Mesoscale vortex space property and geometric parameter calculation and analysis method

Abstract

The invention discloses a mesoscale vortex space property and geometric parameter calculation and analysis method, belongs to the technical field of parameter calculation, is used for mesoscale vortex parameter calculation, and comprises the steps of obtaining mesoscale vortex trajectory data, screening a data range, removing abnormal data, obtaining mesoscale vortex trajectory data in a target range, and calculating mesoscale vortex space distribution. The method comprises the following steps: introducing clustering analysis, obtaining a spatial data set of different clusters of mesoscale vortexes, constructing a mesoscale vortex fitting elliptic equation by combining a least square method and an elliptic standard equation, obtaining a geometrical characteristic data set of the mesoscale vortexes, and carrying out mesoscale vortex multi-element characteristic analysis by combining the spatial data set of different clusters of the mesoscale vortexes. And completing geometric parameter calculation and analysis of the mesoscale vortex. Scientific support is provided for improving a climate prediction model and optimizing ocean resource development and ecological protection, noise and abnormal data are effectively filtered out, high precision and robustness of a fitting result are guaranteed, and reliability of an analysis result is improved.

Description

Technical Field

[0001] The invention discloses a method for calculating and analyzing the spatial properties and geometric parameters of a mesoscale vortex, and belongs to the technical field of parameter calculation. Background Art

[0002] Mesoscale eddies are a ubiquitous dynamic phenomenon in the ocean, usually manifested as water areas with significant rotation. Their scale is generally between tens and hundreds of kilometers, affecting the exchange of matter and energy in the ocean, and has an important impact on the dynamic changes of the marine environment, the biological productivity of the marine ecosystem, and marine climate change. Satellite altimeter data provides an important observation method for the identification and analysis of mesoscale eddies. The current mesoscale eddy analysis method based on remote sensing data has made significant progress in the identification, judgment and tracking of eddies. However, in the systematic study of multiple factors such as the spatial distribution characteristics and geometric characteristics of eddies in a certain area, especially when dealing with complex eddy morphology and a large amount of eddy data, existing methods are often unable to extract and analyze the geometric characteristics of these eddies well, resulting in certain limitations in the geometric description and spatial statistical analysis of eddies. Summary of the invention

[0003] The purpose of the present invention is to provide a method for calculating and analyzing the spatial properties and geometric parameters of a mesoscale vortex, so as to solve the problem in the prior art that it is difficult to accurately perform characteristic analysis of a mesoscale vortex.

[0004] A method for calculating and analyzing the spatial properties and geometric parameters of a mesoscale vortex, comprising obtaining mesoscale vortex trajectory data, screening a data range and eliminating abnormal data, obtaining mesoscale vortex trajectory data within a target range, calculating the spatial distribution of the mesoscale vortex, introducing mean shift clustering analysis, obtaining a spatial data collection of different clusters of mesoscale vortices, constructing a mesoscale vortex fitting elliptic equation by combining the least squares method and the standard ellipse equation, obtaining a mesoscale vortex geometric characteristic data set, performing a mesoscale vortex multi-factor characteristic analysis in combination with the spatial data collection of different clusters of the mesoscale vortex, and completing the calculation and analysis of the geometric parameters of the mesoscale vortex.

[0005] The mesoscale eddy track data within the target range include the mesoscale eddy track point longitude and latitude data, range point longitude and latitude data, time data and track number data.

[0006] Mean shift cluster analysis includes: S1, extracting the longitude and latitude data of the trajectory points of the mesoscale vortex and saving them to the corresponding data points: ; In the formula, It is The longitude of the center of the mesoscale eddy, It is The latitude of the center of the mesoscale eddy, It is data points, which are equal to the center point; S2. Determine the bandwidth parameter by estimating the size of the neighborhood of each point through K nearest neighbors , for each ,choose The distance to the Mth nearest neighbor is The local bandwidth is: ; ; ; In the formula, It is a data point The local bandwidth, yes The distance to the Mth nearest neighbor, is the Mth data point, N is the number of data points; Determine the radial kernel function : ; In the formula, is the normalization constant coefficient, represents the input sample point, is the kernel function width control parameter, It means to find the Euclidean distance.

