Deep learning and physical model coupled method for heavy rainfall nowcasting

Abstract

The application provides a heavy rain nowcasting method based on deep learning and physical model coupling, which comprises the following steps: inputting current radar echo sequence data into a SimVP network to obtain a future radar echo sequence data prediction value output by the SimVP network, wherein the SimVP network is obtained by training through taking radar echo sequence data samples as samples, taking corresponding future radar echo sequence data true observation values as labels and through an adaptive loss function; and substituting the future radar echo sequence data prediction value into a relationship physical model between radar echo data and precipitation intensity to obtain a precipitation intensity prediction value, wherein parameters in the relationship physical model are obtained by fitting according to historical data of different time windows of different weather types. The application improves the heavy rain nowcasting precision.

Description

Technical Field

[0001] This invention relates to the field of meteorological forecasting technology, and in particular to a method for nowcasting heavy precipitation based on the coupling of deep learning and physical models. Background Technology

[0002] Short-duration heavy precipitation and extreme heavy precipitation are defined as precipitation with an intensity of ≥20 mm / h and ≥50 mm / h, respectively. Current numerical models cannot perform precise simulations of localized heavy precipitation at specific times, locations, and quantities. Therefore, operationally, forecasting and early warning of localized heavy precipitation still rely on radar observation data and manual monitoring or extrapolation forecasts within the nowcast lead time (0 to 2 hours).

[0003] Radar echo extrapolation techniques typically employ two methods. One is based on the traditional optical flow method, which extrapolates radar echoes from two or more adjacent moments by calculating their movement vectors and extrapolating the radar echoes for the next 0 to 2 hours. However, because the optical flow method is based on the assumption of grayscale conservation (i.e., constant echo intensity), it cannot predict the evolution of echo intensity, and therefore cannot provide effective forecasts for locally enhanced or quasi-stationary precipitation. The other method utilizes deep learning algorithms, which possess powerful nonlinear mapping and spatiotemporal modeling capabilities. These algorithms can better capture the spatiotemporal variations of precipitation systems using extensive historical data, enabling predictions of the evolution of local convective systems. Models such as PredRNN, PhyDNet, UNet, and Transformer are widely used in the spatiotemporal prediction of short-term radar echoes. However, a common problem with deep learning models is that radar echo intensity rapidly decays and becomes blurred as the prediction time increases. While generative neural network models can alleviate this problem, their prediction accuracy for severe convective weather such as short-duration heavy precipitation is generally low.

[0004] Researchers have proposed a Predictive Recurrent Neural Network (PredRNN) model, which uses a zigzag structure to connect high-level features from the previous time step with low-level features from the current time step, thereby effectively extracting temporal and spatial information during radar echo evolution. To better extract high-order non-stationary features in cloud evolution, researchers have proposed a Memory-in-Memory (MIM) network, applying difference operations to the non-stationary and near-stationary characteristics in spatiotemporal dynamics, effectively improving the model's ability to capture short-term dynamic changes. Others have proposed a MotionRNN model, designing MotionGRU units to learn instantaneous changes using ConvGRU and capturing motion trends through accumulation, improving the radar echo extrapolation model's ability to capture instantaneous changes and complex motion trends. While RNN-based spatiotemporal prediction methods have a strong theoretical foundation, iterative methods suffer from error accumulation problems, meaning that prediction biases accumulate with the extension of forecast lead time, leading to larger errors in later prediction results.

[0005] The above-mentioned model based on recurrent neural networks has achieved spatiotemporal modeling and prediction of radar echo sequences to a certain extent, but there are still some problems: (1) After stacking multiple layers of LSTM units, the gradient is difficult to propagate to the bottom layer of the model, which causes the high echo region in the extrapolation result to gradually weaken and be lower than the actual observation value. (2) Recurrent neural networks, represented by long short-term memory networks, use the output of the previous time step as the input of the next time step, and most models only use a single mean square error as the loss function, which causes the extrapolation result to become increasingly blurred as the time step increases. (3) Some studies have tried to introduce generative adversarial networks (GANs) into radar echo extrapolation, but the training of generative adversarial networks has gradient vanishing and mode collapse problems, which leads to instability in the training process. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides a method for predicting the imminent occurrence of heavy precipitation based on the coupling of deep learning and a physical model. It employs a lightweight deep learning network, SimVP, based entirely on a CNN (Convolutional Neural Network) architecture, and applies it to the prediction of severe convective weather such as short-duration heavy precipitation. By reconstructing the loss function of the deep learning network, it is made more suitable for predicting severe convective echoes. Furthermore, by coupling with a physical model, it can better predict the imminent occurrence area of ​​extreme short-duration heavy precipitation, providing technical support for disaster prevention and mitigation.

[0007] This invention provides a method for predicting heavy precipitation now based on the coupling of deep learning and a physical model, comprising:

[0008] The current radar echo sequence data is input into the SimVP network to obtain the predicted value of the future radar echo sequence data output by the SimVP network. The SimVP network is trained by using radar echo sequence data samples as samples and the corresponding real observation value of the future radar echo sequence data as labels.

[0009] The predicted values ​​of the future radar echo sequence data are substituted into the physical model of the relationship between radar echo data and precipitation intensity to obtain the predicted value of precipitation intensity. The parameters in the physical model are obtained by fitting historical data of different time windows according to different weather types.

[0010] According to the present invention, a method for predicting heavy precipitation now based on deep learning and a physical model coupling is provided, wherein the SimVP network includes:

[0011] A spatial encoder is used to extract spatial features. The spatial encoder uses multiple ordinary convolutional layers to extract spatial features, and stacks convolutional layers, normalization layers and activation functions to extract spatial features.

[0012] A spacetime converter is used to learn temporal evolution. The spacetime converter uses multiple time modules to learn spacetime dependencies and temporal changes, uses the Inception module to construct an encoder-decoder structure, and employs residual connections to preserve spatial features.

[0013] A spatial decoder is used to integrate spatiotemporal information to predict future frames. The spatial decoder uses multiple upsampling layers to decode the latent space into predicted future frames and utilizes transposed convolutional layers, normalization layers, and activation functions to reconstruct ground truth frames.

