Precipitation forecasting method based on Shearlet and L-PWC

Abstract

The invention discloses a precipitation forecasting method based on Shearlet and L-PWC, the precipitation forecasting method is decomposed into a global space, a local space and a time angle, the time feature extraction effect is improved through the consistency evaluation of a reverse optical flow graph and a forward optical flow graph, the decomposition of a picture in a frequency domain is guided by using an optical flow with higher precision, and the time feature extraction efficiency is improved. Feature extraction is carried out on different frequency domains to obtain information to guide directional learning of multi-head attention, and more comprehensive global features are generated through assistance of other frequency band features. Extraction of local space information is guided by time information, feature enhancement of key information is completed, future weather is predicted through gradient decomposition of optical flow and time dependence before and after, and a litsea rotundifolia optimization algorithm is optimized through an ant colony algorithm, so that the algorithm can search for an optimal solution in a wider space, and the optimal solution is obtained. And the possibility that the algorithm falls into local optimum is greatly reduced, so that the ability of the model to deal with complex weather is improved.

Description

Technical Field

[0001] The present invention relates to a precipitation forecasting method based on Shearlet and L - PWC, belonging to the technical field of meteorological precipitation prediction. Background Art

[0002] Precipitation prediction has become increasingly important against the backdrop of frequent global climate change and extreme weather events. However, the complexity and uncertainty of the global climate system pose many challenges to precipitation prediction. In particular, for extreme precipitation events caused by climate change, such as the increasing frequency and intensity of rainstorms, floods, and droughts, traditional prediction methods are difficult to meet the actual needs.

[0003] Traditional numerical weather prediction models face problems with imperfect parameterization schemes in simulating precipitation processes. The cloud microphysical processes, turbulence, and convective activities in the atmosphere are complex and variable, making it difficult to accurately describe them with simple mathematical formulas. The approximation and simplification in the models may lead to biases in predicting precipitation intensity and location. In the face of extreme precipitation events, it is difficult to provide accurate early warning information in a timely manner.

[0004] To improve the accuracy of precipitation prediction, in recent years, artificial intelligence and deep learning technologies have gradually been applied to the meteorological field. By learning a large amount of historical meteorological data, these methods can capture potential patterns that are difficult to discover by traditional models, especially having advantages in processing non - linear and high - dimensional data. For example, the successful application of convolutional neural networks (CNNs) in the field of image processing provides new ideas for the analysis of meteorological image data. By extracting and fusing multi - scale features of meteorological images, the spatial and temporal features of precipitation systems can be captured more comprehensively.

[0005] The application of emerging technologies has brought new opportunities for precipitation prediction. High - spatiotemporal - resolution precipitation observation networks can be constructed through deep learning and machine learning. These models, to a certain extent, make up for the deficiencies of physical models and improve the accuracy and efficiency of prediction. However, the prediction ability for extreme events still needs to be improved; in addition, how to effectively process massive data, avoid overfitting, and improve the generalization ability of the models are also problems that need to be solved. Summary of the Invention

[0006] The technical problem to be solved by the present invention is: to provide a precipitation forecasting method based on Shearlet and L - PWC, which improves the accuracy of precipitation prediction caused by climate change.

[0007] The present invention adopts the following technical solutions to solve the above - mentioned technical problems:

[0008] A precipitation forecasting method based on Shearlet and L - PWC, comprising the following steps:

[0009] Step 1: Obtain a meteorological radar precipitation image dataset, preprocess the obtained dataset, and divide the preprocessed dataset into a training set and a validation set; construct a precipitation forecasting model, including an optical flow estimation network PWC-net, a long short-term memory neural network LSTM, a Transformer network, and a Densenet network;

[0010] Step 2: For the training set, use the optical flow estimation network PWC-net to generate an initial optical flow map for two adjacent frames of images and then refine it three times to obtain a high-resolution optical flow map; use the long short-term memory neural network LSTM to extract the temporal features of the radar precipitation images from the high-resolution optical flow map;

[0011] Step 3: Use Karcher mean calculation and weighted principal component analysis to analyze the motion direction of the initial optical flow map to obtain the motion direction; perform Shearlet transform on each frame of the image in the training set to obtain multiple high-frequency feature maps in different directions and a low-frequency feature map, and find the main direction high-frequency feature map a with the highest correlation with the motion direction from the multiple high-frequency feature maps in different directions; perform Shearlet transform on a again to find the main direction high-frequency feature map b with the highest correlation with the motion direction, and fuse a and b to obtain the main direction high-frequency feature map c;

[0012] Step 4: Use the Transformer network to extract the global spatial features of the radar precipitation images from the main direction high-frequency feature map c, the high-frequency feature maps in the remaining directions obtained from the first Shearlet transform, and the low-frequency feature map; use the Densenet network to extract the local spatial features of the radar precipitation images from two adjacent frames of the training set;

[0013] Step 5: Fuse the global spatial features and local spatial features of the radar precipitation images to obtain the fused spatial features, and fuse the fused spatial features with the temporal features of the radar precipitation images to obtain the spatio-temporal features, that is, the radar precipitation prediction images;

[0014] Step 6: Use the golden jackal optimization algorithm to optimize the hyperparameters in the precipitation forecasting model to obtain the optimal hyperparameters; based on the optimal hyperparameters, use the training set and the validation set to train the weights of the precipitation forecasting model to obtain the optimal weights, thereby obtaining the trained precipitation forecasting model;

[0015] Step 7: Input the current radar meteorological radar precipitation image into the trained precipitation forecasting model to obtain the future precipitation forecasting image, and obtain the future precipitation amount according to the precipitation forecasting image.

