A method for modeling the spatial heterogeneity of lightning ground flash density based on geographic factor regression

Abstract

This invention discloses a method for modeling the spatial heterogeneity of lightning strike density based on geographic factor regression, belonging to the field of lightning protection technology. It includes: spatially gridding topographic and lightning strike data to generate an original lightning strike density distribution map; constructing a lightning strike density downscaling model based on the XGBoost machine learning framework to generate a high-resolution lightning strike density distribution map with the same resolution as the topographic data; constructing a linear regression model to generate a topographic factor-lightning strike density response function decoupled from the influence of latitude and longitude coordinates; and performing cluster analysis on the regression coefficients to extract typical response patterns and calculate a topographic enhancement coefficient to correct the lightning strike probability parameters of the protected object. This invention overcomes the resolution limitations of traditional grid methods, quantifies the influence of key topographic factors on lightning activity, and improves the precision of lightning strike risk assessment.

Description

Technical Field

[0001] This invention belongs to the field of lightning protection technology, and in particular relates to a method for modeling the spatial heterogeneity of lightning ground flash density based on geographic factor regression. Background Technology

[0002] Ground flash (cloud-to-ground discharge), an atmospheric discharge phenomenon that directly causes lightning strikes, poses a significant threat to critical infrastructure such as power and transportation. Ground flash density refers to the average number of ground flashes monitored by lightning location systems per unit area and per unit time, and is a core indicator characterizing the intensity of ground flash activity. Currently, the most common statistical method for ground flash density used by scholars both domestically and internationally is the grid method, which involves dividing a region into grids of equal latitude and longitude to count the frequency of ground flashes. However, this method has an inherent contradiction between spatial resolution and statistical confidence: since lightning is a low-probability event, as the grid resolution increases, the number of lightning events within a single grid decreases sharply, and the statistical results will deviate significantly from the true pattern. The national standard GB / T 40621-2021 stipulates that to meet the confidence requirement of a statistical error of less than 20%, a 10-year observation period and a grid size of not less than 1 km are recommended. This kilometer-level grid resolution is far wider than the scale of typical protected facilities (such as transmission line corridors which are only tens to hundreds of meters wide), making it impossible to identify risk differences within tower units and often resulting in misallocation of lightning protection resources.

[0003] Lightning climatology studies have confirmed that topography significantly enhances lightning activity through mechanisms such as uplift triggering convection and altering local circulation. This phenomenon conforms to the spatial proximity correlation of the first law of geography. This topographic modulation leads to spatial non-stationarity of lightning density, forming significant hotspot areas. Modern geographic information systems can now provide topographic data with resolutions ranging from ten to one hundred meters. This provides a solid physical foundation and reliable data support for establishing a correlation model between topography and lightning density, and further overcoming the resolution limitations of grid-based methods.

[0004] Existing modeling attempts, such as generalized additive models, introduce geographical location parameters to characterize regional specificities, but fail to separate the confounding effects of meteorological background and topographic effects. This results in spatially constrained model adaptability and limited generalization ability. Furthermore, because a quantitative regression relationship between refined topographic factors and lightning activity parameters has not yet been established, it is difficult to further characterize the enhancement or weakening effects of topography on lightning strike risk. The values ​​of some key lightning strike probability parameters in lightning protection engineering calculations still rely on empirical tables using a plains / mountainous area dichotomy, leading to limited accuracy in assessing lightning damage risk to protected objects under complex terrain conditions and a mismatch between lightning protection measures and actual lightning strike risk. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for modeling the spatial heterogeneity of lightning strike density based on geographic factor regression, comprising the following steps: The terrain data of the target area and the lightning flash data recorded by the lightning location system are acquired, and the terrain data and lightning flash data are spatially gridded to generate an original lightning flash density distribution map with the same resolution as the terrain data. A ground flash density downscaling model is constructed based on the XGBoost framework, with the original ground flash density distribution map as the target variable and terrain data and grid coordinates as prediction variables. Multiple decision trees are constructed using the XGBoost model to dynamically divide spatially discrete grid samples with similar "ground flash-terrain" relationships into the same leaf node in order to capture the complex nonlinear relationship between terrain parameters and ground flash density, and generate a high-resolution ground flash density distribution map with the same resolution as the terrain data. Based on the high-resolution lightning density distribution map, a linear regression model is constructed, which includes a global model for describing the overall trend and a local model for capturing spatial heterogeneity. Using topographic factors as predictor variables, a topographic factor-lightning density response function decoupled from the influence of latitude and longitude coordinates is generated. The response function quantifies the enhancing or weakening effect of topographic factors on average lightning activity. Cluster analysis was performed on the regression coefficients of the terrain factor-ground flash density response function output by the local model, and typical integrated response patterns of terrain factors were extracted based on the classification results. The terrain enhancement coefficient of average ground flash density is obtained based on the terrain factor-ground flash density response function and the integrated response mode of terrain factor output by the global model. Based on the terrain enhancement coefficient surrounding the lightning protection target, and conforming to national standards of greater than or equal to 1km... 2 The lightning density statistics of the grid are used to correct the lightning strike probability parameters of the protected objects in order to construct a high-precision spatial heterogeneity model of lightning damage risk.

[0006] Optionally, the terrain data includes a digital elevation model and its derived parameters, and the lightning data includes the timestamps and geographic coordinates of the lightning events; spatial gridding processing of the terrain data and lightning data includes: uniformly resampling the terrain data to a geographic grid of a preset resolution, and statistically analyzing the frequency of lightning events based on the grid to generate an original lightning density distribution map.

