A comprehensive evaluation of the errors inherent in the use of a two-dimensional shell for modeling the ionosphere

[1] Accurately modeling the ionosphere is a critical component to many radionavigation applications. However, in a significant number of cases, these models assume the ionosphere is compacted into a thin shell surrounding the Earth, rather than a full three-dimensional field. While such models allow for ease of use and small storage needs, they are necessarily lacking in detailed information on the actual three-dimensional distribution of electrons in the ionosphere. This paper attempts to quantify all geometric and numerical errors made through the use of a shell model. Such errors can reach as high as 14% on days of no strong ionosphere activity. Ultimately, this paper concludes that the highest levels of accuracy require the total electron content of the ionosphere be modeled three-dimensionally. However, for those who must continue to use a shell model, a new mapping function has been derived which removes as much as 50% of the total errors seen using the previous, standard mapping function for shell models.