Rainfall nowcasting method based on U-KAN grading loss weighting and frequency self-adaption

Abstract

The invention relates to a rainfall nowcasting method based on U-KAN grading loss weighting and frequency self-adaption, which comprises the following steps: (1) carrying out quality control and screening on a radar puzzle, and establishing a data set; (2) dividing a training set, a verification set and a test set, and standardizing; (3) constructing a U-KAN model, selecting training parameters and inputting data: combining a traditional Unet structure with a KAN network to construct the U-KAN model; then performing model training to obtain a prediction result; the prediction result is restored to the original magnitude through destandardization; (4) introducing a loss function based on a root-mean-square error and grade weighting in a model training stage, and performing post-processing on model output by adopting a frequency deviation correction method; (5) integrating and averaging the forecast products processed by the two complementary strategies, and recording the forecast products as U-KANE; and (6) predicting a rainfall result in the next three hours by using radar echo data in the past one hour, and outputting a rainfall short-term and imminent forecast result by the U-KANE.

Description

Technical Field

[0001] The present invention relates to the technical field of precipitation nowcasting, and in particular to a precipitation nowcasting method based on U-KAN hierarchical loss weighting and frequency adaptation. Background Art

[0002] Against the backdrop of global warming, extreme precipitation events are becoming increasingly frequent, sudden, and localized. Their lifespans can be as short as a few hours, and their impact ranges as small as a few kilometers, making them highly susceptible to disasters such as flash floods and urban waterlogging. Traditional weather forecasting models, due to insufficient spatiotemporal resolution and lagging algorithm updates, struggle to capture the rapid evolution of small and medium-scale severe convective systems. Therefore, the development of nowcasting technology with minute-level updates and kilometer-level gridding is imperative. This is crucial for improving severe convective weather warning capabilities and supporting disaster prevention and mitigation efforts.

[0003] Meteorological radar, with its minute-by-minute observation frequency, kilometer-level spatial coverage, and direct detection of the three-dimensional structural features of severe convective systems, has become a core data source for nowcast precipitation forecasts. Radar echo extrapolation algorithms, based on tracking the motion trends of storm cells, can provide 0-2 hour nowcasts of precipitation. Among traditional extrapolation techniques, the optical flow method assumes constant pixel brightness and uses the pixel-by-pixel motion vector calculation of echoes between adjacent frames to infer future positions. The cross-correlation method, on the other hand, uses a local region matching method to determine the overall movement direction of the echo based on the maximum correlation coefficient. However, both methods are limited by the linear motion assumption and struggle to accurately characterize the generation and disappearance evolution of echoes and the nonlinear changes in intensity.

[0004] In recent years, deep learning technology has demonstrated significant advantages in the field of radar echo extrapolation due to its powerful feature extraction and spatiotemporal modeling capabilities. Convolutional neural networks (CNNs) can effectively extract the structural features of convective systems by using local convolution kernels. However, their original design was mainly for static images and they have limitations when processing continuous dynamic echo sequences. Long short-term memory networks (LSTMs) capture temporal dependencies through a gating mechanism. Their variant, ConvLSTM, combines convolution operations to further improve the prediction accuracy of convective system evolution. However, long sequence training is prone to the vanishing gradient problem and has high computational costs. The Transformer model enhances the representation of complex nonlinear evolutionary processes through a self-attention mechanism, but is inferior to CNN and LSTM in capturing local information.

[0005] Unet, a deep convolutional neural network based on a U-shaped symmetric encoder-decoder architecture, has been widely used in precipitation nowcasting tasks. Its encoder extracts image features layer by layer, while the decoder incorporates skip connections to fuse shallow, high-resolution details with deep semantic features. By introducing the Transformer architecture and attention mechanism, the AA-TransUnet model improves its global feature association capabilities. However, this improvement also brings a significant increase in computational complexity, and the opacity of its internal decision-making mechanism further exacerbates the model's "black box" nature, limiting its interpretability. Based on the Kolmogorov-Arnold theorem, the KAN neural network decomposes a multivariate continuous function into a nested composite structure of single-variable functions, parameterized as a learnable B-spline curve.

