## 1. Introduction

[2] The low Earth orbit (LEO) based radio occultation (RO) technique shows dramatic ability in the Earth's lower atmosphere and ionosphere exploration since the success of the Global Positioning System/Meteorology (GPS/MET) experiment aboard the MicroLab 1 satellite in 1995. Many satellite missions after that were launched with GPS RO payload. The RO technique has shown great utility in the weather prediction, climate science, space weather, and ionospheric research [*Anthes et al.*, 2008]. The vertical profiles of refractivity, temperature, pressure, and water vapor in the stratosphere and troposphere and electron density in the ionosphere can be derived from the bending information of the GPS RO signal [*Kuo et al.*, 2004; *Rocken et al.*, 2000; *Schreiner et al.*, 1999]. Of these parameters, the electron density profile (EDP), which can be derived from either the bending angle or the total electron content (TEC), is the important product for the space weather and ionospheric study.

[3] The most commonly used method to derive the EDP from the RO measurements is the so called Abel inversion, aided by several assumptions [*Lei et al.*, 2007; *Schreiner et al.*, 1999; *Syndergaard et al.*, 2006; *Yue et al.*, 2010, 2011a]. The Abel inversion can give reasonable EDPs in the F and above region as well as peak height (hmF2) and density (NmF2) [*Lei et al.*, 2007; *Schreiner et al.*, 2007; *Straus*, 2007; *Yue et al.*, 2010]. However, it has degraded performance in the low altitudes and at low-latitude regions because the spherical symmetry assumption is not totally satisfied in the regions of significant ionospheric horizontal gradients [*Lei et al.*, 2010; *Straus*, 2007; *Yue et al.*, 2010, 2011b]. It can result in several large-scale pseudofeatures such as two plasma caves underneath the equatorial ionization anomaly (EIA) crests, three peaks along the latitude in the low-altitude regions, and the reversal phase wave number 4 structure in the E and F1 layers [*Lei et al.*, 2010; *Yue et al.*, 2010, 2011b]. Many different revised methods, such as the data assimilation retrieval by *Yue et al.* [2011a] and *Nicolls et al.* [2009], the maximum entropy method by *Hysell* [2007], incorporating horizontal gradients by other types of observations by *Schreiner et al.* [1999] and *Hernandez-Pajares et al.* [2000], joint retrieval of several occultations by *Hocke and Igarashi* [2002] and *Tsai and Tsai* [2004], have been proposed to improve the RO EDP retrieval.

[4] In the Abel inversion currently used by the University Corporation for Atmospheric Research (UCAR) Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC) Data Analysis and Archive Center (CDAAC), another important approximation beyond spherical symmetry assumption is the first-order estimation of the LEO satellite orbit electron density [*Syndergaard et al.*, 2004]. Figure 1 gives a general illustration of the Abel inversion with calibrated TEC method and orbit altitude electron density approximation [*Schreiner et al.*, 1999]. Under the assumptions of circular orbit and the same plane of both LEO and GPS satellite movements, the phasmaspheric TEC can be deducted by subtracting the interpolated slant TEC of unoccultation side (TEC_{BC}) into the corresponding tangent points from the occultation side slant TEC (TEC_{AC}), which is called calibrated TEC method. The calibrated TEC between points A and B is related to the electron density through [*Schreiner et al.*, 1999]:

The electron density in each layer can then be derived one by one from the top to the bottom under the assumption of spherical symmetry if we know the electron density in the orbit altitude (N_{e}(r_{orb})). Assuming the electron density is constant around the orbit altitude during the upper most layers, the solution of function (1) can be given as [*Syndergaard et al.*, 2006]:

The orbit altitude electron density can be estimated by the upper most few kilometers calibrated TEC observations using least squares fit method following function (2). Beyond useful for the RO EDP retrieval, these estimated orbit electron densities are also an important on orbit database for the missions with no on orbit observations such as COSMIC. The above step is applicable when sufficient observations in the unoccultation side such as COSMIC satellites are available to make such kind of calibration. We obtain the calibrated TEC by subtracting the topmost slant TEC from the occultation side slant TEC when no or insufficient observations are available in the unoccultation side such as the CHAMP satellite. In this situation, the estimated electron density by formula (2) is the value of the topmost tangent point, not the orbit altitude. So an increment to the calibrated TEC need to be estimated by least squares fit to the observed slant TEC of the occultation side [*Syndergaard et al.*, 2004, 2006]. Then the orbit altitude electron density can be properly estimated using these compensated TEC. *Syndergaard et al.* [2004] compared the CHAMP RO estimated electron density in the orbit altitude with the on orbit observations by the Planar Langmuir Probe (PLP) during 16 months. The correlation coefficient between two types of observations is 0.95. However, some big deviations were also detected. An optional model aided method to derive the orbit altitude electron density and deduct the influence above the satellite altitude was tested by *Jakowski et al.* [2002] for CHAMP mission.

[5] In this paper, we will first evaluate the above method of orbit altitude electron density estimation by CHAMP RO and PLP observations during 2002–2008. Then a series of simulation studies will be implemented to investigate its effect on the Abel inversion error as well as its solar and orbit altitude variations. Further more, the effects of Abel inversions with no predetermined orbit electron density and with an on orbit observation will also be tested.