Ionospheric Slant TEC Modelling Based on GNSS Data with Machine Learning

The ionosphere introduces dispersive delays on GNSS signals, with the magnitude of the error determined by the slant total electron content (STEC) along the satellite–receiver path. Standard correction products, such as Global Ionospheric Maps (GIMs), estimate vertical TEC (VTEC) on coarse spatio-temporal grids, relying on thin-shell assumptions and mapping functions to convert between STEC and VTEC. While effective for many applications, these simplifications limit accuracy, particularly during disturbed ionospheric conditions.

In this work, we present a machine learning–based model for direct STEC prediction, avoiding the need for VTEC mapping. The model is implemented as a ResNet-like multi-layer perceptron (MLP) trained with Gaussian negative log likelihood loss, which allows us to provide uncertainties along with the STEC. To ensure global applicability, the dataset spans observations of the IGS network from 2014 until 2025 and thus more than a full solar cycle, covering diurnal, seasonal, and solar variability. Input features include spatial geometry (station and satellite coordinates, azimuth, elevation), temporal information (time of day, day of year), and space weather indices, enabling the network to capture both spatio-temporal dependencies and heliophysical drivers of ionospheric variability.

The pretrained model shows strong agreement with observed STEC (r = 0.95, R² = 0.90) and generalizes robustly across years without daily fitting. Errors scale with STEC magnitude but remain unbiased, reflecting physically consistent behavior under varying ionospheric conditions. On temporally held-out data, the mean absolute error is ~7.2 TECU, with improved performance for interpolation (~4.6 TECU) compared to extrapolation (~9.2 TECU). Daily fine-tuning additionally improves performance, particularly at low elevation angles where VTEC-based mapping functions are weakest, while maintaining comparable accuracy at high elevations. Performance on unseen stations is competitive with established VTEC-based models and global ionospheric maps.

By directly modelling STEC from raw GNSS observations across a solar cycle, this approach provides a flexible, observation-driven alternative to mapping function based models, with applications in precise GNSS positioning, space weather monitoring, and multi-technique ionospheric research.