[0006] If the powerful nonlinear fitting capability of KAN is combined with the advantages of Unet's cross-scale feature fusion and a U-KAN model is constructed, when processing complex weather radar echo images, precipitation areas with irregular shapes and dynamically changing intensities can be accurately identified, thereby achieving high-quality precipitation nowcasting. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a precipitation nowcasting method based on U-KAN hierarchical loss weighting and frequency adaptation, which can effectively improve the accuracy of precipitation forecast.

[0008] To solve the above problems, the precipitation nowcasting method based on U-KAN hierarchical loss weighting and frequency adaptation described in the present invention includes the following steps:

[0009] ⑴Perform quality control and screening on radar mosaics and establish data sets;

[0010] After removing the non-precipitation echo moments from the original radar mosaic, the mosaic size of the study area was determined. The complete mosaic sequence data with echoes of 30 dBZ or above from -1 hour to 3 hours in the study area was selected. Samples were then selected at 30-minute intervals and used to build a dataset.

[0011] ⑵ Divide the training set, validation set and test set and standardize them:

[0012] The dataset is divided into training set, validation set and test set in a ratio of nearly 8:1:1, and the mean μ of the training set is used for the entire dataset. train and variance σ train Standardization is performed; the training set and validation set are used to train the model, and the test set is used to evaluate the results;

[0013] ⑶Build the U-KAN model, select training parameters and input data:

[0014] The traditional Unet structure is combined with the KAN network, and the fixed activation function is replaced by KAN's nonlinear learnable activation function to construct the U-KAN model. Then, according to the requirements of different forecast timeliness, forecast models for 0-1 hour, 1-2 hours, and 2-3 hours are constructed, with a forecast interval of 6 minutes. Training parameters are selected for model training. The stacked 6-minute historical radar puzzles are used as the feature channel input to the U-KAN model. Features are extracted through convolutional and pooling layers. The KAN layer performs dynamic nonlinear transformations on them, and skip connections are used to fuse features step by step to finally obtain the prediction results. The prediction results are then restored to the original magnitude through denormalization.

[0015] (4) In the model training phase, a loss function based on root mean square error and grade weighting is introduced to obtain a model with weighted loss function, denoted as U-KAN_W; and the frequency deviation correction method is used to post-process the model output, thus obtaining a model with frequency deviation correction, denoted as U-KAN_C;

[0016] (5) Integrate and average the forecast products processed by the two complementary strategies;

[0017] The results of U-KAN_W and U-KAN_C are integrated and averaged to form a dual-path integration model, which is denoted as U-KAN_E;

[0018] (6) Use the radar echo data of the past hour to predict the precipitation results in the next three hours, and U-KAN_E outputs the short-term precipitation forecast results.

[0019] The puzzle size of the research area in step (1) is selected as 256×256.

[0020] The learnable activation function in step (3) is a learnable B-spline function spline(x), and its expression is as follows:

[0021]

[0022] Where: B i (x) is the B-spline basis function; c i is the trainable coefficient.

[0023] The process of constructing the U-KAN model in step (3) is as follows:

[0024] ① In the encoding phase of the model, multiple convolutional blocks are used to gradually extract features and increase feature channels. Subsequently, the maximum pooling layer is used for downsampling, so that the height and width of the feature map are halved each time. After the high-level feature extraction is completed, the KAN module is embedded in the model for nonlinear transformation.

[0025] ② In the model decoding stage, upsampling is performed to restore the image size and reduce the number of channels; the extracted radar echo features of different scales are fused using skip connections; finally, the future combined reflectivity prediction result is output through the deconvolution layer.

[0026] The KAN module consists of a tokenization layer, a KAN layer, depthwise separable convolution, and layer normalization.

[0027] The selection of training parameters in step (3) refers to using the AdamW optimizer, a batch size of 8, and a total training cycle of about 90 cycles.

[0028] The frequency deviation correction method in step (4) is to first calculate the frequency ratio of each precipitation level in the input echo, then map the forecast field time data to the corresponding threshold interval based on the ratio, and finally perform dynamic correction based on the median difference between the precipitation intervals of the input field and the forecast field; its expression is as follows:

[0029]

[0030] Z corr =Z fcst +Δ M (B',B)

[0031] Where: B′ is the corrected precipitation level interval; It is a function to obtain the interval threshold of the forecast sample according to the frequency ratio; F in It is a function that calculates the frequency ratio of different precipitation levels of the input sample; Z in and Z fcst is the input and predicted radar echo; Z corr is the corrected radar echo; Δ M is the function for calculating the median difference of the interval; B is the original precipitation classification interval.

