Method for predicting and analyzing extreme rainstorm event in hilly region based on multi-factor coupling

Abstract

The invention discloses a hilly region extreme rainstorm event prediction and analysis method based on multi-factor coupling, and the method comprises the steps: S1, carrying out the data collection and preprocessing, dividing the preprocessed data into a training data set and a test data set, S2, carrying out the multi-factor feature extraction, extracting main meteorological features, and carrying out the multi-factor feature extraction; the method comprises the following steps: S1, calculating a terrain index to represent the influence of the terrain on rainfall, S3, screening key influence factors, S4, constructing and training a prediction model, and constructing an extreme rainstorm event prediction model by adopting a support vector machine algorithm, and S5, evaluating a prediction result which comprises the accuracy, the recall rate, the precision rate and a comprehensive index F1 value for balancing the recall rate and the precision rate. According to the method, data redundancy and noise are reduced, the efficiency and accuracy of the prediction model are improved, the complex relation among multiple factors can be more accurately captured, and therefore the prediction precision of the extreme rainstorm event is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of meteorological disaster prediction, and in particular to a method for predicting and analyzing extreme rainstorm events in hilly areas based on multi-factor coupling. Background Art

[0002] Against the backdrop of global climate change, extreme rainstorms occur frequently, bringing serious natural disasters such as landslides, mudslides, and floods to hilly areas, posing a huge threat to people's lives and property and the ecological environment.

[0003] AI and machine learning are widely used in weather forecasting, and existing research has extensively explored how machine learning can be applied to rainfall prediction and disaster prevention and mitigation. However, existing rainstorm forecasting methods mostly focus on analyzing a single meteorological element or a few factors, particularly in mountainous and complex terrain. Existing technologies fail to fully consider the coupling effects of multiple factors, such as complex topography, atmospheric circulation, and water vapor transport in hilly areas. This results in insufficient accuracy and reliability in forecasting extreme rainstorm events.

[0004] Therefore, it is of great practical significance to develop a prediction and analysis method for extreme rainstorm events in hilly areas that can comprehensively consider the influence of multiple factors. Summary of the Invention

[0005] In order to solve the above problems, the present invention proposes a prediction and analysis method for extreme rainstorm events in hilly areas based on multi-factor coupling. By comprehensively analyzing multiple meteorological and geographical factors, a prediction model is constructed using a combination of principal component analysis, random forest and support vector machine to improve the prediction accuracy of extreme rainstorm events in hilly areas.

[0006] The present invention is implemented as follows: a method for predicting and analyzing extreme rainstorm events in hilly areas based on multi-factor coupling, comprising the following steps:

[0007] Step S1, data collection and preprocessing: collect the ERA5 dataset of the European Centre for Medium-Range Weather Forecasts, measured data from meteorological stations in the study area, and DEM digital elevation model data reflecting the topographic and geomorphological characteristics of the study area; preprocess the collected data, including quality control and standardization. The quality control includes using a hybrid strategy of a spatiotemporal coupled dynamic threshold method and multivariate joint testing to eliminate outliers and fill missing values, and divide the preprocessed data into a training dataset and a test dataset;

[0008] Step S2, multi-factor feature extraction: use principal component analysis to perform dimensionality reduction, extract main meteorological features, and calculate terrain index to represent the impact of terrain on precipitation;

[0009] Step S3, screening of key influencing factors: using the random forest algorithm to rank the importance of the extracted multi-factor features, and selecting features with higher importance scores as key influencing factors of extreme rainstorm events;

[0010] Step S4, prediction model construction and training: using a support vector machine algorithm to construct an extreme rainstorm event prediction model; using the screened key influencing factors of extreme rainstorm events as input features of the prediction model, and "whether an extreme rainstorm event occurs" as the output label of the prediction model, the prediction model is trained until the model training is completed;

[0011] Step S5, prediction result evaluation: Use the test data set described in step S1 to evaluate the extreme rainstorm event prediction model trained in step S4. The evaluation indicators include accuracy, recall rate, precision rate, and the comprehensive indicator F1 value that balances the recall rate and precision rate.

[0012] Furthermore, the specific steps of removing outliers in step S1 include:

[0013] The first step is to detect the dynamic threshold value of single variable space-time: construct a space-time sliding window for each meteorological variable and calculate the dynamic threshold Q upper (t, s):

[0014]

[0015] Where Q 75 (t, s) is the 75th percentile in the spatiotemporal window, IQR(t, s) is the interquartile range, IQR(t, s) = Q 75 (t, s)-Q 25 (t, s), Q 25 (t, s) is the 25th percentile in the spatiotemporal window; Δh is the mean elevation difference between the weather station and its neighbors, h ref is the reference elevation parameter, k(h) is the terrain adjustment factor, h is the elevation of the weather station, and h meam is the average elevation of the study area, σ h is the elevation standard deviation;

[0016] For suspected outliers exceeding the threshold, the time series curvature Verification, the formula is:

[0017]

[0018] If the following conditions are met, it is considered an outlier:

[0019] and

[0020] Where t is the time step at the current moment, xt is the observed value of the meteorological variable at time t, x t+1 is the observation value of the next time step after time t, x t-1 is the observation value of the previous time step before time t, is the standard deviation of curvature, is the seasonal mean;

[0021] The second step is multivariate joint anomaly detection: calculating the multivariate Mahalanobis distance D M :

[0022]

[0023] Where X is the multivariate observation vector, μ is the mean vector, T is the transpose operator of the matrix or vector, and Σ is the covariance matrix;

[0024] Introducing terrain weight correction threshold D threshold :

[0025]

[0026] Where V is the number of variables, is the 99% quantile of the chi-square distribution with degrees of freedom V, TI is the terrain index of the current point, TI max is the maximum topographic index of the study area, a is the catchment area, and b is the slope;

[0027] If D is satisfied M >D threshold It is determined to be a multivariate coupling outlier;

[0028] The third step is to verify the spatiotemporal density clustering: calculate the composite spatiotemporal distance metric d st :

[0029]

[0030] Where, d space is the spatial Euclidean distance, d time is the time interval, d max is the maximum Euclidean distance between all pairs of spatial points in the study area, ΔT max is the maximum time span within the study time range, Corr(X, Y) is the Pearson correlation coefficient of the variable trend, α, β, and γ are adjustable weight coefficients, α+β+γ=1;