[0016] Compared with the prior art, the present invention adopts the above technical solutions and has the following technical effects:

[0017] The present invention decomposes the precipitation prediction method into the global space, local space, and time perspective, improves the effect of time feature extraction through the consistency evaluation of the backward optical flow map and the forward optical flow map, uses optical flow with higher precision to guide the decomposition of pictures in the frequency domain, performs feature extraction on different frequency domains to obtain information to guide the directional learning of multi-head attention, and generates more comprehensive global features through the assistance of features in other frequency bands. The extraction of local space information is guided by time information to complete the feature enhancement of key information, predicts future weather through the gradient decomposition of optical flow and the time dependence before and after, and optimizes the golden jackal optimization algorithm through the ant colony algorithm, enabling the algorithm to search for the optimal solution in a broader space and greatly reducing the possibility of the algorithm falling into local optima, thereby improving the model's ability to handle complex weather. Brief Description of the Drawings

[0018] Figure 1 is the flowchart of the precipitation prediction method based on Shearlet and L-PWC of the present invention;

[0019] Figure 2 is the working flowchart of the precipitation prediction method of the present invention;

[0020] Figure 3 is the flowchart of extracting time features using PWC-net of the present invention;

[0021] Figure 4 is the flowchart of generating multi-directional frequency bands based on Shearlet transform in the present invention;

[0022] Figure 5 is the flowchart of improving the Transformer network to extract global features of the present invention;

[0023] Figure 6 is the flowchart of extracting local features using the improved Densenet network of the present invention;

[0024] Figure 7 is the flowchart of the block layer in the improved Densenet network of the present invention;

[0025] Figure 8 is the flowchart of the DTRP module for fusing features constructed by the present invention;

[0026] Figure 9 is the flowchart of the optimized golden jackal optimization algorithm of the present invention. Detailed Embodiment

[0027] The following details the embodiments of the present invention, and the examples of the embodiments are shown in the drawings. The embodiments described below with reference to the drawings are exemplary and are only used to explain the present invention and should not be construed as limiting the present invention.

[0028] As Figure 1 and Figure 2 shown, the present invention proposes a precipitation prediction method based on Shearlet and L-PWC, and the specific steps are as follows:

[0029] Step 1: Obtain the meteorological radar precipitation image dataset and preprocess the collected dataset

[0030] The meteorological radar image dataset records the radar echo reflectivity information in each time series and is stored in a three-dimensional data form. Each dimension corresponds to the time series, horizontal coordinate, and vertical coordinate respectively. In order to further process these data and ensure consistency in space and time, it is first necessary to perform two-dimensional plane extraction on the pixel data of each frame (i.e., a single moment in the time series). On this basis, the data is converted into a matrix form in the plane coordinate system, denoted as R * , making it more convenient and efficient to process the subsequent initialization dataset.

[0031] Define a minimum echo reflectivity threshold T dBZ = 10 dBZ, compare the echo reflectivity value of each pixel in each image of the meteorological radar image dataset with the preset minimum threshold. When the reflectivity values of all pixels in the image are lower than this threshold, it is considered that there is no significant precipitation in this image, and it is excluded.

[0032] To further ensure that the proportion of the effective precipitation area is sufficient, calculate the area of the images screened by the threshold. By summing the number of pixels with reflectivity values greater than T dBZ , obtain the precipitation area A rain , and calculate its proportion in the image. When the precipitation area A rain is less than 5% of the total pixel area A total of the image, it is regarded as an invalid precipitation image and excluded. The calculation formula is:

[0033]

[0034] where x represents the pixel in the horizontal direction, y represents the pixel in the vertical direction, and R (x,y) represents the echo reflectivity value of the pixel (x, y). If A rain < 0.05A total , then exclude this image.

[0035] Mark the positions of the missing pixel points in the image, denoted as (x i , y j ). Obtain the four pixel points adjacent to the missing point, obtain the pixel points at the four corners adjacent to the missing point, and fill the missing values through bilinear interpolation. The corresponding echo reflectivity values are The formula is:

[0036]

[0037] Among them, represents the relative position of x i at x i-1 and x i+1 between them; represents the relative position of y j at y j-1 and y j+1 between them.

[0038] Finally, the preprocessed dataset is divided. 80% of the dataset is the training set, and 20% of the dataset is the validation set.

[0039] Step 2: Construct the temporal precipitation prediction model L-PWC network to extract the motion information between radar images

[0040] Construct the temporal feature extraction module PWC-net, perform multiple feature extractions and downsamplings on two consecutive frames of pictures simultaneously to obtain feature maps with different resolutions, form a feature pyramid, then form forward and backward optical flows through image warping and convolutional networks, use deconvolution to improve the resolution of the optical flow map and correct the optical flow direction, and finally generate a temporal feature map with temporal information.

[0041] As Figure 3 shown, denote one of the preprocessed pictures and the previous picture as B and A, and perform 4 consecutive feature extractions in parallel. The steps are to obtain the feature maps A 1 and ρ 1 by passing picture A and picture B through 3×3 convolution, relu activation function, and 2-fold downsampling respectively; perform 3×3 convolution, relu activation function, and 2-fold downsampling on A 1 and B 1 to generate the feature maps A 2 and B 2 , and so on to obtain the feature maps A 1 , A 2 , A 3 , A 4 and the picture B 1 , B 2 , B 3 , B 4 . Use the consecutive frame pictures A 4 and B 4 with the lowest resolution to perform splicing on the channels, and obtain the initial optical flow map d 4 through 3×3 convolution operation.

[0042] Picture B 3 and the optical flow d 4 are warped to generate picture B ′ 3, and enhance the optical flow d through depthwise separable transposed convolution 4 Obtain the optical flow d by increasing the image resolution ′ 4 , put Figure A 3 , B ′ 3 and d ′ 4 Concatenate them in the channel dimension and enter a 3×3 convolution to obtain the forward optical flow map d ′ 3 ; meanwhile, Figure A 3 Generate Figure A ′ 3 by warping according to the optical flow d ′ 3 , put Figure A ′ 3 , B 3 and d ′ 3 Concatenate them in the channel dimension to generate the backward optical flow map g 3 . Check the consistency of the forward and backward optical flow maps and construct a loss function. The regressed optical flow gradually improves the accuracy of optical flow estimation. After 3 times of optical flow refinement, finally obtain the high-resolution optical flow map d 1 . The formula is expressed as:

[0043]

[0044] B′ 3 = Warp(B 3 , d 4 )

[0045] A′ 3 = Warp(A 3 , d 4 )

[0046] where (x, y) represents the position of the pixel, p and q are the coordinates of the convolution kernel, e represents the index of the channel, Y represents the feature map, d represents depthwise separable transposed convolution, K d represents the convolution kernel of depthwise separable transposed convolution, and W e represents the convolution kernel of pointwise convolution, usually a 1×1 convolution kernel. (dx, dy) represents the optical flow displacement, and Warp represents image warping.