[0032] Compared with the prior art, the present invention has the following advantages:

[0033] 1. The model described in the present invention combines the traditional Unet structure with the KAN network, and uses KAN's nonlinear learnable activation function to replace the fixed activation function, thereby improving the expressiveness and interpretability of the model.

[0034] 2. The present invention uses a mosaic of radar reflectivity over a historical period of one hour to train the U-KAN model. The model output is post-processed using a loss function based on root mean square error and level weighting, as well as a frequency deviation correction method. The model is then used to forecast and improve the approaching precipitation in the next 0 to 3 hours. This makes the model sensitive to heavy precipitation events, thereby reducing the risk of missed reports and effectively improving the accuracy of precipitation forecasts.

[0035] 2. The model described in this paper dynamically adjusts the shape of the activation function to accommodate complex nonlinear relationships and deeply integrates global spatiotemporal features with local details, thereby more accurately capturing the nonlinear evolution of the precipitation system. Furthermore, the design of a visual activation function significantly enhances the interpretability of the model's decision-making process. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0037] Figure 1 This is the technical roadmap of the present invention.

[0038] Figure 2 Schematic diagram of the U-KAN model architecture (a) and KAN module (b) of the present invention.

[0039] Figure 3 Visualization of the activation function and eigenvalue output of the KAN layer in this invention (a) and the input radar echo mosaic (b), as well as the Grad-CAM graphs of Unet (c) and U-KAN (d).

[0040] Figure 4 The dual-path integration scheme for precipitation level optimization in the present invention includes: U-KAN_C is a model corrected for frequency deviation; U-KAN_W is a model using a weighted loss function; and U-KAN_E is a dual-path integration model.

[0041] Figure 5 This is a graph showing the successful threat CSI score, hit rate POD, false alarm rate FAR, and spatial neighborhood FSS score of the model in the present invention at different thresholds.

[0042] Figure 6 These are visualization examples of the forecasts of the various models in the present invention: the first row is the observation, the second row is Unet, the third row is SmaAt-Unet, the fourth row is AA-TransUnet, and the fifth row is the forecast results of U-KAN_E. DETAILED DESCRIPTION

[0043] like Figure 1 As shown in FIG, the precipitation nowcasting method based on U-KAN hierarchical loss weighting and frequency adaptation includes the following steps:

[0044] ⑴Perform quality control and screening on radar mosaics and establish data sets;

[0045] After removing non-precipitation echo moments from the original radar mosaic, the mosaic size for the study area was determined, set to 256 × 256. Complete mosaic sequence data with echoes above 30 dBZ from -1 to 3 hours out of the study area was selected. Samples were then selected at 30-minute intervals, and these samples were used to construct the dataset.

[0046] ⑵ Divide the training set, validation set and test set and standardize them:

[0047] The dataset is divided into training set, validation set and test set in a ratio of nearly 8:1:1, and the mean μ of the training set is used for the entire dataset. train and variance σ train The training set and validation set are used to train the model, and the test set is used to evaluate the results.

[0048] ⑶Build the U-KAN model, select training parameters and input data:

[0049] The traditional Unet structure is combined with the KAN network, and the fixed activation function is replaced by the nonlinear learnable activation function of KAN to construct the U-KAN model. Then, according to the requirements of different forecast timeliness, forecast models for 0-1 hour, 1-2 hours, and 2-3 hours are constructed respectively, with a forecast interval of 6 minutes. Training parameters are selected for model training. The stack of historical radar puzzles of each 6 minutes is used as the feature channel and input into the U-KAN model. Features are extracted through convolutional layers and pooling layers, and the KAN layer performs dynamic nonlinear transformation on them. Skip connections are used to fuse features step by step to finally obtain the prediction results. The prediction results are restored to the original magnitude through denormalization.