[0014] According to the present invention, a method for predicting heavy precipitation now based on deep learning and a physical model coupling, before inputting the current radar echo sequence data into the SimVP network to obtain the predicted value of the future radar echo sequence data output by the SimVP network, further includes:

[0015] Radar echo sequence data samples are input into the SimVP network to obtain the predicted values ​​of future radar echo sequence data output by the SimVP network.

[0016] Determine the MSE loss between the predicted value of the future radar echo sequence data corresponding to the radar echo sequence data sample and the corresponding actual observation value, as well as the TV regularization loss of the predicted value of the future radar echo sequence data corresponding to the radar echo sequence data sample.

[0017] The MSE loss and TV regularization loss are fused to obtain a comprehensive loss function, which is then used to train the SimVP network.

[0018] According to the present invention, a method for predicting heavy precipitation now-nearest rainfall based on deep learning and physical model coupling is provided. The comprehensive loss function is obtained by fusing the MSE loss and TV regularization loss using the following formula:

[0019]

[0020] in, For the comprehensive loss function, This represents the predicted value at the i-th time interval in the predicted values ​​of the future radar echo sequence data. This represents the actual observation value at the i-th time interval. This represents the value of the j-th point in the predicted values ​​at time i. This represents the value of the j-th point in the predicted values ​​at time i+1. This represents the value of the (j+1)th point in the predicted values ​​at time i. Indicates weight, Indicates the adjustment coefficient; the weight is based on The threshold range to which it belongs is determined, and the weight corresponds one-to-one with the threshold range.

[0021] According to the present invention, a method for predicting heavy precipitation now based on deep learning and a physical model coupling, before substituting the predicted values ​​of the future radar echo sequence data into the physical model relating radar echo data and precipitation intensity to obtain the predicted precipitation intensity value, the method further includes:

[0022] Establish the correlation between radar echo data and rain gauge observations;

[0023] By substituting historical radar echo data into the aforementioned correlation, the instantaneous rainfall intensity is obtained;

[0024] A target function is constructed based on the difference between the instantaneous rainfall intensity and the corresponding rainfall observed by the rain gauge.

[0025] The coefficients in the correlation are adjusted to minimize the objective function, thus obtaining the physical model of the relationship.

[0026] According to the present invention, a method for predicting heavy precipitation now based on the coupling of deep learning and physical models is provided, wherein the objective function is formulated as follows:

[0027]

[0028] in, Let m be the objective function, and m be the number of historical radar echo data. The instantaneous rainfall intensity is obtained by inverting the i-th historical radar echo data. The rainfall is measured by a rain gauge at the same time as the i-th historical radar echo data.

[0029] According to the present invention, a method for predicting heavy precipitation now based on deep learning and a physical model is provided, wherein the window length of the time window is obtained through the following steps:

[0030] The parameter drift is determined based on the difference between the parameters in the physical model of the relationship between the current time window and the previous time window;

[0031] Determine the adaptive factor based on the drift of the parameters;

[0032] The product of the adaptive factor and the initial window length corresponding to the weather type is used as the window length of the current time window.

[0033] According to the present invention, a method for predicting heavy precipitation now based on the coupling of deep learning and a physical model is provided. The parameter drift is determined using the following formula based on the difference between the parameters in the physical model of the relationship between the current time window and the previous time window:

[0034]

[0035] in, For parameter drift, and This represents the difference in parameters between the physical model of the relationship between the current time window and the previous time window. and These are the parameters in the physical model of the relationship within the current time window. The acceptable drift threshold;

[0036] And / or, the adaptive factor is determined based on the drift of the parameter using the following formula:

[0037]

[0038] in, This is an adaptive factor.

[0039] According to the present invention, a method for predicting heavy precipitation now based on deep learning and a physical model coupling, after taking the product of the adaptive factor and the initial window length corresponding to the weather type as the window length of the current time window, further includes:

[0040] When the current time window length is greater than the initial window length, the exponential decay weight of historical data within the time range exceeding the initial window in the current time window is calculated using the following formula:

[0041]

[0042] in, The exponential decay weight of the i-th historical data is given. For the current time, Let i be the occurrence time of the i-th historical data. This is the preset time decay constant.

[0043] Based on the exponential decay weights, determine whether to use data within the time range to determine the parameters in the physical model of the relationship.

[0044] According to the present invention, a method for predicting heavy precipitation near-term based on deep learning and a physical model coupling, after inputting the current radar echo sequence data into the SimVP network and obtaining the predicted value of the future radar echo sequence data output by the SimVP network, further includes:

[0045] Determine the fitting formula between the observed values ​​of radar echo data and the prediction error of radar echo data;

[0046] Substituting the predicted values ​​of the future radar echo sequence data into the fitting formula yields the prediction error of the predicted values ​​of the future radar echo sequence data.

[0047] The predicted values ​​of the future radar echo sequence data are corrected based on the prediction error to obtain the final predicted values ​​of the future radar echo sequence data.

[0048] This invention provides a method for predicting short-term heavy precipitation based on the coupling of deep learning and physical models. It proposes a spatial neighborhood short-term heavy precipitation prediction method based on the coupling of deep learning and physical models. Through training with radar big data, it can capture the instantaneous changes and complex movement trends of radar echoes. By integrating the adaptive time window dynamic ZR relationship, an inversion model suitable for the current precipitation type is obtained, thereby achieving a more accurate prediction effect for 0-2h short-term heavy precipitation, making short-term heavy precipitation more predictable, especially significantly improving the forecasting capability for extreme heavy precipitation, and providing effective support for heavy precipitation early warning and disaster prevention and mitigation. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0050] Figure 1 This is a flowchart illustrating the heavy precipitation now-prediction method based on the coupling of deep learning and physical models provided by this invention.

[0051] Figure 2This is a schematic diagram of the SimVP-Rw network architecture in the heavy precipitation nowcasting method based on deep learning and physical model coupling provided by the present invention.

[0052] Figure 3 This is a schematic diagram of the adaptive dynamic time window ZR relationship construction process in the heavy precipitation nowcasting method based on deep learning and physical model coupling provided by the present invention.

[0053] Figure 4 This is a schematic diagram of the reflectivity factor attenuation error fitting curve of the SimVP model in the heavy precipitation nowcasting method based on deep learning and physical model coupling provided by the present invention.

[0054] Figure 5 This is a flowchart of the modeling and verification process for the short-term heavy precipitation forecast model in the heavy precipitation now-prediction method based on deep learning and physical model coupling provided by the present invention.

