## 4 Performance Comparison of Different Models
### One-Step Ahead Forecasting  
Based on the five models given in Table 2, one-step ahead forecasting is carried out for the wind data shown in Figure 4. The comparison of measured and forecasted wind speeds is presented in Figure 8. As observed in the figure, the forecasting results by the ARIMA, BPNN, LSTM, and GRU models have slight differences and can generally resemble the measured wind speeds. However, the SVR model presents noticeable deviations from the \begin{table}
\begin{tabular}{c c c} \hline \hline
**No.** & **Model** & **Description** \\ \hline
1 & ARIMA & The autoregressive, differential, and moving average terms have the order of 6, 1, and 2, respectively. \\
2 & BPNN & A relatively simple model is applied, which contains an input layer with six neurons, a hidden layer with six neurons, and an output layer with six neurons. \\
3 & LSTM & The memory cell takes place of the neurons in the hidden layer of BPNN. \\
4 & GRU & The same structure as LSTM is adopted for this model. \\
5 & SVR & The numbers of input and output features equal 6 and 1, respectively. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical models employed for short-term forecasting of tropical storms. measured wind data at each instant, because the tacit assumption of Gaussian distribution to be required by SVR is not well satisfied for the measured winds. In addition, the peak wind speed of this extreme wind event is underestimated by all five models. This is probably attributed to the fact that these statistical methods based on the accumulated historical data are able to capture the primary trend of the time-series, but the abrupt changes around the peak wind speed of tropical-storm winds that present completely different patterns cannot be characterized. This point is thus proved to be a critical and difficult issue for the short-term forecasting of tropical storms using time-series models. In order to further quantify the forecasting errors, the MAE, MRPE, RMSE, and R\({}^{2}\) of the five models are calculated and listed in Table 3. It can be seen from the table that the errors of GRU and LSTM models present negligible differences to the BPNN model, despite the consideration of the memory effect. The MAE, MRPE, RMSE, of the SVR model are 1.67, 6.67%, and 2.24, respectively. The values of these indexes are obviously larger than the other models. Moreover, the R\({}^{2}\) value of the SVR is only 0.40, which indicates relatively bad forecasting compared with the measured wind speeds. Hence, the SVR provides the worst forecasting among the five models. With respect to the ARIMA model, it has the best performance in each index, which means it provides the most accurate prediction from a global point of view. The better performance of the ARIMA model is attributed to the differencing procedure that considers the non-stationarity of wind speeds in the mean sense. Based on the existing observations, the short-term forecasting of tropical-storm winds should emphatically take account of the non-stationary patterns. Figure 9 depicts the density heatmap of the forecasting errors with a comparison to the fitted normal distribution. It is observed that the errors of the ARIMA, BPNN, LSTM, and GRU models are generally satisfied with the normal distribution with small shifts from zero in the mean, especially for the results of the ARIMA and LSTM models. The ARIMA model has the smallest mean of 0.014, whereas the mean of the GRU model has reached 0.373. The error distribution of the SVR model is the flattest, which indicates the largest standard deviation. This observation is consistent with the aforementioned phenomenon that the SVR model provides the worst forecasting with large errors. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **MAE** & **MRPE/\%** & **RMSE** & **R\({}^{2}\)** \\ \hline ARIMA & 1.26 & 5.24 & 1.64 & 0.68 \\ BPNN & 1.29 & 5.35 & 1.69 & 0.66 \\ LSTM & 1.27 & 5.32 & 1.64 & 0.68 \\ GRU & 1.29 & 5.27 & 1.68 & 0.67 \\ SVR & 1.67 & 6.76 & 2.24 & 0.40 \\ \hline \hline \end{tabular}
\end{table}