[0047] Putting two frames of images into the PWC-net network will finally generate a high-resolution optical flow map, namely d 1 . For each pixel point, calculate the gradient of the optical flow map, normalize the gradient, reduce the dynamic range difference between different images, set the segmentation threshold set. Assuming the segmentation is into H + 1 regions, then each particle will contain H thresholds. The thresholds of each particle will update the position according to the velocity.

[0048] Define a particle as a possible combination of thresholds, randomly assign an initial value within the defined range for each parameter of each particle, initialize the velocity for each particle, and randomly set an initial value for each component of the velocity vector, representing the step size of adjustment for each parameter. The fitness of each particle is evaluated by running the Golden Jackal Optimization Algorithm under this parameter combination and measuring its effect in the optimization task. Each particle records the best parameter combination it has found so far, that is, the combination with the maximum fitness value. The particle velocity update formula is as follows:

[0049]

[0050] where, is the velocity of particle i at the (t + 1)-th iteration, ω is the inertia weight, usually set between [0.4, 0.9], e 1 and e 2 are learning factors, usually taking the value of 2, used to control the speed at which the particle approaches the individual best and the global best, r 1 and r 2 are random numbers in the interval [0, 1], increasing the randomness of the velocity, p best,i is the historical best position recorded by particle i, p best,global is the global best position.

[0051] After the particle swarm optimization is completed, select the set of thresholds corresponding to the global optimal solution as the final segmentation threshold. Segment the gradient of the optical flow map according to these thresholds to obtain the optical flow map with H velocity levels. Set 15 groups of parameters, and weighted-fuse the optical flow features of the current frame's velocity levels into 15 optical flow maps.

[0052] Construct a 3-layer LSTM network for time series modeling to establish the long-term dependence of sequential data. Concatenate these 15 optical flow maps and send the concatenated sequence into the first layer of the LSTM network to generate the hidden state at the current time step and the memory cell The LSTM cell includes a forget gate that determines the proportion of memory to be forgotten from the previous moment, an input gate that determines the proportion of input information at the current moment, a candidate memory cell that activates the proportion of input information, an output gate that determines the proportion of the current hidden state to be output, and finally updates the memory cell of the LSTM to generate a new hidden state. The second layer of the LSTM receives the hidden state output by the first layer of the LSTM as input and outputs The third layer of the LSTM receives the output of the second layer as input and performs the same operations as the previous two layers, outputting The formula is:

[0053]

[0054] Among them, represents the hidden state of the k-th layer of LSTM at the previous time step, respectively represent the weight matrix and bias term of the forget gate in the k-th layer of LSTM, σ(·) represents the sigmoid activation function, and tanh(·) represents the tanh activation function. represents the output of the forget gate in the k-th layer of LSTM, is the candidate memory cell, is the output gate, represents the updated memory cell of the k-th layer of LSTM, represents the new hidden state of the k-th layer of LSTM. The 15 groups of parameters are gradually refined, and finally the time feature map is output.

[0055] Step 3: Extract the main motion information of the low-resolution optical flow map through Karcher mean and weighted PCA, and perform Shearlet transform on the image to generate multi-directional frequency bands

[0056] Perform principal direction analysis on the optical flow map d 4 The optical flow map is stored as a three-dimensional array or tensor, where: the first and second dimensions represent the pixel positions of the image, and the third dimension represents the two components of the optical flow: the horizontal displacement u and the vertical displacement v. u and v represent the displacement amounts of the pixel in the horizontal and vertical directions, respectively. A positive value indicates a rightward movement, and a negative value indicates a leftward movement. The horizontal and vertical displacements (u, v) together form the displacement vector of the pixel.

[0057] Construct a direction vector matrix and store the optical flow vectors of each valid motion pixel in the matrix X:

[0058]

[0059] Introduce Karcher mean calculation here, and normalize the optical flow vectors (u l , v l ) to retain only the direction information:

[0060]

[0061] Calculate the Karcher mean as the preliminary main motion direction, and use an iterative method to gradually converge to the Karcher mean:

[0062]

[0063] The finally converged represents the geometric mean of all direction vectors.

[0064] Through Karcher mean calculation, the directional data suitable for non-linear distribution can capture the overall trend in all directions. Combining with weighted principal component analysis, focusing on the main directions with strong movement amplitude, the main direction of movement can be better obtained. Therefore, a weighted covariance matrix is constructed:

[0065]

[0066] where S is the weighted covariance matrix, is the weighted mean, and w l is the magnitude of the displacement vector.

[0067] Through eigenvalue decomposition, the weighted covariance matrix S is expressed as the product of eigenvalues and eigenvectors:

[0068] S·z = λ·z

[0069] where λ is the eigenvalue of the covariance matrix and z is the corresponding eigenvector. Select the largest eigenvalue among them to represent the direction with the largest variance in the data, that is, the main movement direction is denoted as z max .

[0070] Finally, the Karcher mean and the weighted PCA results are combined, and the Karcher mean direction x karcher and the weighted PCA principal component direction x pca are weighted and fused:

[0071] x final = ∈·x karcher +(1 - ∈)·x pca

[0072] where the Karcher mean is a unit vector and ∈ is a tuning parameter.

[0073] As Figure 4 shown, the preprocessed image is subjected to multi-directional Shearlet transform. The input image is f(x, y), where x and y are the spatial coordinates of the image. The Shearlet decomposition of f(x, y) includes high-frequency features in multiple directions and a low-frequency component representing the image contour. Each high-frequency component corresponds to a Shearlet basis function ψ δ,θ (x, y). The Shearlet basis function analyzes the features at different positions in the image through the translation parameter, and rotates the basis function to a specific direction to obtain the high-frequency component in the corresponding direction.

