A thunderstorm cloud charge region volume calculation method based on lightning three-dimensional radiation source

Abstract

The present application relates to thunderstorm cloud charge area volume calculation technical field, especially in kind of thunderstorm cloud charge area volume calculation method based on lightning three-dimensional radiation source, solve the problem that cannot accurately quantify thunderstorm cloud charge area volume, its technical scheme is: including the following steps: S1: data preparation;S2: hierarchical clustering;S3: delaunay triangulation;S4: calculate Alpha-Shapes;S5: convex hull optimization;S6: volume calculation and correction;S7: sub-region volume summation, the beneficial effects of the present application are: with high calculation precision, high calculation efficiency, wide applicability and strong scalability and other advantages, can satisfy the demand of lightning charge area volume calculation, has higher practical value.

Description

Technical Field

[0001] This invention relates to the field of thunderstorm cloud charge region volume calculation technology, and in particular to a method for calculating thunderstorm cloud charge region volume based on a three-dimensional lightning radiation source. Background Technology

[0002] Lightning is one of the most serious natural disasters, causing forest and oil depot fires, power supply and communication system failures or damage, and posing a significant threat to aerospace, mining, and some important and sensitive high-tech equipment. Since the 1980s, the damage caused by lightning has increased significantly, especially in fields closely related to high technology, such as aerospace, defense, communications, power, computers, and electronics industries. The widespread use of large-scale and very large-scale integrated circuits, which are extremely sensitive to electromagnetic interference from lightning, has greatly increased the probability of being struck by lightning.

[0003] Whether lightning can develop to the ground and ultimately form a highly destructive ground flash is closely related to the distribution and size of the charge region in the thunderstorm cloud. While the polarity distribution of thunderstorm charges is difficult to detect directly, lightning location systems can continuously observe the three-dimensional spatiotemporal evolution of lightning channels within thunderstorm clouds. According to the bidirectional leader model mentioned in the paper "Physical processes during development of lightning flashes" (Comptes Rendus Physique, 2002), lightning originates between positive and negative charge regions, and then positive and negative leaders propagate in charge regions of opposite polarities. By analyzing the transmission patterns and spatiotemporal distribution characteristics of lightning discharge channels of different polarities, the polarity of the charge layer can be determined. By superimposing the radiation sources of continuously discharging channels within a given time interval, the main charge polarity distribution of the thunderstorm cloud and the height of the charge region involved in lightning discharge can be inferred. However, research on methods for calculating the volume of the charge region is still lacking. A paper titled "Triggered negativelightning-leaders that propagated into thunderstorm lower positive charge" (Journal of Geophysical Research: Atmospheres, 2021) proposed using the alpha shape (rolling sphere-like method) algorithm to estimate the volume of the charge region in thunderstorm clouds, but did not provide a detailed algorithm.

[0004] Currently, low-frequency lightning location technology can precisely reconstruct lightning channels and depict charge regions. However, due to the lack of methods for calculating the volume of charge regions, it is not yet possible to accurately quantify the volume of charge regions in thunderstorm clouds. Summary of the Invention

[0005] The purpose of this invention is to provide a method for calculating the charge region volume of thunderstorm clouds based on a three-dimensional lightning radiation source. This invention contributes to the study of the physical characteristics of lightning initiation and transmission, and also has significant implications for improving thunderstorm prediction and lightning protection technologies.

[0006] To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0007] A method for calculating the charge region volume of thunderstorm clouds based on a three-dimensional lightning radiation source includes the following steps:

[0008] S1: Data preparation; collect and organize the three-dimensional locations of lightning radiation sources within a certain period of time, and convert these data into three-dimensional point cloud data format;

[0009] S2: Hierarchical clustering; This method divides the charge region into several sub-regions, thus better handling lightning radiation source group data with different shapes and density distributions. The reason for using hierarchical clustering here is that this type of clustering method does not require pre-determining the number of clusters, making it more applicable when dividing the charge region.

[0010] S3: Delaunay triangulation; Delaunay triangulation is performed on the point cloud data of each sub-region, and a spatial weighting strategy based on charge density is introduced to generate a three-dimensional mesh composed of tetrahedrons; this mesh can approximate the shape of the charge region while ensuring that the Delaunay conditions are met.

