Retrieving Vertical Ionospheric Electron Density Profile with an Improved Abel Inversion Algorithm

Vertical electron density profile is an important source of information on the Earth’s ionosphere. It is well known that such vertical electron density profile can be retrieved using LEO (Low Earth Orbit) satellite RO (radio occultation) data. With more and more LEO satellite data available (such as CHAMP, SAC_C, GRACE, COSMIC), the retrieved vertical electron density can be more accurate if some proper models are used. Nowadays, there are two major vertical electron density retrieve methods with the LEO data: tomographic reconstruction and the Abel inversion. Compared with the tomographic reconstruction technology, the Abel inversion method is achieved by small amount of RO data and a simple algorithm. But the drawback of the Abel inversion is that the retrieved vertical electron density profile only shows the vertical electron density average variation over a large area rather than accurate altitude variation in a latitude and longitude position. This problem is caused by the assumption of electron density local spherical symmetry and even distribution. When a RO passes a few thousands kilometers, it is not reasonable to assume the electron density along the RO ray path varies only respect to altitude without considering both latitude and longitude factors. To improve the accuracy of the Abel inversion model, the one dimensional (1D) shape function is introduced. It is defined as the function of altitude, and its value with respect to a point is equal to the vertical TEC (Total Electron Content) at the point divided by the electron density at the point. This definition makes the solved electron density not only depend on altitude (represented by the shape function) but also be related to latitude and longitude (represented by vertical TEC --the function of latitude and longitude). Although the 1D shape function increases the model accuracy, it is still not realistic to assume that the shape function relies only on altitude. In this paper, the two dimensional (2D) shape function is used to further improve the accuracy of the 1D shape function model. The 2D shape function is defined as a function of altitude and the zenith angle with regard to the local center or a GPS (Global Positioning System) receiver. The value of the 2D shape function is first solved by combining ground based GPS data and RO data. Then based on the solved 2D shape function, the vertical electron density profiles in the local area are generated. This paper will describe the details of the proposed method and also discuss the numerical results generated from the proposed 2D model, the 1D shape function model and the IRI model