Three-dimensional numerical ray tracing on a phenomenological ionospheric model

In this paper we present a numerical and step by step ray-tracing method on a phenomenological ionospheric electron density (N_e) model, the TaiWan Ionospheric Model (TWIM), which is constructed from the FormoSat3/Constellation Observing System for Meteorology, Ionosphere and Climate (FS3/COSMIC) ionospheric radio occultation data. With the Earth's magnetic field and horizontal N_e gradient effects included, efficient methods for calculating ray parameters such as the ground range, reflection height, phase path, and group path are presented. The three-dimensional TWIM consists of vertically fitted -Chapman-type layers, with distinct F2, F1, E, and D layers, for which the layer parameters such as peak density, peak density height, and scale height are represented by surface spherical harmonics. This way the continuity of N_e and its derivatives is maintained. This is important for practical schemes for providing reliable radio propagation predictions. The methodology is successfully applied to a practical high-frequency transmitter for oblique incidence ray tracing and further evaluated by comparing synthetic vertical ionograms generated by the method with experimental ionosonde observations.