[0011] S4: Calculate Alpha-Shapes; Apply the Alpha-Shapes algorithm to calculate the outer envelope of the point cloud data; This algorithm effectively describes the complex shape of the charge region by finding a spatial subset that approximates the distribution of the point cloud data.

[0012] S5: Convex Hull Optimization; Convex hull optimization is performed on the outer envelope calculated by Alpha-Shapes; By eliminating the concave parts in the envelope, a convex polyhedron that approximates the charge region is generated.

[0013] S6: Volume Calculation and Correction; Calculate the volume of the convex polyhedron based on its geometric properties; Divide the convex polyhedron into several tetrahedrons and sum the volumes of the tetrahedrons to obtain the total volume of the convex polyhedron;

[0014] S7: Sub-region volume summation; sum the calculated charge region volumes for each sub-region to obtain the volume of the entire charge region.

[0015] Step S1 is as follows:

[0016] This step mainly prepares the 3D point cloud data for subsequent calculations;

[0017] Set each point pi The coordinates are represented as (x i ,y i ,z i ), i = 1, 2, ..., n; x, y, z are used to describe the point cloud position information. The origin is defined according to actual needs, and the absolute coordinates relative to the origin are taken;

[0018] At the same time, each point p i The corresponding charge density is ρ i .

[0019] Step S2 is as follows:

[0020] This step divides the point cloud data into several sub-regions using a hierarchical clustering algorithm.

[0021] The specific implementation of hierarchical clustering algorithms depends on the chosen distance metric and clustering hierarchy.

[0022] The charge region dataset P S Divide into m subregions {C1, C2, ..., C m C1 represents the first region, C2 represents the second region, and so on.

[0023] Define distance metric d(p) i ,p j ) used to calculate data point p i and p j The distance between them;

[0024] Choose a clustering hierarchy and generate a distance matrix D, where D(i,j)=d(C i C j ); i and j represent the i-th and j-th regions among the m sub-regions;

[0025] Distance metrics include Euclidean distance and Manhattan distance. This process can be represented as:

[0026] P→{C1,C2,...,C m}

[0027] Among them, d:P S ×P S →R; R is a real number;

[0028] P is a set of points.

[0029] Step S3 is as follows:

[0030] This step generates a three-dimensional tetrahedral mesh that approximates the actual shape of the charge region by executing the Delaunay triangulation algorithm.

[0031] For each tetrahedron, define its vertices as A, B, C, and D;

[0032] The geometric condition for a tetrahedron to satisfy the Delaunay criterion is that the circumsphere of any tetrahedron does not contain vertices of any other tetrahedron; for each subregion Ci, a tetrahedral mesh T is constructed using Delaunay triangulation. i For each tetrahedron T∈T i The vertex set of T is {A,B,C,D}; the Delaunay criterion requires that the circumsphere of T contains no other vertices.

[0033] Represented as:

[0034] If p ≠ A, B, C, D, then d(p, O) > R, where O and R represent the center and radius of the circumscribed sphere of T, respectively; if p = A, B, C, D, then d(p, O) ≤ R.

[0035] Step S4 is as follows:

[0036] The Alpha-Shapes algorithm generates an outer envelope that approximates the actual shape of the charge region by trimming edges based on Delaunay triangulation. The core of the Alpha-Shapes algorithm is the trimming of boundary conditions.

[0037] Given a parameter Alpha, if the radius of the empty circle formed by the two vertices of an edge in the Delaunay triangulation is less than or equal to Alpha, then retain the edge; otherwise, remove the edge; calculate the Alpha-Shapes outer envelope of the subregion.

[0038] Given the parameter Alpha, for an edge E in a Delaunay triangulation, we can define an empty sphere with radius Alpha; if an empty sphere does not exist between two vertices, the edge is removed, as shown below:

[0039] The radius of the empty sphere B(α) is α, and B(α) does not contain any other points;

[0040] The method for determining the range of alpha values ​​is as follows: Calculate the convex hull of the data point set, and then calculate the shortest side length dmin and the longest side length dmax on the convex hull; these two values ​​serve as the lower and upper limits of the alpha value. Smaller alpha values ​​(closer to dmin) will produce more complex and accurate shapes, but may also lead to overfitting; larger alpha values ​​(closer to dmax) will produce simpler and less accurate shapes. Specific parameter values ​​need to be adjusted based on the actual situation. The initial values ​​for dynamically determining the parameters are given below; values ​​can also be randomly selected from this range.