[0031] Calculate the adaptive density parameters:

[0032] ∈=μ d +2σ d

[0033]

[0034] Where ∈ is the neighborhood radius, μ d is the mean of the distance distribution, σ d is the distance standard deviation, MinPts is the minimum number of cluster points, N total is the total number of samples;

[0035] If a data sample point does not belong to any density cluster and is not covered by more than 80% of neighboring points, it is considered an outlier;

[0036] The fourth step is physical mechanism inversion verification: water vapor flux is measured for the outliers to be removed. Verification, the formula is:

[0037]

[0038] If the following conditions are met, it is considered a true extreme event and the data will be retained:

[0039] (Historical extreme values ​​in the study area)

[0040] Where Q 95 is the 95th percentile of the historical extreme value in the study area, q is the specific humidity, that is, the mass of water vapor per unit mass of wet air, is the three-dimensional wind speed vector, x is the east-west direction, y is the north-south direction, z is the vertical direction, u is the east-west wind speed, east is positive, v is the north-south wind speed, north is positive, and w is the vertical wind speed, upward is positive.

[0041] Furthermore, the step S1 of filling missing values ​​is as follows: using linear interpolation to fill missing values, assuming that the original data sequence is x1, x2, ..., x m , the linear interpolation formula is:

[0042]

[0043] Where x i is a missing value, x i-k is x i The previous adjacent valid data, x i+l is x i The adjacent valid data after that, k and l are the valid data from the missing value position i to the previous adjacent valid data x i-k , the next adjacent valid data x i+l The number of intervals.

[0044] Furthermore, the standardization process in step S1 specifically involves converting the value of each variable into a standard normal distribution with a mean of 0 and a standard deviation of 1 to eliminate the influence of different variable dimensions. The standardization process formula is:

[0045]

[0046] Wherein, is the value after standardization of the j-th variable value of the i-th sample, x ij is the j-th variable value of the i-th sample, is the mean of the j-th variable, s j is the standard deviation of the j-th variable.

[0047] Furthermore, the multi-factor feature extraction described in step S2 specifically includes the following sub-steps:

[0048] Step S21, calculate the covariance matrix S: Let the meteorological station measured data of the training data set described in step S1 be an n×p data matrix X * , where n is the number of samples and p is the total number of meteorological features; calculate the X * covariance matrix S:

[0049]

[0050] Wherein, T is the transpose operator of a matrix or vector, X *T is the transpose matrix of X * , and the covariance matrix S is a p×p real symmetric matrix;

[0051] Step S22, eigenvalue decomposition: For the covariance matrix S obtained in step S21, there exist an orthogonal matrix E and a diagonal matrix Λ such that:

[0052] S = EΛE T

[0053] where the diagonal elements of the diagonal matrix Λ are the eigenvalues λ1≥λ2≥…≥λ p of the covariance matrix S, and the column vectors of the orthogonal matrix E are the corresponding unit orthogonal eigenvectors e1, e2, …, e p ;

[0054] Step S23, dimensionality reduction processing: Select the eigenvectors e1, e2, …, e k corresponding to the first k eigenvalues as column vectors respectively to form a projection matrix P:

[0055] P = (e1, e2, …, e k )

[0056] where the value range of k is 1≤k<p; when selecting the first k eigenvalues, ensure that the cumulative variance contribution rate is greater than or equal to the first preset threshold, and the formula for the cumulative variance contribution rate Cumulative Variance Ratio is:

[0057]

[0058] In the formula, λ i is the i-th eigenvalue sorted from large to small;

[0059] The matrix X of the measured meteorological station data in the training data set in step S1 is projected into a low-dimensional space through the projection matrix P * to obtain the principal component matrix Y:

[0060] Y = XP * P

[0061] Finally, the first k main meteorological features are extracted;

[0062] Step S24, calculate the topographic index: Calculate the topographic index TI for the digital elevation model data of the training data set in step S1:

[0063]

[0064] In the formula, a is the catchment area and b is the slope.

[0065] Furthermore, the screening of the key influencing factors in step S3 specifically includes the following sub-steps:

[0066] Step S31, calculate the overall importance: First, use a random forest to construct multiple decision trees to classify or regress the data. Each decision tree randomly selects a part of the samples and features for training. After training, evaluate its overall importance by calculating the average decrease in impurity of each feature in all decision trees. Let the importance of feature j in the t-th decision tree be I j，t , and the formula for the overall importance of feature j is:

[0067] [[ID=?]]

[0068] In the formula, I j is the overall importance of feature j, α is the number of decision trees, and I j，t is the importance of feature j in the t-th decision tree;

[0069] Step S32, select the key influencing factors: Sort the multi-factor features extracted in step S2 according to the overall importance from large to small, and select the top m features with higher overall importance as the key influencing factors of extreme rainstorm events; among them, the value range of m is 1 ≤ m < q, where q is the total number of multi-factor features extracted in step S2; when selecting the top m features with higher overall importance, ensure that the cumulative importance is greater than or equal to the second preset threshold. The formula for the cumulative importance Cumulative Importance is:

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[0071] Where, I j is the overall importance of feature j sorted from largest to smallest.

[0072] Furthermore, the support vector machine algorithm in step S4 is specifically: for the linearly separable case, the formula for solving the optimization problem by the support vector machine is:

[0073]

[0074] sty i (w T φ(x i )+b)≥1,i=1,2,…,n

[0075] Where w is the weight vector, b is the bias term, and x i is the input sample, φ(x i ) is a function that maps input samples to high-dimensional feature space, y i is the category label of the sample, y i ∈{-1, 1};

[0076] For the case of linear inseparability, the formula for solving the optimization problem using support vector machine is:

[0077]

[0078] sty i (w T φ(x i )+b)≥1-ξ i ,ξ i ≥0, i=1, 2, …, n

[0079] Where, ξ i is the slack variable and C is the penalty factor.

[0080] Furthermore, the specific process of training the prediction model in step S4 until the model training is completed is as follows: during the training process, grid search is used to traverse the kernel function parameter combination, and the model parameters are optimized in combination with cross-validation to select the optimal penalty factor C and kernel function parameters;

[0081] The model training completion specifically includes the following criteria:

[0082] The optimization algorithm meets the convergence conditions: the change of the objective function between adjacent iterations is less than the third preset threshold; the training sample meets the Karush-Kuhn-Tucker condition;

[0083] Preset upper limit of iteration number: If the optimization algorithm does not converge within a fixed number of iterations, it will be forced to stop to avoid infinite loop;

[0084] Stable performance on the test dataset: If the model performance stops improving after a certain number of consecutive rounds on the cross-validation or test dataset, terminate the training early to prevent overfitting.