[0055] Figure 6 This is a scoring diagram of the SimVP-Rw model, wind and thunder model, and physical model in the heavy precipitation nowcasting method based on deep learning and physical model coupling provided by this invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0057] This invention employs SimVP as the foundational deep learning network. Compared to other deep learning models based on Recurrent Neural Networks (RNNs), this network boasts three core advantages: simplicity, efficiency, and strong generalization. It features a pure CNN architecture without RNNs / Transformers, completely abandoning complex gating or memory mechanisms like ConvLSTM and PredRNN++, using only three layers of CNN (encoder-translator-decoder) to complete spatiotemporal modeling, reducing parameter size by 60%. Training is more stable and cost-effective: it avoids oscillations under high learning rates, preventing the vanishing or exploding gradient problems common in RNN-like models. Performance and generalization are strong: its superior performance and generalization capabilities have been validated on multiple datasets. However, this network uses the general loss function of MSE, which, if directly applied to radar echo prediction, cannot solve the problem of predicting strong convective echoes. Therefore, this invention reconstructs the loss function based on the characteristics of strong convective echoes, inventing a SimVP-Rw deep learning model suitable for predicting strong convective weather. This model is trained on a large dataset of meteorological radar sequences to provide short-term forecasts of radar echoes.

[0058] Existing nowcasting methods are all applied to the prediction of radar echoes. For precipitation prediction, it is usually necessary to combine the empirical ZR relationship (Z represents radar echo, R represents precipitation) to convert the echoes into precipitation. However, due to the differences in raindrop spectral characteristics in different regions and for different types of precipitation, precipitation estimation models with a fixed ZR relationship are difficult to solve the problem of inverting various types of precipitation. Furthermore, when the reflectivity factor Z value is large, small changes caused by random errors in Z can have a significant impact on precipitation intensity R. Therefore, this invention constructs a rolling + weighted adaptive time window to dynamically update the ZR relationship to invert precipitation intensity R, which can significantly improve the prediction level of extreme heavy precipitation.

[0059] Therefore, this technology couples a deep learning radar short-term forecast model with a physical model of the adaptive dynamic time window ZR relationship, inventing a forecast model, SimVP-Rw, for disastrous short-duration heavy precipitation. This technology uses a deep learning network and a long-term radar series dataset. By reconstructing and adapting a joint loss function to strong convective echoes, and optimizing parameters through hyperparameter search, it achieves the prediction of radar echo generation and dissipation. The physical model of the adaptive dynamic time window ZR relationship is then coupled to invert the precipitation intensity R, establishing a short-term heavy precipitation forecast model applicable to different seasons and precipitation types. The advantages are summarized as follows:

[0060] (1) The SimVP network has three advantages: it completes spatiotemporal modeling with only three layers of CNN (encoder-translator-decoder), reducing the parameter size by 60%. It is more stable in training, has lower training costs, does not oscillate under large learning rates, and avoids the gradient vanishing / exploding problem of RNN-like models. It has demonstrated better performance and generalization ability on multiple datasets. It liberates spatiotemporal prediction tasks from complex architectures, which is a significant advantage of being lightweight, highly generalizable, and easy to deploy.

[0061] (2) By reconstructing the weighted joint loss function of the strong convection echo, the error of the strong convection echo is smaller and smoother and more continuous. By automatically learning the evolution characteristics of the strong convection echo, the radar echo extrapolation prediction model is trained. This model has the ability to capture instantaneous changes and complex motion trends.

[0062] (3) The advantage of the adaptive dynamic time window ZR relationship physical model is that it adapts to changes in weather processes in real time and effectively reduces the systematic error of radar quantitative precipitation estimation. By dynamically fitting the relationship between radar reflectivity factor Z and observed rainfall R, the precipitation inversion model is adjusted in real time. It is applicable to different precipitation types such as convective, stable, oceanic, and continental precipitation, and significantly improves the forecasting ability of severe weather such as short-term heavy precipitation.

[0063] The following is combined with Figure 1 This invention describes a method for predicting heavy precipitation now based on the coupling of deep learning and a physical model, comprising:

[0064] Step 101: Input the current radar echo sequence data into the SimVP network to obtain the predicted value of the future radar echo sequence data output by the SimVP network. The SimVP network is trained by using radar echo sequence data samples as samples and the corresponding real observation value of the future radar echo sequence data as labels.

[0065] Step 102: Substitute the predicted value of the future radar echo sequence data into the physical model of the relationship between radar echo data and precipitation intensity to obtain the predicted value of precipitation intensity. The parameters in the physical model of the relationship are obtained by fitting historical data of different time windows according to different weather types.

[0066] Training a short-term prediction model for radar reflectivity factors using a deep learning architecture is a key technical challenge this invention aims to address. While deep learning methods can automatically learn the features of input data, data preprocessing and model optimization are crucial during training. Designing the spatiotemporal dependency between input factors and the target variable requires continuously adjusting model parameters based on the loss function output of the target variable. Therefore, data preprocessing, model parameter tuning, network normalization, and sampling strategies are all critical technologies that must be considered to potentially obtain a relatively optimal training model.

[0067] Another challenge is developing a short-duration heavy precipitation prediction model with universal weather type applicability from the radar reflectivity factor forecast model. This requires dynamically fitting the ZR relationship to adapt representative relationships for different precipitation types, such as convective, stable, continental, and oceanic precipitation. The ZR relationship is dynamically updated through a rolling + weighted adaptive time window. Finally, the radar reflectivity factor forecast model and the precipitation inversion physical model are coupled to obtain a short-term heavy precipitation prediction model. After post-processing correction, a spatial neighborhood short-term heavy precipitation prediction model is obtained.

[0068] Accurate and effective forecasting of short-duration heavy precipitation has always been a challenge in meteorological forecasting, especially extreme precipitation caused by stable and slow-moving convective systems, which is a major cause of secondary disasters such as flash floods. Current numerical models cannot yet perform precise, time-, location-, and quantitative simulations of localized heavy precipitation. Therefore, operationally, forecasting and early warning of localized heavy precipitation still rely on extrapolation forecasts based on radar observation data within the next forecast period (i.e., the next 2 hours, 0-2 hours). Deep learning has been proven to better capture the spatiotemporal variation characteristics of precipitation systems through large amounts of historical data, enabling the prediction of the evolution of localized convective systems.

