Optimal Transformer Modeling by Space Embedding for Ionospheric Total Electron Content Prediction

Prediction of ionospheric total electron content (TEC) enables accurate ionospheric delay correction for global navigation satellite system (GNSS) services. Thus, it is crucial to extract the characteristics of the temporal periodicity and spatial correlation for TEC modeling and prediction. The self-attention mechanism of the transformer structure is utilized to capture the long-term characteristics of the TEC in China. The gated recurrent unit (GRU) network and long short-term memory (LSTM) were chosen for comparison because of their capability for nonlinear time series modeling. The results indicate that the proposed model outperforms LSTM by 23% from 2016 to 2018 and GRU by more than 4% from 2016 to 2017. In terms of small, moderate, and intense geomagnetic storms, the relative error at all involved latitude levels was reduced by 40%, 39%, and 5%, respectively, compared with GRU, as well as 44%, 47%, and 12%, respectively, compared with LSTM. Furthermore, the ensemble model (Ense-Trans) based on two proposed spatially embedded transformer models (Trans), compared with the original Trans model, reduced the relative error by 11.38%, 8.78%, and 11.78% in the summer, autumn, and winter of 2018, respectively. It is concluded that Trans has much better performance than GRU and LSTM, and Ense-Trans is better than Trans itself in terms of TEC prediction. This study will be of great significance for ionospheric real-time research and other space weather applications in the future.