[0085] Parameter optimization is complete: When the optimal penalty factor C and kernel function parameters are found through grid search, and the solution of the model on the training set meets the constraints of the optimization problem, the training is considered complete.

[0086] Furthermore, the calculation formula of the accuracy in step S5 is:

[0087]

[0088] Where TP is the number of true positive examples, TN is the number of true negative examples, FP is the number of false positive examples, and FN is the number of false negative examples. The range of Accuracy is [0, 1], where 0 means that the extreme rainstorm event prediction is completely wrong, and 1 means that the extreme rainstorm event prediction is completely correct.

[0089] Furthermore, the F1 value in step S5 is:

[0090]

[0091] Where, the F1 value represents the harmonic mean of the two indicators, Precision and Recall, indicating that the two indicators are equally important. The range of the F1 value is [0, 1], where 0 means that at least one of Precision and Recall is 0, and 1 means that both Precision and Recall are 1.

[0092] The beneficial effects of this invention include: comprehensively considering the impact of multiple meteorological and geographical factors on extreme rainstorm events in hilly areas, reducing data redundancy and noise through multi-factor feature extraction and screening of key influencing factors, and improving the efficiency and accuracy of the prediction model. The use of advanced data analysis and machine learning algorithms such as principal component analysis, random forests, and support vector machines can more accurately capture the complex relationships between multiple factors, thereby improving the accuracy of extreme rainstorm predictions. Through rigorous data preprocessing and model evaluation, the reliability and stability of the method are guaranteed, providing strong technical support for meteorological disaster warning, prevention, and mitigation efforts in hilly areas.

[0093] The present invention will be explained in detail below with reference to the accompanying drawings and specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 The figure is a flow chart of the steps of the method of the present invention. DETAILED DESCRIPTION

[0095] Example 1:

[0096] This embodiment provides a method for predicting and analyzing extreme rainstorm events in hilly areas based on multi-factor coupling. Figure 1 As shown, the following steps are included:

[0097] Step S1, data collection and preprocessing:

[0098] The ERA5 dataset of the European Centre for Medium-Range Weather Forecasts (ECMWF) was collected, including ERA5 hourly data on pressure levels from 1940 to present and ERA5-Land monthly averaged data from 1950 to present. Measured data from meteorological stations in the study area were also obtained, including meteorological elements such as precipitation, temperature, air pressure, wind speed, and wind direction. Digital elevation model (DEM) data reflecting the topographic and geomorphological characteristics of the study area were also obtained.

[0099] Use Python's pandas library to read the data and preprocess the collected data, including quality control and standardization.

[0100] (1) In terms of data quality control, a hybrid strategy of spatiotemporal coupled dynamic threshold method and multivariate joint test is used to detect outliers. The specific steps include:

[0101] The first step is univariate spatiotemporal dynamic threshold detection:

[0102] Using the terrain-adaptive sliding quantile method, a spatiotemporal sliding window is constructed for each meteorological variable (such as precipitation) to calculate the dynamic threshold. The formula is:

[0103]

[0104] Where Q 75 (t, s) is the 75th percentile in the spatiotemporal window, IQR(t, s) is the interquartile range, IQR(t, s) = Q 75 (t, s)-Q 25 (t, s), Q 25 (t, s) is the 25th percentile in the spatiotemporal window; Δh is the mean elevation difference between the weather station and its neighbors, h re′ is the reference elevation parameter, k(h) is the terrain adjustment factor, h is the elevation of the weather station, and h meam is the average elevation of the study area, σ h is the elevation standard deviation.

[0105] The second-order derivative of the mutation point is used to verify the suspected outliers exceeding the threshold, and the time series curvature is used to Verification, the formula is:

[0106]

[0107] If the following conditions are met, it is considered an outlier:

[0108] and

[0109] Where t is the current time step or time index (if the data is observed hourly, t corresponds to the tth hour), x t is the observed value of the meteorological variable at time t (such as precipitation), x t+1 is the observed value of the next time step after time t (such as the precipitation in hour t+1), x t-1 is the observed value of the previous time step before time t (such as the precipitation in the t-1 hour), is the standard deviation of curvature, is the seasonal mean.

[0110] The second step is multivariate joint anomaly detection (terrain-corrected Mahalanobis distance):

[0111] Calculate the multivariate Mahalanobis distance D M :

[0112]

[0113] Where X is the multivariate observation vector, μ is the mean vector, T is the transpose operator of the matrix or vector (i.e., the transpose symbol in linear algebra), and Σ is the covariance matrix.

[0114] Calculate the terrain weight correction threshold D threshold :

[0115]

[0116] Where V is the number of variables, is the 99% quantile of the chi-square distribution with degrees of freedom V, TI is the terrain index of the current point, TI max is the maximum topographic index of the study area, a is the catchment area, and b is the slope.

[0117] If D is satisfied M >D threshold It is determined to be a multivariate coupling outlier.

[0118] The third step is spatiotemporal density clustering verification (ST-DBSCAN improved algorithm):

[0119] Calculate the composite spatiotemporal distance metric dst :

[0120]

[0121] Where, d space is the spatial Euclidean distance, d time is the time interval, d max is the maximum Euclidean distance between all pairs of spatial points in the study area, ΔT max is the maximum time span within the research time range, Corr(X, Y) is the variable trend Pearson correlation coefficient, α, β, and γ are adjustable weight coefficients, and α+β+γ=1. In this embodiment, α=0.4, β=0.3, and γ=0.3 are used.

[0122] Calculate the adaptive density parameters:

[0123] ∈=μ d +2σ d

[0124]

[0125] Where ∈ is the neighborhood radius, μ d is the mean of the distance distribution, σ d is the distance standard deviation, MinPts is the minimum number of cluster points, N total is the total number of samples.

[0126] If a data sample point is an isolated point, that is, it does not belong to any density cluster and is not covered by more than 80% of neighboring points, it is determined to be an outlier.

