## 4 Discussion
### Uncertainty Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Distribution**} & \multicolumn{4}{c}{\(R^{2}\) **for Wind Speed**} & \multicolumn{4}{c}{\(R^{2}\) **for Wind Power**} \\ \cline{3-10}  & & **Site 1** & **Site 2** & **Site 3** & **Site 4** & **Site 1** & **Site 2** & **Site 3** & **Site 4** \\ \hline \multirow{4}{*}{MODA-CM2} & Normal & 0.8899 & 0.8770 & 0.8731 & 0.7568 & 0.6571 & 0.6800 & 0.6008 & 0.5499 \\  & Logistic & 0.9555 & 0.9487 & 0.9432 & 0.8549 & 0.8105 & 0.8522 & 0.7496 & 0.7045 \\  & Stable & 0.9760 & 0.9729 & 0.9671 & 0.9407 & 0.9795 & 0.9911 & 0.9698 & 0.9684 \\  & \(t\)-Location Scale & 0.9846 & 0.9825 & 0.9768 & 0.9466 & 0.9784 & 0.9926 & 0.9634 & 0.9573 \\ \hline \multirow{4}{*}{MODA-CM3} & Normal & 0.8918 & 0.8752 & 0.8776 & 0.7670 & 0.6598 & 0.6813 & 0.6005 & 0.5572 \\  & Logistic & 0.9564 & 0.9468 & 0.9470 & 0.8650 & 0.8131 & 0.8529 & 0.7498 & 0.7132 \\  & Stable & 0.9761 & 0.9710 & 0.9704 & 0.9487 & 0.9831 & 0.9917 & 0.9694 & 0.9749 \\  & \(t\)-Location Scale & 0.9839 & 0.9812 & 0.9796 & 0.9544 & 0.9820 & 0.9933 & 0.9632 & 0.9642 \\ \hline \multirow{4}{*}{MODA-CM4} & Normal & 0.8938 & 0.8766 & 0.8778 & 0.7755 & 0.6639 & 0.6622 & 0.6042 & 0.5599 \\  & Logistic & 0.9579 & 0.9490 & 0.9473 & 0.8739 & 0.8175 & 0.8563 & 0.7545 & 0.7160 \\ \cline{1-1}  & Stable & 0.9772 & 0.9738 & 0.9708 & 0.9568 & 0.9848 & 0.9943 & 0.9726 & 0.9776 \\ \cline{1-1}  & \(t\)-Location Scale & 0.9851 & 0.9839 & 0.9799 & 0.9624 & 0.9838 & 0.9953 & 0.9666 & 0.9682 \\ \hline \multirow{4}{*}{MODA-CM5} & Normal & 0.8931 & 0.8766 & 0.8792 & 0.7767 & 0.6661 & 0.6850 & 0.6069 & 0.5648 \\ \cline{1-1}  & Logistic & 0.9575 & 0.9486 & 0.9482 & 0.8752 & 0.8211 & 0.8582 & 0.7562 & 0.7225 \\ \cline{1-1}  & Stable & 0.9771 & 0.9730 & 0.9712 & 0.9575 & 0.9876 & 0.9942 & 0.9731 & 0.9824 \\ \cline{1-1}  & \(t\)-Location Scale & 0.9832 & 0.9830 & 0.9806 & 0.9629 & 0.9866 & 0.9952 & 0.9671 & 0.9725 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: \(R^{2}\) Values of Each Distribution Fitting. Table 11 shows that the combined model based on MODA and the five sub-models obtained satisfactory uncertainty analysis assessment results, which proves that the proposed model is superior to the other combined models. Using the wind power results for Site 1 as examples at the 15% significance level, the FICP values obtained from each combined model with different numbers of sub-models (MODA-CM2, MODA-CM3, MODA-CM4 and MODA-CM5) were found to be 77.58%, 79.71%, 81.97% and 82.96%, respectively, whereas the FINAW values were 0.0852, 0.0787, 0.0726 and 0.0694, respectively. Furthermore, the proposed model resulted in reductions in AWD values of 0.1119, 0.0645, and 0.0214, respectively, compared with the combined model with five sub-models. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Metric** & **Definition** & **Equation** \\ \hline Upper Bound & Upper bounds of the wind speed forecasting value & \(U(i)=F(i)+\frac{k_{1}-5\omega_{i}^{2}\omega^{2}}{N}\) \\ Lower Bound & Lower bounds of the wind speed forecasting value & \(L(i)=F(i)-\frac{k_{1}-5\omega_{i}^{2}\omega^{2}}{N}\) \\ FICP & Forecast interval coverage probability of testing dataset & \(\textbf{FICF}=\frac{k_{1}-5\omega_{i}^{2}}{N}\) \(\xi\times 100\times\) \\ FINAW & Forecast interval normalized average width of testing dataset & \(\textbf{FICF}=\frac{k_{1}-5\omega_{i}^{2}}{N}\) \((U_{i}-L_{i})\) \\ AWD, & Accumulated width deviation of testing sample \(i\) & \(0\), \(Au_{i}\in[L_{i},L_{i}]\) \\ AWD & Accumulated width deviation of testing dataset & \(\textbf{AMD}=\frac{k_{1}-5\omega_{i}^{2}}{N}\) \(\textbf{AMD}\). \\ \hline \hline \end{tabular} Note: \(F(i)\) is the corresponding point prediction value at point \(i\). \(K\) and \(\sigma\) are the quantile and scale parameters of the logistic DF. \(N\) represents the forecasting length, and \(NR\) is the difference between the maximum and minimum forecasting values. If the actual value is \(Au_{i}\in[L_{i},L_{i}],\ c_{i}=1\); otherwise, \(c_{i}=0\).  
\end{table}