[0069] The short-duration heavy precipitation radar dataset developed by the Meteorological Information Center can be used. First, the combined radar reflectivity data from a single time interval is processed into continuous long-duration radar echo sequences. The continuity of the radar echo sequences is ensured by checking if the time intervals of adjacent files are less than or equal to 6 minutes. This results in several long radar echo sequences of unequal length, which are stored as nc files. In this part, radar reflectivity is converted into a reflectivity factor using the following formula:

[0070] (1)

[0071] The source data was cropped to 128×128 pixels to generate a radar reflectivity factor training dataset with 6-minute intervals. The dataset was then divided into three sets of datasets in an 8:1:1 ratio: training, validation, and testing. The model was continuously optimized through testing and validation.

[0072] The input data for deep learning models needs to be standardized. Data standardization methods, by applying a linear transformation to the features, scale the data to a specified minimum and maximum value, which helps improve model performance and training speed.

[0073] X nor = (XX min ) / (X max -X min (2)

[0074] In the formula X min and X max These represent the minimum and maximum values ​​of the data, respectively. Here, reflectivity factors < 0 are set to 0, and the maximum threshold for radar echo reflectivity factors greater than 80 is set to 80.

[0075] For dataset preprocessing, small patches of weak echoes evolve rapidly. If a large number of these patches are present in the sample, it will negatively impact the learning performance of the deep learning model. Therefore, samples with small echo area coverage and weak echo intensity are removed. Ten time-series combined reflectivity factors are used as input, and 20 time-series data are used as predicted labels (predicting radar echo images for the next 0-2 hours) to construct sequence samples. Since the temporal resolution of a single radar echo data point is 6 minutes, each sequence sample contains 30 radar echo images. To increase the sample size, a sliding window approach is used to select sequence samples, with a sliding step size of 6 steps (a small sliding step size leads to excessive repetition between adjacent sequences), reducing sample overlap and improving model stability. Using echo images from the past 10 time-series as input, the model predicts echo images for the next 20 time-series, thus constructing the radar echo extrapolation model training dataset.

[0076] The underlying network structure used is the SimVP network, which belongs to the CNN-CNN-CNN framework, and its performance has been proven to be superior to other state-of-the-art methods.

[0077] Before using the SimVP network to predict radar echoes, the parameters of the SimVP network are set and optimized. The parameters of the SimVP network are shown in Table 1.

[0078] Table 1 Model Parameter Settings

[0079]

[0080] A physical model of the ZR relationship is dynamically constructed based on an adaptive time window, where Z is the radar reflectivity factor in the radar echo data and R is the precipitation intensity.

[0081] A short-term heavy precipitation prediction model is achieved by fusing a deep learning radar echo extrapolation model and a dynamic ZR relationship physical model. The model continuously inputs combined radar reflectivity factor data from 10 sequences over the past hour into the deep learning model, outputting combined reflectivity factors for 20 sequences over the next 2 hours. The radar reflectivity factor for each sequence is then substituted into the ZR relationship transformation formula.

[0082] (3)

[0083] The instantaneous rainfall intensity R is calculated by formula (3), where parameters a and b are obtained by fitting an adaptive dynamic time window.

[0084] The method for calculating cumulative rainfall is as follows: 10 instantaneous rainfall intensities R are obtained from the 10 sequential reflectance factors predicted by the SimVP-Rw model, and then the hourly cumulative rainfall is obtained by summing them up. This can effectively reflect the evolution of rainfall intensity over 6 minutes. Therefore, it also shows good forecasting performance for extreme precipitation caused by stable and slow-moving convective systems.

[0085] This embodiment proposes a spatial neighborhood heavy precipitation nowcasting method based on deep learning coupled with a physical model. By training with radar big data, it can capture the instantaneous changes and complex motion trends of radar echoes. Coupled with an adaptive time window dynamic ZR relationship, an inversion model suitable for the current precipitation type is obtained, thereby achieving a more accurate prediction effect for 0-2h short-term heavy precipitation, making short-term heavy precipitation more predictable, especially significantly improving the forecasting capability for extreme heavy precipitation, and providing effective support for heavy precipitation early warning and disaster prevention and mitigation.

[0086] Based on the above embodiments, the SimVP network in this embodiment includes an Encoder, a Translator, and a Decoder, all of which are entirely composed of CNNs. The Encoder is used to extract spatial features, the Translator learns temporal evolution, and the Decoder integrates spatiotemporal information to predict future frames.

[0087] The spatial encoder uses Ns ordinary convolutional layers to extract spatial features, stacking ConvNormReLU blocks (Conv2d+LayerNorm+LeakyReLU) to further extract spatial features, encoding high-dimensional past frames into a low-dimensional latent space, i.e., on the upper convolutional channels. Its hidden representation formula is:

[0088] (4)

[0089] in, It is a non-linear activation function, LayerNorm is a normalization layer, the stride of the convolutional layer is 1 (the stride of the downsampling layer is 2), and downsampling is performed once every two convolutional layers. Input and output The shapes are (T,C,H,W) and (T, , , ).

[0090] The temporal-space transformer (Translator) consists of Nt temporal modules that learn spatiotemporal dependencies and temporal variations. It uses the Inception module to construct an Encoder-Decoder structure with convolutional kernel sizes of 3, 5, 7, and 11, and employs residual connections to preserve spatial features. Its hidden representation formula is:

[0091] (5)

[0092] Among them, input and output The shapes are ( ,H,W) and ( , , ) .

[0093] The spatial decoder uses Ns upsampling layers to decode the latent space into predicted future frames, and reconstructs the ground truth frames using unConvNormReLU blocks (ConvTranspose2d+GroupNorm+LeakyReLU) on the upper convolutional channels. The hidden representation formula is:

[0094] (6)

[0095] Among them, input and output The shapes are (T, , , (T,C,H,W), and unConv2d is a transposed convolutional layer.

[0096] Based on the above embodiments, this embodiment further includes the following step before inputting the current radar echo sequence data into the SimVP network to obtain the predicted value of the future radar echo sequence data output by the SimVP network:

[0097] Radar echo sequence data samples are input into the SimVP network to obtain the predicted values ​​of future radar echo sequence data output by the SimVP network.