[0127] The fourth step is physical mechanism inversion verification:

[0128] Water vapor flux is performed on the outliers to be removed Verification, the formula is:

[0129]

[0130] If the following conditions are met, it is considered a true extreme event and the data will be retained:

[0131] (Historical extreme values ​​in the study area)

[0132] Where Q 95 is the 95th percentile of the historical extreme value in the study area, and q is the specific humidity, which is the mass of water vapor per unit mass of wet air and represents the air humidity. It is a three-dimensional wind speed vector, consisting of three directional components u, v, and w. Define x as the east-west direction (horizontal direction in the longitude), y as the north-south direction (horizontal direction in the latitude), and z as the vertical direction (height or altitude). Then u is the east-west wind speed (east is positive), v is the north-south wind speed (north is positive), and w is the vertical wind speed (upward is positive).

[0133] (2) After outliers are detected, if the proportion of outliers is small (in this embodiment, the proportion of outliers is <5%) and does not affect the overall distribution and the data volume is sufficient, these outliers are eliminated.

[0134] (3) For missing values, linear interpolation is used to fill them. The specific method is:

[0135] Assume that the original data sequence is x1, x2, ..., x m , the linear interpolation formula is:

[0136]

[0137] Where x i is a missing value, x i-k is x i The previous adjacent valid data, x i+l is x i The adjacent valid data after that, k and l are the valid data from the missing value position i to the previous adjacent valid data x i-k , the next adjacent valid data x i+l That is, it is necessary to jump forward k positions and backward l positions to find the most recent valid data.

[0138] (4) Because the subsequent steps require the calculation of the covariance matrix, which is sensitive to the variable dimensions, if the dimensions of the original data features differ greatly, such as temperature (°C or °F) and rainfall (mm), directly calculating the covariance matrix will amplify the impact of high-dimensional features on the results. Therefore, the data needs to be standardized first. The specific method of data standardization is to use the StandardScaler class in the scikit-learn library to convert the values ​​of each variable into a standard normal distribution with a mean of 0 and a standard deviation of 1 to eliminate the influence of different variable dimensions (Z-score standardization).

[0139] The standardization formula is:

[0140]

[0141] Where, is the standardized value of the jth variable value of the i-th sample, x ij is the j-th variable value of the i-th sample, is the mean of the jth variable, sj is the standard deviation of the j-th variable. After standardization, the covariance matrix is ​​equivalent to the correlation coefficient matrix of the original data.

[0142] (5) After preprocessing, the dataset is divided into training dataset and test dataset according to a certain ratio.

[0143] Step S2, multi-factor feature extraction:

[0144] The measured data from the weather stations in the training dataset obtained in step S1 are processed using the PCA class in the scikit-learn library, i.e., principal component analysis, to reduce the dimensionality and extract the main meteorological features. This includes the following sub-steps:

[0145] Step S21, calculate the covariance matrix S: Assume that the measured data of the weather station in the training data set in step S1 is the n×p data matrix X * , where n is the number of samples and p is the total number of meteorological characteristics; the calculated X * Covariance matrix S:

[0146]

[0147] Where T is the transposition operator of the matrix or vector (i.e., the transposition symbol in linear algebra), X *T For X * The transposed matrix of the covariance matrix S is a p×p real symmetric matrix (S T =S).

[0148] Step S22, eigenvalue decomposition: According to linear algebra theory, the real symmetric matrix S can be orthogonal diagonalized, that is, there exists an orthogonal matrix E(E T E = I) and a diagonal matrix Λ, such that:

[0149] S=EΛE T

[0150] Among them, the diagonal elements of the diagonal matrix Λ are the eigenvalues ​​of the covariance matrix S λ1≥λ2≥…≥λ p , the column vectors of the orthogonal matrix E are the corresponding unit orthogonal eigenvectors e1, e2,…, e p . Use numerical methods (such as Jacobi method, QR algorithm) to solve eigenvalues ​​and eigenvectors.

[0151] It should be noted that the eigenvalues ​​returned by NumPy for real symmetric matrices are in ascending order from small to large, and the order needs to be reversed to satisfy λ1≥λ2≥…≥λ p The eigenvectors of a real symmetric matrix are naturally orthogonal. and is a unit vector (‖e i‖ = 1), which can be verified by calculating the dot product using NumPy.

[0152] Step S23, dimensionality reduction processing: Select the eigenvectors e1, e2,..., e corresponding to the top k eigenvalues k as column vectors respectively to form the projection matrix P:

[0153] P = (e1, e2,..., e k )

[0154] where the value range of k is 1 ≤ k < p. Since at least 1 principal component must be retained and it must be less than the original feature number p to achieve the purpose of dimensionality reduction (if k = p, there is no dimensionality reduction). [[ID=一十四]] [[ID=一十五]]

[0155] [[ID=一十六]]When selecting the top k eigenvalues, ensure that the cumulative variance contribution rate is greater than or equal to the first preset threshold (in this embodiment, 85% is used, and it can also be changed to commonly used thresholds in the industry such as 90%, 95%, etc.). The formula for the cumulative variance contribution rate Cumulative Variance Ratio is: [[ID=一十七]] [[ID=一十八]]

[0156] [[ID=一十九]] [[ID=二十]] [[ID=二十一]]

[0157] [[ID=二十二]]In the formula, λ [[ID=二十三]] i [[ID=二十四]]is the i-th eigenvalue sorted from large to small. [[ID=二十五]] [[ID=二十六]]

[0158] [[ID=二十七]]When the cumulative variance contribution rate reaches the preset 85%, it is considered that the top k principal components have retained the main information of the original data and can be used as the "main meteorological features". In traditional methods, the principal components with eigenvalues ≥ 1 are often selected because the components with eigenvalues less than 1 carry less information than a single original feature. However, in practical applications, if the cumulative variance contribution rate of the principal components with eigenvalues ≥ 1 does not reach the threshold, additional subsequent principal components need to be supplemented until the threshold requirement is met. If the efficiency of the model is pursued, the threshold can be appropriately reduced (such as 80%) to reduce the value of k; if more detailed information needs to be retained, the threshold can be increased (such as 95%) to increase the value of k. Finally, the optimal k is determined through a scree plot or cross-validation to ensure that the data after dimensionality reduction can retain sufficient information and reduce redundancy. [[ID=二十八]] [[ID=二十九]]

[0159] [[ID=三十]]Project the matrix X of the measured data of the meteorological station [[ID=三十一]] * [[ID=三十二]]onto the low-dimensional space through the projection matrix P to obtain the principal component matrix Y: [[ID=三十三]] [[ID=三十四]]

[0160] [[ID=三十五]]Y = XP [[ID=三十六]] * [[ID=三十七]]P [[ID=三十八]] [[ID=三十九]]

[0161] [[ID=四十]]Finally, the top k main meteorological features are extracted. [[ID=四十一]] [[ID=四十二]]

[0162] Step S24, calculating the topographic index: For the digital elevation model data (topography) in the training dataset obtained in Step S1, use GIS software (such as ArcGIS) to calculate the topographic index to represent the impact of topography on precipitation. The formula is:

[0163]

[0164] In the formula, TI is the topographic index (TopographicIndex), a is the catchment area, and b is the slope.