[0007] Mean shift cluster analysis includes: S3, establishing the update equation of cluster analysis, solving the kernel density estimation : ; Calculate the first-order derivative form of the kernel density estimation function and get The update formula is: ; ; ; In the formula, It is updated , Before the update , and are all known functions. is the function's independent variable; S4, assuming the threshold is , repeat S3 until , then it is judged to be converged and the iteration is stopped; S5, forming different mesoscale vortex clusters, assigning all points with close updated positions to the same cluster, the center of each cluster is equivalent to the point after the mean shift algorithm converges, called the cluster center, and the cluster center represents the gathering area of ​​the mesoscale vortex; S6. Output the clustering results, group all the points in the data set according to the cluster center they converge to, and output the number of trajectory points of each cluster and the geometric range of the cluster to obtain a collection of spatial data of different clusters of mesoscale vortices.

[0008] When constructing the mesoscale eddy fitting ellipse equation, the mesoscale eddy trajectory points of each cluster are fitted into an ellipse shape using the robust least squares method, including T1, the total number of mesoscale eddy trajectory points after cluster analysis is Regions, filter out the latitude and longitude data of the range points in the corresponding area , time data , track number data ; T2. Derive the coefficient conversion relationship between the general equation of the ellipse and the standard equation. The general equation of the ellipse is: ; In the formula, , , , , is the target parameter fitted by the least squares method, and are the horizontal and vertical coordinates of the ellipse points. The ellipse is transformed into a standard form through translation and rotation: ; In the formula, and are the horizontal and vertical coordinates of the ellipse points in standard form, and are the two parameters of the ellipse equation, equivalent to the major and minor axes of the ellipse.

[0009] T2 includes T2.1. Let the coordinates of the point before translation and rotation transformation be , the coordinates of the point after translation transformation are the coordinate origin : ; In the formula, and is the horizontal and vertical coordinates of the ellipse point after translation transformation, and is substituted into the general equation of the ellipse: ; Convert to matrix form: ; After translation, the center of the ellipse is at the origin of the coordinate system: ; ; Solved and The expression is: ; ; Center of the ellipse for: ; ; The matrix form simplifies to: .

[0010] T2 includes T2.2, assuming the rotation angle is : ; Substitute the rotation transformation formula into the simplified matrix of T2.1: ; The offset angle of the rotated ellipse is 0. is 0: ; Deflection angle of the ellipse for: ; The matrix simplifies to: ; for: ; ; T2.3. Obtain the coefficient conversion relationship between the general equation and the standard equation of the ellipse, the calculation formulas for the major and minor axes, the calculation formulas for the deflection angle, and the calculation formulas for the center point.

[0011] The construction of the mesoscale eddy fitting ellipse equation includes T3 and the least squares method to fit the ellipse. The range points in the mesoscale eddy trajectory data set are put into the input variables. The objective function of the fitting is: : ; in, Indicates the number of range point longitude and latitude data corresponding to each mesoscale eddy track point, , Represents the longitude and latitude data of the mesoscale eddy range points , ; Solve the minimum value of the objective function. According to the extreme value principle, find The partial derivatives of: ; Convert to matrix form: ; Simplified to: ; ; In the formula, and Simplify parameters for a matrix.

[0012] T3 includes solving the corresponding The coefficients are used to obtain the ellipse equation and the major axis of the ellipse fitted to each mesoscale vortex. , short axis , deflection angle and the center point for: ; ; ; ; ; So far, a data set of mesoscale eddy geometric characteristics has been obtained.

[0013] The multi-factor feature analysis of mesoscale eddies includes dividing the mesoscale eddies into to ,total range; Calculate the major axis of the mesoscale eddy fitting ellipse within each cluster , short axis , deflection angle and the ratio of the major and minor axes The mean and standard deviation of , It is A feature dataset of data points, They are The major axis, minor axis, deflection angle and major-minor axis ratio of each data point; Calculate the average : ; Calculate standard deviation : ; Output the calculation results to obtain a complete mesoscale eddy spatial data set and geometric characteristic data set, carry out research on the spatial distribution and geometric characteristics of mesoscale eddies, analyze the properties and polar characteristics of mesoscale eddies, draw violin plots, and reveal the geometric characteristics of mesoscale eddies within each classification result and the changing rules between regions.