[0007] Optionally, after generating the original ground flash density distribution map, the method further includes performing two-dimensional low-pass filtering on the distribution map to eliminate small sample statistical noise, generating a smooth ground flash density distribution map, and using the smooth distribution map as the target variable of the downscaling model.

[0008] Optionally, the downscaling model is built on the XGBoost framework, and hyperparameters are tuned with the goal of minimizing the mean squared error. After the model outputs, the reliability of the ground flash density distribution map output by the model is evaluated. The reliability evaluation includes calculating the average confidence level and image entropy value of the ground flash density distribution map output by the model within a preset confidence interval, and comparing it with the original ground flash density distribution map and the smoothing filtering results to verify the improvement effect of the downscaling model in terms of statistical reliability and information richness.

[0009] Optionally, before constructing the linear regression model, the model further includes screening the terrain factors. The screening criteria include: the terrain factors are spatially stable, are continuous numerical variables, and can introduce product combination terms between factors to capture the nonlinear effects caused by the synergistic effect of terrain.

[0010] Optionally, the global model describing the overall trend includes a global least squares regression model; the local model capturing spatial heterogeneity includes a geographically weighted regression model or a multi-scale geographically weighted regression model. First, a global least squares regression model is constructed to generate a unified terrain factor-ground flash density response function for the entire region. When the accuracy of the global least squares regression model is lower than a preset threshold, a geographic weighted regression model or a multi-scale geographic weighted regression model is constructed to generate an independent terrain factor-ground flash density response function for each geographic sample point.

[0011] Optionally, the intercept term of the geographic weighted regression model or the multi-scale geographic weighted regression model is set to the intercept value of the global least squares regression model, so that the topographic factor coefficient reflects its enhancing or weakening effect on the global average lightning activity.

[0012] Optionally, cluster analysis of the regression coefficients includes: removing outliers, extracting coefficient types with significant differences, and calculating the statistical average of the regression coefficients for each cluster category to form a typical integrated response pattern of topographic factors.

[0013] Optionally, the terrain enhancement coefficient is calculated based on the typical response patterns after clustering and combined with low-precision ground flash density statistics that conform to national standards, and is used to correct the lightning strike probability parameters of the protected objects in lightning protection projects.

[0014] Optionally, correcting the lightning strike probability parameters of the protected object includes: determining the geographical location of the protected object, obtaining the terrain conditions of the location, calculating the terrain enhancement coefficient of the location, and correcting the preset benchmark lightning strike probability parameters based on the terrain enhancement coefficient, thereby improving the accuracy of lightning hazard risk assessment for the protected object under complex terrain conditions.

[0015] Optionally, based on the integrated response model of terrain factors, for areas of 1 km or greater that meet national standards...2 The ground flash density statistics of the grid are corrected, specifically by: using the low-precision ground flash density statistics as the intercept term to replace the original intercept value in the integrated response model of terrain factors; obtaining the terrain parameters of the geographical location to be corrected, and calculating the ground flash density of the geographical location after terrain correction according to the factor coefficients determined by the integrated response model of terrain factors.

[0016] Compared with the prior art, the present invention has the following advantages and technical effects: This invention overcomes the spatial resolution bottleneck of traditional grid methods, which are limited by the statistical sample size. By integrating high-resolution terrain data with machine learning downscaling techniques, it achieves same-scale matching between lightning density distribution maps and geographic elevation data. This allows the statistical resolution to be flexibly adjusted according to the accuracy of terrain data, meeting the differentiated and refined lightning protection needs of protected objects under complex terrain conditions. This invention constructs a linear regression model independent of latitude and longitude coordinates, decoupling the confounding effects of meteorological background and terrain effects. It accurately quantifies the enhancing or weakening effects of terrain factors on lightning activity, making the causal relationship between terrain and lightning strike risk clearer, and the model has cross-regional generalization capabilities. This invention uses cluster analysis of regression coefficients to extract typical comprehensive response patterns of terrain factors, supporting the calculation of terrain enhancement coefficients for different geographical locations. It replaces the empirical correction of the traditional plain / mountain dichotomy with data-driven refined response zoning, achieving spatial heterogeneity modeling of lightning strike risk for protected objects. This effectively solves the problem of insufficient protection in high-risk areas and over-protection in low-risk areas in lightning protection engineering, improving the scientificity and accuracy of lightning protection resource allocation. Attached Figure Description

[0017] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention; Figure 2 This is a distribution map of the annual average ground flash density according to an embodiment of the present invention; Figure 3 This is a ranking of the importance of terrain factors output by the XGBoost downscaling model in an embodiment of the present invention. Figure 4 This is a comparison chart of annual average ground flash density at a spatial resolution of 0.01°×0.01° according to an embodiment of the present invention. Figure 5 This is a scatter plot comparing the XGBoost aggregated lightning density and the LLS grid method statistical lightning density at a spatial resolution of 0.01°×0.01° in this embodiment of the invention. Figure 6This is a scatter plot comparing the OLS regression ground flash density and the XGBoost model output ground flash density in an embodiment of the present invention. Figure 7 This is a map showing the average ground flash density distribution output by the GWR model in an embodiment of the present invention. Figure 8 This is a scatter plot comparing the GWR regression ground flash density with the XGBoost model output ground flash density in an embodiment of the present invention. Figure 9 The distribution of five ground flash density regression equations and their regression coefficients on three-dimensional terrain in this embodiment of the invention. Detailed Implementation