[0098] Determine the MSE (Mean Squared Error) loss between the predicted value of the future radar echo sequence data corresponding to the radar echo sequence data sample and the corresponding actual observed value, as well as the TV regularization loss of the predicted value of the future radar echo sequence data corresponding to the radar echo sequence data sample.

[0099] The MSE loss and TV regularization loss are fused to obtain a comprehensive loss function, which is then used to train the SimVP network.

[0100] The model obtained by training the SimVP network using the comprehensive loss function is called the SimVP-Rw network. Figure 2 The SimVP-Rw network architecture flowchart shows that radar echo images from 10 time intervals are input into the SimVP-Rw network to predict radar echo images from the next 20 time intervals. The prediction model is trained and its network weight parameters are updated using a weighted MSE and TV regularization loss function. The optimal prediction model is retained for radar echo extrapolation. The original network, using only MSE as the loss function, often leads to smooth edges in the extrapolated image and rapid loss of details. Furthermore, the radar reflectivity factors in different threshold intervals have varying proportions in the entire dataset, with high-intensity echoes (e.g., ≥40 dBz) being relatively few. Using MSE as the loss function fails to reflect this imbalanced distribution, resulting in poor model performance in predicting strong echoes. A comprehensive loss function consisting of weighted MSE loss and TV regularization loss is adopted to jointly constrain the training process at both the pixel and feature levels. Specifically, different weight coefficients are assigned to the radar reflectivity factors in different threshold intervals, and the mean square error between the predicted and true values ​​is calculated to construct the weighted MSE loss function, thereby improving the problem of imbalanced radar echo data distribution.

[0101] Based on the above embodiments, this embodiment fuses the MSE loss and TV regularization loss to obtain a comprehensive loss function using the following formula:

[0102] (7)

[0103] in, For the comprehensive loss function, This represents the predicted value at the i-th time interval in the predicted values ​​of the future radar echo sequence data. This represents the actual observation value at the i-th time interval. This represents the value of the j-th point in the predicted values ​​at time i. This represents the value of the j-th point in the predicted values ​​at time i+1. This represents the value of the (j+1)th point in the predicted values ​​at time i. Indicates weight, Indicates the adjustment coefficient; the weight is based on The threshold range to which it belongs is determined, and the weight corresponds one-to-one with the threshold range.

[0104] The model training employs a fusion loss function. First, different weight coefficients are assigned to radar reflectivity factors in different threshold ranges, and the mean square error between the predicted and actual values ​​is calculated. The first term constructs a weighted MSE loss function to improve the imbalance in radar echo data distribution, increase the number of strong precipitation echo samples, and ensure smaller errors in high-value areas of strong convection by weighting pixel errors, thereby improving the nowcasting capability of strong convection echoes. The second term is a regularization term, representing the total variation, which introduces a spatial smoothing penalty to ensure smooth and continuous strong convection echoes and suppress checkerboard noise echoes.

[0105] In this embodiment, the fusion loss function, constructed by weighted MSE and TV regularization function, allows the model to fully learn the high-value region while suppressing chessboard pseudo-echoes, effectively improving the prediction score of strong convection echoes.

[0106] Based on the above embodiments, this embodiment further includes the following step before substituting the predicted value of the future radar echo sequence data into the physical model relating radar echo data and precipitation intensity to obtain the predicted value of precipitation intensity:

[0107] Establish the correlation between radar echo data and rain gauge observations;

[0108] By substituting historical radar echo data into the aforementioned correlation, the instantaneous rainfall intensity is obtained;

[0109] A target function is constructed based on the difference between the instantaneous rainfall intensity and the corresponding rainfall observed by the rain gauge.

[0110] The coefficients in the correlation are adjusted to minimize the objective function, thus obtaining the physical model of the relationship.

[0111] The rolling method can calibrate the ZR relationship in real time, providing a representative ZR relationship for local precipitation weather (Z=aR). b This method utilizes past rainfall events for inversion. By calculating the corresponding ZR relationship between the radar reflectivity factor Z and the rainfall intensity R for each precipitation event, the overall sample size of the ZR relationship is increased, thereby reducing the error in precipitation estimation.

[0112] Based on the above embodiments, the formula for the objective function in this embodiment is:

[0113] (8)

[0114] in, Let m be the objective function, and m be the number of historical radar echo data. The instantaneous rainfall intensity is obtained by inverting the i-th historical radar echo data. The rainfall is measured by a rain gauge at the same time as the i-th historical radar echo data.

[0115] In short, the fitting method that makes all rain gauge observations equal to radar estimates implicitly contains an objective function that minimizes the difference between radar estimates and rain gauge observations. The calculation formula is shown in formula (8). Before fitting the ZR relationship, the units of both are converted to mm h. -1 .

[0116] To establish the correlation between radar reflectivity factor and rain gauge observation rainfall, the average value of radar reflectivity factor at two adjacent time points was selected and paired with rain gauge observation rainfall. Then, a fitting method that gradually narrows the range of 'a' values ​​was used to search for 'a' values ​​that satisfy formula (8). During this process, the range of 'a' values ​​was set to [10, 1024], and the range of 'b' values ​​was set to [1.1, 2], in order to eliminate inappropriate ZR relationships. Finally, a dynamic ZR relationship formula suitable for local real-time weather was obtained through fitting, and the precipitation rate was calculated based on it. During fitting, an adaptive dynamic time window was used to adjust the data length to fit the ZR relationship in real time, which can better characterize the type and spatiotemporal changes of the current precipitation system, while taking into account both statistical stability and data volume requirements.

[0117] Based on the above embodiments, the window length of the time window in this embodiment is obtained through the following steps:

[0118] The parameter drift is determined based on the difference between the parameters in the physical model of the relationship between the current time window and the previous time window;

[0119] Determine the adaptive factor based on the drift of the parameters;

[0120] The product of the adaptive factor and the initial window length corresponding to the weather type is used as the window length of the current time window.