[0074] The decomposition formula is:

[0075]

[0076] Among them, g represents the decomposition scale, which controls the level of detail of decomposition. Here, the decomposition is one layer, generally set to 1, and δ=(δ 1 ,δ 2 ) is the translation parameter, indicating the position of the basis function in the image; θ represents the direction, which controls the directionality of the Shearlet basis function and indicates the position of the basis function in the image; ψ is the mother wavelet function, which is the original function for generating the Shearlet basis; L(x, y) represents the low-frequency component, indicating the texture features of the original image; ∑ δ ∑ θ ψ δ,θ (x, y) represents the sum of all high-frequency components.

[0077] By obtaining the high-frequency components in the direction of the basis function, and then according to the known motion direction θ 0 , to ensure that the decomposition focuses on the motion direction θ 0 , calculate the angle difference between each decomposition direction and θ 0 , and select the decomposition direction θ 0 that is closest to the motion direction θ 1 . Then, use the Shearlet transform for multi-level decomposition (set a separate g = 2 or 3 to generate frequency band features) to generate more detailed scale information, thereby amplifying the edge and texture features in the direction of θ 1 . For other direction components, keep the number of decomposition layers unchanged. At the same time, the high-frequency band image represented by θ 1 is passed through multiple layers of convolution as the hidden layer of the LSTM.

[0078] Step 4: Construct spatial predicted precipitation, including a Densenet network and a Transformer network. The Densenet network extracts the local spatial information of the radar precipitation image, and the Transformer network extracts the global spatial information of the radar precipitation image

[0079] As Figure 5 shown, for the high-frequency band image in the main direction, use the deep residual network I-Resnet. First, perform a 5×5 convolution on the image for initial feature extraction, then use a 3×3 pooling layer with a stride of 2 to reduce the size of the feature map. Subsequently, enter a residual block containing a 1×1 convolution and a 3×3 convolution, and add a ReLU activation function between the convolutional layers. The skip connection in the residual block directly adds the input to the output to maintain the initial feature information. Finally, perform average pooling on the output to further compress the feature dimension. The high-frequency band image in the main direction is passed through the SE channel attention mechanism to increase the weight of the main direction features.

[0080] For high-frequency images in the remaining directions, the lightweight network MobileNet is used. First, it enters a 3×3 convolutional layer with a stride of 2 to extract low-level features. Subsequently, it enters the first inverted residual block, which contains a 1×1 convolution with an expansion rate of 3 to increase the number of channels, a 3×3 ordinary convolution to extract features, and another 1×1 convolution to compress the number of channels. ReLU activation is added after each layer. Finally, average pooling is performed to further compress the feature dimension.

[0081] The main direction features and other direction features are concatenated and divided into small blocks of the same size. Each block is flattened into a one-dimensional vector and mapped to the embedding dimension through a linear projection. Position encoding and direction encoding are performed on the segmented small blocks:

[0082]

[0083] I d = Shearlet(θ d )

[0084] where p and d represent the indices of position and direction respectively, that is, a position and a direction in the sequence, represents the dimension index of the position, represents the total dimension of the position.

[0085] The position encoding and direction encoding undergo linear transformation to generate query (Query), key (Key), and value (Value) matrices. These matrices are respectively input into multiple attention heads for processing. For each attention head, the query and key matrices calculate the similarity between spatial positions through dot product operation. Then, the similarity results are scaled and normalized by Softmax to obtain attention weights. Then, the attention weights are applied to the value matrix to achieve weighted summation and generate the output of each attention head. The outputs of these different attention heads are concatenated in the channel dimension to form the aggregated result of multi-head attention.

[0086] Due to the weighting of the SE module, the main direction features will obtain higher attention values in this process, making the weight of the main direction higher. The specific implementation is that in each layer of attention calculation, the Query vector of the main direction obtains a higher weight, so as to ensure the dominant position of the main direction features in the fusion.

[0087] 1×1, 2×2, 3×3, and 6×6 pooling operations are applied to the fused features to generate four feature maps of different scales. Each pooling result is upsampled to the same spatial size as the fused feature map, and then all scale features are concatenated in the channel dimension to obtain multi-scale fused features. The multi-scale fused features and the low-frequency components are concatenated and then integrated through a 3×3 convolutional layer. The integrated features are passed through global average pooling to generate the final global features.

[0088] In Figure 6 , the radar images of the current frame and the previous frame are respectively fed into the Densenet network. The Densenet network includes block layers and transition layers. In Figure 7 , there are 3 cascaded convolutional layers in each block layer. In each convolutional layer, the input features are first normalized using the BN layer and the relu activation function. The 1×1 convolution is used to adjust the number of channels, and the 3×3 depthwise separable convolution is used to extract features. Among them, the high-frequency map representing the motion direction after shearlet decomposition is downsampled and concatenated and fused in the first dense connection block. And each subsequent convolutional layer will receive the output of each previous convolutional layer to form dense connections. After the output, it immediately enters the transition layer. In the transition layer, after the 1×1 convolution, global average pooling is performed on each channel to obtain the global information of the channel. The pooled features are input into the first fully connected layer to compress the feature dimension, and then the feature dimension is restored through the second fully connected layer. Then, the channel weights are normalized through the Sigmoid activation, and each channel is weighted, and finally the feature map is output. At the same time, after the output of the first block layer of the previous frame image, optical flow warping is performed according to the optical flow with the highest resolution, and the warped features are weighted and fused with the features of the current frame in the channel dimension before the transition layer, and finally a local spatial feature map containing picture detail information is generated.

[0089] Step 5: Fuse the local spatial features and the global spatial features in the DTRP module, and then fuse the fused features with the temporal features in the DTRP module to obtain spatio-temporal features

[0090] Construct a feature fusion module, the DTRP module. The local feature map and the global feature map are feature-fused in the DTRP module and then feature-fused with the temporal feature map in the DTRP module to form a future radar precipitation prediction image.

[0091] As Figure 8 shown, according to the cross-attention mechanism, the features with global information are mapped to the query Q (Query) after the 1×1 convolution, and the features with local information are regarded as the key K (Key) and the value V (Value) after the 1×1 convolution.

