# Typhoon Track Prediction Based on Deep Learning
## 3 Experiment Results and Analysis
### Number of Iterations Level  
In this experiment, the performance of the model is compared at the level of the number of iterations based on the loss results of the C-LSTM-based typhoon path prediction model with a different number of iterations. In this experiment, the number of iterations of the C-LSTM-based typhoon path prediction model is set to 25, 50, and 100, respectively, and the obtained loss variation of the training set is shown in Figure 5.  
From Figure 5, we can see that the loss value of the model keeps converging as the number of iterations increases. When the number of iterations is 25, the loss of the training set is 321.94, and the loss of the test set is 213.45. When the number of iterations is 50, the loss of the training set is 140.82, and the loss of the test set is 102.46. When the number of iterations is 100, the loss of the training set is 139.28, and the loss of the test set is 101.902. Moreover, when the number of iterations increases from 50 to 100 iterations, although the time required increases, i.e., the time cost increases, the value of its loss decrease is smaller, so the case of iterations greater than 100 iterations is not considered again.  
In addition, to see the error between the prediction results and the real path of the typhoon based on the C-LSTM typhoon path prediction model with a different number of iterations, this paper takes the typhoon \"Lionrock\" in 2021 as an example and calls the folium library in Python to plot the predicted path and the actual path on a world map. In this paper, the predicted path and the actual path are plotted on the world map by calling the folium library in Python, and the typhoon path is visualized in Figure 6, in which the blue path represents the real path of the typhoon, and the orange path represents the predicted path of the typhoon by using the C-LSTM model.  
Figure 5: Losses of the C-LSTM model with selected cross-entropy loss functions and Adam optimizer for a different number of iterations. (**a**) The loss when the number of iterations is 25, (**b**) the loss when the number of iterations is 50, (**c**) the loss when the number of iterations is 100.  
From Figure 6, we can see that when the number of iterations increases, the predicted path of the typhoon and the real path of the typhoon, though there is always a certain error, gradually converge in the same general direction. For this typhoon, the surface distance error is used as the evaluation index to calculate the average surface distance error between the two, which is calculated as shown in Equation (10).  
\[\Delta d=\sqrt{\Delta x^{2}+\Delta y^{2}}\times\Delta s \tag{10}\]  
where \(\Delta x\) and \(\Delta y\) denote the longitude error and latitude error of the typhoon path prediction results, respectively, and \(\Delta s\) denotes the distance between the predicted longitude and latitude of the typhoon path and the actual longitude and latitude of the typhoon path [28], whose specific expression is shown in Equation (11).  
\[\Delta s=R\times\arccos[\sin\varphi_{1}\sin\varphi_{2}+\cos\varphi_{1}\cos \varphi_{2}\cos(\lambda_{1}-\lambda_{2})] \tag{11}\]  
where \(R\) denotes the radius of the earth, generally taken as 6371 km, and \(\varphi_{1}\) and \(\lambda_{1}\) denote the longitude and latitude of the \(i\)th point, respectively.  
When the number of iterations is 25, its average surface distance error has 56,326 m. When the number of iterations is 50, its average surface distance error has 10,621 m. When the number of iterations is 100, its average surface distance error is only 832 m. That is, when the number of iterations is 100, its average surface distance error is the smallest, and the prediction accuracy is the highest.