A method for extracting the strong precipitation center field in the Jianghuai region

Abstract

The present invention relates to a method for extracting the central field of heavy precipitation in the Jianghuai region, belonging to the technical field of computer objective weather typing. The method includes the following steps: 1) Establish a data set representing the set of heavy precipitation fields; 2) Find the κ-neighborhood heavy precipitation fields of each heavy precipitation field; 3) Calculate the density index of each heavy precipitation field; 4) Calculate the distribution index of each heavy precipitation field; 5) Calculate the geometric mean of the density index and the distribution index of each heavy precipitation field, which is the initial value for determining the central field, and then update the initial value to obtain the central field determination value of each heavy precipitation field; 6) Select the precipitation field dates and precipitation grid point values corresponding to the values greater than 0 from the central field determination values, which are the occurrence dates and precipitation amounts of the central field of the heavy precipitation type. The present invention only requires a single predefined parameter, and the operation result has no randomness, and can accurately extract the central field of the set of heavy precipitation fields whose distribution presents a non-convex shape.

Description

Technical Field

[0001] The present invention relates to a method for extracting the strong precipitation center field in the Jianghuai region, belonging to the technical field of computer objective weather classification. Background Art

[0002] Jianghuai in China is located in the transitional zone between the rainy south and the arid and less rainy north. The annual and seasonal variability of precipitation is very large, the influencing factors are complex, and meteorological disasters such as droughts, floods and typhoons occur frequently. Therefore, for the need of developing more advanced forecasting methods to better prevent and mitigate disasters, it is very necessary to classify the strong precipitation weather in the Jianghuai region.

[0003] The principle of weather classification is to analyze specific meteorological elements by objective or subjective methods to identify several weather types with higher occurrence frequencies, so as to classify the meteorological field into these weather types. Compared with subjective weather classification, objective weather classification is realized by methods such as mathematical statistics and numerical analysis, so it is more objective and comprehensive. The commonly used methods include Spatial Synoptic Classification (SSC), Empirical Orthogonal Function (EOF), wavelet analysis, k-means, hierarchical clustering method, etc. In these methods, it is often necessary to first extract the center field of each weather type, such as the sliding seed day of SSC, reference document: Sheridan S C, 2002. The redevelopment of a weather-type classification scheme for north America; the cluster center of k-means, reference document: Zhang Hongyan, 2021. Split K-means clustering algorithm based on density weighting; the typical mode of EOF, reference document: Qin Ling, 2020. Spatiotemporal characteristics of the main modes of the interannual variation of global spring-autumn monsoon precipitation, and then obtain the classification results. However, these methods all need to specify the number of center fields, and the sliding seed day needs to be subjectively defined by humans; the selection of the cluster center follows certain rules under the improved algorithm of k-means but still has randomness, or additional predefined parameters are added to eliminate randomness. At the same time, the selection of the k-means cluster center is not applicable to non-convex-shaped clusters; EOF uses the method of finding eigenvalues and eigenvectors to extract typical modes, but due to the limitations of data space transformation, it is not applicable to the distribution of non-convex-shaped meteorological fields.

[0004] In view of the deficiencies of the above-mentioned prior art, it is necessary to establish a new method for extracting the typical mode of the meteorological field to obtain the strong precipitation center field in the Jianghuai region. Summary of the Invention

[0005] The present invention provides a method for extracting the central field of heavy precipitation in the Jianghuai region. A new method for extracting typical modes of meteorological fields is applied to obtain the central field of heavy precipitation in the Jianghuai region, facilitating subsequent weather classification of heavy precipitation weather. This method only requires a single predefined parameter, and the operation result has no randomness, and it can accurately extract the central field of the heavy precipitation field set with a non-convex shape distribution.