[0092] Combined with the feature distillation module, the local features are gated and guided into the global features, and the local feature B′ is further weighted and integrated into the global feature A′ to generate Q 0 , enhancing the attention to details. The global features are passed to the local features, and after guiding the selective attention of the local information, K 0 is generated. According to the generated interaction features, through the attention weight Attention(Q 0 ,K 0) is guided by and fused after training:

[0093] L 0 = ||Q - K|| 2

[0094] Q 0 = Q + α 0 ·L 0 ·σ(K)

[0095] K 0 = K + β 0 ·L 0 ·σ(Q 0 )

[0096] O = Attention(Q 0 , K 0 )V

[0097]

[0098] where Q = W q ·A′ + b q , K = W k ·B′ + b k , V = W v ·B′ + b v , L 0 is the distillation loss function, Q 0 and K 0 represent the adjusted features, σ represents the gating mechanism, which is the sigmoid activation function, α 0 and β 0 are adaptive parameters, is the dimension of K 0 , K 0 T represents the transpose of matrix K 0 . The softmax operation normalizes the dot product result to the range [0, 1], making it possible to represent the degree of attention of the global feature to the local feature. O is the finally generated interactive feature containing the information of the two features. Then the fused feature is fused with the time feature to obtain the final spatio-temporal feature.

[0099] Step 6, use the golden jackal optimization algorithm to optimize the model hyperparameters, and use the training set and the validation set to train the weights of the entire model to obtain the optimal weights. Input one hour of radar image data into the model to obtain the predicted image for the next hour and get the future precipitation

[0100] such as Figure 9As shown in the figure, the improved golden jackal optimization algorithm is used to optimize and iterate the hyperparameters in the model. Suppose there are M hyperparameters and N candidate solutions (i.e., N golden jackals), and these parameters will be used as independent variables in the optimization process. First, define a matrix P to store the combinations of each parameter. Each row represents a solution (i.e., a combination of a set of parameters), and each column corresponds to a hyperparameter. The β matrix is as follows:

[0101]

[0102] Among them, represents the initial value of the m-th parameter in the n-th candidate solution, represents the first parameter combination, that is, the first candidate solution.

[0103] When initializing the population, the sequence generated by the Logistic map has nonlinearity and unpredictability, which can provide a kind of randomness and is beneficial to widely exploring the solution space in the initial stage of the algorithm. However, the coverage rate of the Logistic map within the numerical range is uneven, which easily leads to the deviation of the initial population distribution from the optimal region. Therefore, the Tent map is introduced, which can make full use of the advantages of both, ensuring both the chaos of the initial population and increasing the randomness of the generated sequence, so that the initial solutions can be evenly distributed within a larger range. The Logistic map is cascaded with the Tent map to initialize the population, and the formula is:

[0104]

[0105] Among them, represents an initial value in the candidate solution represented by each golden jackal, is the value after mapping, and r is the chaos factor.

[0106] Select the reciprocal of the mean square error as the adaptive fitness function, and the formula is as follows:

[0107]

[0108] Among them, N is the number of samples (golden jackals), F n is the adaptive fitness value, R n is the true value of the n-th sample, is the predicted value of the n-th sample, and the larger the F n value, the better the hyperparameter combination.

[0109] Set the maximum number of iterations and the adaptive fitness threshold, put all the golden jackal individuals in the population into the initial precipitation prediction model for training, and calculate the adaptive fitness of each golden jackal individual through the adaptive function.

[0110] After initializing the population, allocate pheromones to each golden jackal individual, and the pheromone concentration is initialized and updated through the update formula:

[0111] τ n = τ init

[0112]

[0113] where ρ is the pheromone evaporation coefficient, and τ init is a constant of the initial concentration.

[0114] In the hunting of golden jackals, the individuals closer to the optimal solution will have higher pheromones, making it easier to attract other golden jackals to approach. At the same time, in each iteration, the golden jackals gather near the male and female jackals with the best fitness (i.e., the optimal and sub-optimal solutions of the fitness function). Relying on a unique hunting method, the golden jackals are guided by the optimal solution and assisted by the sub-optimal solution, without being limited to a single solution, enhancing the exploration efficiency of the team. Through this joint hunting strategy, the golden jackals not only quickly approach the optimal area but also obtain more solution space information through the assistance of the sub-optimal solution, avoiding falling into local optima. Among them, the golden jackals will dynamically adjust their strategies according to the escape energy E, and the escape energy gradually decreases according to the iteration situation of the golden jackals. When E > 1, the golden jackals will adopt an "attack" strategy and approach the current optimal or sub-optimal solution. When E ≤ 1, the golden jackals will disperse in a larger area and execute a "wide exploration strategy" to continue exploring potential solutions. This mechanism enables the golden jackal team to achieve a dynamic balance between attack and exploration.

[0115] The calculation formula for the escape energy is:

[0116]

[0117] D = ∣C · x prey - x n ∣

[0118] where E n is the escape energy of the nth golden jackal, t is the number of iterations, T is the maximum number of iterations, is the average pheromone concentration of the current population, D is the distance between the golden jackal and the prey, is the position of the male jackal at the (t + 1)th iteration, x n is the position of the nth golden jackal, C is a random factor, x prey is the position of the prey, i.e., the center of the positions of the male and female jackals, and α, β, γ are all adjustment coefficients.

[0119] The formula for the golden jackals to update their positions is:

[0120]

[0121] where represents the position of the nth golden jackal individual after iteration, is the position of the male jackal, is the position of the female jackal, a t is the adjustment factor, which gradually decays with the number of iterations, A * is the control factor used to adjust the amplitude of the jackal position update.

[0122] The addition of pheromone concentration ensures that individuals with lower concentration can move further away from the current optimal solution during the search, expanding the search range of the team. This strategy enables the jackals to continuously explore a larger area and bring back more potential information for the entire team.

[0123] After multiple iterations, there are multiple jackals with the highest fitness. Record their fitness and pheromone values and put them into a module named the historical memory system. When the jackals update their positions, they will refer to these historical optimal positions to enhance the team's attention to the multi-solution area. When the jackals gradually approach the optimal solution, they may sometimes fall into a local optimum, so appropriate perturbations are added to the optimal position. Guided by the random deviation and the historical optimal position, the jackals will re-evaluate the solution at the current position. After each round of exploration, the pheromone concentration will be dynamically adjusted according to the performance. The formula for the historical memory system is:

[0124]

[0125] where, is the historical optimal position.

