## 4 Discussions  
To estimate and demonstrate the predictive capability of the proposed simplified regional prediction model (SRPM) concerning characteristic \(f_{o}\)F\({}_{2}\) values both the temporal (monthly and hourly) and spatial values of \(f_{o}\)F\({}_{2}\) predicted by the SRPM and those predicted by the IRI model (using both the URSI and CCIR coefficients) were compared with the observed values of \(f_{o}\)F\({}_{2}\) obtained from the verification stations (Figure 2) along with the RMSEs and the calculated relative differences (RRMSE) value. The latter two are used here to evaluate the performance from equations (2) and (3). With the aforementioned equation and coefficients reconstructed using least-squares fitting regression, for given geographic coordinates (\(\lambda\), \(\varphi\)) (where \(\lambda\) and \(\varphi\) refer to the geographical latitude and eastern longitude, respectively), month, universal time, and solar activity factor, we summarize the procedure for estimating \(f_{o}\)F\({}_{2}\) as follows: (1) Use the solar activity factor the 12-monthly mean 10.7 cm solar radio flux (\(F_{12}\)), the 12-monthly mean sunspot number (\(R_{12}\)), month (m), and universal time (UT) to calculate the temporal reconstruction variables for each modeling station. (2) Use the temporal relative variables and the geographic coordinates (\(\lambda\), \(\varphi\)) to calculate the \(f_{o}\)F\({}_{2}\) monthly median value. Figures 10 and 11 show some sample plots of the monthly mean values of \(f_{o}\)F\({}_{2}\) predicted values from the SRPM for the years of high solar activity (2013) and low solar activity (2017). They are compared with those determined by the IRI model using both the CCIR and URSI coefficients and measured values obtained from ionosonde stations. Among them, there is no data in Manzhouli and Haikou stations from April to August 2017. As can be seen from Figures 10 and 11, these graphs serve to illustrate that the SRPM and the IRI model successfully predict the general variation shape of behavior of \(f_{o}\)F\({}_{2}\). At the same time, it is found that the results also reflect the annual, semi-annual, seasonal, and monthly variation characteristics and the solar cycle variations of \(f_{o}\)F\({}_{2}\), which confirms  
Figure 9: The sample maps of space weights with measured stations. Measured station labels from 1 to 17 are Akita, Beijing, Chongqing, Guangzhou, Haikou, Irkutsk, Khabarovsk, Magadan, Manzhouli, Okinawa, Seoul, Taipei, Tokyo, Tunguska, Wakkanai, Yakutsk, and Yamagawa, respectively. (**a**) Around noon (universal time is 00:00 clock); (**b**) around sunset (universal time is 10:00 clock); (**c**) around midnight (universal time is 16:00 clock); (**d**) around sunrise (universal time is 22:00 clock). the validity of the modeling. From the whole aspect, the proposed model SRPM compared favorably with the IRI models. Figure 10: Sample plots of different model predicted value and measured value of \(f_{\mathrm{o}}\mathrm{F}_{2}\) for the year 2013 (high solar activity year). From top to bottom panels, stations are ordered from high, middle and low latitude, which are Magadan, Manzhouli, Jeju and Haikou stations. (**a**) Magadan station; (**b**) Manzhouli station; (**c**) Jeju station; (**d**) Haikou station. To estimate the accuracy of the proposed model SRPM, a statistical analysis of the differences between the predicted monthly mean values of \(f_{0}\)F\({}_{2}\) from the proposed model and measured values obtained from verifying stations is made by calculating RMSE and RRMSE. The results are compared with those determined by the IRI model using both the CCIR and URSI coefficients (see Figure 12 and Table 2). Figure 12 presents the RMSEs between measured values of \(f_{0}\)F\({}_{2}\) and predicted values of CCIR, URSI, and SRPM under different conditions, which correspond to two solar activity epochs (high and low), 12 months of the whole year, 24 h of the whole day and three  
and low).