[0006] The present invention adopts the following technical solutions to solve its technical problems:

[0007] A method for extracting the central field of heavy precipitation in the Jianghuai region, comprising the following steps:

[0008] Step 1) Collect daily precipitation station data of the area to be analyzed and convert it into grid data, screen the heavy precipitation day data, and establish a data set representing the heavy precipitation field set;

[0009] Step 2) Calculate the distance matrix of the heavy precipitation fields, and find the κ-neighborhood heavy precipitation fields of each heavy precipitation field, where the κ-neighborhood is a predefined parameter;

[0010] Step 3) Calculate the density index of each heavy precipitation field within the κ-neighborhood range;

[0011] Step 4) Taking each heavy precipitation field as the origin, calculate the radian value of the angle formed by it and all k(k - 1) / 2 pairs of heavy precipitation fields within the κ-neighborhood range. One pair of heavy precipitation fields consists of two heavy precipitation fields, and a set of k - 1 adjacent minimum radian values of the angles is selected, and the distribution index of each origin heavy precipitation field is calculated accordingly;

[0012] Step 5) Calculate the geometric mean of the density index and the distribution index of each heavy precipitation field, which is the initial value for determining the central heavy precipitation field, simply referred to as the initial value for determining the central field. Then, compare within its κ-neighborhood range. If the initial value for determining the central field of a certain heavy precipitation field is less than the initial value for determining the central field of any heavy precipitation field within its κ-neighborhood range, then the determination value of the central field of this heavy precipitation field is set to 0; otherwise, it is set to the original determination value, and the determination value of the central field of each heavy precipitation field is obtained;

[0013] Step 6) Select the precipitation field dates and precipitation grid values corresponding to the values greater than 0 from the central field determination values, which are the occurrence dates and precipitation amounts of the central field of the heavy precipitation type.

[0014] In Step 1), the precipitation station data is first converted into grid data, and then the heavy precipitation day grid data is screened to establish a heavy precipitation field data set, and its representation form is a two-dimensional array where n represents the number of dates, m represents the number of grid points and must be greater than 1, x ij , i ∈ {1...n}, j ∈ {1...m} represents the heavy precipitation value, id i , i ∈ {1...n} represents the date corresponding to the heavy precipitation field on a certain day.

[0015] The distance matrix described in step 2) is composed of the Euclidean distances between the heavy precipitation fields of any two days in DATA, and the form of expression is a two-dimensional array where n represents the number of dates, d ij , i, j ∈ {1...n} and i ≠ j represent the Euclidean distance and d ij = d ji , m represents the number of grid points, inf represents a positive infinite quantity; then the integer k in the range from 2 to n - 1 is a predefined parameter, and the smallest k values are searched row by row in DS and the column numbers where these k values are located are recorded to obtain the κ-neighborhood heavy precipitation field, and the form of expression is a two-dimensional array where: k represents the κ-neighborhood value, kd ij , i ∈ {1...n}, j ∈ {1...k} represent the column numbers where the smallest k values in the i-th row of DS are located.

[0016] The calculation method of the density index described in step 3) uses the formula represents the result of taking the exponential operation of -DS(i, KDS(i, j)) with the natural constant as the base and then summing over j = {1...k}, so as to obtain the density indexes of all heavy precipitation fields, and the form of expression is a one-dimensional array ρ = [ρ 1 , ρ 2 ... ρ i ... ρ n , where i ∈ {1...n}, j ∈ {1...k}, KDS(i, j) is the element in the j-th column of the i-th row of KDS, and DS(i, KDS(i, j)) is the element in the KDS(i, j)-th column of the i-th row of DS.

[0017] The method for obtaining the set of k - 1 adjacent minimum included angle radian values described in step 4) is as follows: First, select all pairs of heavy precipitation fields within the κ-neighborhood range of the origin heavy precipitation field as DDS i = [KDS(i, p), KDS(i, q)], where i ∈ {1...n} represents taking the heavy precipitation field of any date as the origin heavy precipitation field, p = {1...k - 1} and for each element value in p, q takes corresponding values in turn q = {p + 1...k}, KDS(i, p) represents the element in the p-th column of the i-th row of KDS, and KDS(i, q) represents the element in the q-th column of the i-th row of KDS, and the DDS obtained in this way i has the form of a two-dimensional array with k(k - 1) / 2 rows and 2 columns;