[0126] The perturbation formula is:

[0127]

[0128] where, x best , x' best are the positions of the male jackal before and after the perturbation update respectively. Gaussian(0,μ) represents generating a random number from a Gaussian distribution with a mean of 0 and a standard deviation of μ, and γ h is the perturbation coefficient.

[0129] The pheromone dynamic adjustment formula is:

[0130]

[0131] where, is the fitness function of the nth jackal after the (t + 1)th iteration, δ is the historical deviation control parameter, is the pheromone concentration of the nth jackal after the (t + 1)th iteration.

[0132] The optimal hyperparameters are obtained through an optimization algorithm, the optimal weights are obtained by training the model, and a rainfall prediction model is constructed. By inputting the radar rainfall image of one hour, the radar rainfall image of the next hour can be obtained.

[0133] The pixel values of the echo image are converted into radar reflectivity, and then based on the relationship between reflectivity and precipitation, the precipitation is calculated. The formula is:

[0134]

[0135] Z = A 0 ·R F

[0136] Where, Z represents the radar reflectivity of each pixel point, G represents the value of each pixel point, R represents the rainfall, and A 0 and F are both coefficients.

[0137] Based on the same inventive concept, an embodiment of the present application provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the foregoing precipitation prediction method based on Shearlet and L-PWC are implemented.

[0138] Based on the same inventive concept, an embodiment of the present application provides a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the foregoing precipitation prediction method based on Shearlet and L-PWC are implemented.

[0139] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0140] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate for implementing in the process Figure 1 one process or multiple processes and / or blocksFigure 1 means for the functions specified in one or more boxes.

[0141] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to operate in a particular manner, such that the instructions stored in the computer-readable memory produce a manufacture including an instruction means that implements the functions specified in one Figure 1 or more processes and / or boxes Figure 1 means for the functions specified in one or more boxes.

[0142] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus, such that a series of operational steps are performed on the computer or other programmable apparatus to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable apparatus provide steps for implementing the functions specified in one Figure 1 or more processes and / or boxes Figure 1 means for the functions specified in one or more boxes.

[0143] The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the present invention.

Claims

1. A precipitation forecasting method based on Shearlet and L-PWC, characterized in that: The steps include: Step 1: Obtain a weather radar precipitation image dataset, preprocess the acquired dataset, and divide the preprocessed dataset into a training set and a validation set; construct a precipitation forecast model, including an optical flow estimation network PWC-net, a long short-term memory neural network LSTM, a Transformer network, and a Densenet network; Step 2: For the training set, the optical flow estimation network PWC-net is used to generate an initial optical flow map for two adjacent frames of images, and then the optical flow is refined three times to obtain a high-resolution optical flow map; the long short-term memory neural network LSTM is used to extract the temporal features of the radar precipitation image from the high-resolution optical flow map; Step 3, using Karcher mean calculation and weighted principal component analysis to analyze the motion direction of the initial optical flow map, and obtain the motion direction; performing Shearlet transform on each frame image in the training set to obtain multiple high-frequency feature maps in different directions and a low-frequency feature map, and finding the main direction high-frequency feature map a with the highest correlation with the motion direction from the multiple high-frequency feature maps in different directions; Perform Shearlet transform on a again to find the main direction high-frequency feature map b with the highest correlation with the motion direction, and fuse a and b to obtain the main direction high-frequency feature map c; Step 4, using the Transformer network to extract the global spatial features of the radar precipitation image from the high-frequency feature map c in the main direction, the high-frequency feature maps in the remaining directions obtained by the first Shearlet transform, and the low-frequency feature map; The Densenet network is used to extract the local spatial features of radar precipitation images from two adjacent frames of the training set; Step 5, fusing the global spatial features and the local spatial features of the radar precipitation image to obtain fused spatial features, and fusing the fused spatial features with the temporal features of the radar precipitation image to obtain the spatiotemporal features, i.e., the radar precipitation prediction image; Step 6, using the golden jackal optimization algorithm to optimize the hyperparameters in the precipitation forecast model to obtain the optimal hyperparameters; based on the optimal hyperparameters, using the training set and the validation set to train the weights of the precipitation forecast model to obtain the optimal weights, thereby obtaining a trained precipitation forecast model; Step 7, input the current radar weather radar precipitation image into the trained precipitation forecast model to obtain the future precipitation forecast image, and obtain the future precipitation amount according to the precipitation forecast image.

2. The precipitation forecasting method based on Shearlet and L-PWC according to claim 1, characterized in that: The specific process of step 1 is as follows: Step 11, obtaining a weather radar precipitation image data set, performing two-dimensional plane extraction on the echo reflectivity values ​​of the pixel points of each frame of the image in the data set, and converting the extracted echo reflectivity values ​​into a matrix form in a plane coordinate system; Step 12: Preset the minimum echo reflectivity threshold T dBZ , compare the echo reflectivity value of each pixel in each frame of the image with T dBZ , the echo reflectivity values ​​of all pixels are lower than T dBZ Image culling; Step 13: Based on step 12, for the remaining images, for each frame of the image whose echo reflectivity value is greater than T dBZ The number of pixels is summed to obtain the precipitation area A rain , and calculate A rain The proportion in the image, images with a proportion less than 5% will be eliminated; Step 14: Based on step 13, for the pixels in the remaining image where the echo reflectivity values ​​are missing, the missing echo reflectivity values ​​are filled by bilinear interpolation. The formula is as follows: in, represents the echo reflectivity value obtained by bilinear interpolation, and are the echo reflectivity values ​​of the upper left corner, upper right corner, lower left corner and lower right corner of the pixel where the echo reflectivity value is missing, (x i ,y j ) is the pixel position where the echo reflectivity value is missing, (x i-1 ,y j-1 )、(x i+1 ,y j-1 )、(x i-1 ,y j+1 ) and (x i+1 ,y j+1 ) are the pixel positions of the upper left corner, upper right corner, lower left corner and lower right corner of the pixel where the echo reflectivity value is missing; Step 15, divide the data set preprocessed by steps 12 to 14 into a training set and a validation set at a ratio of 8:

2.

