Forecasting Ionospheric Irregularities on GNSS Lines of Sight Using Dynamic Graphs with Ephemeris Conditioning

Earth system infrastructures relying on satellite-based technologies, such as Global Positioning System (GPS) communications, are affected by ionospheric Total Electron Content (TEC) gradients. Modeling these gradients under physical constraints remains challenging due to their dynamic and transient nature. While existing machine learning (ML) models can predict hourly TEC variations, it remains unclear whether their temporal resolution is sufficient to preserve small-scale TEC irregularities within predicted signals. To address this gap, we introduce an interpretable ML-based model, t-STEP, designed to predict TEC at a 30-second resolution and estimate irregularity signatures from the modeled signals. This high cadence enables the derivation of Rate of TEC changes (ROT) and the ROT Index (ROTI) as diagnostic indicators of ionospheric variability. The model is developed using GPS observations from solar cycle 24 at a station located at 5.49°S, 47.49°W. A multi-metric evaluation framework, including dynamic time warping, is used for robustness assessment, while SHAP (SHapley Additive exPlanations) provides insight into feature contributions. The 30-second TEC predictions achieve 91% accuracy with a mean absolute error (MAE) of 4.38 TECU during high solar activity (2015). Compared with the International Reference Ionosphere (IRI-2020), the hourly model improves accuracy by 35%, reduces absolute errors by 57%, and increases prediction skill by 54%. More importantly, the 30-second model captures TEC irregularity dynamics and morphologies during geomagnetic storms of different intensities, outperforming an attention-based Long Short-Term Memory model under the same experimental conditions. This study demonstrates the potential of a single TEC prediction framework for scalable irregularity monitoring without requiring separate models for individual transient events.

Nonstationary Gaussian process (GP) models are powerful tools for capturing input-dependent variability by adapting to observed data. However, with limited sampling and highly parameterized covariance structure, they are often prone to overfitting and overconfident uncertainty estimates, potentially leading to misleading predictions in safety-critical applications. Motivated by ionospheric modeling for satellite-based augmentation systems (SBAS), this paper proposes a Covariance-Boosted Gaussian Process (CBGP) framework centered upon boosting covariance priors to discover nonstationary latent functions for signal and observation variation that capture irregularities in the input domain. An additional layer of GP modeling of "partially-whitened" observations guides latent function relative error estimation that is used to iteratively update weak priors in a gradient descent-like procedure. Following boosting, restrictions are imposed upon prior covariances to prevent overfitting while posterior uncertainties are inflated to prevent model overconfidence. CBGP model efficacy and robustness are demonstrated through out-of-sample testing of both simulated and real-world applications that meet a three-nines integrity standard. The modeling of an extensive ionospheric storm dataset over South America suggests accurate and reliable means to compute SBAS ionospheric corrections in the most challenging space weather environment using regional models that are more informed and responsive than local fitting performed by currently-operating SBAS.

This paper presents a physically-informed fuzzy clustering of vertical sounding ionograms for automatically separating the ionogram into tracks suitable for further interpretation and determining their optimal number. The model is designed for use not only in conditions where the number of tracks is known, but also in disturbed ionospheric conditions where the number of tracks is preliminary unknown. The method is based on an expectation-maximization algorithm, used for clustering, and on parametrically specified distributions of distances from points to parametrically specified curves. The curves used as track models are close to model tracks in the parabolic ionospheric layer model. The resulting model of each track has six parameters: three standard ones (the critical frequency, the lower boundary of the layer, and its half-width), and three additional ones to take into account possible underlying layer effects. By sequentially increasing the number of tracks and optimizing their parameters, the model finds the optimal number of tracks on the ionogram by minimizing the modified Bayesian information criterion. The Sequential Least Squares Quadratic Programming algorithm is used to find the parameters of a single track. The width of each single track is assumed to be unknown constant found during fitting process. To improve the quality of ionogram clustering, automatic adaptive noise filtering is performed before clustering. This filtering is based on a combination of the DBSCAN and Gaussian Mixture algorithms. Also, to improve clustering quality on an ionosonde without hardware separation of the ordinary and extraordinary components, a preliminary approximate removal of points belonging to the extraordinary mode is performed.