[0018] Secondly, calculate the origin heavy precipitation field i and DDS i The radian of the spatial triangle formed by the paired heavy precipitation fields in each row at the origin heavy precipitation field i, the three sides of the spatial triangle are a=DS(i,KDS(i,p)), b=DS(i,KDS(i,q)), c=DS(KDS(i,p),KDS(i,q)), where DS(i,KDS(i,p)) represents the i-th row KDS(i,p) column element of DS, DS(i,KDS(i,q)) represents the i-th row KDS(i,q) column element of DS, DS(KDS(i,p),KDS(i,q)) represents the KDS(i,p)th row KDS(i,q) column element of DS, and the radian calculation formula for the radian of the heavy precipitation field i at the origin is RDS i =acos((a 2 +b 2 -c 2 ) / (2ab)), the obtained RDS i The representation is a one-dimensional array with k(k-1) / 2 rows and 1 column;

[0019] Finally, select k-1 adjacent minimum angle radians, that is, find the RDS first i The smallest element m1 is added to the empty set MRD i , i represents the heavy precipitation field at the origin, and obtains the row where m1 is located in DDS i The two elements of the corresponding row are used as the initial data set DI, and then continuously from DDS i Find the rows where one element belongs to DI and the other element does not belong to DI, and find the corresponding RDS i Find the minimum element mi in the row and add it to MRD i , and place the row where mi is located in DDS i The one of the two elements in the corresponding row that does not belong to DI is added to DI until DI contains DDS i For all k non-repeating elements, KDS(i,p)∪KDS(i,q)=KDS(i,1...k) for a total of k elements. Since DI starts with two elements and increases by one each time until k elements are reached, it increases by k-2 times in total. Therefore, MRD i From the initial element, it increases to a one-dimensional array with k-1 elements, that is, a set of k-1 adjacent minimum angle radian values; the method for calculating the distribution index uses the formula MRD i (j)≤2π (m-1) / k is the condition for MRD i (j) Sum at j = {1...k-1}, where i∈{1...n}, MRDi (j) is the j-th element of MRD i , where m represents the number of grid points and k represents the κ neighborhood value, thus obtaining the distribution indicators of all strong precipitation fields, and the form of expression is a one-dimensional array δ = [δ 1 , δ 2 ... δ i ... δ n .

[0020] Principle description of the steps:

[0021] Step 3) The density indicator describes the density attribute of each strong precipitation field. Because if a strong precipitation field is the central strong precipitation field (central field), the Euclidean distances from it to the strong precipitation fields within its closest κ neighborhood must be very small, that is, the value of its density function is larger. On the contrary, if a strong precipitation field is a non-central field (a strong precipitation field around the central field or an outlier), its Euclidean distance from the strong precipitation fields within the κ neighborhood will generally increase compared with the central field, resulting in a decrease in the value of the density function ρ i . Therefore, the closer a strong precipitation field is to the central field, the higher its density indicator.

[0022] Step 4) The distribution indicator describes the distribution attribute of each strong precipitation field. Its role is to make up for the deficiencies of the density attribute in describing the central field. That is, under the condition that the density indicators are the same, the larger and more uniform the interval radian of the data point distribution within the κ neighborhood of the central field, the higher the value of its distribution indicator, and the more it should be the central field. In addition, when selecting MRD i (j) ≤ 2π (m-1) / k as the condition for summing MRD i (j) is because although MRD i (j) is better if it is larger, it cannot exceed a certain threshold. Otherwise, this radian value will be considered to have too large a difference from other radian values, resulting in uneven distribution. Since the distribution indicator of the central field requires that the radian values of MRD i should be as uniform as possible, the radian values that cause uneven distribution will not be included in the distribution indicator. Here, the threshold is selected using the total radian mean value, that is, the total radian 2π (m-1) of the m-dimensional space represented by the number of grid points m divided by k.

[0023] In short, the constituent element of the density indicator is distance, and the constituent element of the distribution indicator is radian. The two form a complete polar coordinate system, so the characteristics of the central field can be comprehensively depicted.