3. The precipitation forecasting method based on Shearlet and L-PWC according to claim 1, characterized in that: The specific process of step 2 is as follows: Step 21, for two adjacent frames in the training set, i.e., the current frame image B and the previous frame image A, perform 3×3 convolution, relu activation function and 2-fold downsampling on B in sequence to obtain feature map B1; perform 3×3 convolution, relu activation function and 2-fold downsampling on B1 in sequence to obtain feature map B2; and so on to obtain feature maps B3 and B4; similarly, perform the same operation on A to obtain feature maps A1, A2, A3 and A4; concatenate A4 and B4 in the channel dimension and pass a layer of 3×3 convolution to generate an initial optical flow map d4; Step 22, B3 performs image distortion based on d4 to generate feature map B ′ 3, and deconvolve d4 to obtain the feature map d ′ 4. Place A3 and B ′ 3 and D ′ 4 Splicing in the channel dimension, and then passing a layer of 3×3 convolution to obtain the forward optical flow map d ′ 3; Step 23, A3 according to d ′ 3. Perform image distortion to generate feature map A ′ 3. A ′ 3. B3 and d ′ 3. Generate the reverse optical flow map g3 by splicing in the channel dimension. ′ 3 and g3 are checked for consistency, and optical flow correction is performed to obtain the optical flow map d3; Step 24, perform the same optical flow refinement operation as in Step 22 and Step 23 on B2 and A2 to obtain an optical flow map d2; perform the same optical flow refinement operation as in Step 22 and Step 23 on B1 and A1 to obtain a high-resolution optical flow map d1; Step 25, calculate the gradient of each pixel on d1 and normalize the gradient, use the particle swarm optimization algorithm to determine the segmentation threshold H of the gradient of the optical flow map d1, segment the gradient of d1 according to the segmentation threshold, and obtain an optical flow map of H speed levels; Step 26, construct a 3-layer long short-term memory neural network LSTM to splice the optical flow maps of H speed levels to obtain a time feature map; each layer of the long short-term memory neural network LSTM includes a forget gate, an input gate, a candidate memory unit, an output gate, a memory unit and a hidden state; the specific formula is as follows: in, represents the output of the forget gate in the k-th layer LSTM at time step t, represents the hidden state of the k-1th layer LSTM at time step t, represents the hidden state of the k-th layer LSTM at time step t-1, They represent the weight matrix and bias term of the forget gate in the k-th layer LSTM, respectively. represents the output of the input gate in the k-th layer LSTM at time step t, W i k , They represent the weight matrix and bias term of the input gate in the k-th layer LSTM, respectively. is a candidate memory unit, is the output gate, They represent the memory units updated by the k-th layer LSTM at time steps t and t-1, respectively. represents the hidden state of the k-th layer LSTM at time step t, W I k , They represent the weight matrix and bias term of the candidate memory unit in the k-th layer LSTM, respectively. They represent the weight matrix and bias term of the output gate in the k-th layer LSTM, σ(·) represents the sigmoid activation function, tanh(·) represents the tanh activation function, and k=1,2,3.

4. The precipitation forecasting method based on Shearlet and L-PWC according to claim 3, characterized in that: The specific process of step 3 is as follows: Step 31, perform Karcher mean calculation and weighted principal component analysis on the initial optical flow map d4, obtain the Karcher mean direction and the weighted principal component direction, perform adaptive weighted fusion on the Karcher mean direction and the weighted principal component direction, and obtain the motion direction θ0; Step 32, perform Shearlet transform on each frame image in the training set to obtain high-frequency feature maps in multiple different directions, calculate the absolute value of the angle difference between each direction and the motion direction θ0, take the direction with the smallest absolute value as the main direction with the highest correlation with the motion direction, perform Shearlet transform on the high-frequency feature map a of the main direction again, find the high-frequency feature map b of the main direction with the highest correlation with the motion direction, and fuse a and b to obtain the high-frequency feature map c of the main direction.

5. The precipitation forecasting method based on Shearlet and L-PWC according to claim 4, characterized in that: The specific process of step 4 is as follows: Step 41, using a deep residual network to extract features from the main direction high-frequency feature map c to obtain the main direction high-frequency features, using a lightweight network to extract features from the high-frequency feature maps of the remaining directions obtained by the first Shearlet transform to obtain the high-frequency features of the remaining directions, the main direction high-frequency features are spliced ​​with the high-frequency features of the remaining directions after the SE channel attention mechanism to obtain the high-frequency features; The deep residual network includes a 5×5 convolutional layer, a maximum pooling layer, a 1×1 convolutional layer, a 3×3 convolutional layer and a global average pooling layer connected in sequence, and the output of the maximum pooling layer is concatenated with the output of the 3×3 convolutional layer as the input of the global average pooling layer; The lightweight network includes a 3×3 convolution layer, a 1×1 convolution layer, a 3×3 depth convolution layer, a 1×1 convolution layer, and a global average pooling layer connected in sequence; Step 42, using the feature encoding module of the Transformer network to divide the high-frequency features into blocks, and perform position encoding and direction encoding on the blocks, and the position encoding and direction encoding are obtained by the directional multi-head attention module of the Transformer network to obtain the fused features; Step 43, performing 1×1, 2×2, 3×3 and 6×6 pooling operations on the fused features respectively to generate feature maps of four different scales, upsampling the feature maps of each scale to the same spatial size as the fused features, and concatenating the features of all scales after upsampling in the channel dimension to obtain multi-scale fused features; fusing the multi-scale fused features with the low-frequency feature map obtained by the first Shearlet transform, and then performing 3×3 convolution to obtain the global spatial features of the radar precipitation image; Step 44, the current frame image and the previous frame image in the training set are respectively sent to the Densenet network, the Densenet network includes a first block layer, a transition layer and a second block layer connected in sequence, the transition layer includes a 1×1 convolution layer, a global average pooling layer, a first fully connected layer and a second fully connected layer connected in sequence, the first fully connected layer is followed by a relu activation function, and the second fully connected layer is followed by a sigmoid activation function; the output of the previous frame image in the first block layer is optically distorted according to the initial optical flow map of the previous frame image, and then merged with the output of the current frame image in the first block layer as the input of the current frame image in the transition layer; the output of the previous frame image in the second block layer is optically distorted according to the initial optical flow map of the previous frame image, and then spliced ​​with the output of the current frame image in the second block layer, and the splicing result is output through the SE channel attention mechanism to obtain the local spatial features of the radar precipitation image; the initial optical flow map of the previous frame image is obtained by the optical flow estimation network PWC-net according to the previous frame and the previous two frames of the current frame image; The structures of the first block layer and the second block layer are the same, both of which include three cascaded convolution modules. Each convolution module includes a BN layer, a relu activation function, a 1×1 convolution layer, a BN layer, a relu activation function, a 3×3 depth-separable convolution layer, and a dense connection layer connected in sequence; the output of the 3×3 depth-separable convolution layer in the first convolution module and the output of the 2x downsampling of the high-resolution optical flow map are used as the input of the dense connection layer in the first convolution module; the high-resolution optical flow map of each block layer in the previous frame image is obtained through the optical flow estimation network PWC-net based on the previous frame and the previous two frames of the current frame image; the dense connection layer in the first convolution module The output of the set connection layer is used as the input of the first BN layer in the second convolution module; the output of the 3×3 depth-separable convolution layer in the second convolution module and the output of the densely connected layer in the first convolution module are used as the input of the densely connected layer in the second convolution module; the output of the densely connected layer in the second convolution module is used as the input of the first BN layer in the third convolution module; the output of the 3×3 depth-separable convolution layer in the third convolution module, the output of the densely connected layer in the first convolution module and the output of the densely connected layer in the second convolution module are used as the input of the densely connected layer in the third convolution module; the output of the densely connected layer in the third convolution module is used as the output of the block layer.

