Four-Dimensional Topside Electron Density Modeling Using Multi-Stage Deep Learning Approaches

Accurate modeling of topside ionospheric electron density is essential for improving GNSS positioning and understanding upper-atmosphere dynamics. A new four-dimensional (spatial and temporal) topside electron density model is developed using global GNSS radio occultation data within an L2-regularized artificial neural network framework. The model combines both empirical and physical variables, including geomagnetic coordinates, temporal parameters, solar flux ((Formula presented.)), geomagnetic activity index ((Formula presented.)), and key ionospheric parameters (NmF2 and hmF2). To support the modeling framework, two sub-models are first constructed to estimate NmF2 and hmF2 when direct measurements are unavailable. The full model is trained using COSMIC-1 data and evaluated against independent datasets, including COSMIC-1, GRACE, and incoherent scatter radar (ISR). The results show that the proposed sub-models reduce relative errors by 4.5% for hmF2 and 11.0% for NmF2 compared with IRI-2016. For the full topside (Formula presented.) modeling, the proposed approach achieves improvements of 35%, 36%, and 53% relative to IRI-2016 when evaluated against COSMIC-1, GRACE, and ISR datasets, respectively. A systematic analysis of input variables further indicates that both physical drivers and ionospheric structural parameters play essential roles in determining model performance. The new model incorporated with NmF2 and hmF2 sub-models still achieves a 16% improvement over IRI-2016 based on ISR data. In addition to statistical improvements, the model reproduces key ionospheric features, including the equatorial ionization anomaly (EIA) and the midlatitude summer nighttime anomaly (MSNA), under different solar activity conditions. These results demonstrate that the proposed model captures not only the statistical variability but also the underlying physical behavior of the topside ionosphere.