[0050] Where: the learnable activation function is the learnable B-spline function spline(x), which is expressed as follows:

[0051]

[0052] Where: B i (x) is the B-spline basis function; c i is the trainable coefficient.

[0053] The process of building the U-KAN model is as follows;

[0054] ① During the model's encoding phase, multiple convolutional blocks are used to gradually extract features and increase feature channels. Subsequently, a max pooling layer is used for downsampling, halving the height and width of the feature map each time. After high-level feature extraction, a KAN module is embedded in the model for nonlinear transformation. The KAN module consists of a tokenization layer, a KAN layer, depthwise separable convolution, and layer normalization. The tokenization layer uses convolution operations to segment the input high-dimensional feature map into flattened two-dimensional image patches, forming a continuous sequential representation. The KAN layer performs nonlinear transformations by replacing fixed node activation functions with learnable B-spline functions. Other components further enhance the model's feature extraction capabilities.

[0055] ② In the model decoding stage, upsampling is performed to restore the image size and reduce the number of channels; the extracted radar echo features of different scales are fused using skip connections; finally, the future combined reflectivity prediction result is output through the deconvolution layer.

[0056] The choice of training parameters refers to using the AdamW optimizer, a batch size of 8, and a total training of about 90 cycles.

[0057] F(·) refers to the model obtained by training in the present invention, X test The data in the test set needs to be denormalized after being input into the trained model for prediction. The process of denormalization to restore to the original magnitude is as follows:

[0058] Model F(·) for X test The prediction results It is expressed in the following mathematical formula:

[0059]

[0060] (4) In the model training stage, a loss function based on root mean square error and grade weighting is introduced to obtain a model with weighted loss function, denoted as U-KAN_W; and the frequency deviation correction method is used to post-process the model output, to obtain a model with frequency deviation correction, denoted as U-KAN_C.

[0061] Among them, the frequency deviation correction method is to first calculate the frequency ratio of each precipitation level in the input echo, then map the forecast field time data to the corresponding threshold interval based on the ratio, and finally perform dynamic correction based on the median difference between the precipitation intervals of the input field and the forecast field to eliminate the systematic deviation. Its expression is as follows:

[0062]

[0063] Z corr =Z fcst +Δ M (B′,B)

[0064] Where: B′ is the corrected precipitation level interval; It is a function to obtain the interval threshold of the forecast sample according to the frequency ratio; F in It is a function that calculates the frequency ratio of different precipitation levels of the input sample; Z in and Z fcst is the input and predicted radar echo; Z corr is the corrected radar echo; Δ M is the function for calculating the median difference of the interval; B is the original precipitation classification interval.

[0065] (5) Integrate and average the forecast products processed by the two complementary strategies;

[0066] The results of U-KAN_W and U-KAN_C are integrated and averaged to form a dual-path integration model, which is denoted as U-KAN_E.

[0067] (6) Use the radar echo data of the past hour to predict the precipitation results in the next three hours, and U-KAN_E outputs the short-term precipitation forecast results.

[0068] Example

[0069] In order to illustrate the effectiveness of the present invention, radar echo data from the summer of August 2020 to August 2022 in North China were selected for model training, and data from June to August 2023 were selected for evaluation. Figure 1 The specific process is as follows:

[0070] ⑴Perform quality control and screening on radar mosaics and establish data sets;

[0071] Moments containing non-precipitation echoes, such as ground object echoes, were removed from the original radar mosaic to prevent outliers from interfering with model training. The mosaic size for the study area was then determined, set to 256×256. Complete mosaic sequences containing echoes above 30 dBZ were selected from the entire period from -1 hour to 3 hours within the study area. Samples were then selected at 30-minute intervals and used to construct the dataset.

[0072] In actual production and life, we pay attention to heavy rainfall. This treatment allows the model to specifically learn the evolution law of convective precipitation.

[0073] ⑵ Divide the training set, validation set and test set and standardize them:

[0074] The dataset is divided into training set, validation set and test set in a ratio of nearly 8:1:1, and the mean μ of the training set is used for the entire dataset. train and variance σ trainThe training set and validation set are used to train the model, and the test set is used to evaluate the results.