[0014] Compared with the prior art, the present invention has the following beneficial effects: the present invention deeply analyzes the spatial distribution and geometric characteristics of mesoscale eddies, which can not only reveal their dynamic mechanisms, but also provide scientific support for improving climate prediction models, optimizing marine resource development and ecological protection; effectively filters out noise and abnormal data, ensures the high precision and robustness of the fitting results, and improves the reliability of the analysis results, which is of great significance for grasping the spatial structural properties of mesoscale eddies in different sea areas and the long-term change characteristics of the properties of mesoscale eddies under the background of climate warming. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic flow chart of the method of the present invention; Figure 2 This is a schematic diagram of the cluster analysis process of mesoscale cold eddies in the northern part of the experimental sea area; Figure 3 It is a schematic diagram of the first process of fitting an ellipse in the range of a mesoscale eddy; Figure 4 It is a schematic diagram of the second process of fitting the ellipse in the range of mesoscale eddies; Figure 5 Is Figure 2 Schematic diagram of the obtained cluster analysis results and ellipse fitting results; Figure 6 It is the probability distribution of the 9 regions under the long axis length of the cold vortex; Figure 7 It is the probability distribution of the 9 regions under the short axis length of the cold vortex; Figure 8 It is the probability distribution of the 9 regions under the ratio of the long and short axes of the cold vortex; Fig. 9 This is the probability distribution of 9 regions under the deflection angle of the cold vortex major axis. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention is described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0017] A method for calculating and analyzing the spatial properties and geometric parameters of a mesoscale vortex, comprising obtaining mesoscale vortex trajectory data, screening a data range and eliminating abnormal data, obtaining mesoscale vortex trajectory data within a target range, calculating the spatial distribution of the mesoscale vortex, introducing mean shift clustering analysis, obtaining a spatial data collection of different clusters of mesoscale vortices, constructing a mesoscale vortex fitting elliptic equation by combining the least squares method and the standard ellipse equation, obtaining a mesoscale vortex geometric characteristic data set, performing a mesoscale vortex multi-factor characteristic analysis in combination with the spatial data collection of different clusters of the mesoscale vortex, and completing the calculation and analysis of the geometric parameters of the mesoscale vortex.

[0018] The mesoscale eddy track data within the target range include the mesoscale eddy track point longitude and latitude data, range point longitude and latitude data, time data and track number data.

[0019] Mean shift cluster analysis includes: S1, extracting the longitude and latitude data of the trajectory points of the mesoscale vortex and saving them to the corresponding data points: ; In the formula, It is The longitude of the center of the mesoscale eddy, It is The latitude of the center of the mesoscale eddy, It is data points, which are equal to the center point; S2. Determine the bandwidth parameter by estimating the size of the neighborhood of each point through K nearest neighbors , for each ,choose The distance to the Mth nearest neighbor is The local bandwidth is: ; ; ; In the formula, It is a data point The local bandwidth, yes The distance to the Mth nearest neighbor, is the Mth data point, N is the number of data points; Determine the radial kernel function : ; In the formula, is the normalization constant coefficient, represents the input sample point, is the kernel function width control parameter, It means to find the Euclidean distance.

[0020] Mean shift cluster analysis includes: S3, establishing the update equation of cluster analysis, solving the kernel density estimation : ; Calculate the first-order derivative form of the kernel density estimation function and get The update formula is: ; ; ; In the formula, It is updated , Before the update , and are all known functions. is the function's independent variable; S4, assuming the threshold is , repeat S3 until , then it is judged to be converged and the iteration is stopped; S5, forming different mesoscale vortex clusters, assigning all points with close updated positions to the same cluster, the center of each cluster is equivalent to the point after the mean shift algorithm converges, called the cluster center, and the cluster center represents the gathering area of ​​the mesoscale vortex; S6. Output the clustering results, group all the points in the data set according to the cluster center they converge to, and output the number of trajectory points of each cluster and the geometric range of the cluster to obtain a collection of spatial data of different clusters of mesoscale vortices.

[0021] When constructing the mesoscale eddy fitting ellipse equation, the mesoscale eddy trajectory points of each cluster are fitted into an ellipse shape using the robust least squares method, including T1, the total number of mesoscale eddy trajectory points after cluster analysis is Regions, filter out the latitude and longitude data of the range points in the corresponding area , time data , track number data ; T2. Derive the coefficient conversion relationship between the general equation of the ellipse and the standard equation. The general equation of the ellipse is: ; In the formula, , , , , is the target parameter fitted by the least squares method, and are the horizontal and vertical coordinates of the ellipse points. The ellipse is transformed into a standard form through translation and rotation: ; In the formula, and are the horizontal and vertical coordinates of the ellipse points in standard form, and are the two parameters of the ellipse equation, equivalent to the major and minor axes of the ellipse.