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0020] Current lightning protection theoretical modeling relies on empirical data. Although studies have confirmed a significant correlation between topographic factors and ground flash density, existing research has long remained at the level of empirical rule summaries, such as "mountainous areas have a higher risk of lightning strikes than plains." This limitation is particularly prominent in lightning protection engineering calculations—using transmission line backflashover tripping rates as a primary method. For example, in calculation: ; In the formula: Number of lightning strikes per year; For the rate of attack; This refers to the stroke rate; For the arc-building rate; This represents the probability that a lightning-struck pole exceeds its lightning withstand level. The strike rate (the ratio of the number of lightning strikes to the total number of lightning strikes on the line) is highly dependent on empirical tables. Table 1 The above calculation method only roughly corrects the strike rate by dividing the terrain into two categories (plains / mountains), which is difficult to reflect the enhancement or weakening effect of terrain factors on lightning strike risk. This leads to a mismatch between lightning protection measures and the actual lightning strike risk (insufficient protection in high-risk areas and excessive protection in low-risk areas), resulting in waste of resources and safety hazards.

[0021] Example 1 like Figure 1As shown, this embodiment provides a method for modeling the spatial heterogeneity of lightning flash density based on geographic factor regression, including the following steps: Acquire terrain data of the target area and lightning flash data recorded by the lightning location system, and perform spatial gridding processing on the terrain data and lightning flash data to generate an original lightning flash density distribution map with the same resolution as the terrain data; A ground flash density downscaling model is constructed based on the XGBoost framework, with the original ground flash density distribution map as the target variable and terrain data and grid coordinates as prediction variables. Multiple decision trees are constructed using the XGBoost model to dynamically divide spatially discrete grid samples with similar "ground flash-terrain" relationships into the same leaf node in order to capture the complex nonlinear relationship between terrain parameters and ground flash density, and generate a high-resolution ground flash density distribution map with the same resolution as the terrain data. Based on high-resolution lightning density distribution maps, a linear regression model is constructed, including a global model to describe the overall trend and a local model to capture spatial heterogeneity. Using topographic factors as predictors, a topographic factor-lightning density response function decoupled from the influence of latitude and longitude coordinates is generated. The response function quantifies the enhancing or weakening effect of topographic factors on average lightning activity. Cluster analysis is performed on the regression coefficients of terrain factors output by the local model to extract typical comprehensive response patterns of terrain factors, supporting the calculation of terrain enhancement coefficients in different geographical locations. This is used to correct the lightning strike probability parameters of the protected objects. Data-driven refined response zoning replaces the empirical correction of the plain or mountainous dichotomy, realizing spatial heterogeneity modeling of lightning strike risk.

[0022] Furthermore, the terrain data includes a digital elevation model and its derived parameters, and the lightning data includes the timestamps and geographic coordinates of lightning events. Spatial gridding processing of the terrain data and lightning data includes: uniformly resampling the terrain data to a geographic grid of a preset resolution, and statistically analyzing the frequency of lightning events based on the grid to generate an original lightning density distribution map.

[0023] After generating the original ground flash density distribution map, a two-dimensional low-pass filter is applied to the distribution map to eliminate small sample statistical noise and generate a smooth ground flash density distribution map. This smooth distribution map is then used as the target variable for the downscaling model.

[0024] Specifically, high-precision terrain data (including DEM and its derived terrain parameters) of the target area is acquired. When the original resolution is ≤0.001°, it is uniformly resampled to a 0.001°×0.001° grid in the projected coordinate system. Based on this grid, at least 5 years of lightning location system lightning data are integrated, and the lightning density (times / km) of each grid is calculated. 2(Year), generate the original ground flash density distribution map with the same resolution as the terrain data; eliminate small sample statistical noise through two-dimensional low-pass filtering, and output a smooth ground flash density distribution map.

[0025] Furthermore, the downscaling model is built on the XGBoost framework, and hyperparameters are tuned with the goal of minimizing the mean squared error. After the model output, the reliability of the ground flash density distribution map output by the model is evaluated. The reliability evaluation includes calculating the average confidence level and image entropy value of the ground flash density distribution map output by the model within a preset confidence interval, and comparing it with the original ground flash density distribution map and the smoothing filtering results to verify the improvement effect of the downscaling model in terms of statistical reliability and information richness.

[0026] Specifically, when constructing the downscaling model, the smoothed lightning density is used as the target variable, and the terrain data and grid coordinates are used as the prediction variables. The lightning density downscaling model is constructed based on the XGBoost framework, and the hyperparameters are tuned by minimizing the mean square error.

[0027] The model outputs the average confidence level of lightning frequency (lightning frequency = lightning density × grid area × statistical years) within a preset confidence interval (not exceeding ±20%), along with the image entropy value of the lightning density distribution map. These results are compared with the statistical results of the LLS grid method and the smoothing filter results to comprehensively evaluate the improvement effect of the downscaling model in terms of statistical reliability and information richness. In the preferred embodiment below, the confidence interval is set to ±20% (other interval ranges can be used as needed). Meanwhile, the statistical errors at different regional scales were examined by combining geospatial aggregation analysis: for the ground flash density distribution map output by the model, when the grid ground flash frequency (cumulative value within the statistical period) is <80 times, the grid is aggregated to a cumulative frequency ≥80 times, and compared with the high confidence ground flash density map of the same scale drawn by LLS measured data to verify the spatial scaling invariance of the ground flash density distribution map.

[0028] When generating the results, the importance of the features in the model output is ranked, and an annual average ground flash density distribution map aligned with the resolution of the terrain data is drawn based on the model output.