[0075] ⑶Build the U-KAN model, select training parameters and input data:

[0076] This model combines the traditional Unet structure with the KAN network, using KAN's nonlinear learnable activation function to replace the fixed activation function, thereby improving the model's expressiveness and interpretability.

[0077] The U-KAN model is constructed by Figure 2 As shown in Figure a, during the model's encoding phase, multiple convolutional blocks are used to gradually extract features and increase the number of feature channels. Subsequently, a max pooling layer is used for downsampling, halving the height and width of the feature map each time. After high-level feature extraction, a KAN module is embedded in the model for nonlinear transformation. During the model's decoding phase, upsampling is performed to restore the image size and reduce the number of channels. The extracted radar echo features at different scales are fused using skip connections. Finally, a deconvolution layer outputs the future combined reflectivity prediction. The prediction is then denormalized to restore it to its original magnitude.

[0078] Figure 2 Figure b shows the internal structure of the KAN module. The KAN module consists of a tokenization layer, a KAN layer, depthwise separable convolution, and layer normalization. The tokenization layer uses convolution operations to segment the input high-dimensional feature map into flat two-dimensional image blocks, forming a continuous sequence representation. In the KAN layer, based on the Kolmogorov-Arnold theorem, the high-dimensional function is decomposed into a single variable combination, and the fixed node activation function is replaced by a learnable B-spline function. The spline function spline(x) is expressed as follows:

[0079]

[0080] Where: B i (x) is the B-spline basis function; c i is the trainable coefficient.

[0081] In the experimental setup, a B-spline structure with 9 initial mesh segments is adopted, and dynamic mesh refinement is used to enhance the local resolution.

[0082] Interpretability: Figure 3 The U-KAN visualization activation function design and the heat map generated by Grad-CAM (gradient weighted class activation mapping) are shown. The KAN layer combines the advantages of SiLU and B-spline functions to multiply the activated feature matrix with the learnable weight matrix to generate a highly nonlinear feature value output ( Figure 3 a). Figure 3As shown in Figures bd, the heatmap generated by Grad-CAM clearly illustrates the areas the model focuses on when making decisions. Compared to Unet, U-KAN highlights are more concentrated and accurately positioned on the heatmap, demonstrating U-KAN's superior feature extraction and nonlinear representation.

[0083] Based on the requirements of different forecast timelines, this paper constructs forecast models for 0-1 hour, 1-2 hours, and 2-3 hours, with a forecast interval of 6 minutes. This allows for more flexible model parameter adjustment while effectively limiting the accumulation of errors with forecast duration. A stack of historical 6-minute radar mosaics is used as the feature channel input into the U-KAN model. Features are extracted through convolutional and pooling layers, and the KAN layer performs dynamic nonlinear transformations on them. Skip connections are used to fuse features step by step to ultimately obtain the forecast results.

[0084] The selection of U-KAN model training parameters refers to using the AdamW optimizer, a batch size of 8, and a total training of approximately 90 epochs.

[0085] (4) In the model training stage, a loss function based on root mean square error and grade weighting is introduced to obtain a model with weighted loss function, denoted as U-KAN_W; and the frequency deviation correction method is used to post-process the model output, to obtain a model with frequency deviation correction, denoted as U-KAN_C.

[0086] The first optimization strategy is adopted. A loss function based on the root mean square error (RMSE) and precipitation level weighting is introduced into the model for training and prediction. Specifically, after assigning a weight to each spatial point according to the level, the RMSE of the entire spatial field is calculated. The loss function and its weights are as follows:

[0087]

[0088] Where: i and j represent the rows and columns of the spatial field respectively; W is the weight assigned to the grid point; y is the result of the observation; is the prediction result of the model in each iteration; I is the echo intensity of the corresponding pixel.

[0089] The second optimization strategy is adopted. A frequency-informed forecast bias correction method is proposed based on the consistency of radar echo frequency distribution for different precipitation levels over a short period of time. This method first calculates the frequency proportion of each precipitation level in the input echo. Based on this proportion, the forecast field time data is mapped to the corresponding threshold interval. Finally, a dynamic correction is performed using the median difference between the precipitation intervals of the input and forecast fields to eliminate systematic bias. Its expression is as follows:

[0090]

[0091] Zcorr =Z fcst +Δ M (B',B)

[0092] Where: B′ is the corrected precipitation level interval; It is a function to obtain the interval threshold of the forecast sample according to the frequency ratio; F in It is a function that calculates the frequency ratio of different precipitation levels of the input sample; Z in and Z fcst is the input and predicted radar echo; Z corr is the corrected radar echo; Δ M is the function for calculating the median difference of the interval; B is the original precipitation classification interval, which is the same as the intensity classification setting of the weight formula in the first optimization strategy.