[0041] S41: Initialization: Set an initial range for Alpha values ​​and the number of iterations N;

[0042] S42: Alpha value setting: Select an Alpha value from the given range as the starting point.

[0043] S43: Alpha-Shapes Calculation: Calculate the Alpha-Shapes of all sub-regions based on the current Alpha value;

[0044] S44: Geometric Feature Evaluation: Based on the obtained Alpha-Shapes, evaluate the geometric features of the calculated results; for example, factors such as convexity, compactness, and hole size can be considered. Set one or more evaluation metrics to quantify the difference between the generated Alpha-Shapes and the actual shapes at the current Alpha value.

[0045] S45: Alpha Value Update: Adjust the Alpha value based on the evaluation results. If the current Alpha value yields a good evaluation metric, fine-tune it around that value; if the evaluation metric is poor, try other values ​​within the Alpha range. Specific adjustment strategies include binary search and gradient descent, with the appropriate strategy chosen based on the specific problem.

[0046] S46: Iteration and Termination: Repeat steps S43 to S45 until the iteration count N is met or an Alpha value that meets a preset criterion is found. For example, stop iterating when the change in Alpha value between two iterations is less than a certain threshold or the evaluation index reaches a preset target value.

[0047] Step S5 is as follows:

[0048] For each sub-region C i Alpha-Shapes envelope A i Construct its convex hull H i Given A i A set of points P i Define a convex hull H i Such that for every point p∈P i H i Satisfying the convexity condition; expressed as:

[0049] For each point p, q∈H i And since p ≠ q, we have: (pq)·(rq) ≥ 0 for all points r ∈ P. i , convex hull H i All points within the triangle have acute or right angles between themselves and p and q.

[0050] Step S6 is as follows:

[0051] The shape of the lightning radiation source group has concave parts. It is necessary to calculate the volume of the concave parts generated by Alpha-Shapes and subtract the volume of these concave parts from the total volume of the convex polyhedron to obtain a more accurate sub-region charge region volume.

[0052] For each tetrahedron of a convex polyhedron, calculate its volume V. t As shown below:

[0053]

[0054] Where A, B, C, and D represent the four vertices of a tetrahedron; x represents the cross product of vectors; · represents the dot product of vectors; |(·)| represents the magnitude of the vector.

[0055] Divide the subregion of the convex polyhedron into several tetrahedrons, and sum the volumes of the tetrahedrons to obtain the total volume V of the convex polyhedron. c :

[0056] V c =∑V t

[0057] The shape of the lightning radiation source group has concave portions. Calculate the volume V of the concave portions generated by Alpha-Shapes. a And from the total volume V of the convex polyhedron c Subtracting the volume of these concave portions from the middle yields a more accurate sub-region charge volume Vr.

[0058] Volume V of the concave part a The calculation method is as follows: The Alpha-Shapes envelope surface is divided along the concave portion to obtain the concave boundary surface; all points on the concave boundary surface are divided into internal and external points, where internal points are located inside the concave portion and external points are located outside the concave portion; the volume V of the concave portion is calculated. a The formula is:

[0059] V a =∫∫∫ρ(r)dv

[0060] Where the integration range is the interior of the concave region, and ρ(r) is the charge density at point r;

[0061] The volume Vr of the sub-region charge region is obtained:

[0062] V r =V c -V a .

[0063] Step S7 is as follows:

[0064] The formula for the volume V of the entire charge region is as follows:

[0065] V=∑V r .

[0066] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0067] 1. Higher accuracy: By introducing Alpha-Shapes and dynamically adjusting the Alpha value, the actual charge region shape can be approximated more accurately, thereby improving the accuracy of the calculation results.

[0068] 2. Higher computational efficiency: By employing hierarchical clustering and Delaunay triangulation techniques, the charge region is divided into multiple sub-regions for calculation, improving computational efficiency. Furthermore, techniques such as convex hull optimization can further reduce computational errors.

[0069] 3. Wider applicability: The core technology of this solution is universal and can be applied to different types of charge region volume calculation problems, and can flexibly cope with different datasets and calculation requirements.