[0022] T2 includes T2.1. Let the coordinates of the point before translation and rotation transformation be , the coordinates of the point after translation transformation are the coordinate origin : ; In the formula, and is the horizontal and vertical coordinates of the ellipse point after translation transformation, and is substituted into the general equation of the ellipse: ; Convert to matrix form: ; After translation, the center of the ellipse is at the origin of the coordinate system: ; ; Solved and The expression is: ; ; Center of the ellipse for: ; ; The matrix form simplifies to: .

[0023] T2 includes T2.2, assuming the rotation angle is : ; Substitute the rotation transformation formula into the simplified matrix of T2.1: ; The offset angle of the rotated ellipse is 0. is 0: ; Deflection angle of the ellipse for: ; The matrix simplifies to: ; for: ; ; T2.3. Obtain the coefficient conversion relationship between the general equation of the ellipse and the standard equation, the calculation formulas for the major and minor axes, the calculation formulas for the deflection angle, and the calculation formulas for the center point.

[0024] The construction of the mesoscale eddy fitting ellipse equation includes T3 and the least squares method to fit the ellipse. The range points in the mesoscale eddy trajectory data set are put into the input variables. The objective function of the fitting is: : ; in, Indicates the number of latitude and longitude data of the range points corresponding to each mesoscale eddy track point, , Represents the longitude and latitude data of the mesoscale eddy range points , ; Solve the minimum value of the objective function. According to the extreme value principle, find The partial derivatives of: ; Convert to matrix form: ; Simplified to: ; ; In the formula, and Simplify parameters for a matrix.

[0025] T3 includes solving the corresponding The coefficients are used to obtain the ellipse equation and the major axis of the ellipse fitted to each mesoscale vortex. , short axis , deflection angle and the center point for: ; ; ; ; ; So far, a data set of mesoscale eddy geometric characteristics has been obtained.

[0026] The multi-factor feature analysis of mesoscale eddies includes dividing the mesoscale eddies into to ,total range; Calculate the major axis of the mesoscale eddy fitting ellipse within each cluster , short axis , deflection angle and the ratio of the major and minor axes The mean and standard deviation of , It is A feature dataset of data points, They are The major axis, minor axis, deflection angle and major-minor axis ratio of each data point; Calculate the average : ; Calculate standard deviation : ; Output the calculation results to obtain a complete mesoscale eddy spatial data set and geometric characteristic data set, carry out research on the spatial distribution and geometric characteristics of mesoscale eddies, analyze the properties and polar characteristics of mesoscale eddies, draw violin plots, and reveal the geometric characteristics of mesoscale eddies within each classification result and the changing rules between regions.

[0027] The present invention obtains a mesoscale eddy trajectory data set obtained by processing satellite altimeter data identification, and takes the Mesoscale Eddy Trajectory Atlas Product META3.2 DT provided by AVISO as an example to screen the longitude and latitude data (LON, LAT) of the mesoscale eddy trajectory points within the target range, the longitude and latitude data (ELON, ELAT) of the range points, the time data (TIM), and the trajectory number data (TRACK).

[0028] When the present invention processes the kernel density estimation, finding the extreme value of the kernel density estimation is equivalent to finding the zero point of its first-order derivative. Then the first-order derivative of the kernel density estimation function at the zero point is expressed as: ; In the formula, Represents the gradient. The steps to infer the first-order derivative form of the kernel density estimation function are as follows: ; make : .

[0029] The process of the present invention is as follows Figure 1 As shown, it includes obtaining mesoscale eddy trajectory data, screening data range and eliminating abnormal data, obtaining mesoscale eddy trajectory data within the target range, calculating the spatial distribution of mesoscale eddy, introducing Mean shift clustering analysis, obtaining spatial data collection of different clusters of mesoscale eddy, combining the least squares method and the standard ellipse equation, constructing the mesoscale eddy fitting ellipse equation, obtaining the mesoscale eddy geometric characteristic data set, combining the spatial data collection of different clusters of mesoscale eddy to perform mesoscale eddy multi-factor characteristic analysis, and completing the calculation and analysis of the geometric parameters of the mesoscale eddy.