[0121] To maintain consistency in timescale between station observation data and radar combined reflectivity factors, and considering the time required for the radar to complete one volume scan and the fact that the precipitation retrieved from the echo is aerial rainfall that also takes time to reach the ground, a 10-minute window is selected after the radar scan begins to calculate the cumulative observed precipitation within this time period. Here, precipitation is converted to precipitation intensity. To improve the efficiency of parameter fitting and reduce fitting errors, fitting is performed separately for different precipitation types. Considering the occurrence patterns of different types such as systematic mixed cloud precipitation, typhoon precipitation, and summer severe convective precipitation, the ZR relationship is dynamically fitted by adaptively adjusting the data time window. This approach can better characterize the type and spatiotemporal variations of precipitation systems while balancing statistical stability and data volume requirements.

[0122] The adaptive dynamic time window scheme consists of three steps, as illustrated in the diagram below. Figure 3 As shown:

[0123] ① Divide the original radar-rain gauge matching samples into 3 independent sub-databases according to weather type: convective type (strong echo, high gradient), stratiform type (uniform, low gradient), and mixed type (typhoon spiral rainband, Meiyu front, etc.).

[0124] ② Set the initial time window according to the life history characteristics of different precipitation types, as shown in Table 2, and then use "rolling + weighting" to adaptively adjust the time window.

[0125] ③ Introduce a "forgetting factor" to utilize historical data. For older samples that are past the initial window but still have reference value, use an exponentially decaying weight.

[0126] Table 2 Initial Time Window Settings

[0127]

[0128] Based on the above embodiments, this embodiment determines the parameter drift degree according to the difference between the parameters in the physical model of the relationship under the current time window and the previous time window using the following formula:

[0129] (9)

[0130] in, For parameter drift, and This represents the difference in parameters between the physical model of the relationship between the current time window and the previous time window. and These are the parameters in the physical model of the relationship within the current time window. The acceptable drift threshold;

[0131] And / or, the adaptive factor is determined based on the drift of the parameter using the following formula:

[0132] (10)

[0133] in, This is an adaptive factor.

[0134] Window length = initial window × adaptive factor k, where k is automatically adjusted by the parameter drift α within the last three time windows. a and b represent Z = aR... b The coefficients, Δa and Δb, are the differences between the results of the current window and the previous window, used to measure the parameter drift. . The tolerable drift threshold is (empirically taken as 0.15); if Then k→2 (can be extended to 24h); if Then k→0.5 (shortened to 3–6h).

[0135] Based on the above embodiments, this embodiment, after using the product of the adaptive factor and the initial window length corresponding to the weather type as the window length of the current time window, further includes:

[0136] When the current time window length is greater than the initial window length, the exponential decay weight of historical data within the time range exceeding the initial window in the current time window is calculated using the following formula:

[0137] (11)

[0138] in, The exponential decay weight of the i-th historical data is given. For the current time, Let i be the occurrence time of the i-th historical data. This is a preset time decay constant, in hours;

[0139] Based on the exponential decay weights, determine whether to use data within the time range to determine the parameters in the physical model of the relationship.

[0140] Take T decay =6h, the weight of samples within 6 hours is close to 100%; while the weight of samples outside 24 hours is set to 2%. The time decay constant T is... decay Shortened to 6 hours, making it more suitable for strong convection scenarios.

[0141] Therefore, using "drift α + exponential forgetting" for time window adaptation can achieve more reasonable and accurate dynamic updates of ZR relationships in business than a fixed time window.

[0142] Based on the above embodiments, this embodiment, after inputting the current radar echo sequence data into the SimVP network and obtaining the predicted value of the future radar echo sequence data output by the SimVP network, further includes:

[0143] Determine the fitting formula between the observed values ​​of radar echo data and the prediction error of radar echo data;

[0144] Substituting the predicted values ​​of the future radar echo sequence data into the fitting formula yields the prediction error of the predicted values ​​of the future radar echo sequence data.

[0145] The predicted values ​​of the future radar echo sequence data are corrected based on the prediction error to obtain the final predicted values ​​of the future radar echo sequence data.

[0146] In the spatial neighborhood short-term heavy precipitation prediction model, the deep learning model SimVP-Rw is post-processed. Since the deep learning model still suffers from echo attenuation and fuzzy smoothing issues for extrapolation forecasts longer than 1 hour, statistical post-processing correction methods can effectively correct the radar echo attenuation problem. This invention establishes a post-processing correction formula (12) for the 0-2 hour radar reflectivity factor for systematic mixed cloud precipitation and local convective cloud precipitation. The fitting formula for the observation and forecast errors of the radar reflectivity factor is as follows: Figure 4 As shown:

[0147] Systemic hybrid cloud

[0148] Localized convective clouds (12)

[0149] Among them, st is the forecast sequence with a value of 1-20. By fitting the equation, the attenuation problem of different types of heavy precipitation echoes can be effectively corrected.

[0150] Figure 5 A flowchart illustrating the modeling and validation process for short-term heavy precipitation forecasting models is presented. Furthermore, due to the localized nature of short-term heavy precipitation, precise, quantitative forecasting at specific locations is extremely challenging. Therefore, a spatial neighborhood method is proposed, significantly improving the forecast score for short-term heavy precipitation and enhancing the operational applicability of heavy precipitation warnings, thus contributing to better economic and social benefits of disaster prevention and mitigation. Here, for different precipitation levels of 20 mm / h and 50 mm / h, based on the optimal TS score, a neighborhood radius of 10-15 km is selected for expansion for both systematic and localized heavy precipitation systems, effectively improving the forecast score for heavy precipitation.

[0151] This study examines the hourly precipitation intensity in a specific region from May to July 2025, scoring short-duration heavy precipitation events with hourly rainfall intensities reaching 20 mm / h and 50 mm / h. A national-level wind and thunder model is used for comparison, with data intervals of 3 hours. The performance of the SimVP-Rw model, the physical model, and the national-level wind and thunder model are compared. The physical model is a short-duration heavy precipitation statistical model constructed based on dual-polarization radar characteristics. The wind and thunder model is used as the primary comparison model to illustrate the technical advantages of this invention. Results are shown in [Figure number missing]. Figure 6 Tables 3 and 4.

