# 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
To test the combined model on different tidal types and stations, the harmonic analysis, SVR, and combined models were trained on the tidal level data from four stations with different tidal types, and their predictive performances were evaluated in each case. Nawiliwili, The Battery, and Texas Point tidal stations were selected for tidal prediction comparison experiments, which have different tidal types. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**The Size of Sample Set** & \(p^{i}\) & \(E_{\text{MA}}/\text{m}^{2}\) & \(E_{\text{MS}}/\text{m}\) & \(E_{\text{RMS}}/\text{m}\) & \(r\) & **Time /s** \\ \hline One month & 3 & 0.0415324 & 0.0023897 & 0.0498613 & 0.9738146 & 56.042 \\ Three months & 2 & 0.0413146 & 0.0022134 & 0.0495362 & 0.9738124 & 37.312 \\ Six months & 4 & 0.0412874 & 0.0021045 & 0.0494135 & 0.9738113 & 64.617 \\ Twelve months & 3 & 0.0411763 & 0.0020983 & 0.0493245 & 0.9738137 & 143.982 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Sample-size comparison tidal prediction errors in the SVR model. The second column lists “\(p^{i}\)”, which refers to the fact that when the prediction time step is 1, the total tidal level from \(t-1\) to \(t-p^{\prime}\) moment is used to predict the total tidal level at time \(t\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & \(p^{i}\) & \(E_{\text{MA}}/\text{m}^{2}\) & \(E_{\text{MS}}/\text{m}\) & \(E_{\text{RMS}}/\text{m}\) & \(r\) & **Time/s** \\ \hline Harmonic Analysis & - & 0.1439167 & 0.0326057 & 0.1805706 & 0.52892 & 32.547131 \\ BP & 3 & 0.1381779 & 0.0194776 & 0.1395623 & 0.61248 & 7.404504 \\ PSO-SVR & 3 & 0.0415324 & 0.0023897 & 0.0498613 & 0.97381 & 56.04157 \\ Combined model & 3 & 0.0152928 & 0.0005121 & 0.0226293 & 0.99066 & 148.28581 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance comparison of different models simulating the tidal behavior at Bay Waveland Yacht Club. The second column lists “\(p^{i}\)”, which refers to the fact that when the prediction time step is 1, the residual values from \(t-1\) to \(t-p^{\prime}\) moment are used to predict the value at time \(t\). The last column lists the processing time required for the various methods. The ARIMA model was established for the tidal data of different tidal stations to determine the lagged rank of the time series \(p\), so the input of the non-astronomical tidal part was determined. The error results are shown in Table 8. At all four stations, the combined model outperformed the pure harmonic analysis and pure SVR models. In order to further measure the prediction accuracy, the relative magnitude of the astronomical tide and non-astronomical tide parts of the sample data of four tidal station was calculated, and the following Table 8 was obtained. As shown in Tables 8 and 9, it can be seen that the larger the relative magnitude of the astronomical tide, the higher the accuracy of the harmonic analysis. The harmonic analysis method is suitable for predicting tidal stations with a high relative magnitude of astronomical tides. The input of the SVR also significantly affects the prediction accuracy of the combined models. To verify the robustness of the input of SVR in the combined model determined according to the lagged rank \(p\) of the residual sequence in the ARIMA model, the combined model was trained on the tide level data from the Bay Waveland Yacht Club tidal station, and its predictive performance was compared for different inputs. The prediction results are shown in Table 10. Here, the first column lists \"\(p\)\", 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 \(t\). Increasing the \(p^{\prime}\) from 1 to 3 reduced the error in the combined model, but increasing the \(p^{\prime}\) further increased the error. The minimized error at \(p^{\prime}=3\) is consistent with the test results of the lagged rank \(p\) of the residual sequence in the ARIMA model.