# Forecasting the Distortion in Solar Radiation during Midday
## 3 Results and Discussion
### Testing the Performance of the Proposed Technique in the First Location (Riyadh City)  
Figure 1 shows the results of 5 days (1-5) of January. The left side shows the solar radiation (w/m\({}^{2}\)) with time in minutes for each day. The order of the solar radiation plots is from 1 to 5 sorted downward (the top is the 1 st day). The right side shows the values of the \(DI\) for each day (the x axis represents the day number in the year starting at 1 for the first day of January and ending with 365 for the last day of December) sorted from left to right (the most left is the 1 st day). The solar radiation of the 1 st and 2 nd days is distorted especially the 2 nd day and, therefore, the values of the \(DI\) are high for these 2 days (both are >70). The value of the \(DI\) of the 2 nd day is higher than that of the 1 st day. For the 3 rd and 4 th days, the solar radiation is stable and hence their values of \(DI\) are low (approximately 40). The solar radiation of the 5 th day has little distortion and hence its \(DI\) is in the medium range.  
Figure 2 shows the results of another 5 days (11-15) from January. Obviously, the solar radiation of days 12-15 is distorted and their distortion indices are high. Since the DIs of days (12-15) are greater than 60, the forecasted solar radiation is distorted in the midday hours. It is clear that the solar radiation during midday time is distorted which proves the accuracy of the proposed approach in predicting the fluctuation in the solar radiation during midday time by measuring the radiation during the early hours of the day. For day 11, the \(DI\) is relatively low (<60) and its solar radiation is nearly stable with very little distortion in the noon time.  
Figure 3 shows the results of days 1-5 of February. As the figure shows, the \(DI\) is high (>60) for days 1-3 whose radiation is distorted especially days 2 and 3. The \(DI\) of day 4 is low and its radiation is clean (\(DI<40\)). However, the radiation of the 5 th day is distorted  
but its \(DI\) is low, which means that the proposed method failed to predict the distortion on this day. The reason behind this failure needs further investigation.  
Figure 4 shows the solar radiation and DIs of days 11-15 of February. The DIs of all days are correct except for that of day 15 whose \(DI\) is 28 and its radiation was much distorted.  
Figure 1: The solar radiation of days 1–5 of January (**left**) and the distortion index (\(DI\)) (**right**).  
Figure 3: The solar radiation of days 1–5 of February (**left**) and the distortion index (\(DI\)) (**right**).  
Figure 2: The solar radiation of days 11–15 of January (**left**) and the distortion index (\(DI\)) (**right**).  
Moreover, the approach was examined in another two months in the summer season (July and August). Figures 5 and 6 show the results of the proposed method for days 1-5 and days 13-17 of July. The DIs of the all days in these two figures are correct and gave an accurate prediction of the distortion in solar radiation except for the 5 th day of July.  
Figures 7 and 8 show good agreement between the \(DI\) and the solar radiation of days 1-5 and 13-17 of August except for day 16 whose solar radiation is clean and its \(DI\) is 47. However, this disagreement is relatively tolerant because the \(DI\) is in the medium range.  
Figure 4: The solar radiation of days 11–15 of February (**left**) and the distortion index (\(DI\)) (**right**).  
Figure 5: The solar radiation of days 1–5 of July (**left**) and the distortion index (\(DI\)) (**right**).  
Figure 6: The solar radiation of days 13–17 of July (**left**) and the distortion index (\(DI\)) (**right**).  
Some other results obtained from this location (Riyadh city) for some days in the remaining months are listed in Appendix A (Figures A1-A12).