## 5 Conclusions  
A different empirical model of \(f_{0}\)F\({}_{2}\) based on an EOF and modified surface interpolation method was proposed. This model for predicting the ionospheric characteristics of the F2 layer instead of the CCIR/URSI coefficient was adopted in calculating \(f_{0}\)F\({}_{2}\). It has four main important features: (a) The ionospheric index \(F_{10.7}\) and sunspot number were introduced together in the model to assist in the temporal reconstruction; (b) this model expresses \(f_{0}\)F\({}_{2}\) with harmonic functions representing the annual, semi-annual, seasonal, monthly and solar cycle variations; (c) the geomagnetic coordinates were applied instead of geographic coordinates for calculating ionosphere distance and using the spatial reconstruction; (d) this model has a very simple mathematical formulation that is more effective in representing temporal and spatial characteristics of \(f_{0}\)F\({}_{2}\). The predicted results obtained from the SRPM agree well with the measurements. A statistical analysis has proved its potential in that it not only agrees well with the measurements but also performs better than the CCIR and URSI over East Asia region. To use the SRPM the new model requires only the following inputs: latitude, longitude, month, hour, the twelve-month running value of the monthly flux of solar radio waves at 10.7 cm, and the twelve-month running mean value of the monthly sunspot number. It is a simplified empirical model but has more accuracy than IRI. On the basis of the results obtained in this work, one may justify support this model for both regional and global \(f_{0}\)F\({}_{2}\) modeling. Future research is directed towards validating this modeling approach for other ionospheric \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Statistical Analysis Item**} & \multicolumn{3}{c}{**RMSE (MHz)**} & \multicolumn{3}{c}{**Relative RMSE (\%)**} & \multicolumn{2}{c}{**Percent Difference**} & \multicolumn{1}{c}{\multirow{2}{*}{**Percent Difference**}} \\ \cline{3-3} \cline{5-10}  & & **IRI-CCIR** & & **IRI-URSI** & & **SRPM** & **IRI-CCIR** & & **IRI-URSI** & & **SRPM** \\  & & & & & & & & & **and SEPM (\%)** & & **and SEPM (\%)** \\ \hline solar & high & 1.23 & 1.22 & 0.71 & 22.12 & 22.06 & 12.38 & 9.74 & 9.68 \\ activity & low & 0.88 & 0.89 & 0.45 & 19.04 & 20.02 & 11.22 & 7.82 & 8.80 \\ epochs & spring & 1.29 & 1.28 & 0.57 & 25.32 & 26.01 & 11.92 & 13.39 & 14.09 \\ seasonal & summer & 1.07 & 1.14 & 0.65 & 18.76 & 20.03 & 13.48 & 5.28 & 6.55 \\ autumn & 0.79 & 0.75 & 0.64 & 12.05 & 11.88 & 11.14 & 0.91 & 0.74 \\ winter & 0.99 & 0.92 & 0.66 & 24.97 & 23.46 & 14.77 & 10.20 & 8.69 \\ midnight & 1.21 & 1.29 & 0.70 & 17.23 & 19.11 & 10.84 & 6.38 & 8.27 \\ local time & sunrise & & & & & & & & \\ sectors & (5-0.90-9.0) & 1.34 & 1.35 & 0.72 & 33.84 & 33.72 & 18.69 & 15.15 & 15.03 \\  & moon & & & & & & & & \\  & (100:00-14.00) & 1.14 & 1.09 & 0.72 & 16.46 & 15.34 & 10.56 & 5.90 & 4.78 \\  & sunset & & & & & & & & \\  & (160:00-2000) & 0.83 & 0.85 & 0.56 & 11.03 & 11.87 & 8.77 & 2.26 & 3.10 \\  & high & & & & & & & & \\ latitude regions & middle & & & & & & & & \\  & (30”N-6”N) & 0.91 & 0.85 & 0.63 & 24.21 & 23.43 & 16.27 & 7.93 & 7.16 \\  & low & & & & & & & & \\  & (\(\leq\)30”N) & 1.58 & 1.62 & 0.65 & 23.98 & 26.60 & 8.71 & 15.27 & 17.89 \\  & average & 1.08 & 1.08 & 0.63 & 20.42 & 20.74 & 12.25 & 8.17 & 8.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RMSE and relative value between measured values of \(f_{0}\)F\({}_{2}\) and predicted values of CCIR, URSI, and SRPM for two solar activity epochs, four seasons, four local time periods and three latitude regions. parameters such as propagation factor of 3000 km, and with modification confirming its suitability for other regions as well as globally.