Correcting GNSS Radio Occultation Residual Ionospheric Errors using Attention-Based Physics-Guided Neural Networks in Various Geographic Regions

GNSS Radio Occultation (GNSS-RO) provides globally distributed bending angle observations that improve numerical weather prediction and climate monitoring. Accurate neutral atmosphere retrieval requires removing ionospheric effects from RO bending angles, commonly via the standard dual-frequency linear combination of L1 and L2 bending angles. While this approach mitigates first-order ionospheric effects, a residual ionospheric error (RIE) remains due to frequency-dependent ray-path separation within complex ionospheric structures, leading to systematic biases in stratosphere and mesosphere products.

Previous research demonstrated RIEs are proportional to the squared difference between the L1 and L2 bending angles, scaled by a coefficient, called kappa, providing the basis for the kappa correction framework [1]. Subsequent studies improved its practical performance by characterizing the dependence of kappa on geophysical parameters (e.g., solar activity, local time, solar zenith angle, geomagnetic latitude) and incorporating these trends into enhanced parameterizations [2,3]. Under the assumption of a symmetric ionosphere, RIE tends to be predominantly negative, and the kappa correction can reduce the resulting negative bias. However, robust accuracy improvements remain challenging under widely varying electron densities across diverse geographic regions. Under a strongly asymmetric ionosphere—where the RIE can become positive—a kappa correction fails to reduce, or even amplify, the error. This limitation motivates a deep-learning-based correction that adapts to complex, geographic-dependent ionospheric structures.

This study develops a physics-guided neural network (PGNN) to correct RIE by learning the residual error relative to a physics-based baseline (i.e., the kappa correction) using geophysical parameters [4]. Training labels are generated from ray-tracing simulations through an ionosphere-only environment modeled by NeQuick-3D. The proposed architecture incorporates a feature-wise attention gate that adaptively weights the input variables. This method enables the model to capture condition-dependent ionospheric structures that are poorly represented by fixed-form kappa parameterizations, particularly under strong ionospheric asymmetry during high solar activity.

For validation, we compare our model against a kappa correction baseline, a purely data-driven neural network, and a transformer-based PGNN on an independent test set. Across diverse geographic regions, the proposed PGNN with feature-wise attention consistently achieves the best agreement with the true RIE, yielding a highest correlation coefficient of 0.935 and a lowest RMSE of 6.398 nrad. These results indicate that combining a kappa-based physical prior with attention-guided residual learning provides a robust correction across geographic regions.

References

[1] Healy, S. B., & Culverwell, I. D. (2015). A modification to the standard ionospheric correction method used in GPS radio occultation. Atmospheric Measurement Techniques, 8(8), 3385–3393.https://doi.org/10.5194/amt-8-3385-2015

[2] Angling, M. J., Elvidge S., & Healy, S. B. (2018). Improved model for correcting the ionospheric impact on bending angle in radio occultation measurements. Atmospheric Measurement Techniques, 11(4), 2213–2224.https://doi.org/10.5194/amt-11-2213-2018

[3] Park, J., Chang, J., Sun, K., & Lee, J. (2025). Residual ionospheric error correction in GNSS radio occultation bending angles: parametric analysis using electron density profiles derived from COSMIC-II data. EGU General Assembly 2025, EGU25-18658. https://doi.org/10.5194/egusphere-egu25-18658

[4] Daw, A., Watkins, W., Read, J., Karpatne, A., & Kumar, V. (2021). Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling. arXiv preprint arXiv:1710.11431. https://doi.org/10.48550/arXiv.1710.11431