[0165] Step S3, screening of key influencing factors:

[0166] Use the RandomForestClassifier class in the scikit-learn library to build a random forest model. Use the random forest algorithm to rank the importance of the multi-factor features extracted in Step S2. According to the ranking result of importance, select the features with higher importance scores as the key influencing factors of extreme rainstorm events. Specifically, it includes the following sub-steps:

[0167] Step S31, calculating the overall importance: First, use the random forest to build multiple decision trees to classify or regress the data. Each decision tree randomly selects a part of the samples and features for training. After training, evaluate its overall importance by calculating the average decrease in impurity (Gini index) of each feature in all decision trees.

[0168] Let the importance of feature j in the t-th decision tree be I j，t , and the formula for the overall importance of feature j is: [[ID=2%]]

[0169]

[0170] In the formula, I j is the overall importance of feature j, α is the number of decision trees, and I j，t is the importance of feature j in the t-th decision tree. [[ID=%%]]

[0171] Step S32, selecting the key influencing factors: Sort the multi-factor features extracted in Step S2 in descending order of overall importance, and select the top m features with higher importance scores as the key influencing factors of extreme rainstorm events.

[0172] Among them, the value range of m is 1 ≤ m < q, where q is the total number of multi-factor features extracted in Step S2; because at least 1 key influencing factor is retained and must be less than the total number of features q to achieve the screening purpose (if k = q, then there is no screening).

[0173] When selecting the top m features with higher overall importance, ensure that the cumulative importance is greater than or equal to a second preset threshold (such as 80%, 85% or 90%, 85% is used in this embodiment). The Cumulative Importance formula is:

[0174]

[0175] Where, I j is the overall importance of feature j sorted from largest to smallest.

[0176] When the cumulative importance reaches the preset 85%, the top m features are considered to have covered the key factors that have the greatest impact on extreme rainstorm events and can be used as input features for subsequent model training. It is also possible to set a minimum threshold for the importance score of a single feature (such as greater than 5%) and only select the top m features with an importance score above this threshold to avoid including features that have a weak contribution to the model. It is also possible to combine professional knowledge of extreme rainstorms in hilly areas to ensure that key geographical features such as the terrain index are included first. Even if their importance score is slightly lower, the value of m can be adjusted through manual intervention.

[0177] Alternatively, determine the optimal m through cross-validation or grid search: train and test the model for different values ​​of m (e.g., m = 5, 10, 15), and select the m that yields the highest prediction accuracy. Balance model complexity and generalization to avoid underfitting due to too few features and overfitting due to too many features.

[0178] Step S4, prediction model construction and training:

[0179] (1) The SVC class in the scikit-learn library, namely the support vector machine (SVM) algorithm, is used to build an extreme rainstorm event prediction model. The basic idea of ​​SVM is to find an optimal hyperplane in the feature space so that samples of different categories can be separated to the greatest extent. For the linearly separable case, the goal of SVM is to solve the following optimization problem:

[0180]

[0181] sty i (w T φ(x i )+b)≥1, i=1,2,…,n

[0182] Where w is the weight vector, b is the bias term, and x i is the input sample, φ(x i ) is a function that maps input samples to high-dimensional feature space, y i is the category label of the sample, y i ∈{-1, 1}.

[0183] For the case of linear inseparability, the slack variable ξ is introduced i ≥0 and penalty factor C, the optimization problem becomes:

[0184]

[0185] sty i (w T φ(x i )+b)≥1-ξ i ,ξ i ≥0, i=1, 2, …, n

[0186] Where, ξ i is the slack variable and C is the penalty factor.

[0187] (2) Use the key influencing factors of extreme rainstorm events screened in step S3 as the input features of the prediction model and "whether an extreme rainstorm event occurs" as the output label of the prediction model to train the prediction model. The specific process is:

[0188] During the training process, GridSearchCV is used to traverse the kernel function parameter combinations using grid search, and cross-validation (CV) is combined to optimize the model parameters to select the optimal penalty factor C and kernel function parameters (such as gamma, etc.).

[0189] Model training completion specifically includes the following criteria:

[0190] SVM finds the optimal hyperplane by solving a convex optimization problem. The core criterion for training completion is that the optimization algorithm meets the convergence condition: the objective function between adjacent iterations The change is less than the third preset threshold (10 in this embodiment) -6 ); The training samples meet the Karush-Kuhn-Tucker conditions, that is, the Lagrange multipliers of the support vectors are non-zero and the constraints of the non-support vectors are strictly satisfied.

[0191] Preset upper limit on the number of iterations: If the optimization algorithm does not converge within a fixed number of iterations (e.g., 1000), it is forced to stop to avoid infinite loops. This is set by the max_iter parameter of scikit-learn.

[0192] Stable performance on the test dataset: On the cross-validation or test dataset, if the model performance no longer improves after a certain number of consecutive rounds (such as 10 rounds), terminate the training early to prevent overfitting.

[0193] Parameter optimization is completed: when the optimal penalty factor C and kernel function parameters are found through grid search, and the solution of the model on the training set meets the constraints of the optimization problem (such as the slack variable constraint y in the case of linear inseparability), i (w T φ(x i )+b)≥1-ξ i ), the training is considered complete.