[0024] Step 5) Since the initial determination value of the center field of each heavy precipitation field represents the possibility of the heavy precipitation field becoming the center field, that is, the larger the initial determination value, the more likely it is to be the center field. However, due to the lack of a threshold standard, the initial determination value cannot accurately represent whether a certain heavy precipitation field is the center field. Therefore, another idea is considered to solve the above problem, that is, introducing a judgment principle for the center field - the initial determination value of a certain heavy precipitation field must be greater than or equal to the initial determination values of all heavy precipitation fields within its κ neighborhood range before its initial determination value can be considered valid and retained. Otherwise, the final center field determination value is zero. The principle on which this judgment principle is based is that the initial determination value of the center point of each type of data point in the dataset is the highest within its local range (κ neighborhood). For the data points around the center point, since there must be some data points closer to the center point within their κ neighborhood with higher initial determination values, the final determination values of the data points around the center will be set to zero. Similarly, for the outlier data points, since there must be some data points closer to the periphery of the center within their κ neighborhood with higher initial determination values, the final determination values of the outlier data points will also be set to zero. In this way, the data points around the center and the outlier data points are filtered out, and only the data points with a determination value greater than zero at the center point are left.

[0025] The beneficial effects of the present invention are as follows:

[0026] 1. Extract the center field with a single predefined parameter, and the result is stable without randomness

[0027] The present invention only uses the k value representing the κ neighborhood as a parameter without specifying the number of center fields. By calculating the density index and distribution index of each heavy precipitation field, then converting them into the initial determination value of the center field, and then according to the judgment principle (a certain heavy precipitation field can be determined as the center field only when its initial determination value is greater than or equal to the initial determination values of all heavy precipitation fields within its κ neighborhood range), the center field determination result is obtained. There is no random content in the technical solution, so the result is stable without randomness.

[0028] 2. Can accurately extract the center field of the heavy precipitation field set with a non-convex shape distribution Brief Description of the Drawings

[0029] Figure 1 It is a comparison diagram of different distribution indexes for data with the same density index.

[0030] Figure 2 It is a simulated dataset diagram.

[0031] Figure 3 It is a schematic diagram of the centers of 2 categories obtained by the EOF method.

[0032] Figure 4 It is a schematic diagram of the centers of 2 categories obtained by the method of the present invention.

[0033] Figure 5It is the flowchart for extracting the heavy precipitation center field of the present invention.

[0034] Figure 6(a) is a schematic diagram of the first heavy precipitation center field (July 21, 2002) in the Yangtze-Huaihe region of China from 1981 to 2015; Figure 6(b) is a schematic diagram of the second heavy precipitation center field (June 14, 2004) in the Yangtze-Huaihe region of China from 1981 to 2015; Figure 6(c) is a schematic diagram of the third heavy precipitation center field (July 1, 2003) in the Yangtze-Huaihe region of China from 1981 to 2015; Figure 6(d) is a schematic diagram of the fourth heavy precipitation center field (July 3, 2007) in the Yangtze-Huaihe region of China from 1981 to 2015; Figure 6(e) is a schematic diagram of the fifth heavy precipitation center field (June 20, 1998) in the Yangtze-Huaihe region of China from 1981 to 2015. Detailed implementation manners

[0035] The present invention will be further described in detail below with reference to the accompanying drawings.

[0036] Figure 1 It is an example to illustrate the significance of the distribution index. The distribution index depicts the distribution attributes of each heavy precipitation field, and its role is to make up for the deficiencies of the density attribute in describing the center field. For example Figure 1 As can be seen from the comparison of the two distributions shown, the κ-neighborhood value k of the center (center field) in the upper right circle is k = 12, and the κ-neighborhood value of the center in the lower left circle is also k = 12, and the Euclidean distances from the two centers to the κ-neighborhood points are all correspondingly equal. Therefore, the density indexes of the two distributions are equal. However, the data points (heavy precipitation fields) in the upper right circle are more evenly distributed. So its center is more likely to be the center field than the center in the lower left. Therefore, the distribution function value of the upper right center is higher than that of the lower left center. As shown by the solid arrow range in Figure 1 , where: MRD i represents the set of k - 1 adjacent minimum included angle radian values within the κ-neighborhood of the center (i.e., the origin heavy precipitation field i). MRD i (j) is the j-th element of MRD i where j ∈ {1... k - 1}.