[0030] The cluster analysis process of the mesoscale cold eddy in the northern part of the experimental sea area of ​​the present invention is as follows Figure 2 As shown in the figure, the number of each part (a total of 9 areas) and the corresponding number of sample points are shown. The first process of fitting the ellipse in the mesoscale eddy range is as follows Figure 3 As shown, the black line is the fitting process line, the blue line is the fitting ellipse, the center coordinates are (110.9331, 13.4133), the offset angle is -8.7258°, the major axis is 0.78541, the minor axis is 1.0815, and the equation is: ; The second process of fitting the ellipse of the mesoscale eddy range is as follows Figure 4 As shown, multiple ellipse fittings are performed according to different points. Figure 2 The cluster analysis results and ellipse fitting results are shown in Figure 5 As shown, it contains the ellipse parameters of each of the 9 regions. Figure 5 In They are two equal angles symmetrical about the major axis of the ellipse.

[0031] The probability distribution of the 9 regions under the long axis length of the cold vortex is as follows Figure 6 As shown in the figure, the probability distribution of the 9 regions under the short axis length of the cold vortex is as follows Figure 7 As shown in the figure, the probability distribution of the nine regions under the long-short axis ratio of the cold vortex is as follows Figure 8 As shown in Figure 2, the probability distribution of the nine regions under the deflection angle of the cold vortex major axis is as follows: Fig. 9 The present invention deeply analyzes the spatial distribution and geometric characteristics of mesoscale eddies, which can not only reveal their dynamic mechanisms, but also provide scientific support for improving climate prediction models, optimizing marine resource development and ecological protection; effectively filter out noise and abnormal data, ensure the high accuracy and robustness of fitting results, and improve the reliability of analysis results, which is of great significance for grasping the spatial structure properties of mesoscale eddies in different sea areas and the long-term change characteristics of mesoscale eddies under the background of climate warming.

[0032] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features may be replaced by equivalents, and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating and analyzing the spatial properties and geometric parameters of a mesoscale vortex, characterized in that: It includes obtaining mesoscale eddy trajectory data, screening data range and eliminating abnormal data, obtaining mesoscale eddy trajectory data within the target range, calculating the spatial distribution of mesoscale eddy, introducing Mean shift cluster analysis, obtaining spatial data collection of different clusters of mesoscale eddy, combining the least squares method and the standard ellipse equation, constructing a mesoscale eddy fitting ellipse equation, obtaining a mesoscale eddy geometric characteristic data set, combining the spatial data collection of different clusters of mesoscale eddy to perform multi-factor characteristic analysis of mesoscale eddy, and completing the calculation and analysis of the geometric parameters of the mesoscale eddy.

2. A method for calculating and analyzing the spatial properties and geometric parameters of a mesoscale vortex according to claim 1, characterized in that: The mesoscale eddy track data within the target range include the mesoscale eddy track point longitude and latitude data, range point longitude and latitude data, time data and track number data.

3. A method for calculating and analyzing the spatial properties and geometric parameters of a mesoscale vortex according to claim 2, characterized in that: Mean shift cluster analysis includes: S1. Extracting the longitude and latitude data of the trajectory points of the mesoscale vortex and saving them to the corresponding data points: ； In the formula, It is The longitude of the center of the mesoscale eddy, It is The latitude of the center of the mesoscale eddy, It is data points, which are equal to the center point; S2. Determine the bandwidth parameter by estimating the size of the neighborhood of each point through K nearest neighbors , for each ,choose The distance to the Mth nearest neighbor is The local bandwidth is: ； ； ； In the formula, It is a data point The local bandwidth, yes The distance to the Mth nearest neighbor, is the Mth data point, N is the number of data points; Determine the radial kernel function : ； In the formula, is the normalization constant coefficient, represents the input sample point, is the kernel function width control parameter, It means to find the Euclidean distance.

4. A method for calculating and analyzing the spatial properties and geometric parameters of a mesoscale vortex according to claim 3, characterized in that: Mean shift cluster analysis includes: S3, establishing the update equation of cluster analysis, solving the kernel density estimation : ； Calculate the first-order derivative form of the kernel density estimation function and get The update formula is: ； ； ； In the formula, It is updated , Before the update , and are all known functions. is the function's independent variable; S4, assuming the threshold is , repeat S3 until , then it is judged to be convergent and the iteration is stopped; S5, forming different mesoscale vortex clusters, assigning all points with close updated positions to the same cluster, the center of each cluster is equivalent to the point after the mean shift algorithm converges, called the cluster center, and the cluster center represents the gathering area of ​​the mesoscale vortex; S6. Output the clustering results, group all the points in the data set according to the cluster center they converge to, and output the number of trajectory points of each cluster and the geometric range of the cluster to obtain a collection of spatial data of different clusters of mesoscale vortices.

