## 4 Results and Discussion
### WRF-Alone Forecasts of Solar Radiation  
With proper configurations of the WRF model, a 12-month time series of the solar radiation forecasts are generated for two sites, respectively. The forecasting skills of WRF model have been verified with observed data. Figure 5a,c depict the comparison of diurnal variations (over one-year) of predicted and observed solar radiation for the Maizuru and Qinghai sites, respectively. It is observed that the WRF raw forecasts of solar radiation can capture well the pattern of the corresponding observations for both sites. Overestimations of WRF forecasts have been found. Figure 4: Taylor diagrams for Maizuru (**left**) and Qinghai (**right**) sites. The diagrams show normalized standard derivations and correlations of solar radiation forecasts for five experiments referred to observations (REF) in winter (January) and summer (July). The number of samples for each experiment is 336. Figure 5: The 12-month mean solar radiation (W/m\({}^{2}\)) series from 12:00 a.m. to 11:00 p.m. (**a**) and the monthly averaged series of 2018 solar radiation (**b**) for the Maizuru site; (**c**) and (**d**) display similar results but for the Qinghai site in 2017. Note that the time mentioned is local time. The marked black and red lines stand for forecasts and the corresponding observations, respectively. The monthly variations of predicted and observed solar radiation are plotted in Figure 5b,d for the Maizuru and Qinghai sites, respectively. From Figure 5b, we can find slight overestimation for each month except for July. Similarly, the forecasts of the Qinghai site also meet the observed data well and have overestimations for most of the months. Furthermore, the forecasting ability of WRF model under different sky conditions (defined in Section 2.3) is investigated, and the results are summarized in Table 2. Note that the statistical performance of hourly solar radiation forecasts under different sky conditions is calculated based on their occurrence frequency in the whole year, which is displayed in the second row of Table 2.  
Table 2 reveals that the WRF model can predict well the solar radiation for all three sky conditions since the relatively small values of MBE and RMSE can be obtained for both Maizuru and Qinghai sites. It is also observed that the nRMSE of the whole time series (denoted by \"All-year\") reaches a relatively small value of 0.2 and 0.1 for Maizuru and Qinghai sites, respectively. Considering all the above results, we may conclude that the WRF model has a relatively high ability of forecasting short-term solar radiation while there are slight differences among different sky conditions and different locations. Such differences can also be found in Figure 6.  
A period of five-day forecasts of the Maizuru site is chosen as an example to show the different performances under three sky conditions. It is also used to explain the reason that we conduct the clearness index-based Kalman filter for the sake of improving the raw forecasts. Figure 6a-c show comparative forecasts of solar radiation (hourly interval) for clear, cloudy and overcast sky conditions, respectively. It can be found that the forecasting patterns under clear sky conditions are very similar. Relatively large variation has been observed in WRF forecasts of solar radiation as well as observations under cloudy sky conditions (Figure 6b). In addition, it can be observed in Figure 6c that the values of solar radiation forecasts are much smaller than the values under the clear and cloudy sky conditions. Such a significant difference in forecasting errors among three kinds of sky conditions might limit the performance of KF_TS for improving the forecasting accuracy. In other words, searching analogues using the clearness index will enhance the role of the Kalman filter in reducing forecasting errors. In the following sections, the performance of the Kalman filter on time-sequence (KF_TS) and clearness index-based Kalman filter (KF_Kt) are discussed.