[0194] Step S5, prediction result evaluation:

[0195] The extreme rainstorm event prediction model trained in step S4 is evaluated using the test dataset obtained in step S1. The evaluation metrics used include accuracy, recall, precision, and F1-score to assess model performance. Accuracy represents the overall prediction accuracy, reflecting the model's ability to distinguish between extreme and non-extreme rainstorm events. Recall represents the model's ability to capture positive examples (i.e., extreme rainstorm events), preventing missed extreme rainstorm events (which can lead to missed disaster warnings and increased risk). Precision represents the reliability of positive predictions, reducing false positives (which can lead to excessive disaster prevention and increased social costs). The F1-score is a comprehensive metric that balances recall and precision, ensuring a balance between missed and false positives. Evaluation metrics are calculated using the classification_report function in the scikit-learn library.

[0196] The calculation formula for accuracy is:

[0197]

[0198] Where TP is the number of true positive examples (predicted to be positive and actually positive), TN is the number of true negative examples (predicted to be negative and actually negative), FP is the number of false positive examples (predicted to be positive but actually negative), and FN is the number of false negative examples (predicted to be negative but actually positive). The range of Accuracy is [0,1], where 0 means that the extreme rainstorm event prediction is completely wrong (all samples are misjudged), and 1 means that the extreme rainstorm event prediction is completely correct (no misjudgment).

[0199] The recall rate Recall is:

[0200]

[0201] Where Recall ranges from [0, 1], where 0 means that no positive examples are correctly identified (TP = 0, all positive examples are misclassified as negative examples), and 1 means that all positive examples are correctly identified (FN = 0, no missed examples).

[0202] The precision is:

[0203]

[0204] Wherein, the range of Precision is [0,1], 0 means that all predicted positive examples are false positives (TP=0, all predicted positive examples are negative examples), and 1 means that all predicted positive examples are correct (FP=0, no false positive examples).

[0205] The F1 value is:

[0206]

[0207] Wherein, F1 value represents the harmonic mean of Precision and Recall, indicating that the two indicators are equally important. Compared with the arithmetic mean, it is more sensitive to the imbalance between the two indicators. The range of F1 value is [0, 1], where 0 means that at least one of Precision and Recall is 0, and 1 means that both Precision and Recall are 1 (TP = 1, FP = 0, FN = 0).

[0208] All indicators have values ​​between 0 and 1, and the closer the value is to 1, the better the model performance:

[0209] Accuracy focuses on overall correctness and is suitable for scenarios with balanced classes. However, accuracy may be ineffective when data classes are imbalanced, such as when there are few samples of extreme rainstorm events. For example, if 95% of negative examples are predicted as negative, 95% accuracy is achieved, but recall is 0. In this case, recall, precision, and F1 score better reflect the model's predictive ability for positive examples.

[0210] Recall and precision respectively focus on the "capture ability" and "prediction reliability" of positive examples, and are suitable for the evaluation of extreme events (few positive examples).

[0211] The F1 value forces a balance between recall and precision, is suitable for scenarios with imbalanced categories, and can be used as a core evaluation metric for extreme rainstorm prediction.

[0212] Due to the high-risk characteristics of extreme rainstorms in hilly areas, we should focus on recall rate and F1 value to avoid missed judgments and maintain a comprehensive balance.

[0213] Example 2:

[0214] This embodiment is the application example data of embodiment 1:

[0215] The study area is Xingguo County, Ganzhou City, Jiangxi Province. The area has a typical red soil hilly landform with an average slope of 25° to 35°, an average annual precipitation of 1500 to 1800 mm, and extreme rainstorms (daily precipitation ≥ 100 mm) occurring 2 to 3 times a year. Historically, rainstorms have caused serious mountain torrents and mudslides.

[0216] Meteorological data collection: Hourly meteorological data (12 characteristics such as precipitation intensity, temperature, humidity, and wind speed) from 2015 to 2024 were collected from the Xingguo County Meteorological Station and ECMWF's ERA5 reanalysis data.

[0217] Outlier processing: Detect outliers in precipitation intensity. For example, if the precipitation intensity reaches 120 mm / h at a certain time in July 2023, which exceeds the dynamic threshold, it will be replaced with the 3-hour sliding window mean.

[0218] Topographic data collection and processing: 30m resolution digital elevation model (DEM) was used to extract three features, namely slope, aspect and altitude, and a composite terrain index was constructed in combination with land use types (forest land, cultivated land and water area).

[0219] Label data: 280 samples of extreme rainstorm events (daily precipitation ≥ 100 mm) are labeled, with 15% positive examples and class imbalance.

[0220] Dataset Partitioning and Simulated Data Augmentation: The dataset was split into training and test datasets in a 7:3 ratio, with the training dataset containing 196 samples and the test dataset containing 84 samples. 1,000 simulated extreme rainstorm events were then generated based on historical data. The model's generalization capabilities were enhanced by randomly perturbing precipitation intensity (±20%) and terrain parameters (slope ±5°).

[0221] Model construction, training, and parameter optimization: The radial basis function (RBF) kernel was selected as the kernel function of the SVM.

[0222] RBF kernel SVM parameter optimization: The grid search range is C = [0.1, 1, 10, 100], gamma = [0.001, 0.01, 0.1, 1]. The optimal parameters C = 10 and gamma = 0.01 were obtained through training, and the F1 value reached 0.85 through 5-fold cross-validation.

[0223] Comparative experiments revealed that the linear kernel SVM's performance was limited by the significant nonlinearity of the terrain, resulting in an F1 of 0.78. The polynomial kernel SVM, however, was prone to overfitting due to the high-order polynomials, resulting in an F1 of 0.80. The advantage of the RBF kernel SVM lies in its improved separability of complex terrain features through nonlinear mapping, resulting in stronger generalization capabilities on simulated data.

[0224] The model training is completed using the following criteria: the objective function value changes by less than 10% in 50 consecutive iterations. -6 , meeting the convergence conditions; the cross-validation F1 value fluctuation is less than 1%, and the accuracy of the training data set is stable at 93%. In addition, considering the actual business application, in terms of real-time inference efficiency, the single-sample prediction time is less than 0.1 seconds, meeting the real-time requirements of the early warning system.

[0225] Model evaluation results: In terms of test data set performance indicators, accuracy = 0.91, recall rate = 0.88, precision rate = 0.86, F1 = 0.87; significantly reducing the risk of missed judgments and the social costs caused by misjudgments, the overall performance is better than the traditional model.

[0226] Confusion matrix and error analysis: The confusion matrix is

[0227]

[0228] Missed detections (FN = 6) often occur in deep mountainous areas with complex terrain, such as Meijiao Town in Xingguo County, and require optimization based on satellite remote sensing data. Misjudged detections (FP = 5) are primarily due to short bursts of heavy rainfall (<3 hours) that do not meet the extreme criteria. This can be improved by extending the time window (e.g., 6 hours).

