## 5 Forecasting of Mean Wind Speeds  
The forecasting of the 1 min maximum wind speed is relatively challenging owing to the existence of some high-frequency components. The mean wind speed of tropical-storm winds is another important focus. Thus, multi-step forecasting of the mean wind speed is also conducted to investigate the performances of linear and nonlinear models. Figure 12 shows the mean wind speed of Rumbia, which is averaged by a time interval of 1 min. Meanwhile, the original wind speed is also plotted in Figure 13, and the comparison shows that mean wind speed has a lower rangeability and changing rate. In the forecasting, the data are divided following a scheme with the same maximum wind speed as that shown in Figure 4.  
Figure 11: Multi-step forecasting errors of different models for the 1 min maximum wind speed. (**a**) MSE; (**b**) MRPE; (**c**) RMSE; (**d**) R\({}^{2}\).  
Figure 12: Mean wind speed of the tropical storm Rumbia.  
To characterize the errors in forecasting the mean wind speed, the MAE, MRPE, RMSE, and R\({}^{2}\) values of different models at different forecasting steps are calculated, as shown in Figure 13. It is found that the errors of the BPNN, LSTM, GRU, and SVR models still increase as the forecasting step increases. However, the differences in the errors of BPNN, LSTM, and GRU decrease compared with the results of maximum wind speed shown in Figure 11. The ARIMA model offers the best forecasting of the mean wind speed among all five models and its errors change little when increasing the forecasting steps, which means the ARIMA model can achieve high accuracy in multi-step forecasting of wind speeds in the mean sense.  
Moreover, the forecasting accuracy of these models improved compared with those in the 1 min maximum wind speed forecasting. As a typical example, herein, the accuracy improvement of the ARIMA model is presented in Table 4 because it outperforms other models. It can be seen from the table that the MAE, MRPE, and RMSE of the forecasting results are reduced by more than 18%, 8%, and 20%, respectively, and the reduction proportions are not related to the forecasting step. As for the R\({}^{2}\) of the forecasting results of maximum wind speed and mean wind speed, the latter increases by at least 17.5% compared with the former. In summary, these statistical models can achieve preferable performance in terms of forecasting mean wind speed.  
Based on the aforementioned discussions, the ARIMA model is found to be suitable for short-term forecasting of tropical storms for both the maximum and mean wind speeds. Especially for the mean wind speed, the forecasting error with six steps ahead is almost the same as that of the one with one step ahead. For the BPNN, LSTM, GRU, and SVR models, they present relatively large prediction errors for either the maximum or the mean wind speed, as the non-stationarity is not well represented by these models. Hence, for the purpose of early warning, the ARIMA model is suggested as an effective approach to forecast the wind speeds of tropical storms.  
Figure 13: Multi-step forecasting errors of different models for the mean wind speed. (**a**) MSE; (**b**) MRPE; (**c**) RMSE; (**d**) R\({}^{2}\).