Ray tracing technique for global 3-D modeling of ionospheric electron density using GNSS measurements

For space geodetic techniques, operating in microwave band, ionosphere is a dispersive medium; thus, signals traveling through this medium are in the first approximation, affected proportional to the inverse of the square of their frequencies. This effect allows gaining information about the parameters of the ionosphere in terms of total electron content (TEC) or the electron density (N-e). Making use of this phenomenon, space geodetic techniques have turned into a capable tool for studying the ionosphere in the last decades. Up to now, two-dimensional (2-D) models of Vertical TEC (VTEC) have been widely developed and used by different communities; however, due to the fact that these models provide information about the integral of the whole electron content along the vertical or slant raypath, these maps are not useful when information about the ionosphere at different altitude is required. This paper presents a recent study which aims at developing a global 3-D model of the electron density, using measurements from Global Navigation Satellite Systems and by applying the ray tracing technique to the upper atmosphere. The developed modeling approach represents the horizontal variations of the electron density, with two sets of spherical harmonic expansions of degree and order 15. The height dependency of the electron density is represented by a multilayered Chapman profile function for the bottomside and topside ionosphere, and an appropriate model for the plasmasphere. In addition to the geodetic applications of the developed models, within this study, the 3-D models of electron density can include geophysical parameters like maximum electron density and its corresponding height. High-resolution modeling of these parameters allows an improved geophysical interpretation, which is essential in all studies of the upper atmosphere, space weather, and for the solar-terrestrial environment.