# A Model-Assisted Combined Machine Learning Method for Ionospheric TEC Prediction
## 3 Results and Discussion
The curve graph of actual observed TEC data and the scatter graph of predicted data of each model in a low solar activity year (2020) are shown in Figure 9c. The curve graph of the prediction error of the corresponding models is shown in Figure 9d. Monthly performance indicators (average of 50 runs) of the above six models in a high solar activity year (2015) and low solar activity year (2020) are calculated, and variation curves are drawn, as shown in Figure 10. In the months with high TEC fluctuations, the prediction effect of the model is poor. In March, April, and May 2015, actual observed TEC data were larger than the normal condition, and the forecast data of MMAapGA-BP-NN showed large errors. In March and April 2020, actual observed TEC data were smaller than normal, and the MMAapGA-BP-NN forecast data had larger errors than in other months. But in general, compared with other models, the prediction results of MMAapGA-BP-NN are more accurate and stable. Figure 8: In the low solar activity year (2020), the scatter diagram and normal distribution diagram of the performance indicators of BP-NN, GA-BP-NN, and MMAapGA-BP-NN running 50 times: **(a)** the scatter diagram of the performance indicators of BP-NN, GA-BP-NN, and MMAapGA-BP-NN running 50 times; **(b)** the normal distribution diagram of iteration times when the three models running 50 times; **(c)** the normal distribution diagram of RMSE when the three models running for 50 times; **(d)** the normal distribution diagram of \(\rho\) when the three models running 50 times. Figure 10: _Cont_. Figure 9: Actual observed TEC data predicted TEC data and prediction error with IRI-2020, SMI-F10.7, SMI-SSN, BP-NN, GA-BP-NN, and MMAdapGA-BP-NN in a high solar activity year (2015) and low solar activity year (2020): (**a**) predicted TEC data of each model and actual observed TEC data in a high solar activity year (2015); (**b**) prediction error of each model in a high solar activity year (2015); (**c**) predicted TEC data of each model and actual observed TEC data in low solar activity year (2020); (**d**) prediction error of each model in a low solar activity year (2020). Taking 6:00 to 18:00 as daytime and the rest of the time as night, the diurnal deviation of the predicted results is analyzed. The deviation of TEC data in daytime and night predicted by MMAdapGA-BP-NN in the high solar activity year (2015) and low solar activity year (2020) is shown in Figure 11. The prediction error is large when actual observed TEC data fluctuate violently. Overall, the prediction error is smaller at night than during the daytime. The performance indexes of MMAdapGA-BP-NN in daytime and night in the high solar activity year (2015) and low solar activity year (2020) are calculated, as shown in Table 2. In the year of high solar activity (2015), MAE, MRE, RMSE, and \(\rho\) of MMAdapGA-BP-NN during the night decreased by 45.31%, 48.30%, 35.62%, and 14.63% compared with daytime. In the low solar activity year (2020), MAE, MRE, RMSE, and \(\rho\) of MMAdapGA-BP-NN during the night decreased by 48.65%, 60.70%, 39.42%, and 7.78% compared with daytime. Figure 10: (**a–d**) are the variation curves of monthly performance indicators (MAE, MRE, RMSE, and \(\rho\) of IRI-2020, SML-F10.7, SML-SSN, BP-NN, GA-BP-NN, and MMAdapGA-BP-NN in a high solar activity year (2015); (**e–h**) are the variation curves of monthly performance indicators of the six models in a low solar activity year (2020); (**f–l**) are the variation curves of monthly performance indicators of the average of two years of data. Monthly performance indicators of MMAapGA-BP-NN in the high solar activity year (2015) and low solar activity year (2020) are calculated, respectively, and variation curves are drawn, as shown in Figure 12. Around April 2015 and March 2020, TEC data fluctuated sharply, and the prediction error was large. Obviously, the prediction error of TEC data during the daytime is generally larger than that at night.