In this paper, the observations from CHAMP radio occultation (RO) and Planar Langmuir Probe (PLP) during 2002–2008 and Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC) observations during 2007.090–2007.120 are used to evaluate the orbit altitude electron density estimation and its effect on the Abel inversion from RO measurements. Comparison between PLP observed and RO estimated orbit electron density on board CHAMP shows that RO estimation tends to overestimate the true orbit electron density by 10% averagely. The average relative deviation is ∼20% and decreases slightly with the increase of the ionospheric peak height and the satellite orbit. It is larger at nighttime than daytime and peaks around sunrise time. Simulations based on COSMIC observations using NeQuick model indicate that the solar activity and the satellite orbit altitude variations will not influence the ratio of the successfully retrieved electron density profiles to the observed occultation events and the relative Abel inversion error of the electron density as well. Different orbit electron density derivation methods, including estimation by the RO total electron content, given by an independent on orbit observation, and assumed to be equal to the topmost point, will have no essential influence on the Abel retrieved electron density. Adding an on orbit observation even has a negative effect on the Abel retrieved electron density around the orbit altitude, which is contrary to our imagination.
 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.
 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 (TECBC) into the corresponding tangent points from the occultation side slant TEC (TECAC), 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 (Ne(rorb)). 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.  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.  for CHAMP mission.
 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.
2. Evaluating the Orbit Altitude Electron Density Estimation Method Using the CHAMP RO and PLP Data
 CHAMP was launched with both the GPS RO receiver and on orbit PLP observation in 2000 [Jakowski et al., 2002]. Figure 2 depicts the variations of the solar 10.7 cm radiation flux (F107), the CHAMP satellite orbit altitude and the available daily data point number for both PLP and RO observations during 2002–2008. As can be seen, the CHAMP daily orbit altitude decays from ∼420 km during the solar maximum of 2002 to ∼330 km in solar minimum of 2008. There are averagely ∼130/day observations available to make the comparison.
Figure 3 shows the general comparison between CHAMP PLP observed and RO estimated orbit altitude electron density for all the available data during 2002–2008 for low-latitude, midlatitude and high-latitude regions, respectively. The RO estimated orbit altitude electron densities generally accord well with the on orbit PLP observations. The correlation coefficient of two data sets varies between 0.89 and 0.96. The mean relative deviation (in absolute value) of RO estimated from the PLP observed electron density is ∼21%, 18% and 22% in low, middle and high latitudes, respectively. The above estimation method performs better in middle latitude than in low and high latitudes. However, some cases show significant deviations as reported by Syndergaard et al. . It indicates that the above estimation method has degraded performance during some specific RO configurations.
Figure 4 is the corresponding statistical result on the relative deviation of RO estimated orbit altitude electron density from that of the PLP observations. A notable feature is that the RO estimation method tends to overestimate the electron density by ∼10% systematically. It can be concluded that ∼60% deviations locate between −10% and 30%. The overestimation might be due to the approximation of constant electron density around the orbit used in our RO estimation method, since the electron density always decrease with the increase of altitude in the topside ionosphere.
Figure 5 shows the peak height (Figure 5a), the orbit altitude (Figure 5b) and local time (Figure 5c) variations of mean relative deviation (in absolute value) of RO estimated from PLP observed orbit electron density. Generally, the mean relative deviation decreases with the increase of the peak height and the orbit altitude. It is 22% (16%) when hmF2 is 200 km (380 km). It changes from 18% (25%) around 330 km orbit altitude to 15% (20%) at 430 km orbit altitude during daytime (nighttime), which indicates the degraded performance of our orbit electron density estimation method from RO signal with the decrease of the satellite orbit altitude. As we know, the electron density gradient above the peak height usually decreases with the altitude. This will result in a better performance of our estimation method in the higher orbit altitude since we use the constant electron density approximation in the topmost kilometers. Note that the ratio that the orbit altitude is equal or lower than the peak height is ∼5% averagely for CHAMP. It is a little larger in solar maximum than in solar minimum. Figure 5 also shows that the mean relative deviation is larger in nighttime than during the daytime and peaks around the sunrise time (∼0500–0700). In our estimation, we assume that both the LEO and GPS satellites move in the same plane. During nighttime, the background electron density is much lower than the daytime. The calibrated TEC should have a relatively larger uncertainty during nighttime especially around the topmost kilometers. This can also be concluded from the peak height variation of the estimation error. During sunrise time, the electron density changes significantly along the orbit, which will result in larger error of our estimation because of constant orbit electron density assumption. The relative deviation is used here to represent our method performance since both the solar flux and orbit altitude changes very much during 2002–2008. Using relative deviation can eliminate the effect of solar radiation variation. We also looked at the absolute deviation and its variations with respect to orbit altitude and local time mainly follow the corresponding background electron density variations. No significant latitude and seasonal variations of the relative deviation are detected (figures not shown).