[0093] Two complementary optimization strategies are adopted, such as Figure 4 As shown in the figure, a loss function (root mean square error) weighted by precipitation level is designed in the original U-KAN model for training and prediction; and the frequency deviation correction method is used to correct the original U-KAN forecast results based on the frequency distribution of radar echoes in the past hour.

[0094] (5) Integrate and average the forecast products processed by the two complementary strategies;

[0095] The results of U-KAN_W and U-KAN_C are integrated and averaged to form a dual-path integration model, which is denoted as U-KAN_E.

[0096] like Figure 4 As shown in Figure 2, the results of the two complementary optimization strategies are integrated and averaged, and the final nowcast is output by U-KAN_E. Its performance is evaluated on the test set. The baseline models compared with U-KAN_E include Unet, SmaAt-Unet, and AA-TransUnet. The results are as follows:

[0097] Depend on Figure 5It can be seen that the CSI scores of each model show a rapid decrease from 0 to 1 hour and a slow decrease from 1 to 3 hours with changes in forecast time. At thresholds of 30 dBZ and 40 dBZ, the U-KAN_E model achieves the highest CSI score for successful threats, especially after a 0.5-hour forecast. Compared to Unet, U-KAN_E's score improves by 27.5%. Furthermore, at higher thresholds, the difference in POD scores between U-KAN_E and the baseline model is greater. This is because U-KAN_E has stronger ability to fit nonlinear relationships and express local details, enabling it to more effectively capture the evolution of heavy precipitation areas and convective systems. The baseline model's forecasts, on the other hand, tend to produce smoothed results, making them less able to predict extreme events. Furthermore, compared to the CSI score, the FSS score demonstrates a more significant improvement in the accuracy of U-KAN_E's forecasts, exceeding 35%.

[0098] (6) Use the radar echo data of the past hour to predict the precipitation results in the next three hours, and U-KAN_E outputs the short-term precipitation forecast results.

[0099] In order to evaluate the performance of each model forecast in the entire precipitation evolution process, a rare extreme precipitation event in the study area at the end of July 2023 was selected as a case for analysis. Figure 6 The precipitation evolution and model forecast results for this event are presented. In the early stages of the cyclone's formation, only U-KAN_E accurately captured the area of ​​strong radar echoes. During the mature development phase of the cyclone, all models were able to accurately predict the location and shape of the cyclone center, and the precipitation intensity predicted by U-KAN_E was closest to the actual situation. As the cyclone gradually contracted and gathered into stratiform mixed clouds, decaying and dissipating toward the northeast, the performance of the baseline model continued to decline. The strong echo center was completely unpredictable by AA-TransUnet. In summary, only U-KAN_E was able to maintain a high level of forecasting throughout this precipitation event.

[0100] Overall, the U-KAN model can better extract the nonlinear characteristics of radar echoes. Through hierarchical loss weighting and frequency-adaptive optimization, the model's overall score significantly improves compared to existing models. It also boasts shorter prediction times and higher accuracy than traditional radar extrapolation algorithms. Furthermore, this method demonstrates high timeliness and accuracy in severe convective weather forecasting, providing 0- to 3-hour nowcast precipitation forecasts for scenarios such as urban disaster prevention and aviation support, demonstrating significant application value.