[0152] The period from May to July encompasses systematic precipitation during the plum rain season, localized convective precipitation in summer, and typhoon precipitation. As seen from the scoring indicators, the SimVP-Rw model significantly outperforms the physical model and the meteorological model in terms of 1-hour forecast lead time, achieving a maximum 1-hour TS of 0.251, while the physical model and meteorological model have TS values ​​of 0.181 and 0.173 respectively, representing an improvement of 43% over the meteorological model. The SimVP-Rw model has a POD (Position Optimization Distributed) of 47%, while the physical model and meteorological model have 41% and 22% respectively. The BIAS (Breakthrough Index) of the SimVP-Rw model is 0.34, the physical model is 0.65, and the meteorological model is 0.52. Here, the BIAS index is the value minus 1, representing the magnitude of the deviation; the closer the index is to 0, the smaller the deviation, indicating that the actual and forecast frequencies are close. Because deep learning models show a decreasing trend with increasing forecast lead time, the advantage of the 2-hour SimVP-Rw model diminishes, with the TS decreasing to 0.101, slightly higher than the physical model and the wind and thunder model, but with the smallest BIAS bias. The quantitative score (ME) index characterizes the quantitative forecast score for 50 mm / h. It can be seen that the SimVP-Rw model has the highest score for heavy precipitation exceeding 50 mm, averaging 0.062, with an improvement rate of 59% compared to the wind and thunder model, indicating that it has a certain forecasting capability for extreme precipitation exceeding 50 mm.

[0153] Table 3. Hourly Rating Results for May-July 2025

[0154]

[0155] Table 4. Second-hour scoring results from May to July 2025

[0156]

[0157] The advantages and applicability of the short-term heavy precipitation prediction model of this invention are illustrated below by comparing three forecasting models (SimVP-Rw model, physical model, and wind and thunder model) for three cases: mixed cloud system heavy precipitation on June 14, 2025, typhoon precipitation on July 30, 2025, and local convective heavy precipitation on August 4, 2025.

[0158] The main testing indicators include: TS, POD (hit rate), FAR (false alarm rate), BIAS (biasedness amplitude), and ME score for extreme heavy precipitation (50 mm / h), calculated using the following formula:

[0159] ; ; (13)

[0160] (14)

[0161] (15)

[0162] In formulas 13 to 15, NA represents the number of correctly predicted stations (times), NB represents the number of false reports (times), and NC represents the number of missed reports (times). In formula (14), BIAS characterizes the deviation magnitude; the closer this value is to 0, the more likely the number of forecasts and actual occurrences are equal, indicating no systematic bias. In formula (15)... The hourly precipitation is observed at the i-th grid point. ME represents the corresponding hourly precipitation forecast, and ME is the deviation score of the precipitation. The larger the error, the lower the score.

[0163] 1) Case of heavy precipitation in a mixed cloud system

[0164] June 14, 2025, was a typical period of systemic heavy rainfall during the plum rain season. The comparative evaluation scores of the three models are shown in Tables 5 and 6. The SimVP-Rw model outperformed the physical model and the wind-thunder model, with a 1-hour forecast TS of 0.35, compared to 0.24 for the wind-thunder model, representing an improvement rate of 45%. The SimVP-Rw model achieved a POD of 64%, while the wind-thunder model achieved 29%, representing an improvement rate of 120%. Its ME score also reached 0.124, outperforming the other models. The model's 2-hour forecast score was close to that of the physical model, but the physical model had a higher BIAS, indicating a higher likelihood of false alarms. Compared to the wind-thunder model, the SimVP-Rw model still showed a significant advantage, with a TS improvement rate of 58%. The ME score remained significantly superior in the 2-hour period. For systemic heavy rainfall, the SimVP-Rw model of this invention significantly outperformed other models in both quantitative and qualitative assessments.

[0165] Table 5. Scoring results for the first hour on June 14, 2025.

[0166]

[0167] Table 6. Scoring results for the second hour on June 14, 2025.

[0168]

[0169] 2) Cases of localized convective heavy rainfall

[0170] On August 4, 2025, a localized convective heavy precipitation event occurred under the control of a stable, low-motion weather system under the influence of a subtropical high. The comparison and verification of the three models are shown in Table 7. The SimVP-Rw model achieved a 1-hour forecast TS score of 0.39, while the physical model and the wind-thunder model scored 0.25, representing an improvement rate of 56%. The SimVP-Rw model had a hit rate of 54%, and a POD improvement rate of 92% compared to the wind-thunder model. The SimVP-Rw model's BIAS was close to 0, and its score for extreme heavy precipitation of 50 mm / h reached 0.164, significantly higher than the other models. However, for localized convective precipitation, due to its rapid formation and dissipation, and shorter forecast lead time, the 1-hour forecast performed better, significantly outperforming the physical model and the wind-thunder model.

[0171] Table 7. Scoring results for the first hour on August 4, 2025

[0172]

[0173] July 30, 2025, is a case study of typhoon precipitation. The comparison and verification of the three models are shown in Tables 8 and 9. Typhoon precipitation belongs to a tropical maritime precipitation system, with precipitation efficiency significantly different from continental precipitation. While the echo intensity is moderate, the precipitation efficiency is high. The model of this invention effectively predicted the evolution characteristics of the spiral rainband of the typhoon system and accurately predicted the intensity of extreme precipitation based on the adaptive dynamic ZR relationship. The scores show that the SimVP-Rw model significantly outperforms the wind and thunder and physical models in the 1st and 2nd hour forecasts of short-duration heavy typhoon precipitation. The improvement rates of the 1-hour and 2-hour TS scores relative to the wind and thunder models are 98% and 76%, respectively. From the BIAS bias analysis, the SimVP-Rw model has the closest BIAS to 0, with the smallest bias. In particular, the ME index for extreme precipitation of 50 mm / h is significantly higher than other models, reaching 0.275, while the wind and thunder model significantly underestimates the magnitude of typhoon precipitation with high precipitation efficiency and fails to predict extreme heavy precipitation.

[0174] Table 8. Scoring results for the first hour on July 30, 2025.

[0175]

[0176] Table 9. Scoring results for the second hour on July 30, 2025.

[0177]

[0178] This invention proposes a spatial neighborhood short-term heavy precipitation nowcasting method coupled with deep learning and a physical model. The model consists of a three-layer CNN framework. It extracts spatial features through a spatial encoder, learns temporal evolution through a spatiotemporal transformer (Translator) to achieve temporal potential dynamic modeling, and then reconstructs the features through a spatial decoder. Therefore, based on training with large radar datasets, a loss function is reconstructed to train a radar reflectivity factor short-term prediction model. This model is then fused with an adaptive dynamic ZR relationship physical model to achieve short-term heavy precipitation forecasting. Simultaneously, a statistical post-processing correction method is used to compensate for the shortcomings of deep learning, making short-term heavy precipitation and other destructive convective weather more predictable. Therefore, this invention is of great significance for further improving the short-term forecasting capability of short-term heavy precipitation and extreme precipitation, increasing the lead time for warnings, and contributing to disaster prevention and mitigation.