[0029] Furthermore, before constructing the linear regression model, the terrain factors are screened. The screening criteria include: the terrain factors are spatially stable, are continuous numerical variables, and can be combined with product terms between factors to capture the nonlinear effects caused by the synergistic effect of terrain.

[0030] Specifically, to maintain consistency with the core parameter system of the downscaling model, a secondary screening is performed based on the topographic factors (excluding latitude and longitude coordinates) input to the downscaling model. The screening criteria are: the topographic factors have a stable spatial distribution (no drastic jumps between adjacent spatial units, typically, the aspect does not show abrupt changes >90° on both sides of the ridgeline), continuous numerical variables are used (such as continuous values ​​of slope from 0° to 90°, discrete classification is prohibited), and multiplicative combination terms between factors (such as slope × altitude) are introduced to capture the nonlinear effects caused by the synergistic effects of topography.

[0031] Furthermore, global models describing overall trends include global least squares regression models; local models capturing spatial heterogeneity include geographic weighted regression models or multi-scale geographic weighted regression models. First, a global least squares regression model is constructed to generate a unified terrain factor-ground flash density response function for the entire region. When the accuracy of the global least squares regression model is lower than a preset threshold, a geographic weighted regression model or a multi-scale geographic weighted regression model is constructed to generate an independent terrain factor-ground flash density response function for each geographic sample point.

[0032] In this model, the intercept term of the geographic weighted regression model or the multi-scale geographic weighted regression model is set to the intercept value of the global least squares regression model, so that the topographic factor coefficient reflects its enhancing or weakening effect on the global average lightning activity.

[0033] Specifically, based on the selected terrain factors, an Ordinary Least Squares (OLS) regression model is first established. This model generates a terrain factor-ground flash density response function that is independent of latitude and longitude coordinates for the entire region.

[0034] Using the ground flash density distribution map output by the machine learning downscaling module as the baseline, the model must simultaneously satisfy: Root Mean Square Error (RMSE) < 5 times / (km) 2 • per year), mean absolute error (MAE) < 5 times / (km) 2 ·year), coefficient of determination (R) 2 >0.8.

[0035] If any indicator in the OLS model fails to reach a threshold, a geographically weighted regression (GWR) or multiscale geographically weighted regression (MGWR) model is constructed. This model generates a terrain factor-spot lightning density response function for each geographic sample point, independent of latitude and longitude coordinates. It is important to note that, to ensure the terrain factor coefficients directly reflect their enhancing or weakening effect on average spot lightning activity, the intercept term of this response function can preferably be set to the intercept value of the regression equation obtained from the least squares global regression. The performance of the GWR model needs to be validated using the same indicators mentioned above.

[0036] Furthermore, cluster analysis of the regression coefficients includes: removing outliers, extracting coefficient types with significant differences, and calculating the average regression coefficient for each cluster category to form a typical comprehensive response pattern of topographic factors.

[0037] Specifically, when using GWR / MGWR modeling, cluster analysis is further performed on the regression coefficients of various topographic factors output by the model. After removing outliers, coefficient types with significant differences are extracted. Coefficients are aggregated for each cluster, and their average values ​​are calculated. These average coefficients represent the parameters of the geoflash density regression model for the specific topographic feature area corresponding to that category, ultimately forming a typical comprehensive response pattern of topographic factors. When using OLS modeling, the global regression equation itself is the only typical response pattern, directly representing the global average impact of topographic factors on ground flash density.

[0038] Furthermore, the terrain enhancement coefficient is calculated based on the typical response patterns after clustering, and combined with parameters greater than or equal to 1 km that meet national standards. 2 The ground flash density statistics of the grid are used to correct the lightning strike probability parameters of the protected objects in lightning protection projects.

[0039] Furthermore, correcting the lightning strike probability parameters of the protected object includes: determining the geographical location of the protected object, obtaining the terrain conditions of that location, calculating the terrain enhancement coefficient, and correcting the preset baseline lightning strike probability parameters based on the terrain enhancement coefficient, thereby achieving lightning strike risk assessment at the tower scale. It should be noted that for any given geographical location, only its terrain parameters need to be obtained (regardless of the statistical method or precision of these parameters) to calculate the corresponding terrain enhancement coefficient, thus correcting the lightning strike probability parameters before considering the influence of terrain factors. This method is not limited to the aforementioned grid method and can be extended to a wider range of terrain conditions.

[0040] Specifically, the terrain enhancement coefficient is calculated based on the typical response patterns obtained from clustering: ; In the formula: The average regression coefficient of a certain type of terrain factor after clustering; To standardize the terrain factor, based on this terrain enhancement coefficient, the relevant parameters of the lightning strike probability of the protected object in the lightning protection engineering calculation are corrected. Data-driven refined response zoning replaces the empirical correction of the plain / mountain dichotomy, realizing spatial heterogeneity modeling of lightning strike risk.

[0041] Furthermore, the integrated response model based on terrain factors is applied to terrain surfaces of 1 km or greater that meet national standards. 2 The ground flash density statistics of the grid are corrected, specifically by: using the low-precision ground flash density statistics as the intercept term to replace the original intercept value in the integrated response model of terrain factors; obtaining the terrain parameters of the geographical location to be corrected, and calculating the ground flash density of the geographical location after terrain correction according to the factor coefficients determined by the integrated response model of terrain factors.