3. Evaluating the Effect of the Orbit Altitude Electron Density Estimation on the Abel Inversion Using the Simulation
 It is difficult to obtain the EDP error by doing the same comparison work as section 2 because no independent EDP observations with good temporal and spatial coverage are available [Yue et al., 2010]. To evaluate the effect of the orbit altitude electron density estimation on the Abel inversion, a series similar simulation works as Yue et al. [2010, 2011b] have been done. During these simulation works, we mainly focus on the following two aspects: (1) The effects of solar activity and orbit altitude variations on the orbit electron density estimation and Abel inversion, which is done for satellite mission planning purpose. (2) The effect of different orbit altitude electron density derivation on the Abel inversion.
 The COSMIC RO observations during 2007.090–120, when is the transitional time of COSMIC satellite altitudes, are chosen to do the simulation in this study. Detailed description of the COSMIC satellites and its data processing can be found in some previous papers [e.g., Kuo et al., 2004; Lei et al., 2007; Rocken et al., 2000; Schreiner et al., 2007; Syndergaard et al., 2006; Yue et al., 2010]. Figure 6 gives the orbit altitude range of the six COSMIC satellites and the distribution of the number of the occultations versus the orbit altitude during the selected month. There are totally 81297 occultation events selected. The COSMIC satellite orbits have good coverage in both high (∼800 km) and low (∼550 km) altitudes, which is convenient for us to study the effects of the orbit altitude variation.
 The NeQuick model is used to simulate the occultation slant TEC as we did in the work of Yue et al. [2010, 2011a, 2011b], also submitted manuscript, 2010] first. Then the retrieval error can be obtained by comparing the Abel retrieved EDP from the simulated TEC with the NeQuick model EDP along the tangent points. NeQuick is an empirical ionospheric model using the Epstein function to represent the altitude profile of the electron density based on the Consultative Committee on International Radio (CCIR) NmF2 and hmF2 map [Leitinger et al., 2002]. For every simulated occultation event, three Abel inversions as listed in Table 1 with different types of orbit altitude electron density derivation are implemented. Note that the “on orbit observation” in Abel 2 is actually also given by the NeQuick model in our simulation work. In Abel 3, we essentially assume the orbit altitude electron density is the same as that of the topmost tangent point. The topmost point electron density can be calculated by the topmost calibrated TEC without input of the orbit electron density. All the above simulations have been done for every occultation event during both low (F107 = 80) and high (F107 = 200) solar activities, respectively.
Table 1. Three Abel Inversions With Different Orbit Altitude Electron Density Derivations and the Corresponding Correlation Coefficients With the Simulated Truth and the Mean Value of the Absolute Value of the Relative Deviation From the Simulated Truth for NmF2, hmF2, TEC and the Topmost Point, Respectively
Orbit Electron Density Derivation
Correlation Coefficient Between Retrieved and Simulated Truth
3.1. The Effects of the Solar Activity and Satellite Orbit Altitude Variations
 Of the selected 81297 occultation events, 67687 and 67667 high-quality EDPs are successfully retrieved during the simulation under the same CDAAC parameters configuration for the low and high solar activities, respectively. Furthermore, the ratio of successfully retrieved EDP number to the number of occultations has no significant dependency on the orbit altitude (figure not shown here). These indicate that the changes in both the solar activity and the orbit altitude would not influence the ratio of the retrieved EDP to the observed occultation event. However, it should be noted that the orbit altitude is an important parameter on determining the observed number of occultation event [Mousa et al., 2006]. The number of occultations will increase with the decrease of the satellite orbit altitude. In addition, the ratio that the ionosphere peak height is equal or higher than the satellite orbit altitude when the orbit is ∼500 km changes from <0.5% during low solar activity to ∼5% in high solar activity from our modeling results. It is impossible to get the right peak density and height for this kind of occultation. The real situation might be worse than the modeling results. This should be paid attention to when designing the satellite orbit altitude.
Figure 7 shows the orbit altitude electron density estimation error dependency on the solar activity and the orbit altitude from the simulation work during 1300–1500 LT. The corresponding statistical parameters are also given. It is found that the orbit electron density estimation error (in relative deviation) has no obvious dependency on either the solar activity or the orbit altitude. The mean value of the absolute value of the relative deviation is ∼12% for the four selected situations. The estimated orbit electron density tends to overestimate the “truth” in either high or low solar activities (orbit altitudes) by ∼2%. Since the model result is much smoother and the orbit altitude used in the simulation is higher than the CHAMP orbit, both the mean relative deviation and the systematic overestimation are smaller than those of the CHAMP results given in section 2. The relative error of the orbit electron density estimation is slightly higher in nighttime than during the daytime, which is the same as CHAMP results displayed in section 2 (figure not shown).