[0037] Since the number of grid points of the heavy precipitation field in the Yangtze-Huaihe region, that is, the data dimension, is very high and cannot be intuitively represented by a graph, a simplified two-dimensional data set is used to prove the beneficial effects of the present invention in the case of non-convex shaped heavy precipitation field distributions. As Figure 2 shown, the simulated data set has 240 two-dimensional data, which are divided into two categories. Among them, category 1 is convex-shaped and category 2 is non-convex-shaped. Therefore, there should be two center points (i.e., center fields) located at the center positions of category 1 and category 2 respectively.

[0038] Comparing the EOF method and the method of the present invention, it can be found that the EOF method, asFigure 3 As shown, its typical number of modes = 2. The centers of Category 1 and Category 2 are marked at the boundary positions of the data. This is because when calculating eigenvalues and eigenvectors through spatial transformation of the data, a linear transformation (or restricted non-linear transformation) method is used. Therefore, for data with a relatively complex distribution, such as a simulated data set with non-convex shaped categories and the boundaries of the two categories in contact, it is impossible to obtain large variances in the orthogonal directions through spatial transformation, resulting in a very poor effect of the EOF method in identifying the data category centers. In contrast, the method of the present invention, as Figure 4 shown, with k = 78, does not require spatial transformation. Instead, it automatically evaluates and judges the category centers through the density index and distribution index of the data, so that the two category centers of the simulated data set can be accurately found.

[0039] The flow chart of the present invention is as Figure 5 , using the daily 00:00 (Universal Time) 24-hour accumulated precipitation station data in the Yangtze-Huaihe region of China (26°N - 36°N, 110°E - 123°E) from 1981 to 2015 as the precipitation station data set.

[0040] First, convert the precipitation station data set from station data to grid data, which is implemented using the obj_anal_ic_Wrap function in the NCAR Command Language (NCL). The precipitation grid data set is obtained. The input parameters of this function are set as follows: zlon = longitudes of 694 stations in the Yangtze-Huaihe region; zlat = latitudes of 694 stations in the Yangtze-Huaihe region; z = precipitation of 694 stations in the Yangtze-Huaihe region; glon = grid longitude sequence in the Yangtze-Huaihe region (grid range 110 - 123, grid interval 1); glat = grid latitude sequence in the Yangtze-Huaihe region (grid range 26 - 36, grid interval 1); rscan = continuous radius of influence ([10, 5, 3]); option = no local smoothing (False). The returned precipitation grid data are precipitation values of 154 grid points at each grid interval within the above grid range.

[0041] Secondly, the screening criteria for heavy precipitation day data are as follows: Based on the precipitation grid data set, objectively identify continuous heavy rain (heavy rain) areas (the number of grid points with 24-hour accumulated precipitation reaching the heavy rain (heavy rain) or above level (≥50 mm (25 mm)) ≥ 15 and connected in a continuous area). "Connected in a continuous area" means that each grid point in this area is at least connected to another grid point (including diagonal connection). Using the precipitation grid data where continuous heavy rain (heavy rain) areas appear as heavy precipitation day data, a data set representing the heavy precipitation field set is obtained.

[0042] Finally, using the heavy precipitation field dataset and the predefined parameter k = 15, by the method of calculating the density index, distribution index, and central field determination value in the present invention, several heavy precipitation fields with a central field determination value > 0 are obtained as the central fields of several heavy precipitation types, and the output results are as follows Figures 6(a) to 6(e) .

