Temporal extrapolation of TEC using WNN during 2007–2018 and comparison against GIM,IRI2016 and Kriging

In this paper, a new method of temporal extrapolation of the ionosphere total electron content (TEC) is proposed. Using 3-layer wavelet neural networks (WNNs) and particle swarm optimization (PSO) training algorithm, TEC time series are modeled. The TEC temporal variations for next times are extrapolated with the help of training model. To evaluate the proposed model, observations of Tehran GNSS station (35.69°N, 51.33°E) from 2007 to 2018 are used. The efficiency of the proposed model has been evaluated in both low and high solar activity periods. All observations of the 2015 and 2018 have been removed from the training step to test the proposed model. On the other hand, observations of these 2 years are not used in network training. According to the F10.7, the 2015 has high solar activity and the 2018 has quiet conditions. The results of the proposed model are compared with the global ionosphere maps (GIMs) as a traditional ionosphere model, international reference ionosphere 2016 (IRI2016), Kriging and artificial neural network (ANN) models. The root mean square error (RMSE), bias, dVTEC = |VTEC_GPS ? VTEC_Model| and correlation coefficient are used to assess the accuracy of the proposed method. Also, for more accurate evaluation, a single-frequency precise point positioning (PPP) approach is used. According to the results of 2015, the maximum values of the RMSE for the WNN, ANN, Kriging, GIM and IRI2016 models are 5.49, 6.02, 6.34, 6.19 and 13.60 TECU, respectively. Also, the maximum values of the RMSE at 2018 for the WNN, ANN, Kriging, GIM and IRI2016 models are 2.47, 2.49, 2.50, 4.36 and 6.01 TECU, respectively. Comparing the results of the bias and correlation coefficient shows the higher accuracy of the proposed model in quiet and severe solar activity periods. The PPP analysis with the WNN model also shows an improvement of 1 to 12 mm in coordinate components. The results of the analyzes of this paper show that the WNN is a reliable, accurate and fast model for predicting the behavior of the ionosphere in different solar conditions.