[0070] 4. Enhanced scalability: This solution employs a combination of various technologies, allowing for the addition or reduction of certain computational steps as needed to meet diverse computational requirements.

[0071] This invention has advantages such as high calculation accuracy, high calculation efficiency, wide applicability and strong scalability, and can meet the needs of calculating the volume of lightning charge region, thus having high practical value. Attached Figure Description

[0072] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0073] Figure 1 This is a schematic diagram of the steps of the present invention.

[0074] Figure 2 This is a schematic diagram of the lightning three-dimensional radiation source localization data set of the present invention;

[0075] Figure 3 This is a partial Delaunay triangulation diagram of the horizontal layered profile of the lightning three-dimensional radiation source localization data of the present invention;

[0076] Figure 4 The diagram shows the horizontal layered profile of the three-dimensional lightning radiation source location data extracted by the Alpha-Shapes algorithm of this invention; (a) is a schematic diagram of the horizontal layered profile of the three-dimensional lightning radiation source location data, and (b) is a schematic diagram of the profile extracted by the Alpha-Shapes algorithm. Detailed Implementation

[0077] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0078] Example 1

[0079] A method for calculating the charge region volume of thunderstorm clouds based on a three-dimensional lightning radiation source includes the following steps:

[0080] S1: Data preparation; collect and organize the three-dimensional locations of lightning radiation sources within 20 minutes, and convert this data into a three-dimensional point cloud data format;

[0081] S2: Hierarchical clustering; This method divides the charge region into several sub-regions, thus better handling lightning radiation source group data with different shapes and density distributions. The reason for using hierarchical clustering here is that this type of clustering method does not require pre-determining the number of clusters, making it more applicable when dividing the charge region.

[0082] S3: Delaunay triangulation; Delaunay triangulation is performed on the point cloud data of each sub-region, and a spatial weighting strategy based on charge density is introduced to generate a three-dimensional mesh composed of tetrahedrons; this mesh can approximate the shape of the charge region while ensuring that the Delaunay conditions are met.

[0083] S4: Calculate Alpha-Shapes; Apply the Alpha-Shapes algorithm to calculate the outer envelope of the point cloud data; This algorithm effectively describes the complex shape of the charge region by finding a spatial subset that approximates the distribution of the point cloud data.

[0084] S5: Convex Hull Optimization; Convex hull optimization is performed on the outer envelope calculated by Alpha-Shapes; By eliminating the concave parts in the envelope, a convex polyhedron that approximates the charge region is generated.

[0085] S6: Volume Calculation and Correction; Calculate the volume of the convex polyhedron based on its geometric properties; Divide the convex polyhedron into several tetrahedrons and sum the volumes of the tetrahedrons to obtain the total volume of the convex polyhedron;

[0086] S7: Sub-region volume summation; sum the calculated charge region volumes for each sub-region to obtain the volume of the entire charge region.

[0087] Step S1 is as follows:

[0088] This step mainly prepares the 3D point cloud data for subsequent calculations;

[0089] Set each point p iThe coordinates are represented as (x i ,y i ,z i ), i = 1, 2, ..., n; x, y, z are used to describe the point cloud position information. The origin is defined according to actual needs, and the absolute coordinates relative to the origin are taken;

[0090] At the same time, each point p i The corresponding charge density is ρ i .

[0091] Step S2 is as follows:

[0092] This step divides the point cloud data into several sub-regions using a hierarchical clustering algorithm.

[0093] The specific implementation of hierarchical clustering algorithms depends on the chosen distance metric and clustering hierarchy.

[0094] The charge region dataset P S Divide into m subregions {C1, C2, ..., C m C1 represents the first region, C2 represents the second region, and so on.

[0095] Define distance metric d(p) i ,p j ) used to calculate data point p i and p j The distance between them;

[0096] Choose a clustering hierarchy and generate a distance matrix D, where D(i,j)=d(C i C j ); i and j represent the i-th and j-th regions among the m sub-regions;

[0097] Distance metrics include Euclidean distance and Manhattan distance. This process can be represented as:

[0098] P→{C1,C2,...,C m}

[0099] Where d: P×P→R; R is a real number;

[0100] P is a set of points.

