# High-Precision Combined Tidal Forecasting Model
## 3 Combined Tidal Forecasting Model Based on Harmonic Analysis and ARIMA-SVR
### Model Checking
#### 3.2.4 Analysis of Prediction Results of the Combined Model  
Next, the astronomical tidal level and the non-astronomical tidal level were linearly added to obtain the overall tidal prediction throughout November 2018. Figure 14 compares the predicted tidal levels with the observed (not de-noised) data, and Figure 15 plots the predicted errors. The combined model yielded much more accurate results than the pure harmonic analysis method. The \(E_{\mathrm{RMS}}\) of the combined model was 0.022293 m, which is obviously smaller than that in the harmonic analysis method. Figure 16 linearly regresses the predictions of the combined model against the observed (not de-noised) data. The combined model clearly predicted the observed tidal level with a high accuracy. Figure 14: Comparison of the (not de-noised) observations and the water levels predicted by the combined model. Figure 13: Error distribution map of the non-astronomical tidal level. To verify the effect of de-noising, the tide level was predicted using the original data (without de-noising) and the predicted error was calculated by the above steps. The errors in the predictions are compared with those of the de-noised data in Table 4. Clearly, the wavelet transform smoothed the data and improved the prediction accuracy. This result confirms the feasibility and effectiveness of de-noising the sample data prior to analysis. To further verify the prediction accuracy of the combined model, the total tidal levels at the Bay Waveland Yacht Club station were predicted by single harmonic analysis, the combined model, the SVR model, and another common method called back propagation neural networks (the BP model) [24]. The parameters of the SVR model were optimized by the PSO algorithm. For a fair comparison, the sample data and parameters were identical in all methods. The prediction performances of the four \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data** & \(\mathbf{E_{\text{MA}}/\text{m}^{2}}\) & \(\mathbf{E_{\text{MS}}/\text{m}}\) & \(\mathbf{E_{\text{RMS}}/\text{m}}\) \\ \hline With de-noising & 0.0152928 & 0.0005121 & 0.0226293 \\ Without de-noising & 0.0245718 & 0.0015876 & 0.0398451 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the predicted tide level errors with and without de-noising. Figure 16: Linear regression plot of the predicted versus observed tidal heights. The predicted results were calculated by the combined model. Figure 15: Error distribution map of the combined model. methods are compared in Table 5. The proposed combined model required a longer training time, but yielded more accurate tidal predictions with lower errors than the other models. The prediction accuracy of a model depends on the size of the training set. Accordingly, the prediction accuracies of the SVR and combined models were compared on training sets with different sample sizes (samples collected over 1, 3, 6, or 12 months). In this comparison, the test set remained fixed. ARIMA modeling is performed on the training sets of different sample sizes, and the lagged order of time series \(p\) is determined, and the input of the model is determined thereby. Again, the data were the tidal levels at the Bay Waveland Yacht Club tidal station. The prediction results of the SVR model and the combined model are shown in Tables 6 and 7, respectively. As the sample size increased, the \(E_{\text{RMS}}\) of the tidal levels predicted by the SVR model (Table 6) changed substantially around 0.049, whereas those of the combined model (Table 7) fluctuated around 0.022 m. By contrast, the error indicators of tidal prediction were lower in the combined model than in the SVR model. The combined model thus exhibited a more accurate and stable prediction performance than the SVR model alone, within a significantly lower runtime than the SVR model. This result confirms the efficiency of the combined model. As mentioned above, the Bay Waveland Yacht Club tidal station experiences a diurnal tide.