6. The precipitation forecasting method based on Shearlet and L-PWC according to claim 5, characterized in that: The specific process of step 5 is as follows: Step 51, according to the cross attention mechanism, the global spatial features of the radar precipitation image are mapped to the query matrix Q after 1×1 convolution, and the local spatial features of the radar precipitation image are mapped to the key matrix K and the value matrix V after 1×1 convolution; Step 52, combined with the feature distillation module, guides the local spatial features to the global spatial features to generate the interactive feature Q0, transfers the global spatial features to the local spatial features to generate the interactive feature k0, and according to the generated interactive features, guides and fuses the attention weights to obtain the fused spatial feature O, the formula is as follows: L0=∣∣qK∣∣ 2 Q0=Q+α0·L0·σ(K) K0=K+β0·L0·σ(Q0) O=Attention(Q0,K0)V Among them, L0 is the distillation loss function, α0 and β0 are adaptive parameters, σ represents the gating mechanism, and σ is the sigmoid activation function. is the dimension of the interaction feature K0; Step 53, according to the same steps as step 51-step 52, the fused spatial features are fused with the temporal features of the radar precipitation image to obtain a radar precipitation prediction image.

7. The precipitation forecasting method based on Shearlet and L-PWC according to claim 6, characterized in that: The golden jackal optimization algorithm described in step 6 is as follows: Step 61, assume that the precipitation forecast model has M hyperparameters and N candidate solutions, each candidate solution corresponds to a golden jackal, and define a matrix P to store the hyperparameters and candidate solutions, that is: Among them, each row represents a candidate solution, and each column corresponds to a hyperparameter. represents the random value of the mth hyperparameter in the nth candidate solution, n=1,…,N, m=1,…,M; assigns an initial pheromone concentration to each golden jackal; Step 62, using the Logistic map cascaded in the Tent map to initialize the random value of each hyperparameter in each candidate solution, the formula is: in, represents the initialization value of the mth hyperparameter in the nth candidate solution, and r is the chaos factor; Step 63, for the t+1th iteration, all golden jackals are put into the precipitation forecast model for optimization, the fitness value of each golden jackal is calculated by the fitness function, the one with the highest fitness value is selected as the male jackal, and the one with the second highest fitness value is selected as the female jackal; the fitness function formula is as follows: Among them, F n is the fitness value of the nth golden jackal, N is the number of golden jackals, R n , are the true value and predicted value of the nth golden jackal respectively; Step 64, update the pheromone concentration of each golden jackal: Among them, τ n , τ′ n are the pheromone concentrations before and after the renewal of the nth golden jackal, and ρ is the pheromone volatility coefficient; Step 65, calculate the escape energy of each golden jackal: D=∣C·x prey -x n ∣ Among them, E n is the escape energy of the nth golden jackal, t is the number of iterations, T is the maximum number of iterations, is the average pheromone concentration of all golden jackals at present, D is the distance between the golden jackal and the prey, is the position of the male jackal at the t+1th iteration, x n is the position of the nth golden jackal, C is a random factor, x prey is the location of the prey, i.e., the center of the location of the male and female jackals, α, β, γ are all adjustment coefficients; Update the position of each golden jackal according to the escape energy: in, is the position of the nth golden jackal at the t+1th iteration, a t is the adjustment factor, is the position of the female jackal at the t+1th iteration, A * is the control factor used to adjust the amplitude of the golden jackal's position update, is the position of the male jackal corresponding to the hth optimal solution in history; Step 66, disturb and update the position of the male jackal: Among them, x best , x′ best are the positions of the male jackal before and after the disturbance update, respectively. Gaussian(0,μ) represents a random number generated from a Gaussian distribution with a mean of 0 and a standard deviation of μ. h is the disturbance coefficient; Step 67, dynamically adjust the pheromone of each golden jackal: in, are the pheromone concentrations of the nth golden jackal after the t+1th iteration, is the fitness function of the nth golden jackal after the t+1th iteration, and δ is the historical deviation control parameter; Step 68, determine whether the preset maximum number of iterations has been reached, if not, return to step 63 to continue iterating, otherwise, output the optimal solution for each hyperparameter.

8. The precipitation forecasting method based on Shearlet and L-PWC according to claim 7, characterized in that: In step 7, the future precipitation is obtained based on the precipitation forecast image, and the formula is as follows: Z=A0·R F Among them, Z represents the echo reflectivity of each pixel, G represents the gray value of each pixel, R represents the precipitation, and A0 and F are coefficients.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that: When the processor executes the computer program, the steps of the precipitation forecasting method based on Shearlet and L-PWC are implemented as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the precipitation forecasting method based on Shearlet and L-PWC are implemented as described in any one of claims 1 to 8.

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