# Forecasting Ionospheric foF2 Based on Deep Learning Method
## 3 Results and Discussion
### The Forecasting Performance
For the year 2015 of high solar activity, the forecasting errors RMSE of the LSTM model is 0.833 MHz, \(\rho\) is 0.907 and PD is 9.35%, while those of  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Station**} & \multirow{2}{*}{**Year**} & \multicolumn{3}{c}{**BPNN**} & \multicolumn{3}{c}{**GABP**} & \multicolumn{3}{c}{**IRI2016**} & \multicolumn{3}{c}{**LSTM**} \\ \cline{3-14}  & & **RMSE** & \multirow{2}{*}{\(\rho\)} & **PD (\%)** & & **RMSE** & \multirow{2}{*}{\(\rho\)} & **PD (\%)** & & **RMSE** & \multirow{2}{*}{\(\rho\)} & **PD (\%)** & & **RMSE** \\  & & **(MHz)** & & & **(MHz)** & & & **(MHz)** & & & **(MHz)** & & **(MHz)** \\ \hline \multirow{2}{*}{DAR} & 2015 & 1.784 & 0.842 & 16.72 & 1.803 & 0.846 & 16.25 & 1.819 & 0.837 & 18.39 & 1.148 & 0.937 & 12.67 \\  & 2019 & 1.054 & 0.873 & 17.24 & 1.095 & 0.869 & 17.44 & 1.575 & 0.860 & 25.56 & 0.913 & 0.898 & 14.65 \\ \hline \multirow{2}{*}{SAY} & 2015 & 1.5 & 0.908 & 13.95 & 1.462 & 0.913 & 13.78 & 1.823 & 0.894 & 15.36 & 1.134 & 0.948 & 11.07 \\  & 2019 & 1.497 & 0.882 & 25.90 & 1.425 & 0.893 & 24.65 & 1.758 & 0.887 & 27.56 & 0.937 & 0.945 & 14.39 \\ \hline SHY & 2015 & 1.717 & 0.876 & 15.63 & 1.685 & 0.882 & 15.64 & 1.859 & 0.867 & 16.06 & 1.084 & 0.953 & 11.18 \\ \hline \multirow{2}{*}{BRI} & 2015 & 1.033 & 0.849 & 12.02 & 1.058 & 0.841 & 12.18 & 1.147 & 0.831 & 13.29 & 0.833 & 0.907 & 9.35 \\  & 2019 & 0.768 & 0.728 & 13.18 & 0.785 & 0.722 & 13.80 & 0.980 & 0.757 & 16.59 & 0.676 & 0.757 & 11.44 \\ \hline \multirow{2}{*}{WUH} & 2015 & 1.254 & 0.843 & 13 & 1.198 & 0.858 & 12.15 & 1.317 & 0.843 & 14.69 & 1.194 & 0.862 & 11.98 \\  & 2019 & 0.786 & 0.878 & 14.44 & 0.791 & 0.885 & 14.55 & 1.392 & 0.859 & 25.13 & 0.648 & 0.919 & 11.68 \\ \hline \multirow{2}{*}{CAM} & 2015 & 0.963 & 0.867 & 13.04 & 0.953 & 0.869 & 12.87 & 1.026 & 0.853 & 13.79 & 0.751 & 0.921 & 9.53 \\  & 2019 & 0.656 & 0.746 & 12.06 & 0.648 & 0.749 & 11.92 & 1.033 & 0.760 & 20.13 & 0.593 & 0.790 & 10.12 \\ \hline \multirow{2}{*}{CAN} & 2015 & 0.955 & 0.86 & 13.31 & 0.879 & 0.881 & 12.21 & 0.998 & 0.847 & 13.84 & 0.661 & 0.935 & 8.66 \\  & 2019 & 0.652 & 0.772 & 12.72 & 0.670 & 0.768 & 13.19 & 0.802 & 0.776 & 15.68 & 0.529 & 0.827 & 10.19 \\ \hline \multirow{2}{*}{BEJ} & 2015 & 0.852 & 0.914 & 10.67 & 0.832 & 0.919 & 10.41 & 0.875 & 0.91 & 11.28 & 0.666 & 0.949 & 8.07 \\  & 2019 & 0.593 & 0.860 & 11.64 & 0.587 & 0.865 & 11.38 & 0.888 & 0.847 & 16.74 & 0.514 & 0.887 & 9.55 \\ \hline \multirow{2}{*}{HOB} & 2015 & 0.976 & 0.85 & 14.17 & 0.918 & 0.869 & 13.47 & 1.031 & 0.826 & 15.23 & 0.803 & 0.903 & 10.89 \\  & 2019 & 0.587 & 0.800 & 12.28 & 0.597 & 0.797 & 12.27 & 0.788 & 0.811 & 16.88 & 0.592 & 0.795 & 11.92 \\ \hline \multirow{2}{*}{MOH} & 2015 & 0.913 & 0.892 & 13.76 &the BPNN, GABP, and IRI2016 models are 1.033 MHz, 0.849, 12.02%, 1.058 MHz, 0.841, 12.18% and 1.147 MHz, 0.831, 13.29%, respectively. The LSTM model tends superior to other models in each station indicates the advantages of the deep learning method in the forecasting of foF2 time series. It's mainly due to the special \"gate\" structures, the dependency for long-term variation of foF2 is learned by the LSTM model, so the trend of time serial can be well obtained. Meanwhile, all the other three models are superior to the IRI2016 model, possibly because the IRI2016 model is an empirical ionosphere model based on worldwide available data of ground-based and satellite observations, it can be used as ionospheric background, without the function of ionospheric forecasting. Figure 5 illustrates the root-mean-square error, relative deviation of the four prediction models for each ionosonde station. The stations are arranged from left to right according to the latitude from low to high. Figure 5 shows that the overall root-mean-square error of the 4 prediction models is larger in the low latitude area, but the forecasting performance of each model in the middle latitude area is better than that in the low latitude area.