[0179] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that the solutions described in the foregoing embodiments can be modified, or some technical features can be equivalently replaced; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for nowcasting heavy precipitation based on the coupling of deep learning and a physical model, characterized in that, include: The current radar echo sequence data is input into the SimVP network to obtain the predicted value of the future radar echo sequence data output by the SimVP network. The SimVP network is trained by using radar echo sequence data samples as samples and the corresponding real observation value of the future radar echo sequence data as labels, and through an adaptive loss function. The predicted values ​​of the future radar echo sequence data are substituted into the physical model of the relationship between radar echo data and precipitation intensity to obtain the predicted value of precipitation intensity. The parameters in the physical model of the relationship are obtained by fitting historical data of different time windows according to different weather types. The window length of the time window is obtained through the following steps: The parameter drift is determined based on the difference between the parameters in the physical model of the relationship between the current time window and the previous time window; Determine the adaptive factor based on the drift of the parameters; The product of the adaptive factor and the initial window length corresponding to the weather type is used as the window length of the current time window; The parameter drift is determined using the following formula based on the difference between the parameters in the physical model of the relationship between the current time window and the previous time window: ； in, For parameter drift, and This represents the difference in parameters between the physical model of the relationship between the current time window and the previous time window. and These are the parameters in the physical model of the relationship within the current time window. The acceptable drift threshold; The adaptive factor is determined based on the drift of the parameter using the following formula: ； in, This is an adaptive factor.

2. The method for nowcasting heavy precipitation based on the coupling of deep learning and physical models according to claim 1, characterized in that, The SimVP network includes: A spatial encoder is used to extract spatial features. The spatial encoder uses multiple ordinary convolutional layers to extract spatial features, and stacks convolutional layers, normalization layers and activation functions to extract spatial features. A spacetime converter is used to learn temporal evolution. The spacetime converter uses multiple time modules to learn spacetime dependencies and temporal changes, uses the Inception module to construct an encoder-decoder structure, and employs residual connections to preserve spatial features. A spatial decoder is used to integrate spatiotemporal information to predict future frames. The spatial decoder uses multiple upsampling layers to decode the latent space into predicted future frames and utilizes transposed convolutional layers, normalization layers, and activation functions to reconstruct ground truth frames.

3. The method for nowcasting heavy precipitation based on the coupling of deep learning and physical models according to claim 1, characterized in that, Before inputting the current radar echo sequence data into the SimVP network to obtain the predicted value of the future radar echo sequence data output by the SimVP network, the process also includes: Radar echo sequence data samples are input into the SimVP network to obtain the predicted values ​​of future radar echo sequence data output by the SimVP network. Determine the MSE loss between the predicted value of the future radar echo sequence data corresponding to the radar echo sequence data sample and the corresponding actual observation value, as well as the TV regularization loss of the predicted value of the future radar echo sequence data corresponding to the radar echo sequence data sample. The MSE loss and TV regularization loss are fused to obtain a comprehensive loss function, which is then used to train the SimVP network.

4. The method for nowcasting heavy precipitation based on the coupling of deep learning and physical models according to claim 3, characterized in that, The combined loss function is obtained by fusing the MSE loss and TV regularization loss using the following formula: ； in, For the comprehensive loss function, This represents the predicted value at the i-th time interval in the predicted values ​​of the future radar echo sequence data. This represents the actual observation value at the i-th time interval. This represents the value of the j-th point in the predicted values ​​at time i. This represents the value of the j-th point in the predicted values ​​at time i+1. This represents the value of the (j+1)th point in the predicted values ​​at time i. Indicates weight, Indicates the adjustment coefficient; the weight is based on The threshold range to which it belongs is determined, and the weight corresponds one-to-one with the threshold range.

5. The method for nowcasting heavy precipitation based on the coupling of deep learning and physical models according to claim 1, characterized in that, Before substituting the predicted values ​​of the future radar echo sequence data into the physical model relating radar echo data and precipitation intensity to obtain the predicted precipitation intensity values, the process also includes: Establish the correlation between radar echo data and rain gauge observations; By substituting historical radar echo data into the aforementioned correlation, the instantaneous rainfall intensity is obtained; A target function is constructed based on the difference between the instantaneous rainfall intensity and the corresponding rainfall observed by the rain gauge. The coefficients in the correlation are adjusted to minimize the objective function, thereby obtaining the parameters of the physical model of the relationship.

6. The method for nowcasting heavy precipitation based on the coupling of deep learning and physical models according to claim 5, characterized in that, The formula for the objective function is: ； in, Let m be the objective function, and m be the number of historical radar echo data. The instantaneous rainfall intensity is obtained by inverting the i-th historical radar echo data. The rainfall is measured by a rain gauge at the same time as the i-th historical radar echo data.

7. The method for nowcasting heavy precipitation based on the coupling of deep learning and physical models according to claim 1, characterized in that, After multiplying the adaptive factor by the initial window length corresponding to the weather type as the window length of the current time window, the method further includes: When the current time window length is greater than the initial window length, the exponential decay weight of historical data within the time range exceeding the initial window in the current time window is calculated using the following formula: ； in, The exponential decay weight of the i-th historical data is given. For the current time, Let i be the occurrence time of the i-th historical data. The preset time decay constant; Based on the exponential decay weights, determine whether to use data within the time range to determine the parameters in the physical model of the relationship.

8. The method for nowcasting heavy precipitation based on the coupling of deep learning and physical models according to claim 1, characterized in that, After inputting the current radar echo sequence data into the SimVP network to obtain the predicted value of the future radar echo sequence data output by the SimVP network, the process also includes: Determine the fitting formula between the observed values ​​of radar echo data and the prediction error of radar echo data; Substituting the predicted values ​​of the future radar echo sequence data into the fitting formula yields the prediction error of the predicted values ​​of the future radar echo sequence data. The predicted values ​​of the future radar echo sequence data are corrected based on the prediction error to obtain the final predicted values ​​of the future radar echo sequence data.

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