Ray tracing in realistic 3D ionospheric model

For the most accurate ray-tracing in an anisotropic ionosphere with realistic 3D electron density gradients, it is found that the ionosphere model should be a continuous function of the spatial co-ordinates and thus also the electron density. The spatial derivatives of the refractive index should also be continuous for first, second and higher order derivatives. To perform ray-tracing in a 3D ionosphere model such as International Reference Ionosphere (IRI), the vertical profile must first be accurately fitted by some analytical basis functions. Unlike parabolic or quasi-parabolic basis functions, exponential functions, taken to some exponent n, make a good choice because they and their derivatives are always continuous. These are then used to match the vertical electron density profile of an IRI modelled ionosphere. To accomplish this, a 3D fit to the IRI ionosphere is determined over the desired area of latitude and longitude in which the ray-tracing is to be performed. Results are presented for transionospheric paths through the equatorial ionosphere where the large electron density gradients associated with the equatorial anomaly cause refraction and significant differences in time delay of transionospheric signals. These are then presented for different elevation angles of propagation from 10 to 90 degrees and show the significant variation and complex effects arising from the latitudinal electron density gradients.