# 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
However, even at the largest \(p^{\prime}\) (\(p^{\prime}=12\) ), the error was lower in the combined model than in the harmonic analysis method. Therefore, the combined model is more accurate and more suitable for short-term tidal level prediction than the simple harmonic model. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**\(p^{{}^{\prime}}\)** & \(\mathbf{E_{\text{MA}}}\)/\(\mathbf{\text{m}}^{2}\) & \(\mathbf{E_{\text{MS}}}\)/\(\mathbf{\text{m}}\) & \(\mathbf{E_{\text{RMS}}}\)/\(\mathbf{\text{m}}\) & \(\mathbf{r}\) \\ \hline
1 & 0.0218577 & 0.0009071 & 0.0301173 & 0.9916444 & 29.233 \\
2 & 0.0163588 & 0.0005606 & 0.0236780 & 0.9948650 & 40.472 \\
3 & 0.0152412 & 0.0005076 & 0.0225293 & 0.9953641 & 130.600 \\
4 & 0.0153038 & 0.0005076 & 0.0225293 & 0.9953641 & 169.639 \\
6 & 0.0154409 & 0.0005186 & 0.0227718 & 0.9952334 & 281.034 \\
12 & 0.0793346 & 0.0073769 & 0.0858892 & 0.9904756 & 556.413 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The input of SVR model comparisons of prediction accuracy of the combined method at Bay Waveland Yacht Club Tidal Station. The first column lists “\(p^{\prime}\)”, which refers to the fact that when the prediction time step is 1, the residual values from \(t-1\) to \(t-p^{\prime}\) moment is used to predict the value at time \(t\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Tidal Stations** & **Tidal Type** & \(p^{{}^{\prime}}\) & \multicolumn{2}{c}{**Combined Model**} & \multicolumn{2}{c}{**SVR Model**} & \multicolumn{2}{c}{**Harmonic Analysis**} \\ \cline{4-9}  & & \(\mathbf{E_{\text{RMS}}}\)/\(\mathbf{m}\) & \(\mathbf{r}\) & \(\mathbf{E_{\text{RMS}}}\)/\(\mathbf{m}\) & \(\mathbf{r}\) & \(\mathbf{E_{\text{RMS}}}\)/\(\mathbf{m}\) & \(\mathbf{r}\) \\ \hline Naviliwili & Semidirurnal mixed tide & 3 & 0.0157421 & 0.9967487 & 0.0637458 & 0.9267340 & 0.0517735 & 0.9760012 \\ The Battery & Semidirurnal tide & 2 & 0.0345787 & 0.9945872 & 0.2547214 & 0.8998741 & 0.2661074 & 0.9014375 \\ Texas Point & Diurnal mixed tide & 2 & 0.0424531 & 0.9857817 & 0.0845512 & 0.9459475 & 0.1908219 & 0.7382920 \\ Bay Waveland Yacht Club & Diurnal tide & 3 & 0.0152928 & 0.9906615 & 0.0498613 & 0.9738146 & 0.1805706 & 0.7188010 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Tidal-type comparisons of prediction errors in the harmonic analysis, SVR, and combined models. The third column lists “\(p^{\prime}\)”, which refers to the fact that when the prediction time step is 1, the value from \(t-1\) to \(t-p^{\prime}\) moment is used to predict the value at time \(t\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Tidal Stations** & **The Astronomical Tide** & **The Non-Astronomical Tide** \\ \hline Naviliwili & 88.1535\% & 11.8465\% \\ The Battery & 85.9369\% & 14.0631\% \\ Texas Point & 74.2308\% & 25.7692\% \\ Bay Waveland Yacht Club & 60.406\% & 39.594\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The relative magnitude of the astronomical tide and the un-astronomical tide parts of four tidal stations.