[0042] The following uses Fangchenggang City as a case study: (1) Data preprocessing; The terrain data used was DEM data acquired by the Shuttle Radar Topography Mission SRTM, with an original spatial resolution of 90 m × 90 m. Based on this data, three key parameters characterizing terrain features—slope, aspect, and landform—were calculated using standard algorithms from Geoscene software, with all derived parameters maintaining the original 90-meter resolution.

[0043] In an embodiment of the present invention, preferably, the original DEM and derived terrain parameters are resampled to a 0.001°×0.001° geographic grid in the WGS 1984 UTM Zone49N projection system.

[0044] In this embodiment, the lightning data consists of fifteen consecutive years of LLS lightning records for the region (2010-2024), with valid data selected from joint positioning by at least three detection stations. Each record includes a timestamp and geographic coordinates (longitude and latitude). The region is divided into geographic grids with a resolution of 0.001° × 0.001°, and marine areas are excluded. It should be noted that to maximize the number of lightning samples, no lightning aggregation processing was performed in this embodiment; each record corresponds to an independent return stroke event (including the first or subsequent return strokes). Furthermore, potential cloud-to-ground lightning records were not actively removed, resulting in a slightly higher estimated lightning density, but this does not affect the core conclusions of the topographic impact analysis.

[0045] In this embodiment, based on the aforementioned LLS data, the total number of ground flashes within each grid cell is statistically analyzed, and the ground flash density of that cell (unit: flashes / km) is calculated. 2 / year). The resulting annual average lightning density distribution map, as shown in... Figure 2 As shown in (a) above, a two-dimensional low-pass filter is used to suppress small sample statistical noise, preserve spatial distribution trend characteristics, and generate a smooth flash density map, as shown in (a). Figure 2 As shown in (b), the noise is significantly reduced and the terrain relevance is enhanced after smoothing.

[0046] (2) Machine learning downscaling; In an embodiment of the present invention, a downscaling model is constructed using the XGBoost gradient boosting framework. The model uses the minimization of mean squared error as the objective function, smoothed ground flash density as the objective variable, and resampled terrain data and latitude and longitude coordinates as prediction variables; the hyperparameters are tuned using a two-stage Bayesian optimization strategy.

[0047] In an embodiment of the invention, 898,651 samples were input into the XGBoost model. After iterative training and prediction using 997 XGBoost trees, a high-resolution (0.001° × 0.001°) spatial distribution map of ground flash density at the same scale as the geographic elevation data was generated, such as... Figure 2 As shown in (c) above. The importance ranking of topographic factors (excluding latitude and longitude) is as follows: Figure 3 As shown.

[0048] In this embodiment, the confidence level of the lightning frequency in each grid within the ±20% error interval and the Shannon entropy of the lightning density distribution map are calculated based on the Poisson process. The improvement effect of the downscaling model on confidence level and information richness is evaluated by comparing the results with the statistical results of the LLS grid method and the results of smoothing filtering. The calculation results of key indicators are shown in Table 2 (confidence level (±20% confidence interval) and entropy calculation results of the average lightning density distribution map): Table 2 In this embodiment, the LLS grid direct statistical method has a confidence level of only 0.009% due to sample dispersion. Smoothing filtering increases the confidence level to 26.32% by expanding the grid through a fixed window, while the XGBoost model significantly improves the confidence level to 28.85% by expanding the equivalent statistical area through grid clustering. The ground flash density distribution obtained directly from the LLS grid method has a one-dimensional Shannon entropy of only 4.03, which is highly concentrated and contains many zero-value regions, resulting in limited information content. After smoothing, the entropy value increases to 18.34, and the XGBoost model output reaches a maximum of 19.58, representing an increase of 385% compared to the LLS grid direct statistical data and an increase of 6.7% compared to the smoothed data.

[0049] In this embodiment, geospatial aggregation analysis is further used to examine statistical errors at different regional scales: the 0.001°×0.001° resolution lightning density distribution map output by XGBoost is aggregated to a resolution of 0.01°×0.01° using 10×10 grid cells. This aggregation result is compared with the lightning density distribution at the same resolution (0.01°×0.01°) obtained directly using the LLS grid method. Figure 4 As shown. The numerical comparison results of the two graphs are as follows. Figure 5 As shown, the root mean square error (RMSE) is only 0.94. Due to the high confidence level of the direct statistical results from the LLS grid at this resolution, the confidence probability of its distribution values ​​within the ±20% error range is as high as 98.20%. The deviation between the aggregated results and the high-confidence benchmark remains at a low level, fully demonstrating that the 100-meter resolution ground flash density distribution map output by the XGBoost regression model has good spatial scaling invariance, further verifying the reliability of the XGBoos downscaling model output results.

[0050] (3) Spatial regression modeling; In this embodiment, to maintain consistency with the core parameter system of the downscaling model, a secondary screening is performed based on the topographic factors (elevation, aspect, slope, and landform type) input to the downscaling model: aspect does not meet the model's requirement for parameter space stability due to local abrupt changes (such as abrupt changes in the windward / leeward side within a small area of ​​a mountain ridgeline); landform type, as a discrete variable, is difficult to participate in continuous spatial regression modeling. Therefore, elevation, slope, and their product (used to capture the nonlinear relationship between topographic factors) are ultimately selected as the core parameters.

[0051] Based on the selected topographic factors, a global least squares (OLS) regression model is first established. This model generates a topographic factor-ground flash density response function independent of latitude and longitude coordinates for the entire domain. ; In the formula, This refers to the standardized altitude. The standardized slope; This is an interaction term for two parameters, used to capture the nonlinear coupling effect of terrain factors.

