A Multichannel CNN for Global Empirical Ionospheric Modeling

Conventional empirical global ionospheric models, such as the Klobuchar model and the International Reference Ionosphere (IRI), utilize a limited set of parameters to represent global ionospheric Total Electron Content (TEC). These models are extensively employed in Global Navigation Satellite Systems (GNSS) positioning. However, the accuracy of these models is inherently restricted by their reliance on predefined mathematical functions, particularly during periods of intense space weather activity. While Artificial Neural Networks (ANNs) offer significant advantages in modeling nonlinear relationships and have demonstrated promising results for ionospheric prediction, their efficacy specifically for the domain of empirical ionospheric modeling remains largely unexplored. This study aims to fill this gap by proposing a multi-channel Convolutional Neural Network (CNN) method for empirical ionospheric modeling. The base architecture, CEIMv1, integrates fundamental solar-geometric parameters. Building upon this foundation, CEIMv2 incorporates the solar-geomagnetic indices as additional inputs, while CEIMv3 further extends the input data by including Mean Global Electron Content (MGEC) data. Validation against reference products shows that CEIMv2 and CEIMv3 achieve root-mean-square errors (RMSEs) of 6.40 TECU and 4.06 TECU, corresponding to accuracy gains of 26.0% and 17.1% over IRI-2020 and 46.6% and 49.9% compared to the Klobuchar model. Notably, CEIMv3 exhibits a minimal variation in precision of merely 3.66 TECU between high- and low-activity solar years, significantly outperforming conventional models. These results demonstrate a shift from traditional function-based methods toward a data-driven, multi-channel machine learning strategy, offering significantly improved ionospheric delay correction for single-frequency GNSS users.