[0101] Step S3 is as follows:

[0102] This step generates a three-dimensional tetrahedral mesh that approximates the actual shape of the charge region by executing the Delaunay triangulation algorithm.

[0103] For each tetrahedron, define its vertices as A, B, C, and D;

[0104] The geometric condition for a tetrahedron to satisfy the Delaunay criterion is that the circumsphere of any tetrahedron does not contain vertices of any other tetrahedron; for each subregion Ci, a tetrahedral mesh T is constructed using Delaunay triangulation. i For each tetrahedron T∈T i The vertex set of T is {A,B,C,D}; the Delaunay criterion requires that the circumsphere of T contains no other vertices.

[0105] Represented as:

[0106] If p ≠ A, B, C, D, then d(p, O) > R, where O and R represent the center and radius of the circumscribed sphere of T, respectively; if p = A, B, C, D, then d(p, O) ≤ R.

[0107] Step S4 is as follows:

[0108] The Alpha-Shapes algorithm generates an outer envelope that approximates the actual shape of the charge region by trimming edges based on Delaunay triangulation. The core of the Alpha-Shapes algorithm is the trimming of boundary conditions.

[0109] Given a parameter Alpha, if the radius of the empty circle formed by the two vertices of an edge in the Delaunay triangulation is less than or equal to Alpha, then retain the edge; otherwise, remove the edge; calculate the Alpha-Shapes outer envelope of the subregion.

[0110] Given the parameter Alpha, for an edge E in a Delaunay triangulation, we can define an empty sphere with radius Alpha; if an empty sphere does not exist between two vertices, the edge is removed, as shown below:

[0111] The radius of the empty sphere B(α) is α, and B(α) does not contain any other points;

[0112] The method for determining the range of alpha values ​​is as follows: Calculate the convex hull of the data point set, and then calculate the shortest side length dmin and the longest side length dmax on the convex hull; these two values ​​serve as the lower and upper limits of the alpha value. Smaller alpha values ​​(closer to dmin) will produce more complex and accurate shapes, but may also lead to overfitting; larger alpha values ​​(closer to dmax) will produce simpler and less accurate shapes. Specific parameter values ​​need to be adjusted based on the actual situation. The initial values ​​for dynamically determining the parameters are given below; values ​​can also be randomly selected from this range.

[0113] S41: Initialization: Set an initial range of Alpha values ​​(e.g., Alpha_min, Alpha_max) and the number of iterations N;

[0114] S42: Alpha value setting: Select an Alpha value as the starting point from the given range of Alpha values. For example, you can select the midpoint of the range ((Alpha_min+Alpha_max) / 2).

[0115] S43: Alpha-Shapes Calculation: Calculate the Alpha-Shapes of all sub-regions based on the current Alpha value;

[0116] S44: Geometric Feature Evaluation: Based on the obtained Alpha-Shapes, evaluate the geometric features of the calculated results; for example, factors such as convexity, compactness, and hole size can be considered. Set one or more evaluation metrics to quantify the difference between the generated Alpha-Shapes and the actual shapes at the current Alpha value.

[0117] S45: Alpha Value Update: Adjust the Alpha value based on the evaluation results. If the current Alpha value yields a good evaluation metric, fine-tune it around that value; if the evaluation metric is poor, try other values ​​within the Alpha range. Specific adjustment strategies include binary search (interpretation) and gradient descent (interpretation), with the appropriate strategy chosen based on the specific problem.

[0118] S46: Iteration and Termination: Repeat steps S43 to S45 until the iteration count N is met or an Alpha value that meets a preset criterion is found. For example, stop iterating when the change in Alpha value between two iterations is less than a certain threshold or the evaluation index reaches a preset target value.

[0119] Step S5 is as follows:

[0120] For each sub-region C i Alpha-Shapes envelope A i Construct its convex hull H i Given A i A set of points P i Define a convex hull H i Such that for every point p∈P i H i Satisfying the convexity condition; expressed as:

[0121] For each point p, q∈H i And since p ≠ q, we have: (pq)·(rq) ≥ 0 for all points r ∈ P. i , convex hull H iAll points within the triangle have acute or right angles between themselves and p and q.

