## 3 The Method Presented in This Paper
### Cold Wave Recognition Process  
#### 3.1.1 Cold Wave Weather Recognition Model Based on Improved U-Net  
The U-Net model is a deep learning architecture designed for data segmentation [37]. It consists of a contracting path on the left and an expansive path on the right, forming a U-shaped structure, hence the name \"U-Net.\" The specific structure is shown in Figure 5. The contracting path follows a typical CNN structure, consisting of two convolutional layers followed by a max pooling layer. The dimensionality of cold wave features doubles after each pooling operation. The contracting path uses \(Relu\) as the activation function. \[Relu(x)=max\{0,x\} \tag{5}\]  
The input value is \(x\). It is compared with 0; if \(x>0\), the output is \(x\), and if \(x\leq 0\) the output is 0. Figure 5: U-Net classification model structure. In the expansive path, a transposed convolution operation is performed to double the spatial resolution of the cold wave feature data generated by the contracting path. The feature data are then concatenated with the corresponding feature from the contracting path, further increasing the spatial resolution. Two convolutional layers are subsequently applied for feature extraction, and this structure is repeated. The U-Net can learn more features of cold spells from limited data by increasing the dimensionality through convolution and concatenating data features, thus improving the model's generalization ability to recognize cold spells, making it superior to conventional classification models. The number of feature channels in the final convolution layer is set to match the number of categories, and the convolution kernel size is set to \(1\times 1\). The corresponding cold wave feature data are predicted using the cross-entropy loss function. Finally, the \(Softmax\) f function is used to obtain the probability distribution, which classifies whether a cold wave occurs based on the input features. The \(Softmax\) function is expressed as follows:  
\[Softmax(z_{i})=\frac{e^{z_{i}}}{\sum\limits_{j=1}^{K}e^{z_{j}}} \tag{6}\]  
\(z_{i}\) is the \(i\)-th element of the input vector, \(K\) is the total number of classes, and \(e\) is the base of the natural logarithm. The cross-entropy loss function is defined as follows:  
\[E=\sum\limits_{x\in\Omega}\omega(x)\log(p_{l}x) \tag{7}\]  
where \(\omega(x)\) represents the regulation function, \(p_{l}x\) represents the recognition label function, and \(l=\{1,\cdots,K\}\) represents the label of each feature. Fusing different data types to fully leverage multi-dimensional information has become a key strategy for improving model performance. In this paper, a multi-modal U-Net classification model is proposed, which combines time features such as season and month with cold wave feature data in the compressed channel of the model. Cold wave events exhibit distinct seasonal patterns, and incorporating multi-modal data allows the U-Net model to effectively capture temporal information, thus significantly enhancing the accuracy of cold wave event recognition. This method not only strengthens the model's ability to capture cold wave occurrence patterns but also enhances the accuracy of cold wave recognition. The parameters of the multimodal U-Net classification model are shown in Table 2.