# A Model Output Deep Learning Method for Grid Temperature Forecasts in Tianjin Area
## 3 Methods
### MODL Method  
The core of the MODL is 3D Fully Convolutional Neural Networks (3D FCNN). Acknowledged convolution neural networks (CNN) architectures (such as AlexNet [44] or GoogLeNet [45]) require a fixed-size input image and they use a pooling layer to gradually reduce the spatial resolution of the representation. The spatial knowledge of the features will be completely lost due to the classifier's fully connected layer. Although the sliding window method can be used to solve the above problems, many redundant convolution operations affect the running speed of the model. Unlike traditional CNNs, FCNNs only consist of convolutional layers, which can be applied to images of any size. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters Abbreviation** & **Range** \\ \hline n\_estimators & (50,120,160,200,250) \\ max\_depth & (1,2,3,5,7,9,11,13) \\ min\_samples\_leaf & (1,5,10,20,30,40) \\ max\_features & (3,5,7,9) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter combination range. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Predictor** & **Abbreviation** & **Level** & **Score (\%)** \\ \hline
10-m U wind component & 10u & - & 9.249 \\
10-m V wind component & 10v & - & 10.006 \\
2 m dewpoint & 2d & - & 4.893 \\ temperature & 2t & - & - \\ Convective available & cape & - & 0.126 \\ potential energy & lcc & - & 0.032 \\ Low cloud cover & lmsl & - & 9.091 \\ Mean sea level pressure & msl & 850 hPa & 4.766 \\ Relative humidity & r & 925 hPa & 3.946 \\ Relative humidity & r & 950 hPa & 4.104 \\ Temperature & T & 850 hPa & 7.481 \\ Temperature & T & 925 hPa & 14.426 \\ Total cloud cover & tcc & - & 3.030 \\ Total precipitation & tp & - & 2.052 \\ Visibility & vis & - & 7.797 \\ U wind component & u & 850 hPa & 1.042 \\ U wind component & u & 925 hPa & 4.766 \\ U wind component & u & 950 hPa & 4.893 \\ V wind component & v & 850 hPa & 2.241 \\ V wind component & v & 925 hPa & 2.620 \\ V wind component & v & 950 hPa & 3.441 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Weather elements, abbreviations, and correlations. Because the spatial graphs of class scores are obtained in a single dense inference step, FCNN can avoid redundant convolution and pooling operations, thereby making them more computationally efficient. The post-processing of temperature prediction is greatly affected by spatial information. NWP data are also grid data in units of time and space. The size of the model input space is uncertain when the model is applied in other regions. Therefore, the structure of the FCNN is more suitable for the MODL model. The 3D FCNN is composed of three convolutional layers, and each convolutional layer is composed of several \(7\times 7\times 7\) convolution kernels. The output of each convolutional layer is noted as the feature map. The \(k\)-th output of the \(l\)-th convolutional layer can be written as:  
\[y_{l}^{k}=f\Bigl{(}\sum\
olimits_{n=1}^{m_{l-i}}W_{i}^{k,n}\otimes x_{l-1}^{n }+b_{l}^{k}\Bigr{)}, \tag{4}\]  
where \(m_{l}\) is the number of the convolution kernels in layer l of the network, \(x_{l-1}^{n}\) is the \(n\)-th input of the \(l\)-th layer convolution, \(W_{i}^{k,n}\) is the kernel convolved with the previous output features, \(b_{l}^{k}\) is the bias, and \(f\) is a non-linear activation function. The feature map that is generated by convolution is slightly smaller than its input volume. The output feature map will be two pixels smaller in each dimension than the input feature map. For a convolution kernel of size \(3\times 3\times 3\), each convolution operation will reduce 2 units on the space-time scale of the output tensor. In order to make the output tensor the same size as the input tensor, three solutions have been used to compare. The first one is to use bilinear interpolation to reduce output tensor after each convolution to the same size as the input tensor. The second is to choose a larger input area as MODL input, which can be calculated by the number of convolution modules and the size of convolution kernel.