5. A method for calculating and analyzing the spatial properties and geometric parameters of a mesoscale vortex according to claim 4, characterized in that: When constructing the mesoscale eddy fitting ellipse equation, the mesoscale eddy trajectory points of each cluster are fitted into an ellipse shape using the robust least squares method, including T1, the total number of mesoscale eddy trajectory points after cluster analysis is Regions, filter out the latitude and longitude data of the range points in the corresponding area , time data , track number data ; T2. Derive the coefficient conversion relationship between the general equation of the ellipse and the standard equation. The general equation of the ellipse is: ； In the formula, , , , , is the target parameter fitted by the least squares method, and are the horizontal and vertical coordinates of the ellipse points. The ellipse is transformed into a standard form through translation and rotation: ； In the formula, and are the horizontal and vertical coordinates of the ellipse points in standard form, and are the two parameters of the ellipse equation, equivalent to the major and minor axes of the ellipse.

6. A method for calculating and analyzing the spatial properties and geometric parameters of a mesoscale vortex according to claim 5, characterized in that: T2 includes T2.

1. Let the coordinates of the point before translation and rotation transformation be , the coordinates of the point after translation transformation are the coordinate origin : ； In the formula, and is the horizontal and vertical coordinates of the ellipse point after the translation transformation, and is substituted into the general equation of the ellipse: ； Convert to matrix form: ； After translation, the center of the ellipse is at the origin of the coordinate system: ； ； Solved and The expression is: ； ； Center of the ellipse for: ； ； The matrix form simplifies to: 。 7. A method for calculating and analyzing the spatial properties and geometric parameters of a mesoscale vortex according to claim 6, characterized in that: T2 includes T2.2, assuming the rotation angle is : ； Substitute the rotation transformation formula into the simplified matrix of T2.1: ； The offset angle of the rotated ellipse is 0. is 0: ； Deflection angle of the ellipse for: ； The matrix simplifies to: ； for: ； ； T2.

3. Obtain the coefficient conversion relationship between the general equation and the standard equation of the ellipse, the calculation formulas for the major and minor axes, the calculation formulas for the deflection angle, and the calculation formulas for the center point.

8. A method for calculating and analyzing the spatial properties and geometric parameters of a mesoscale vortex according to claim 7, characterized in that: The construction of the mesoscale eddy fitting ellipse equation includes T3 and the least squares method to fit the ellipse. The range points in the mesoscale eddy trajectory data set are put into the input variables. The objective function of the fitting is: : ； in, Indicates the number of range point longitude and latitude data corresponding to each mesoscale eddy track point, , Represents the longitude and latitude data of the mesoscale eddy range points , ; Solve the minimum value of the objective function. According to the extreme value principle, find The partial derivatives of: ； Convert to matrix form: ； Simplified to: ； ； In the formula, and Simplify parameters for a matrix.

9. A method for calculating and analyzing the spatial properties and geometric parameters of a mesoscale vortex according to claim 8, characterized in that: T3 includes solving the corresponding The coefficients are used to obtain the ellipse equation and the major axis of the ellipse fitted to each mesoscale vortex. , short axis , deflection angle and the center point for: ； ； ； ； ； So far, a data set of mesoscale eddy geometric characteristics has been obtained.

10. A method for calculating and analyzing the spatial properties and geometric parameters of a mesoscale vortex according to claim 9, characterized in that: The multi-factor feature analysis of mesoscale eddies includes dividing the mesoscale eddies into to ,total range; Calculate the major axis of the mesoscale eddy fitting ellipse within each cluster , short axis , deflection angle and the ratio of the major and minor axes The mean and standard deviation of , It is A feature dataset of data points, They are The major axis, minor axis, deflection angle and major-minor axis ratio of each data point; Calculate the average : ； Calculate standard deviation : ； Output the calculation results to obtain a complete mesoscale eddy spatial data set and geometric characteristic data set, carry out research on the spatial distribution and geometric characteristics of mesoscale eddies, analyze the properties and polar characteristics of mesoscale eddies, draw violin plots, and reveal the geometric characteristics of mesoscale eddies within each classification result and the changing rules between regions.

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