Abstract:
Objectives: Accurate prediction of the ionospheric total electron content (TEC) is essential for the positioning, navigation and timing services of Global Navigation Satellite Systems (GNSS). Existing attention-based TEC prediction models mostly extract information along a single dimension and rely on recurrent architectures, which limits the representation of the spatiotemporal coupling of ionospheric variability. A dual-attention Temporal Convolutional Network Transformer model, DA-TCNT, is therefore proposed to strengthen the identification of key spatial regions and informative feature channels within a non-recurrent framework and to examine its performance under different levels of geomagnetic activity.
Methods: TEC grids over 70°E-140°E and 15°N-55°N (2.5°×5° resolution, 255 grid points) were derived from the standard IONosphere map EXchange (IONEX) files of the Center for Orbit Determination in Europe (CODE) of the International GNSS Service (IGS) for 2000-2023, and linear interpolation unified the original 2- hour and 1-hour intervals to 1 hour. Seven space-weather parameters from the NASA Space Physics Data Facility (SPDF) and the OMNIWeb database—solar radio flux index F10.7, planetary Kp index, disturbance storm time (Dst) index, geomagnetic equivalent three-hour-range amplitude (ap) index, auroral electrojet (AE) index, southward interplanetary magnetic field Bz component and sunspot number R—were aligned with the TEC series. Sliding windows with 48-hour inputs, 24- hour targets and a one-day step generated 8764 samples, which were stratified by Kp into quiet (Kp < 4), active (4 ≤ Kp < 7) and disturbed (Kp ≥ 7) pools and split 8:1:1 into training, validation and test sets (7011/877/876). DA-TCNT comprises four cascaded stages: a spatial-attention module at the input that exploits the auxiliary parameters to weight TEC across geographical locations; a temporal convolutional network (TCN) with dilated causal convolutions for local multi-scale feature extraction that avoids future information leakage; a Transformer encoder with multi-head selfattention for global dependency modelling; and a squeeze-and-excitation channel-attention module for feature-channel recalibration. Performance was measured by the coefficient of determination (R
2), root mean square error (RMSE) and mean absolute error (MAE), averaged over per-date test files, through ablation experiments (Pre-DA with both modules front-loaded, No-SA, No-CA, NoDA), comparisons with the convolutional gated recurrent unit (ConvGRU), convolutional long short-term memory (ConvLSTM), attention-based long short-term memory (Att-LSTM), long short-term memory (LSTM) and a standalone TCN, geomagnetically stratified testing, and gridwise error mapping.
Results: DA-TCNT attained R
2 = 0.9397, RMSE = 2.7047 TEC units (TECU) and MAE = 1.9032 TECU on the test set, exceeding all ablation variants. Relative to No-DA (RMSE 3.9154 TECU, MAE 2.7668 TECU), the dual attention reduced RMSE and MAE by 30.92% and 31.21%; relative to Pre-DA, the staged placement of the two modules reduced them by 28.42% and 29.25%. Grid-wise analysis showed that error growth after removing either attention module concentrated at 15°N-30°N, and in the averaged spatial-attention map 65.71% of grid points within this equatorial ionization anomaly (EIA) belt carried weights above 0.5, versus 50.67% north of 30°N. Against the baselines, DA-TCNT reduced RMSE and MAE by 11.05% and 11.00% relative to the strongest one, LSTM (RMSE 3.0409 TECU), and by 12.61% and 13.06% relative to AttLSTM; 79.34% of per-file RMSE values and 79.79% of MAE values fell within one standard deviation of their means, and the fitted regression line (y = 0.98x + 0.16 TECU) closely followed the ideal line. Under quiet, active and disturbed conditions, RMSE rose from 2.461 to 3.361 and 6.626 TECU while R
2 declined from 0.941 to 0.857; DA-TCNT remained more accurate than AttLSTM in all three regimes, with RMSE lower by 12.92%, 12.47% and 4.70%, respectively. In the disturbed case of 24 March 2023, errors expanded into spatially continuous and temporallypersistent bands over eastern China and the low-to-mid latitudes, while the model still reproduced the large-scale spatial pattern of TEC.
Conclusions: Placing spatial attention at the input and channel attention after the Transformer within a TCN-Transformer backbone is more effective than front-loading both modules, indicating that separating spatial screening from channel purification benefits regional TEC forecasting. Embedding seven physically meaningful space-weather parameters into the attention computation improves interpretability and generalization across geomagnetic regimes. Prediction accuracy nevertheless degrades under strong geomagnetic storms, although the overall TEC evolution is still captured, and extreme-event forecasting requires further improvement. Future work will benchmark DA-TCNT against authoritative operational products such as the CODE 1-day predicted global ionosphere map (C1PG) under unified spatiotemporal matching standards.