Claims

1. A precipitation nowcasting method based on U-KAN hierarchical loss weighting and frequency adaptation includes the following steps: ⑴Perform quality control and screening on radar mosaics and establish data sets; After removing the non-precipitation echo moments from the original radar mosaic, the mosaic size of the study area was determined. The complete mosaic sequence data with echoes of 30 dBZ or above from -1 hour to 3 hours in the study area was selected. Samples were then selected at 30-minute intervals and used to build a dataset. ⑵ Divide the training set, validation set and test set, and standardize them: The dataset is divided into training set, validation set and test set in a ratio of nearly 8:1:1, and the mean μ of the training set is used for the entire dataset. train and variance σ train Standardization is performed; the training set and validation set are used to train the model, and the test set is used to evaluate the results; ⑶Build the U-KAN model, select training parameters and input data: The traditional Unet structure is combined with the KAN network, and the fixed activation function is replaced by KAN's nonlinear learnable activation function to construct the U-KAN model. Then, according to the requirements of different forecast timeliness, forecast models for 0-1 hour, 1-2 hours, and 2-3 hours are constructed, with a forecast interval of 6 minutes. Training parameters are selected for model training. The stacked 6-minute historical radar puzzles are used as the feature channel input to the U-KAN model. Features are extracted through convolutional and pooling layers. The KAN layer performs dynamic nonlinear transformations on them, and skip connections are used to fuse features step by step to finally obtain the prediction results. The prediction results are then restored to the original magnitude through denormalization. (4) In the model training phase, a loss function based on root mean square error and grade weighting is introduced to obtain a model with weighted loss function, denoted as U-KAN_W; and the frequency deviation correction method is used to post-process the model output, thus obtaining a model with frequency deviation correction, denoted as U-KAN_C; (5) Integrate and average the forecast products processed by the two complementary strategies; The results of U-KAN_W and U-KAN_C are integrated and averaged to form a dual-path integration model, which is denoted as U-KAN_E; (6) Use the radar echo data of the past hour to predict the precipitation results in the next three hours, and U-KAN_E outputs the short-term precipitation forecast results.

2. The precipitation nowcasting method based on U-KAN hierarchical loss weighting and frequency adaptation according to claim 1, characterized in that: The puzzle size of the research area in step (1) is selected as 256×256.

3. The precipitation nowcasting method based on U-KAN hierarchical loss weighting and frequency adaptation according to claim 1, characterized in that: The learnable activation function in step (3) is a learnable B-spline function spline(x), and its expression is as follows: Where: B i (x) is the B-spline basis function; c i is the trainable coefficient.

4. The precipitation nowcasting method based on U-KAN hierarchical loss weighting and frequency adaptation according to claim 1, characterized in that: The process of constructing the U-KAN model in step (3) is as follows: ① In the encoding phase of the model, multiple convolutional blocks are used to gradually extract features and increase feature channels. Subsequently, the maximum pooling layer is used for downsampling, so that the height and width of the feature map are halved each time. After the high-level feature extraction is completed, the KAN module is embedded in the model for nonlinear transformation. ②In the model decoding stage, upsampling is performed to restore the image size and reduce the number of channels; The extracted radar echo features of different scales are fused using skip connections; Finally, the future combined reflectivity prediction result is output through the deconvolution layer.

5. The precipitation nowcasting method based on U-KAN hierarchical loss weighting and frequency adaptation according to claim 4, characterized in that: The KAN module consists of a tokenization layer, a KAN layer, depthwise separable convolution, and layer normalization.

6. The precipitation nowcasting method based on U-KAN hierarchical loss weighting and frequency adaptation according to claim 1, characterized in that: The selection of training parameters in step (3) refers to using the AdamW optimizer, a batch size of 8, and a total training cycle of about 90 cycles.

7. The precipitation nowcasting method based on U-KAN hierarchical loss weighting and frequency adaptation according to claim 1, characterized in that: The frequency deviation correction method in step (4) is to first calculate the frequency ratio of each precipitation level in the input echo, then map the forecast field time data to the corresponding threshold interval based on the ratio, and finally perform dynamic correction based on the median difference between the precipitation intervals of the input field and the forecast field; its expression is as follows: Z corr =Z fcst +Δ M (B′,B) Where: B′ is the corrected precipitation level interval; It is a function to obtain the interval threshold of the forecast sample according to the frequency ratio; F in It is a function that calculates the frequency ratio of different precipitation levels of the input sample; Z in and Z fcst is the input and predicted radar echo; Z corr is the corrected radar echo; Δ M is the function for calculating the median difference of the interval; B is the original precipitation classification interval.

Images