[0052] Output using the XGBoost model ( Figure 2 (c) is used as the baseline value for comparison. The OLS regression scatter plot of ground flash density is shown below. Figure 6 As shown. Coefficient of determination R 2 With a value of only 0.21, far below the 0.8 threshold, it indicates that the global uniform response function cannot capture the spatial heterogeneity of terrain effects. Therefore, an upgrade to the GWR / MGWR model is necessary.

[0053] Based on the above verification results, in this embodiment, a GWR model with a fixed bandwidth d of 1000 meters is constructed (it should be noted that the embodiment uses a geographic weighted regression GWR model which requires a fixed bandwidth, while the multi-scale geographic weighted regression MGWR model uses a variable bandwidth; the claims and invention content cover both GWR and MGWR implementations). This model generates a terrain factor-ground flash density response function independent of latitude and longitude coordinates for each geographic sample point (grid point): ; In the formula, This refers to the standardized altitude. The standardized slope; This is an interaction term between two parameters, used to capture the nonlinear coupling effect of terrain factors; , , These are the spatial variation coefficients of various topographic factors, with each sample point having an independent value; For the intercept term, in the embodiments of the present invention, the intercept term is preferably set as the intercept value of the regression equation obtained by OLS global regression, so that the topographic factor coefficient can intuitively reflect its enhancing or weakening effect on the global average state.

[0054] The lightning density distribution obtained based on the above regression equation is as follows: Figure 7 As shown in the figure, the scatter plot comparing the GWR regression lightning density with the high-resolution lightning density output by the XGBoost downscaling model is as follows. Figure 8 As shown. Output of the XGBoost model ( Figure 2 Using (c) as the baseline, the model's root mean square error (RMSE) = 1.82, mean absolute error (MAE) = 1.27, and coefficient of determination (R²) = 1.82. 2 =0.93, all three statistical indicators are less than the set threshold, confirming that GWR has successfully constructed the local response relationship between ground flash density and topographic parameters.

[0055] (4) Cluster analysis and spatial heterogeneity modeling of lightning strike risk; In this embodiment of the invention, a two-step method is used to perform cluster analysis on the regression coefficients of various terrain factors output by the GWR model. After removing sample points with abnormal coefficient fluctuations, five categories of coefficients with significant differences are extracted. For each cluster category, the average value of the terrain factor coefficients corresponding to the sample points it contains is calculated. These average coefficients represent the parameters of the geoflash density regression model for the specific terrain feature area corresponding to that category, ultimately forming a typical comprehensive response pattern of terrain factors. The regression equations of each typical pattern and the distribution of their average coefficients in three-dimensional terrain space are shown below. Figure 9 As shown.

[0056] Based on the typical response patterns obtained from clustering, the terrain enhancement coefficient for each location can be calculated: ; Based on this terrain enhancement coefficient, the relevant parameters of the lightning strike probability of the protected object in the lightning protection engineering calculation are corrected. By constructing a spatially continuous terrain response partition, the empirical correction of the plain / mountain dichotomy is replaced, thus realizing the spatial heterogeneity modeling of lightning strike risk. In an embodiment of the present invention, the calculation of the backflashover tripping rate of transmission lines is taken as an example: ; In the formula: Number of lightning strikes per year; For the rate of attack; This refers to the stroke rate; For the arc-building rate; This represents the probability that the lightning current exceeds the backflashover withstand level. The strike rate is one of these probabilities. The value of is highly dependent on the empirical table: The hit rates for different terrains are shown in Table 3.

[0057] Table 3 This embodiment performs spatial correction of the hit rate based on the terrain enhancement coefficient according to the following steps: Establish the affiliation between towers and grid cells, and determine the geographical location of each tower; Calculate the terrain enhancement factor at this location. ; Using terrain enhancement coefficient The correction formula for the strike rate of the tower is as follows: ; in, This is the corrected stroke rate. Based on this, the value is 1 / 4 when there is 1 ground wire and 1 / 6 when there are 2 ground wires.

[0058] The core technical solution of this invention is as follows: (1) Overall technical framework; This invention constructs a three-tiered technology chain based on a unified terrain parameter system: "XGBoost downscaling → spatial regression → cluster analysis and lightning strike risk modeling." First, the XGBoost model is used to fuse low-confidence lightning location system data with high-resolution terrain parameters to generate a lightning density distribution map at the same scale as geographic elevation data. Next, spatial regression technology is used to construct a terrain-lightning response function independent of latitude and longitude. Finally, cluster analysis is performed on the model output to extract typical terrain-based comprehensive response patterns. These response patterns support the calculation of terrain enhancement coefficients, which are used to correct relevant parameters of the lightning strike probability of protected objects in lightning protection engineering calculations, achieving spatial heterogeneity modeling of lightning strike risk. This technical path realizes a complete technical closed loop from data downscaling and spatial regression modeling to engineering applications.

[0059] (2) XGBoost downscaling method; This invention employs a machine learning downscaling modeling method based on XGBoost. It eliminates statistical noise in lightning location system data through two-dimensional low-pass filtering and expands the equivalent statistical sample size using an XGBoost grid clustering mechanism, generating a lightning density distribution map with the same resolution as geographic elevation data. This method overcomes the terrain resolution limitations of traditional grid methods while significantly improving statistical reliability. In this embodiment, the method increases the average confidence level of lightning frequency within a ±20% error range from 0.009% using the grid method to 28.85%, while simultaneously increasing the Shannon entropy value of the lightning density distribution map from 4.03 to 19.58, effectively resolving the contradiction between high resolution and high confidence.