[0043] As can be seen from Figs. 6(a)-(e), there are five heavy precipitation central fields in the Jianghuai region of China from 1981 to 2015, corresponding to five heavy precipitation weather classification types. Among them, the first type (Fig. 6(a)) shows the characteristic of overall consistent and relatively more precipitation in the Jianghuai region, with less precipitation in the northeast and southeast; the second type (Fig. 6(b)) presents the characteristic of more precipitation in the central part of the Jianghuai region and less precipitation in the north and south, and the large precipitation center is located in the central part of the Jianghuai region; the third and fourth types (Figs. 6(c)(d)) both show the spatial distribution characteristic of more precipitation in the north and less precipitation in the south of the Jianghuai region. However, for the third type (Fig. 6(c)), the entire northern part of the Jianghuai region is included in the large precipitation center, while for the fourth type (Fig. 6(d)), the precipitation center is mainly located in the coastal area in the east of the northern Jianghuai region, with less precipitation in the northwest; the fifth type (Fig. 6(e)) is opposite to the distribution characteristics of the third and fourth types, presenting the characteristic of more precipitation in the south and less precipitation in the north of the Jianghuai region, and the large precipitation center is located in the southeast of the Jianghuai region.

Claims

1. A method for extracting the strong precipitation center field in the Jianghuai region, characterized in that, it includes the following steps: Step 1) Collect the daily precipitation station data of the area to be analyzed and convert it into grid data, screen the strong precipitation day data among them, and establish a data set representing the strong precipitation field set; Step 2) Calculate the distance matrix of the strong precipitation fields, and find the κ-neighborhood strong precipitation fields of each strong precipitation field, where the κ-neighborhood is a predefined parameter; Step 3) Calculate the density index of each strong precipitation field within the κ-neighborhood range; Step 4) Taking each strong precipitation field as the origin, calculate the radian value of the angle formed by the spatial line segments formed by it and all k(k - 1) / 2 pairs of strong precipitation fields within the κ-neighborhood range, where a pair of strong precipitation fields are two strong precipitation fields, and screen to obtain a set of k - 1 adjacent minimum radian values of the angle, and calculate the distribution index of each origin strong precipitation field based on this; k is the κ-neighborhood value; Step 5) Calculate the geometric mean of the density index and the distribution index of each strong precipitation field, which is the initial value for determining the central strong precipitation field, simply referred to as the initial value for determining the central field, and then compare it within its κ-neighborhood range. If the initial value for determining the central field of a certain strong precipitation field is less than the initial value for determining the central field of any strong precipitation field within its κ-neighborhood range, then the value for determining the central field of this strong precipitation field is set to 0, otherwise it is set to the original value for determination, to obtain the value for determining the central field of each strong precipitation field; Step 6) Select the precipitation field dates and precipitation grid values corresponding to the values greater than 0 from the values for determining the central field, which are the occurrence dates and precipitation amounts of the central field of the strong precipitation type.

2. The method for extracting the strong precipitation center field in the Jianghuai region according to claim 1, characterized in that, The precipitation station data described in step 1) is first converted into grid data, and then the grid data of heavy precipitation days is screened to establish a heavy precipitation field dataset, the form of which is a two-dimensional array where n represents the number of dates, m represents the number of grid points and must be greater than 1, x ij , i ∈ {1...n}, j ∈ {1...m} represents the heavy precipitation value, id i , i ∈ {1...n} represents the date corresponding to the heavy precipitation field on a certain day.

3. The method for extracting the strong precipitation center field in the Jianghuai region according to claim 1, characterized in that, The distance matrix described in step 2) is composed of the Euclidean distances between the heavy precipitation fields of any two days in DATA, and its representation form is a two-dimensional array where n represents the number of dates, and d ij , i, j ∈ {1...n} and i ≠ j represent the Euclidean distance, and d ij = d ji , m represents the number of grid points, inf represents a positive infinite quantity; then the integer k in the range of 2 to n - 1 is a predefined parameter, and the smallest k values are searched row by row in DS and the column numbers where these k values are located are recorded to obtain the κ-neighborhood heavy precipitation field, and its representation form is a two-dimensional array where: k represents the κ-neighborhood value, and kd ij , i ∈ {1...n}, j ∈ {1...k} represent the column numbers where the smallest k values in the i-th row of DS are located.