 According to Yue et al. , the Abel inverted electron density has systematic deviation because of the spherical symmetry assumption. Figure 8 gives an example of the relative error distribution with respect to the local time and the geomagnetic latitude for NmF2, hmF2 and TEC from our modeling results during the solar maximum. The relative errors of all three parameters have significant geomagnetic latitude and local time dependency. The error is more significant in low-latitude regions and after noontime until sunrise time, which is the same as that of the lower-altitude electron density [Yue et al., 2010]. However, their amplitude is smaller than that of the lower-altitude electron density as reported by Yue et al. . The range of relative error is −20%∼40% for NmF2, ±5% for hmF2 and −25%∼60% for TEC, respectively. We also plot the same picture as Figure 8 for different orbit altitude situations under both high and low solar activities (figures not shown). No significant solar activity and orbit altitude dependencies are detected. The error distributions keep the same latitude and local time dependence except slightly difference in the value. As discussed by Yue et al. , the above error distribution is mainly resulted by the spherical symmetry assumption, which is not fully satisfied in the low-latitude regions. The changes in solar activity and orbit altitude therefore have a relatively smaller influence on the retrieval error.
3.2. The Effect of Different Orbit Altitude Electron Density Derivation on the Abel Inversion
Figure 9 is an occultation case retrieved by different Abels (Abel 1–3) as listed in Table 1 for both the real and the simulated data. Note that there is no Abel 2 retrieval on the real data since no independent orbit observations are available on COSMIC satellites. From either the real data or the simulated data, we can see that the three Abel retrievals give almost the same electron density profile, except some discrepancies on the topmost points. We looked through many cases and the situation is almost the same as this one. The big difference between the retrieved and “simlated truth” is resulted from the calibration error.
Table 1 lists the correlation coefficient and the mean value of the relative deviation between the Abel inversions and the simulated truth for NmF2, hmF2, TEC and the topmost point, respectively. From either the correlation coefficient or the mean relative deviation, it can be concluded that all three Abel inversions have almost the same performance on the NmF2, hmF2 and TEC retrieval. However, the Abel 2 retrieval has a degraded performance on the topmost point retrieval in comparison with Abel 1 or 3 retrievals. It indicates that adding an on orbit observation even has a negative effect on the Abel retrieved electron density below the orbit altitude, which is contrary to our imagination. This might relate to the calibration method used, which will have a relatively larger error on the top most points and then determine a different electron density profile on the top. The average retrieval error by three Abel inversions is 6%, 0.7%, 14% for NmF2, hmF2 and TEC, respectively. The mean relative error for the topmost point changes from 11% by Abel 1 and 3 to 17% by Abel 2. The real situation should be worse because a smooth model is used here. We also checked the error distributions with respect to the latitude and local time. The three Abel inversions give almost the same features as Figure 8 for NmF2, hmF2 and TEC.
 In this paper, the Abel inversion especially the orbit altitude electron density estimation method is described. Both the CHAMP and COSMIC observations are used to evaluate the orbit altitude electron density estimation accuracy and its effects on the Abel inversion. The conclusions are given as follows:
 Through comparing the orbit altitude electron density observed by PLP and estimated by RO measurements on board the CHAMP satellite during 2002–2008, it is found that the RO estimation tends to overestimate the true orbit electron density by 10% averagely, which can be explained by the constant electron density approximation around the orbit. The average relative deviation of the RO estimated orbit electron density from that of PLP observed is ∼20% and decreases slightly with the increase of the peak height and the satellite orbit altitude. The orbit electron density estimation method performs better in midlatitude than low-latitude and high-latitude regions. The relative error of the current orbit altitude electron density estimation method is larger at nighttime than daytime and peaks around sunrise time.
 Totally 81297 occultation events observed by the COSMIC satellites during 2007.90–120 are selected to do the simulation using NeQuick model. It is found that the changes in the solar activity and the satellite orbit altitude will not influence the ratio of the successfully retrieved EDPs number to the observed occultation events. The occurrence rate that the peak height is equal or higher than the orbit altitude increases very much from low solar activity to high solar activity especially for lower orbit altitude. The mean value of the absolute value of the relative deviation of orbit electron density is ∼12% and the estimated orbit electron density tends to overestimate the “truth” in either high or low solar activities (orbit altitudes) by ∼2% by our simulation work. The changes in solar activity and orbit altitude does not influence the relative Abel retrieval error of electron density from the simulation. Different orbit electron density derivation methods, including estimation by function (2), given by an independent on orbit observation, and assumed to be equal to the topmost point, will have no essential influence on the Abel retrieved electron density. Adding an on orbit observation even has a negative effect on the Abel retrieved electron density especially around the orbit altitude, which is contrary to our imagination.
 This work is supported by the National Science Foundation under grant AGS-0961147. Special thanks should be given to the ISDC of GFZ for providing the CHAMP data. We are thankful to Jiuhou Lei from Colorado University for his help in preparing the CHAMP PLP data.