[0060] (3) Local regression modeling method considering spatial heterogeneity; This invention constructs a geographic weighted regression modeling method based on high-resolution topographic factors, mainly including the following technical steps: First, establishing a mechanism for screening topographic parameters and constructing interaction terms, selecting continuous numerical variables that satisfy spatial distribution stability, and introducing multiplicative combination terms between factors to capture the nonlinear effects caused by topographic synergy; Second, adopting a hierarchical modeling strategy and a fixed intercept term strategy, first establishing a global least squares regression model, and when the model error index does not reach the threshold, upgrading to a geographic weighted regression or multi-scale geographic weighted regression model, and fixing the intercept of the response function to the global least squares regression value, so that the topographic factor coefficients can directly quantify their enhancing or weakening effect on the global average lightning activity. This method, by establishing a regression model independent of latitude and longitude coordinates, effectively reduces the interference of meteorological background factors, can accurately statistically analyze the enhancing or weakening effect of topography on lightning density, and obtain a topographic-lightning response relationship with regional universality.

[0061] (4) Spatial heterogeneity modeling of lightning strike risk; This invention achieves spatial heterogeneity modeling of lightning strike risk, mainly including the following method: First, cluster analysis is performed on the regression coefficients of various terrain factors output by the geographic weighted regression model to extract typical comprehensive response patterns of terrain factors; then, the terrain enhancement coefficient is calculated based on the response patterns, and this coefficient is used to correct the relevant parameters of the lightning strike probability of the protected object in traditional lightning protection engineering calculations. This method replaces the traditional plain / mountain dichotomy empirical correction with data-driven refined response zoning, achieving an accurate characterization of the spatial distribution law of lightning strike risk and providing a scientific basis for differentiated lightning protection design.

[0062] The advantages of this invention are as follows: (1) Compared with the traditional grid method which is constrained by the statistical sample size (GB / T 40621-2021 requires a grid size of ≥1 km to ensure confidence), this invention uses machine learning to downscale and fuse high-precision terrain data to achieve same-scale matching between lightning density and high-resolution geographic elevation data, so that the statistical resolution can be flexibly adjusted according to the accuracy of the terrain data. At the same time, the XGBoost grid clustering mechanism is used to expand the equivalent statistical sample size, increasing the average confidence in the ±20% error interval from 0.009% to 28.85%, and the Shannon entropy value from 4.03 to 19.58, fundamentally solving the inherent contradiction between spatial resolution and statistical confidence in lightning protection engineering.

[0063] (2) To address the problem of mixed meteorological background and topographic effects caused by the introduction of latitude and longitude coordinates in traditional modeling methods (such as generalized additive models), this invention innovatively adopts a local regression modeling method that considers spatial heterogeneity. Through topographic factor selection and intercept optimization (fixed to the OLS global intercept value), a topographic factor-ground flash density response function independent of latitude and longitude coordinates is established. In empirical data analysis, this method achieves RMSE=1.82 and R0.05. 2 With an accuracy of 0.93, the spatial coefficients output by the model can quantify the intensity of the "enhancing" or "weakening" effect of each grid terrain on lightning activity, thus clearly depicting the local differences in lightning activity under the influence of different terrains.

[0064] (3) To overcome the limitations of traditional lightning protection theory, which relies on empirical thresholds and ignores the influence of geographical factors, this invention clusters the output of a linear regression model to extract comprehensive response patterns of typical terrain factors, and uses these response patterns to support the calculation of terrain enhancement coefficients. Based on these coefficients, relevant parameters of the lightning strike probability of protected objects in lightning protection engineering calculations are used to replace the empirical correction values ​​of the plain / mountain dichotomy with data-driven refined response zoning, thus realizing spatial heterogeneity modeling of lightning strike risk.

[0065] This invention can achieve the following technical objectives: (1) Achieving flexible and adaptable high-resolution lightning density statistics: Under the constraint of limited LLS data, by integrating high-resolution terrain data and machine learning downscaling technology, a dual improvement is achieved based on the XGBoost grid clustering mechanism: both accurately analyzing the nonlinear correlation between terrain factors and lightning density, and expanding the equivalent statistical sample size to enhance reliability. Thus, a lightning density model with the same scale as geographic elevation data is constructed, so that the statistical resolution can be flexibly adapted according to the accuracy of terrain data, fundamentally solving the spatial resolution bottleneck problem of traditional grid methods, and meeting the differentiated and refined lightning protection needs under complex terrain conditions.

[0066] (2) Realize spatial regression modeling of terrain-lightning density: Based on the spatial alignment of high-resolution terrain factors and LLS data, a local regression modeling method considering spatial heterogeneity is adopted to construct a terrain-lightning response function independent of latitude and longitude coordinates, thereby accurately quantifying the enhancement / weakening effect of terrain factors on lightning activity, reflecting the influence of complex terrain on lightning activity, and decoupling the mixed effect of terrain factors and meteorological background factors.

[0067] (3) Achieving spatial heterogeneity modeling of lightning strike risk: By performing cluster analysis on the output results of the regression model, the comprehensive response pattern of typical terrain factors is extracted, and the calculation of the terrain enhancement coefficient is supported based on the response pattern. The core value of this coefficient is to correct the relevant parameters of the lightning strike probability of the protected object in the calculation of lightning protection engineering, replace the empirical correction of the plain / mountain dichotomy with data-driven refined response zoning, realize spatial heterogeneity modeling of lightning strike risk for linear projects such as transmission lines and point facilities such as wind turbines, and improve the accuracy of lightning damage risk assessment for protected objects under complex terrain conditions.

