## 3 Results and Discussion  
### Model Training Results  
The following generally accepted quality indicators were used in the work (in Equations (2)-(5), \(I\)--true value; \(I^{\prime}\)--predicted value; and \(n\)--number of samples in the test dataset):  
\[MAE=\frac{1}{n}\sum_{h=1}^{n}\big{|}I_{h}-I^{\prime}{}_{h}\big{|}, \tag{2}\]  
Figure 2: General pipeline of the forecasting algorithm with the output interpretation. \[nMAE=\frac{1}{n\overline{l}}\sum_{h=1}^{n}\left|I_{h}-I^{\prime}_{h}\right|\times 1 00\%,\ \overline{I}=\sum_{h=1}^{n}\left|I_{h}-I^{\prime}_{h}\right|\!, \tag{3}\]  
\[RMSE=\sqrt{\frac{1}{n}\sum_{h=1}^{n}\left(I_{h}-I^{\prime}_{h}\right)^{2}}, \tag{4}\]  
\[R^{2}=1-\frac{\sum_{h=1}^{n}\left(I_{h}-I^{\prime}_{h}\right)^{2}}{\sum_{h=1}^ {n}\left(I_{h}-\overline{I}\right)^{2}}. \tag{5}\]  
The testing results are shown in Table 7. For the kNN algorithm, the standard-scale normalisation of numerical features was applied (Equation (6)):  
\[z=\frac{x-mean}{std}, \tag{6}\]  
where \(z\) is a normalized value, \(x\) is an initial value of a one sample from a feature (before normalization), \(mean\) is a mean value of the feature, and \(std\) is a standard deviation of the feature. Figures 3-6 show the visualization of the ensemble models' accuracy using MAE; Figure 4 presents a comparison of the models' nMAEs; Figure 5 shows the same using R\({}^{2}\). The experiments allow us to draw the following conclusions:  
* The desired dependencies between the solar irradiance and other features were not even approximately linear, since the Ridge linear regression model showed an accuracy much lower than other models and R\({}^{2}\) was only 0.5. * The use of detailed cloud descriptions performed by the proposed algorithm significantly increased the accuracy of all ensemble models; the achieved averaged improvements were:
* MAE by 15%;
* nMAE by 15%;
* RMSE by 12.7%;
* R\({}^{2}\) by 5%. * It should be noted that the overall cloud level as a percentage of the sky covered by clouds was used in all experiments. Thus, the difference in accuracy was ensured by the proposed algorithm for processing text descriptions of cloudiness in natural language. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Using Cloud** & **MAE** & **nMAE**, & **RMSE**, & \multirow{2}{*}{**R\({}^{2}\)**} \\  & **Descriptions** & **W/m\({}^{2}\)** & **\%** & **W/m\({}^{2}\)** & \\ \hline Ridge & no & 154.1 & 32.8 & 190.2 & 0.49 \\ Ridge & yes & 151.6 & 32.3 & 187.8 & 0.5 \\ kNN & no & 84.0 & 17.9 & 116.5 & 0.81 \\ kNN & yes & 95.9 & 20.4 & 134.0 & 0.75 \\ AB & no & 85.3 & 18.2 & 108.5 & 0.83 \\ AB & yes & 80.0 & 17.0 & 100.6 & 0.86 \\ RF & no & 70.7 & 15.1 & 97.6 & 0.87 \\ RF & yes & 58.6 & 12.5 & 83.1 & 0.91 \\ XGB & no & 77.8 & 16.6 & 105.4 & 0.84 \\ XGB & yes & 63.7 & 13.6 & 91.4 & 0.88 \\ CB & no & 75.9 & 16.2 & 103.8 & 0.85 \\ CB & yes & 63.1 & 13.4 & 90.1 & 0.89 \\ LGBM & no & 76.7 & 16.3 & 104.4 & 0.85 \\ LGBM & yes & 62.6 & 13.3 & 88.9 & 0.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Description of the final dataset. * The decrease in accuracy for the kNN when using cloud descriptions may have been due to the fact that the kNN is less suitable for working with binary features. * The best accuracy was obtained with the random forest algorithm; the CatBoost and LightGBM algorithms gave accuracies close to it. * The resulting accuracy of random forest--R\({}^{2}\) = 0.91, nMAE = 12.5%--for the 3-h-ahead forecast of solar irradiance at tilted plane at the Earth's surface corresponds to the state-of-the-art accuracy when taking into account differences in meteorological conditions between different territories. Figures 7 and 8 show two days from the testing dataset with a comparison of actual values and predicted values. A description  
Figure 5: RMSE of ensemble models on a testing dataset with and without cloud descriptions. Figure 6: R\({}^{2}\) of ensemble models on a testing dataset with and without cloud descriptions. Figure 7: An example of a day from a testing dataset.