[0122] Step S6 is as follows:

[0123] The shape of the lightning radiation source group has concave parts. It is necessary to calculate the volume of the concave parts generated by Alpha-Shapes and subtract the volume of these concave parts from the total volume of the convex polyhedron to obtain a more accurate sub-region charge region volume.

[0124] For each tetrahedron of a convex polyhedron, calculate its volume V. t As shown below:

[0125]

[0126] Where A, B, C, and D represent the four vertices of a tetrahedron; x represents the cross product of vectors; · represents the dot product of vectors; |(·)| represents the magnitude of the vector.

[0127] Divide the subregion of the convex polyhedron into several tetrahedrons, and sum the volumes of the tetrahedrons to obtain the total volume V of the convex polyhedron. c :

[0128] V c =∑V t

[0129] The shape of the lightning radiation source group has concave portions. Calculate the volume V of the concave portions generated by Alpha-Shapes. a And from the total volume V of the convex polyhedron c Subtracting the volume of these concave portions from the middle yields a more accurate sub-region charge volume Vr.

[0130] Volume V of the concave part a The calculation method is as follows: The Alpha-Shapes envelope surface is divided along the concave portion to obtain the concave boundary surface; all points on the concave boundary surface are divided into internal and external points, where internal points are located inside the concave portion and external points are located outside the concave portion; the volume V of the concave portion is calculated. a The formula is:

[0131] V a =∫∫∫ρ(r)dv

[0132] Where the integration range is the interior of the concave region, and ρ(r) is the charge density at point r;

[0133] The volume Vr of the sub-region charge region is obtained:

[0134] V r =V c -V a .

[0135] Step S7 is as follows:

[0136] The formula for the volume V of the entire charge region is as follows:

[0137] V=∑V r .

[0138] Example 2

[0139] Based on Example 1, referring to Figure 2 , Figure 2 The dataset shows a three-dimensional localization of low-frequency lightning radiation sources within one minute. The radiation sources are mainly clustered at three heights: 2.5-6km, 6-8km, and 8-11km. Based on the leader development theory, it can be inferred that the lightning has a tripolar charge structure with negative positive and negative charges. Figure 3 A local Delaunay triangulation network of the horizontal layer section of a 3D localization dataset of low-frequency lightning radiation sources over a 1-minute period is presented, and the charge region plane of this layer is constructed using triangular mesh partitioning. Figure 4 (a) and (b) show the horizontal layer cross-sectional profiles of a 1-minute dataset of three-dimensional localization of low-frequency lightning radiation sources using Alpha-Shapes.

[0140] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the charge region volume of thunderstorm clouds based on a three-dimensional lightning radiation source, characterized in that, Includes the following steps: S1: Data preparation; collect and organize the three-dimensional locations of lightning radiation sources within a certain period of time, and convert these data into three-dimensional point cloud data format; S2: Hierarchical clustering; The charge region is divided into several sub-regions using a hierarchical clustering method; S3: Delaunay triangulation; Delaunay triangulation is performed on the point cloud data of each sub-region to generate a three-dimensional mesh composed of tetrahedrons; S4: Calculate Alpha-Shapes; Apply the Alpha-Shapes algorithm to calculate the outer envelope of the point cloud data; S5: Convex hull optimization; The outer envelope calculated by Alpha-Shapes is optimized by convex hull optimization; by eliminating the concave part in the envelope, a convex polyhedron that approximates the charge region is generated. S6: Volume Calculation and Correction; Calculate the volume of a convex polyhedron based on its geometric properties; Divide the convex polyhedron into several tetrahedrons and sum the volumes of the tetrahedrons to obtain the total volume of the convex polyhedron. S7: Sub-region volume summation; sum the calculated charge region volumes for each sub-region to obtain the volume of the entire charge region.

2. The method for calculating the volume of the charge region of a thunderstorm cloud based on a three-dimensional lightning radiation source according to claim 1, characterized in that, Step S1 is as follows: Set each point The coordinates are represented as ; Used to describe point cloud location information, the origin is defined according to actual needs, and the absolute coordinates relative to the origin are taken; At the same time, each point The corresponding charge density is .