[0068] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for modeling the spatial heterogeneity of lightning ground flash density based on geographic factor regression, characterized in that, Includes the following steps: The terrain data of the target area and the lightning flash data recorded by the lightning location system are acquired, and the terrain data and lightning flash data are spatially gridded to generate an original lightning flash density distribution map with the same resolution as the terrain data. A ground flash density downscaling model is constructed based on the XGBoost framework, with the original ground flash density distribution map as the target variable and terrain data and grid coordinates as prediction variables. Multiple decision trees are constructed using the XGBoost model to dynamically divide spatially discrete grid samples with similar ground flash-terrain relationships into the same leaf node, in order to capture the complex nonlinear relationship between terrain parameters and ground flash density, and generate a high-resolution ground flash density distribution map with the same resolution as the terrain data. A linear regression model is constructed based on the high-resolution lightning density distribution map. The linear regression model includes a global model for describing the overall trend and a local model for capturing spatial heterogeneity. Using topographic factors as predictor variables, a topographic factor-lightning density response function decoupled from the influence of latitude and longitude coordinates is generated. The response function quantifies the enhancing or weakening effect of topographic factors on average lightning activity. Cluster analysis was performed on the regression coefficients of the terrain factor-ground flash density response function output by the local model, and typical integrated response patterns of terrain factors were extracted based on the clustering results. The terrain enhancement coefficient of average ground flash density is obtained based on the terrain factor-ground flash density response function and the integrated response mode of terrain factor output by the global model. Based on the terrain enhancement factor around the lightning protection object, and in line with the national standard of greater than or equal to 1 km 2 The grid lightning density statistical data, the lightning probability parameter of the protected object is corrected, to build a high-precision lightning disaster risk spatial heterogeneity model.

2. The modeling method according to claim 1, characterized in that, The terrain data includes a digital elevation model and its derived parameters, and the lightning data includes the timestamp and geographic coordinates of the lightning event; Spatial gridding processing of the terrain data and ground flash data includes: uniformly resampling the terrain data to a geographic grid of a preset resolution, and statistically analyzing the frequency of ground flash events based on the geographic grid to generate an original ground flash density distribution map.

3. The modeling method according to claim 2, characterized in that, After generating the original ground flash density distribution map, the method further includes performing two-dimensional low-pass filtering on the distribution map to eliminate small sample statistical noise, generating a smooth ground flash density distribution map, and using the smooth ground flash density distribution map as the target variable of the downscaling model.

4. The modeling method according to claim 1, characterized in that, The downscaling model is built on the XGBoost framework, and hyperparameters are tuned with the goal of minimizing the mean squared error. After the model outputs, the reliability of the ground flash density distribution map output by the model is evaluated. The reliability evaluation includes calculating the average confidence level and image entropy value of the ground flash density distribution map output by the model within a preset confidence interval, and comparing it with the original ground flash density distribution map and the smoothing filtering results to verify the improvement effect of the downscaling model in terms of statistical reliability and information richness.

5. The modeling method according to claim 1, characterized in that, Before constructing the linear regression model, the importance of terrain factors is screened, and a product combination term between factors can be introduced to capture the nonlinear effects caused by terrain synergy.

6. The modeling method according to claim 1, characterized in that, The global model describing the overall trend includes a global least squares regression model; the local model capturing spatial heterogeneity includes a geographic weighted regression model or a multi-scale geographic weighted regression model. First, a global least squares regression model is constructed to generate a unified terrain factor-ground flash density response function for the entire region. When the accuracy of the global least squares regression model is lower than a preset threshold, a geographic weighted regression model or a multi-scale geographic weighted regression model is constructed to generate an independent terrain factor-ground flash density response function for each geographic sample point.

7. The modeling method according to claim 6, characterized in that, The intercept term of the geographic weighted regression model or multi-scale geographic weighted regression model is set to the intercept value of the global least squares regression model so that the topographic factor coefficient reflects its enhancing or weakening effect on the global average lightning activity.

8. The modeling method according to claim 1, characterized in that, Cluster analysis of regression coefficients includes: removing outliers, extracting coefficient types with significant differences, and calculating the statistical average of regression coefficients for each cluster category to form a typical comprehensive response pattern of terrain factors.

9. The modeling method according to claim 1, characterized in that, The terrain enhancement coefficient is calculated based on the typical response patterns after clustering, and combined with a value greater than or equal to 1 km that meets national standards. 2 The ground flash density statistics of the grid are used to correct the lightning strike probability parameters of the protected objects in lightning protection projects; The correction of the lightning strike probability parameters of the protected object includes: determining the geographical location of the protected object, obtaining the terrain conditions of the location, calculating the terrain enhancement coefficient, and correcting the preset benchmark lightning strike probability parameters according to the terrain enhancement coefficient, thereby improving the accuracy of lightning hazard risk assessment for the protected object under complex terrain conditions.

10. The modeling method according to claim 9, characterized in that, Based on the integrated response model of terrain factors, for areas of 1 km or greater that meet national standards 2 The ground flash density statistics of the grid are corrected, specifically by: using the low-precision ground flash density statistics as the intercept term to replace the original intercept value in the integrated response model of terrain factors; obtaining the terrain parameters of the geographical location to be corrected, and calculating the ground flash density of the geographical location after terrain correction according to the factor coefficients determined by the integrated response model of terrain factors.

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