Global 4D Ionospheric STEC Prediction based on DeepONet for GNSS Rays

Abstract

The ionosphere is a vitally dynamic charged particle region in the Earth's upper atmosphere, playing a crucial role in applications such as radio communication and satellite navigation. The Slant Total Electron Contents (STEC) is an important parameter for characterizing wave propagation, representing the integrated electron density along the ray of radio signals passing through the ionosphere. The accurate prediction of STEC is essential for mitigating the ionospheric impact particularly on Global Navigation Satellite Systems (GNSS). In this work, we propose a high-precision STEC prediction model named DeepONet-STEC, which learns nonlinear operators to predict the 4D temporal-spatial integrated parameter for specified ground station - satellite ray path globally. As a demonstration, we validate the performance of the model based on GNSS observation data for global and US-CORS regimes under ionospheric quiet and storm conditions. The DeepONet-STEC model results show that the three-day 72 hour prediction in quiet periods could achieve high accuracy using observation data by the Precise Point Positioning (PPP) with temporal resolution 30s. Under active solar magnetic storm periods, the DeepONet-STEC also demonstrated its robustness and superiority than traditional deep learning methods. This work presents a neural operator regression architecture for predicting the 4D temporal-spatial ionospheric parameter for satellite navigation system performance, which may be further extended for various space applications and beyond.

Figures (19)

• Figure 1: Illustration of the 4D DeepONet-STEC architecture. Using $\{(\tilde{\textbf{x}}_i, \tilde{t}_i, \tilde{y}_i)\}_{i=1}^M$ to train, the model can predict given ray $(\textbf{x}, t) \in \mathcal{D}$ to get the output STEC value $y$. The 4D DeepONet-STEC comprises two main components: the Branch network and the Trunk network. Both neural networks adopt a fully connected structure. The Branch network takes the output value of the $u$ function at fixed point location, representing the mapped STEC value, as its input. The input for the Trunk network includes the coordinates of the corresponding rays in the observed data, as well as sine and cosine encoded time. An activation function ReLu is applied to the output of each hidden layer. The branch network has the input layer with 300 neurons, 30 hidden layer with 64 neurons, and the output layer with 300 neurons.
• Figure 2: US-CORS station distribution for the training (red), validation (blue) and test (green) data for (a) all available sites; (b) the down-sampling sites.
• Figure 3: Global station distribution for the training, validation and test data after down-sampling. Tree test sites (green triangle) and four validation sites (blue triangle) are selected globally, respectively, while the red square refers to the training sites.
• Figure 4: Temporal dataset of the geomagnetic index Kp&Dst and retrieved STEC value at a single station (GODE) during solar ionospheric quiet (a-b) and storm (c-d) time periods.
• Figure 5: US CORS observation dataset predicted STEC of single-station, single-satellite (G08) for three test stations for (a) one-month data and (b) only the three-day prediction period. The blue dots represents the observation, while the red dots represents the predicted STEC values in quiet periods.