Development and Evaluation of an AI Model for Simulating GNSS radio occultation Bending Angle through Ray Tracing

Abstract. Given computational cost and complexity of the ray-tracing observation operator and its adjoint operator for Global Navigation Satellite System (GNSS) Radio Occultation (RO) data assimilation, this study develops an AI model for simulating nonlocal bending angles using a Transformer encoder. The model uses ERA5 reanalysis data and COSMIC-2 RO geometry to learn the nonlocal mapping from atmospheric states along finite ray paths of bending angle simulated by ray tracing. A Transformer encoder extracts ray-path features, which are aggregated using target-dependent multi-head attention to predict bending angles. Training employs a composite loss function that combines weighted absolute errors below 8 km, layer-dependent relative error above 8 km, and constraints on layer-mean biases. The model is trained over East Asia from 30 June to 4 July 2024 and independently evaluated from 4 July to 8 July 2024. The AI model reproduces the vertical structure of bending angles simulated by ray tracing. The mean fractional difference is near 0 % above 8 km, below 2 % between 3 and 8 km, and within 8 % below 3 km. Compared with the local Abel operator, the AI model exhibits less error dispersion. Incorporating tropopause height information reduces systematic bias near 18 km. Automatic differentiation also facilitates development of the AI model’s adjoint. Relative sensitivity analyses of AI-simulated bending angles with respect to temperature and specific humidity further show that the AI model captures the nonlocal response patterns of the ray-tracing operator, with similar along-track distributions and sensitivity magnitudes. CPU timing results indicate that AI model and its adjoint calculations are approximately 1.5–3 times faster than ray tracing, demonstrating the potential for improved computational efficiency in forward ray-tracing and backward-adjoint calculations.