4. The method for extracting the strong precipitation center field in the Jianghuai region according to claim 3, characterized in that, The calculation method of the density index described in step 3) uses the formula represents the result of taking the exponential operation of -DS(i, KDS(i, j)) with the natural constant as the base and then summing over j = {1... k}, so as to obtain the density index of all heavy precipitation fields, and the representation form is a one-dimensional array ρ = [ρ 1 , ρ 2 ... ρ i ... ρ n , where i ∈ {1... n}, j ∈ {1... k}, KDS(i, j) is the element in the i-th row and j-th column of KDS, and DS(i, KDS(i, j)) is the element in the i-th row and KDS(i, j)-th column of DS.

5. The method for extracting the strong precipitation center field in the Jianghuai region according to claim 3, characterized in that, The method for obtaining the set of k - 1 adjacent minimum radian values of the angle in step 4) is as follows: First, select all pairs of strong precipitation fields within the κ-neighborhood of the origin strong precipitation field as DDS i =[KDS(i,p), KDS(i,q)], where i∈{1...n} represents taking the strong precipitation field on any date as the origin strong precipitation field, p={1...k - 1} and for each element value in p, q corresponds to the value q={p + 1...k} in sequence. KDS(i,p) represents the element in the p-th column of the i-th row of KDS, and KDS(i,q) represents the element in the q-th column of the i-th row of KDS. The DDS obtained in this way i is in the form of a two-dimensional array with k(k - 1) / 2 rows and 2 columns; Secondly, calculate the strong precipitation field i at the origin and DDS i The radian of the angle at the strong precipitation field i at the origin formed by the spatial triangles formed by the paired strong precipitation fields in each row. The three side lengths of the spatial triangle are a = DS(i, KDS(i, p)), b = DS(i, KDS(i, q)), c = DS(KDS(i, p), KDS(i, q)), where DS(i, KDS(i, p)) represents the element in the KDS(i, p)-th column of the i-th row of DS, DS(i, KDS(i, q)) represents the element in the KDS(i, q)-th column of the i-th row of DS, and DS(KDS(i, p), KDS(i, q)) represents the element in the KDS(i, q)-th column of the KDS(i, p)-th row of DS. The calculation formula for the radian of the angle at the strong precipitation field i at the origin is RDS i = acos((a 2 + b 2 - c 2 ) / (2ab)), and the obtained RDS i is in the form of a one-dimensional array with k(k - 1) / 2 rows and 1 column; Finally, k - 1 adjacent minimum included - angle radian values are screened out. That is, first find the minimum element m1 of RDS i and add it to the empty set MRD i . Let i represent the strong precipitation field at the origin, and obtain the two elements in the corresponding row of the row where m1 is located in DDS i as the initial data set DI. Then, continuously search in DDS i for those rows where one element belongs to DI and the other element does not belong to DI. Search for the minimum element mi in the corresponding RDS i row and add it to MRD i . And add the element that does not belong to DI among the two elements in the corresponding row of the row where mi is located in DDS i to DI until DI contains all k non - repeating elements of DDS i , that is, until KDS(i,p)∪KDS(i,q)=KDS(i,1...k) for a total of k elements. Since DI starts from two elements and increases by one each time until k elements, a total of k - 2 times of increase, so MRD i increases from the initial one element to a one - dimensional array with k - 1 elements, which is the set of k - 1 adjacent minimum included - angle radian values. The method for calculating the distribution index uses the formula which means summing MRD i (j) with the condition that MRD (m-1) (j)≤2π i / k for j∈{1...k - 1}, where i∈{1...n}, MRD i (j) is the j - th element of MRD i , m represents the number of grid points, k represents the neighborhood value, so as to obtain the distribution indexes of all strong precipitation fields, and the manifestation form is a one - dimensional array δ=[δ 1 ,δ 2 ...δ i ...δ n .

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