## 4 Calculation Results and Discussion
### Comparison of Forecasting Models  
To verify the effectiveness and universality of the proposed CM-MDLN forecasting method, we compare the forecasting results of different methods based on the same data set mentioned above in this subsection. The following six methods are compared: support vector regression (SVR), gradient boosting regression tree (GBRT), random forest (RF), long-short-term memory network (LSTM), and, separately, MLP and CNN. The above comparison methods are all based on the Keras deep learning framework in the Python development environment. The SVR, GBRT, and RF models are implemented by calling the Sklearn machine learning library. The SVR model takes the radial basis function (RBF) as the kernel function, and the penalty coefficient \(C\) is set to 10. The GBRT and RF models take default parameter values. The LSTM model takes a three-layer network, with 64, 32, and 16 neurons in each of the three layers. The separate MLP and CNN models have the same network parameter settings as the proposed model. Since several methods such as SVR, GBRT, RF, LSTM, and separate MLP cannot directly process the spatial distribution data of precipitation, it is necessary to reduce the two-dimensional spatial distribution data of precipitation to the one-dimensional vector data before using these methods. To verify the universality of the proposed method, the HC data set is randomly divided into a training set, validation set, and testing set according to proportions of 80%, 10%, and 10%, respectively. Since the proportion of non-precipitation periods in a year is higher than that of precipitation periods, the data of the precipitation periods and non-precipitation periods contained in the randomly divided data sets are relatively evenly distributed, and the calculated results are more convincing. Among them, the training set is used for model training, the validation set is used for tuning model parameters, and the testing set is used to test the forecasting effect of the model. The comparison of the forecasted value and the true value of each model in HC city and GL city are shown in Figures 13 and 14 (the three straight lines in each figure represent \(y=1.1\)\(x\), \(y=x\), and \(y=0.9\)\(x\) from top to bottom). In the results of HC city and GL city, almost all the points of the proposed model fall between the two lines \(y=(1\pm 0.1)x\) and are closer to the diagonal line \(y=x\), which indicates that the forecasted values of this model are closer to the true values and that the forecasting accuracy is higher than that of other models. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Evaluation Metrics**} & \multicolumn{2}{c}{**Is the Spatial Distribution of Precipitation Considered?**} \\ \cline{2-3}  & **No** & **Yes** \\ \hline \(AC\) (\%) & 85.02 & 93.39 \\ \(MAPE\) (\%) & 11.77 & 5.63 \\ \(RMSE\) (MWh) & 528.66 & 217.15 \\ \(R^{2}\) (\(\times 10^{-1}\)) & 8.347 & 9.721 \\ \(APE\) \(<\) 10\% (d) 1 & 47 & 82 \\ \(APE\) \(<\) 10\% (\%) 2 & 51.09 & 89.13 \\ \(APE\) \(<\) 5\% (d) 3 & 25 & 43 \\ \(APE\) \(<\) 5\% (\%) 4 & 27.17 & 46.74 \\ \hline \hline \end{tabular}  
* The number of days with APE less than 10%. 2 The percentage of days with APE less than 10%. 3 The number of days with APE less than 5%. 4 The percentage of days with APE less than 5%.  
\end{table} 
Table 3: Statistics of evaluation metrics for forecasting results before and after considering the spatial distribution of precipitation in GL city. Figure 13: Scatter plots for seven methods in HC city: (**a**) SVR; (**b**) GBRT; (**c**) RF; (**d**) LSTM; (**e**) MLP; (**f**) CNN; (**g**) proposed CM-MDLN method. The \(x\)-axis represents the true value, and the \(y\)-axis represents the forecasted value corresponding to the true value. The three straight lines represent \(y=1.1x\), \(y=x\), and \(y=0.9\)\(x\) from top to bottom. Figure 14: Scatter plots for seven methods in GL city: (**a**) SVR; (**b**) GBRT; (**c**) RF; (**d**) LSTM; (**e**) MLP; (**f**) CNN; (**g**) proposed CM-MDLN method.