[0229] Compared with the existing system:

[0230] (1) In this embodiment, the evaluation index F1=0.87. The advantage lies in the strong nonlinear feature extraction capability, which reduces the missed detection rate by 40% compared with the traditional model, and the model size is less than 1MB, which can be run in real time on edge devices.

[0231] (2) The model of a water conservancy department has an evaluation index of F1 = 0.72. The model is based on linear regression and has poor adaptability to complex terrain and a high misjudgment rate.

[0232] (3) The Lingxi large model of a meteorological bureau has an evaluation index of F1=0.82 and an excellent score for heavy rainfall forecast during the flood season. However, it relies on cloud computing and requires high computing power support. The edge device deployment is difficult and costly, making it unsuitable for areas with weak networks.

[0233] Finally, it should be noted that the above is only used to illustrate the technical solution of the present invention and is not limiting. Although the present invention has been described in detail with reference to the preferred solution, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the solution of the present invention.

Claims

1. A method for predicting and analyzing extreme rainstorm events in hilly areas based on multi-factor coupling, characterized by: It includes the following steps: Step S1, data collection and preprocessing: Collect the ERA5 dataset of the European Centre for Medium-Range Weather Forecasts, the measured data of meteorological stations within the study area, and the DEM digital elevation model data reflecting the topographic and geomorphic characteristics of the study area; perform preprocessing on the collected data, including quality control and standardization processing. The quality control includes using a hybrid strategy of a spatio-temporal coupled dynamic threshold method + multivariate joint test to remove outliers and fill missing values, and dividing the preprocessed data into a training dataset and a test dataset; Step S2, multi-factor feature extraction: Use the principal component analysis method for dimensionality reduction processing, extract the main meteorological features, and calculate the topographic index to represent the impact of topography on precipitation; Step S3, screening of key influencing factors: Use the random forest algorithm to rank the importance of the extracted multi-factor features, and select the features with higher importance scores as the key influencing factors of extreme rainstorm events; Step S4, prediction model construction and training: Use the support vector machine algorithm to construct a prediction model for extreme rainstorm events; use the key influencing factors of extreme rainstorm events selected as the input features of the prediction model, and "whether an extreme rainstorm event occurs" as the output label of the prediction model, and train the prediction model until the model training is completed; Step S5, prediction result evaluation: Use the test dataset described in Step S1 to evaluate the prediction model for extreme rainstorm events trained in Step S4. The evaluation indicators include accuracy, recall rate, precision rate, and the comprehensive index F1 value that balances the recall rate and precision rate.

2. The method for predicting and analyzing extreme rainstorm events in hilly areas based on multi-factor coupling according to claim 1 is characterized in that: The specific steps for removing outliers in Step S1 include: The first step is to detect the dynamic threshold value of single variable space-time: construct a space-time sliding window for each meteorological variable and calculate the dynamic threshold Q upper (t, s): Where Q 75 (t, s) is the 75th percentile in the spatiotemporal window, IQR(t, s) is the interquartile range, IQR(t, s) = Q 75 (t, s)-Q 25 (t, s), Q 25 (t, s) is the 25th percentile in the spatiotemporal window; Δh is the mean elevation difference between the weather station and its neighbors, h ref is the reference elevation parameter, (h) is the terrain adjustment factor, h is the elevation of the weather station, and h me)m is the average elevation of the study area, σ h is the elevation standard deviation; For suspected outliers exceeding the threshold, the time series curvature Verification, the formula is: If the following conditions are met, it is determined as an outlier: Where t is the time step at the current moment, x t is the observed value of the meteorological variable at time t, x t+1 is the observation value of the next time step after time t, x t-1 is the observation value of the previous time step before time t, is the standard deviation of curvature, is the seasonal mean; The second step is multivariate joint anomaly detection: calculating the multivariate Mahalanobis distance D M : In the formula, X is the multivariate observation vector, μ is the mean vector, T is the transpose operator of the matrix or vector, and Σ is the covariance matrix; Introducing terrain weight correction threshold D threshold : Where V is the number of variables, is the 99% quantile of the chi-square distribution with degrees of freedom V, TI is the terrain index of the current point, TI m)x is the maximum topographic index of the study area, a is the catchment area, and b is the slope; If D is satisfied M >D threshold It is determined to be a multivariate coupling outlier; The third step is to verify the spatiotemporal density clustering: calculate the composite spatiotemporal distance metric d st : Where, d sp)ce is the spatial Euclidean distance, d time is the time interval, d m)x is the maximum Euclidean distance between all pairs of spatial points in the study area, ΔT m)x is the maximum time span within the study time range, Corr(X, Y) is the Pearson correlation coefficient of the variable trend, α, β, and γ are adjustable weight coefficients, α+β+γ=1; Calculate the adaptive density parameter: ∈=μ d +2s d Where ∈ is the neighborhood radius, μ d is the mean of the distance distribution, σ d is the distance standard deviation, MinPts is the minimum number of cluster points, N total is the total number of samples; If the data sample point does not belong to any density cluster and is not covered by more than 80% of the neighboring points, it is determined as an outlier; The fourth step is physical mechanism inversion verification: water vapor flux is measured for the outliers to be removed. Verification, the formula is: If the following conditions are met, it is determined as a real extreme event and the data is retained: Where Q 95 is the 95th percentile of the historical extreme value in the study area, q is the specific humidity, that is, the mass of water vapor per unit mass of wet air, is the three-dimensional wind speed vector, x is the east-west direction, y is the north-south direction, z is the vertical direction, u is the east-west wind speed, east is positive, v is the north-south wind speed, north is positive, and w is the vertical wind speed, upward is positive.

3. The method for predicting and analyzing extreme rainstorm events in hilly areas based on multi-factor coupling according to claim 1 is characterized in that: The filling of missing values ​​in step S1 is specifically: using linear interpolation to fill the missing values, assuming that the original data sequence is x1, x2, ..., x m , the linear interpolation formula is: Where x i is a missing value, x i-k is x i The previous adjacent valid data, x i+l is x i The adjacent valid data after that, k and l are the valid data from the missing value position i to the previous adjacent valid data x i-k , the next adjacent valid data x i+l The number of intervals.

