# A Model Output Deep Learning Method for Grid Temperature Forecasts in Tianjin Area
## 3 Methods
### MODL Method
#### 3D Fully Convolutional Neural Network Model (MODL-PLAIN)  
The proposed MODL-PLAIN conducts post-processing using a stack of locally connected convolutional layers. Figure 5 shows the model structure. The low-level convolution in the red dotted frame on the left is used for general feature extraction. The high-level convolution in the blue dotted frame on the right uses these features to regress temperature predictions. Figure 3: The training and operational process of model output deep learning (MODL). The feature extraction part of MODL-PLAIN is composed of three convolution modules. For the problem examined in this paper, the scale of the convolution kernel is set to \(3\times 3\times 3\). The feature extraction part can integrate a square area with a length of eight pixels pitch with the output pixel as the center point in space and time information with eight-time intervals around the output time point as the center. Figure 6 uses a geographical location in Tianjin as an example to visualize the impact of feature extraction. The location of the red dot, which is the center of the forecast area on each map, in the figure is \(117.25^{\circ}\) E \(39.25^{\circ}\) N. The information that MODL-PLAIN can integrate is the purple part of the picture, which contains 80% of Tianjin area. In the longitude direction, it can include an area of 172 km from the output point in the east-west direction. On the other hand, the information of the area of 222 km from the output point in the north-south direction can be included in the latitude direction. Therefore, the model can find the relationship between the output points of the numerical forecast over a large spatial range at the same time dimension. In the time direction, the 3-h interval model can be fully considered by the temperature change of one day before and after the output grid (\(3\) h \(\times\) 8 = 24 h). The temperature change of two days before and after the output grid (\(6\) h \(\times\) 8 = 48 h) can be fully considered by the 6-h interval model. Figure 4: The base framework of MODL. Figure 5: 3D Fully Convolutional Neural Network Model (MODL-PLAIN) structure. The seven-channel tensor on the left is the input of the model, which is the seven weather elements of the numerical forecast model. The single-channel tensor on the right is the output of the model, which is the forecast result of MODL-PLAIN. The three green tensors in the middle are the output feature tensors of the middle convolutional layer. The feature tensor has the same shape and different channels. For the activation function, we used Scale Exponential Linear Unit (SeLU) [46] instead of the popular Rectified Linear Unit (ReLU) [47]. This function can be formulated as  
\[f(x)=\lambda\left\{ \begin{array}{ll}x&if\ x>0\\ ae^{x}-\alpha&if\ x\leq 0\end{array} \right., \tag{5}\]  
where the \(x\) defines the input signal, \(f(x)\) represents the output of the activation function, and \(\alpha\) is a scaling coefficient for when \(x\) is negative. This activation function can modify the rectifier to its input, improving the accuracy of the network with a few extra calculation costs. ReLU directly sets the inputs to zero, while SeLU obtains the parameter a by calculation, so that the network has the ability to be self-normalization. Although SeLU has provided the convolution module with regularization capabilities, the additional regularization module [48] can still improve the regression effect of the model. Therefore, each convolution module in the feature extraction part on the left side of the figure adds a regularization operation. 3D Fully Convolutional Neural Network Model Based on U-Net Structure (MODL-U)  
The convolution structure of MODL-PLAIN can integrate the spatiotemporal information in a certain range. Therefore, the feature tensors that are extracted by the middle-hidden layer are considered to have the same effect as the weather system of different scales. This characteristic tensor that affects temperature prediction is called weather-like system in this paper.