results are substituted into the... Grid data from one observation station was obtained. , express Remove the first observation station from the list. All remaining observation stations after the first observation station, ,when The bandwidth corresponding to the minimum value is the bandwidth of the optimal weighting function.

5. The meteorological data fusion and correction method based on geographically weighted regression according to any one of claims 1-4, characterized in that, The meteorological grid data mentioned in S1 is determined according to the research object, and the meteorological grid data includes wind speed grid data, precipitation grid data or temperature grid data.

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