# Linking Singular Spectrum Analysis and Machine Learning for Monthly Rainfall Forecasting
## 4 Results and Discussion  
The current study constructed the monthly rainfall forecasting models for 1-, 2-, and 3-month lead-time for two reservoir watersheds (i.e., Deji and Shihmen) in different regions of Taiwan. The standard models (i.e., LS-SVR and RF) and the hybrid models (i.e., SSA-LSSVR and SSA-RF) have comparable processes for the data modeling. The difference is that the standard models used the raw data as model input, whereas the hybrid models used the decomposed input data generated by SSA instead of raw data. Table 4 presents the forecasting performances for 1-, 2-, and 3- month lead-time for the standard and hybrid models during the validation period by the criteria of RMSE and NSE. Figure 2: Structure of the hybrid model (i.e., SSA-LSSVR, and SSA–RF). As observed from Table 4, it is found that RMSE and NSE exhibit very poor values for the standard models using original data when compared to the hybrid models using data generated by SSA. There is also evidence that the standard models have been poorly validated for all three lead-times (i.e., 1-, 2-, and 3- month lead-time). Using only the original data as input for rainfall forecasting seems less efficient than using the data generated by SSA. The LS-SVR's output is noise-sensitive and may not be effective when the level of noise is high. Therefore, the LS-SVR coupling with the SSA filtering the raw rainfall data will reduce the noise effects. Furthermore, the trained LS-SVR in conjunction with the SSA thus paid greater attention to the noise sensitivity, increasing the overall forecasting performance of the hybrid model. Ref [68] suggested that the coupled model (the SSA with predictive model) has superior performance as compared to those directly using the raw data and is therefore well suited for forecasting noisy time series. Figures 3 and 4 illustrate the time-series graphs of the observed and 1-month lead-time forecasted rainfalls by the standard models during the validation process for Deji and Shihmen Reservoir watersheds respectively. From the figures, we find that the forecasted values from the hybrid models are closer to the observed values than the values forecasted by the standard models. The scatterplots of observed vs. values forecasted by the standard models (LS-SVR and RF) and the hybrid models (SSA-LSSVR and SSA-RF) in Deji and Shihmen Reservoir watersheds are also illustrated in Figures 5 and 6 for 1-,2-, and 3-month lead-time forecasts, respectively. The rainfalls forecasted by the hybrid models were found to be very closely limited to the line of equality, whereas the rainfalls forecasted by the standard models are not close to the line of equality. This also reveals that the standard models without a data preprocessing technique are not efficient to forecast rainfalls and the hybrid models are able to approximate different rainfall properties much better than the standard models. Moreover, the performances of the hybrid models (SSA-LSSVR and SSA-RF) vary in both reservoir watersheds. For example, the SSA-LSSVR forecasts better than the SSA-RF in Deji reservoir watershed for all three lead-times. NSE values above 0.75 may characteristically be considered as a \"very good\" performance [94]. From Table 4, it is clear that all the values of NSE by the SSA-LSSVR in the Deji Reservoir watershed are greater than 0.75 and the values of the RMSE of the SSA-LSSVR are lower than the values of SSA-RF. Hence, the SSA-LSSVR outperforms the SSA-RF in the Deji Reservoir watershed. In the Shihmen Reservoir watershed, it can be seen that the NSE values of SSA-RF for each of the three lead-times belong to the \"very good\" performance class, whereas the NSE values of SSA-LSSVR indicate \"good\" performance between 0.65 and 0.75 for all three lead-times. Similarly, the RMSE values of SSA-RF are lower than the values of SSA-LSSVR for 1- and 2-month lead-time, while the RMSE value of the SSA-RF is close to the value of SSA-LSSVR for 3- month lead-time.