4. The method for predicting and analyzing extreme rainstorm events in hilly areas based on multi-factor coupling according to claim 1 is characterized in that: The specific standardization processing in Step S1 is: Convert the values of each variable into a standard normal distribution with a mean of 0 and a standard deviation of 1 to eliminate the influence of different variable dimensions. The standardization processing formula is: Where, is the standardized value of the jth variable value of the i-th sample, x ij is the j-th variable value of the i-th sample, is the mean of the jth variable, s j is the standard deviation of the j-th variable.

5. The method for predicting and analyzing extreme rainstorm events in hilly areas based on multi-factor coupling according to claim 1 is characterized in that: The specific multi-factor feature extraction in Step S2 includes the following sub-steps: Step S21, calculate the covariance matrix S: Assume that the measured data of the weather station of the training data set in step S1 is an n×p data matrix X * , where n is the number of samples and p is the total number of meteorological characteristics; the calculated X * Covariance matrix S: Where T is the transpose operator of the matrix or vector, X *T For X * The transposed matrix of , the covariance matrix S is a real symmetric matrix of p×p; Step S22, eigenvalue decomposition: For the covariance matrix S obtained in Step S21, there exist an orthogonal matrix E and a diagonal matrix Λ such that: S=EΛE T Among them, the diagonal elements of the diagonal matrix Λ are the eigenvalues ​​of the covariance matrix S λ1≥λ2≥…≥λ p , the column vectors of the orthogonal matrix E are the corresponding unit orthogonal eigenvectors e1, e2,…, e p ; Step S23, dimensionality reduction processing: select the eigenvectors e1, e2, ..., e corresponding to the first k eigenvalues k As column vectors, they constitute the projection matrix P: P=(e1,e2,…,e k ) where the value range of k is 1 ≤ k < p; when selecting the first k eigenvalues, ensure that the cumulative variance contribution rate is greater than or equal to the first preset threshold. The formula for the cumulative variance contribution rate Cumulative Variance Ratio is: Where λ i is the i-th eigenvalue sorted from large to small; The matrix X of the weather station measured data of the training data set in step S1 is transformed by the projection matrix P * Projecting into low-dimensional space yields the principal component matrix Y: Y=X * P Finally, extract the first k main meteorological features; Step S24, calculate the topographic index: Calculate the topographic index TI for the digital elevation model data of the training dataset in Step S1: In the formula, a is the catchment area and b is the slope.

6. The method for predicting and analyzing extreme rainstorm events in hilly areas based on multi-factor coupling according to claim 1 is characterized in that: The specific screening of key influencing factors in Step S3 includes the following sub-steps: Step S31, calculate the overall importance: first use random forest to build multiple decision trees to classify or regress the data, each decision tree randomly selects a part of samples and features for training, after the training is completed, the overall importance of each feature is evaluated by calculating the average impurity reduction of all decision trees, and the importance of feature j in the tth decision tree is set to I j，t , the overall importance of feature j is calculated as: Where, I j is the overall importance of feature j, α is the number of decision trees, I j，t is the importance of feature j in the t-th decision tree; Step S32, select key influencing factors: Sort the multi-factor features extracted in Step S2 in descending order of overall importance, and select the top m features with higher overall importance as the key influencing factors for extreme rainstorm events; where the value range of m is 1 ≤ m < q, and q is the total number of multi-factor features extracted in Step S2; When selecting the top m features with higher overall importance, ensure that the cumulative importance is greater than or equal to the second preset threshold. The formula for cumulative importance CumulativeImportance is: Where, I j is the overall importance of feature j sorted from largest to smallest.

7. The method for predicting and analyzing extreme rainstorm events in hilly areas based on multi-factor coupling according to claim 1 is characterized in that: The specific support vector machine algorithm described in Step S4 is: For the linearly separable case, the formula for the support vector machine to solve the optimization problem is: s.t.y i (w T φ(x i )+b)≥1,i=1,2,…,n Where w is the weight vector, b is the bias term, and x i is the input sample, φ(x i ) is a function that maps input samples to high-dimensional feature space, y i is the category label of the sample, y i ∈{-1, 1}; For the linearly inseparable case, the formula for the support vector machine to solve the optimization problem is: style i (w T φ(x i )+b)≥1-ξ i ,x i ≥0, i=1, 2,…, n Where, ξ i is the slack variable and C is the penalty factor.

8. The method for predicting and analyzing extreme rainstorm events in hilly areas based on multi-factor coupling according to claim 1 is characterized in that: The specific process of training the prediction model until the model training is completed described in Step S4 is: During the training process, use grid search to traverse the combination of kernel function parameters, optimize the model parameters in combination with cross-validation, and select the optimal penalty factor C and kernel function parameters; The completion of the model training specifically includes the following criteria: The optimization algorithm meets the convergence condition: The change in the objective function between adjacent iterations is less than the third preset threshold; The training samples meet the Karush-Kuhn-Tucker conditions; Preset the upper limit of the number of iterations: If the optimization algorithm does not converge within a fixed number of iterations, stop it forcibly to avoid infinite loops; The performance of the test data set is stable: On the cross-validation or the test data set, if the model performance does not improve after a continuous specific number of rounds, terminate the training in advance to prevent overfitting; The parameter optimization is completed: When the optimal penalty factor C and kernel function parameters are found through grid search, and the solution of the model on the training set satisfies the constraints of the optimization problem, it is regarded as the training is completed.

9. The method for predicting and analyzing extreme rainstorm events in hilly areas based on multi-factor coupling according to claim 1, characterized in that: The calculation formula for the accuracy Accuracy described in Step S5 is: In the formula, TP is the number of true positives, TN is the number of true negatives, FP is the number of false positives, and FN is the number of false negatives; The range of Accuracy is [0, 1], 0 indicates that the prediction of extreme rainstorm events is completely wrong, and 1 indicates that the prediction of extreme rainstorm events is completely correct.

10. The method for predicting and analyzing extreme rainstorm events in hilly areas based on multi-factor coupling according to claim 1, characterized in that: The F1 value described in Step S5 is: In the formula, the F1 value represents the harmonic mean of the two indicators Precision and Recall, indicating that the two indicators are equally important; The range of the F1 value is [0, 1], 0 indicates that at least one of Precision and Recall is 0, and 1 indicates that both Precision and Recall are 1.

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