t-STEP: An interpretable model for Total Electron Content predictions and irregularities estimations

Technical Summary: t-STEP – An Interpretable Model for TEC Predictions and Irregularities Estimations

Problem Statement
Global Positioning System (GPS) communications and other satellite-based infrastructures are frequently compromised by ionospheric Total Electron Content (TEC) gradients. These gradients cause phase advances, group delays, and positioning errors that impact sectors ranging from precision agriculture to military intelligence. While machine learning (ML) models have improved TEC prediction accuracy, a critical gap remains: existing models typically operate at low temporal resolutions (e.g., hourly). This cadence prevents the accurate derivation of rate-of-change metrics, specifically the Rate of TEC Index (ROTI), which are essential for diagnosing ionospheric irregularities and transients. Consequently, current ML approaches struggle to preserve the morphologies of sudden TEC gradients within predicted signals without explicitly training specialized models for each transient type.

Methodology
The authors introduce t-STEP (Temporal Sampling and TEc Prediction), a novel ML-based framework designed to predict TEC at a 30-second resolution. The study utilizes a single ground-based GPS receiver located in Brazil (5.49°S, 47.49°W) covering Solar Cycle 24 (2009–2015).

• Data Processing: The model ingests dual-frequency GPS signals to compute slant TEC (sTEC), which is converted to vertical TEC (vTEC) using a thin-shell ionospheric model at 350 km. To ensure data consistency, the authors employed an XGBoost inference routine to reconstruct missing ionosonde data (foF2 and hmF2) from the Embrace and GIRO DIDBase databases, using solar and geomagnetic parameters as constraints.
• Feature Engineering: The input feature space includes temporal covariates (encoded via Fourier transformations for seasonality and diurnal cycles), satellite IPP information, ionosonde parameters (NmF2, hmF2, foF2), and space weather indices (Kp, SymH, Vx).
• Model Architecture: The study compares four architectures: Long Short-Term Memory (LSTM) with attention mechanisms, LightGBM, Categorical Boosting, and Random Forest. LightGBM was selected as the primary model due to its superior performance in capturing irregularities. The model was trained on data from 2009–2014 and tested on the high solar activity year of 2015.
• Evaluation Framework: Performance was assessed using standard metrics (RMSE, MAE, R², Concordance Correlation Coefficient) and Dynamic Time Warping (DTW) to evaluate the alignment of transient shapes and morphologies. Interpretability was achieved using SHAP (Shapley Additive exPlanations) to analyze feature attributions. The model was benchmarked against the International Reference Ionosphere (IRI-2020) and an LSTM+Attention model.

Key Contributions

1. High-Resolution Prediction: The first development of an ML-based TEC prediction model operating at a 30-second cadence, enabling the direct derivation of ROT and ROTI from modeled signals.
2. Irregularity Detection from Modeled Signals: The first demonstration of detecting TEC irregularities (ROTI) directly from a single, general-purpose TEC prediction model without training redundant models for specific transients.
3. Interpretability: Identification of key drivers for TEC variability using SHAP analysis, revealing how physical constraints (like storm indices) dynamically influence predictions.
4. Reproducible Workflow: Establishment of a complete informatics workflow for TEC prediction, benchmarking, and irregularity estimation.

Results

• Prediction Accuracy: The t-STEP model achieved a test accuracy of 91% (R²) with a Mean Absolute Error (MAE) of 4.38 TECU during the high solar activity period of 2015.
• Benchmarking: The hourly variant of t-STEP outperformed the IRI-2020 model by approximately 35% in R² accuracy, a 57% reduction in absolute errors (MAE), and a 54% gain in prediction skill.
• Irregularity Retention: Under three distinct geomagnetic storm conditions (weak, moderate, and strong), t-STEP successfully captured significant ROTI dynamics and morphologies. In contrast, the LSTM+Attention model, while competitive in raw TEC prediction for moderate storms, failed to preserve irregularity morphologies, with its ROTI signals appearing distorted and engulfed by noise artifacts.
• Feature Importance: SHAP analysis confirmed that the model adheres to physical laws. Under quiet conditions, temporal features and electron density (NmF2) dominated; during storms, the SymH index rose in importance, demonstrating the model's sensitivity to space weather dynamics.
• Ablation Studies: Removing ionosonde-derived parameters (Iz) significantly degraded the model's ability to capture irregularity physics, confirming their role as essential energy constraints.

Significance and Claims
The paper claims that t-STEP demonstrates the feasibility of achieving scalable detection of TEC irregularities using a single, unified model. By predicting at 30-second intervals, the model bridges the gap between standard TEC forecasting and the need for high-resolution irregularity diagnostics. The authors posit that for chaotic prediction tasks involving ionospheric transients, gradient-boosting ensemble methods (like LightGBM) may outperform deep learning counterparts (like LSTM) in retaining signal morphologies, though they note this hypothesis requires further validation. The study concludes that while the current implementation is limited to a single station, the results provide a promising foundation for scaling the model to track small-scale transients across multiple stations.