## 3 Results and Discussion
### The Interpretation Examples  
For the RF (the model gave the smallest forecast error), the SHAP algorithm described above was applied, and visual interpretations of the forecasts were constructed. The first eight most important features are shown during visualisation. One interpretation explains the results of one model run to produce one forecast value of solar irradiance 3 h ahead. In this case, the features associated with the position of the Sun and the intensity of solar irradiance at the top of the atmosphere (day, hour and irradiance at the atmosphere boundary) were combined during interpretation, since they are determined by date and time and have a general meaning for a user. Figures 9-14 present the SHAP visualisation of the model forecasts for different days. Each horizontal bar shows the significance of a correspondence feature. A positive value indicates that the feature leads to an increase in the forecast relative to the average target value; a negative value indicates the opposite. The larger the absolute value of the feature's bar, the stronger the feature's significance on the result (forecast). Figure 8: An example of a day from a testing dataset. At 13:00 without using the cloud description, the forecast is underestimated (Predicted Cloud Cover line). Figure 9: Example of interpretation, 7 May, 10:00. Figure 11: Example of interpretation, 9 May, 10:00. Figure 12: Example of interpretation, 17 May, 10:00. Figure 10: Example of interpretation, 8 May, 10:00. Examples of forecasts interpretation using the SHAP visualisation approach:
* Figure 9 shows that the model took into account the average percentage of low-level clouds (ALow = 60%) to reduce the forecast value, which is logical, since low-level clouds have a greater impact on the scattering of solar radiation. Also, the model took into account the absence of high cirrus clouds (HiCi = False) to improve the forecast, which is also logical. * For the following day and the same hour of the day, the forecast was slightly lower; from Figure 10, it is immediately clear that the reason was the presence of high cirrus clouds (HiCi = True). * Figure 11 shows an example of another close day and the same hour of day, and the model forecast was significantly higher than for the example in Figures 9 and 10. The model result is explained by the absence of low and medium clouds (ALow = 0%). From a comparison of Figures 9-11, we can conclude that the interpretation algorithm makes it possible for user to quickly understand why forecasts are so different for coinciding hours and close days of the year. Without interpretation of the results, the user would not be able to evaluate the logic of the model. Our analysis of the interpretations obtained allows us to note that the feature often used in other studies to take into account cloudiness--the percentage of cloud coverage of the sky (Cov)--did not have much influence in the presence of features that describe  
Figure 14: Example of interpretation, 19 May, 16:00. Figure 13: Example of interpretation, 13 May, 16:00.  
cloudiness in more detail. For example, as seen in Figure 12, at 100% sky cover, the absence of low clouds and high cirrus made it possible for the model to improve the forecast despite cloudy weather. Although experiments have shown that of all the binary features that describe cloud types, the presence of high cirrus clouds (HiCi) has a significant influence, other features also contribute and reduce the average forecast error. Examples are shown in Figures 13 and 14, which demonstrate that the presence of Fractonimbus clouds (HiFbrn) had noticeable effects on the forecast. Interpretations of forecasts allow one to not only explain an individual forecast during operation but also check the logic of the model at the stages of its validation and testing. The first use case is for the user, and the second one is for the developer. In addition, the visualisation method used makes it possible to identify errors in the source data during operation of the intelligent information system.