3. The method for calculating the volume of the charge region of a thunderstorm cloud based on a three-dimensional lightning radiation source according to claim 2, characterized in that, Step S2 is as follows: The charge region dataset P S Divided into m sub-regions ; Represents the first area, This represents the second area, and so on. Define distance metric d(p) i ,p j ) used to calculate data point p i and p j The distance between them; Select a clustering hierarchy and generate a distance matrix D, where ; i and j represent the i-th and j-th regions in the m sub-regions; This process can be represented as: ； in, R is a real number; P is a set of points.

4. The method for calculating the volume of the charge region of a thunderstorm cloud based on a three-dimensional lightning radiation source according to claim 3, characterized in that, Step S3 is as follows: For each tetrahedron, define its vertices as A, B, C, and D; The geometric condition for a tetrahedron to satisfy the Delaunay criterion is: the circumsphere of any tetrahedron does not contain vertices of any other tetrahedron; for each subregion C i A tetrahedral mesh is constructed using Delaunay triangulation. ; For each tetrahedron T ∈ The vertex set of T is {A, B, C, D}; the Delaunay criterion requires that the circumsphere of T contains no other vertices; expressed as: ,if ,So ,in and They represent The center and radius of the circumscribed sphere; if ,So .

5. The method for calculating the charge region volume of thunderstorm clouds based on a three-dimensional lightning radiation source according to claim 4, characterized in that, Step S4 is as follows: Given a parameter Alpha, if the radius of the empty circle formed by the two vertices of an edge in a Delaunay triangulation is less than or equal to Alpha, then retain the edge; otherwise, prune the edge. Calculate the Alpha-Shapes outer envelope of the subregion. Given a parameter Alpha, for an edge E in a Delaunay triangulation, define an empty sphere with radius Alpha; if the empty sphere between two vertices does not exist, prune the edge, as shown below: E satisfies the condition. Empty sphere The radius is ,and Excludes other points; The method for determining the Alpha value follows a dynamic parameter optimization process: First, calculate the convex hull of the data point set, and then calculate the shortest side length dmin and the longest side length dmax on the convex hull to set the initial search range for the Alpha value. Then, perform the following steps: S41: Initialization: Set an initial range for Alpha values ​​and the number of iterations N; S42: Alpha value setting: Select an Alpha value from the given range of Alpha values ​​as the starting point; S43: Alpha-Shapes Calculation: Calculate the Alpha-Shapes of all sub-regions based on the current Alpha value; S44: Geometric feature evaluation: Evaluate the geometric features of the calculated results based on the obtained Alpha-Shapes; S45: Alpha value update: Adjust the alpha value based on the evaluation results; S46: Iteration and Termination: Repeat steps S43 to S45 until the iteration count N is satisfied or an Alpha value that satisfies the preset criteria is found.

6. The method for calculating the volume of the charge region of a thunderstorm cloud based on a three-dimensional lightning radiation source according to claim 5, characterized in that, Step S5 is as follows: For each sub-region Alpha-Shapes envelope Construct its convex hull Given A set of points Define a convex hull Such that for every point p∈ , Satisfying the convexity condition; expressed as: For each point p, q ∈ and ,have: For all points , convex hull All points within the triangle have acute or right angles between them and p and q.

7. The method for calculating the volume of the charge region of a thunderstorm cloud based on a three-dimensional lightning radiation source according to claim 6, characterized in that, Step S6 is as follows: For each tetrahedron of a convex polyhedron, calculate its volume. As shown below: ； Where A, B, C, and D represent the four vertices of a tetrahedron; x represents the cross product of vectors; · represents the dot product of vectors; |(·)| represents the magnitude of the vector. Divide the convex polyhedron into several tetrahedrons and sum the volumes of the tetrahedrons to obtain the total volume of the convex polyhedron. : ； Volume of concave part The calculation method is as follows: The Alpha-Shapes envelope surface is divided along the concave portion to obtain the concave boundary surface; all points on the concave boundary surface are divided into internal and external points, where internal points are located inside the concave portion and external points are located outside the concave portion; the volume of the concave portion is then calculated. The formula is: ； The integration range is within the concave portion. It is the charge density at point r; The volume Vr of the sub-region charge region is obtained: 。 8. The method for calculating the volume of the charge region of a thunderstorm cloud based on a three-dimensional lightning radiation source according to claim 7, characterized in that, Step S7 is as follows: The formula for the volume V of the entire charge region is as follows: 。

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