Interactive comment on “ Electron density profiles probed by radio occultation of FORMOSAT-7 / COSMIC-2 at 520 and 800 km altitude ”

retrievals? Through the analysis of the RO observations obtained at different COSMIC orbit altitudes and simulation study, the authors find the effect of satellite altitude on the Abel inversion is not significant. Generally speaking, this study would have been valuable if this question had never been answered before. However Yue et al. [2011] has investigated this question, as announced clearly in their abstract, “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”. This study therefore seems a bit redundant, and not good enough for publication. Yue, X., W. S. Schreiner, C. Rocken, and Y.-H. Kuo (2011), Evaluation of the orbit altitude electron density estimation and its effect on the Abel inversion from radio occultation measurements, Radio Sci., 46, RS1013, doi:10.1029/2010RS004514. ”


Introduction
On 15 April 2006, six microsatellites of FORMOSAT-3/COSMIC (F3/C) were launched to the parking orbit of about 516 km altitude and subsequently lifted to the mis-sion orbit at about 800 km, both with an inclination of 72 • .Each microsatellite has been receiving GPS signals to carry out radio occultation (RO), which yields abundant information about neutral atmospheric temperature and moisture as well as space weather estimates of slant total electron content (TEC), electron density profiles, and an amplitude scintillation index, S4 (Schreiner et al., 2007).The Abel inversion (cf.Hajj and Romans, 1998) has been employed to invert the electron density from the RO TEC.With the success of F3/C, the United States and Taiwan are moving forward with a follow-on RO mission named FORMOSAT-7/COSMIC-2 (F7/C2), which will ultimately place 12 satellites in orbit with two launches with 24-28.5 • inclination and 520-550 km altitude in 2016 and with 72 • inclination and 720-750 km altitude in 2018 (Lee et al., 2013;Yue et al., 2014;Yen, 2015).Scientists find that the local spherical symmetry assumption in the standard (Abel) RO inversion processes results in systemic biases, especially the EIA (equatorial ionization anomaly) at low latitudes, where the horizontal gradient is most significant (cf.Liu et al., 2010b).Lei et al. (2007) indicated that to conduct the Abel inversion, the electron density at the satellite altitude should be assumed.Yue et al. (2011) conducted simulations based on F3/C observations using NeQuick model and found that the solar activity and the satellite orbit altitude variations do 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.They also show that different orbit electron density derivation methods have no essential influence on the Abel retrieved electron density.Their statistical results indicate that the orbit electron density estimation error has no obvious dependency on either the solar activity or the orbit altitude.It is essential to know and evaluate the difference between the two electron density profiles retrieved from the sounding geometries of satellites orbiting at 500 and 800 km altitudes for combining the two electron density profiles to construct the global three-dimensional electron density structure.In this paper, we examine the effect of satellite altitude on the Abel inversion by firstly comparing the electron density profiles ranging from 100 to 500 km altitude observed by satellites at 500 and 800 km altitude and their differences during the early F3/C mission period.Observing system simulation experiments (OSSEs) by means of the standard F3/C Abel inversion are used to produce above the observation.Cross comparisons among the observation and the OSSE shall have a better understanding on the electron density profiles observed at 520-550 and 720-750 km altitude for the upcoming F7/C2 mission during both solar minimum and solar maximum.

F3/C electron density profiles observed at 500 and 800 km altitude
One half of F3/C satellites were orbiting at the parking orbit 500 km altitude and the other half at the mission orbit 800 km altitude in March and April 2007 (Fig. 1).The satellites at 500 and 800 km altitude probed 5812 and 5425 electron density profiles during 12:00-14:00 UT in March and April of 2007.During the study period, satellite LEO4 was transferred from 500 to 800 km altitude, and therefore its electron density profiles probed below and above 600 km altitude are classified into 500 and 800 km altitude, respectively.The electron density profiles are gridded with 5 • in latitude, 20 • in longitude, and 5 km in altitude and the median of the electron density in each grid is computed.Figure 2 displays that the global electron density N, F2 peak electron density NmF2, and height hmF2 observed at the 500 and 800 km satellite altitude, and their difference.The longitude cuts in −120, −60, 0, 60, and 120 • stand for the electron density at 05:00, 09:00, 13:00, 17:00, and 21:00 LT, respectively.It can be seen that structures of the electron density observed from 500 km satellite altitude (N 500 ) and from 800 km satellite altitude (N 800 ) at 09:00, 13:00, 17:00, and 21:00 LT are similar, respectively.Since the accuracy in the lower ionosphere is relatively low, we focus on the electron density in the topside ionosphere (i.e., the region above the F2 peak).It can be seen that the N 500 is slightly greater (less) than N 800 in the equatorial (off-equator) ionosphere, while N 500 is slightly weaker than N 800 in the South Pole region at 09:00 LT.N 500 is greater than N 800 in the EIA region at 13:00 LT; N 500 is weaker (greater) than N 800 in the northern (southern) EIA region at 17:00 LT; and N 500 is weaker than N 800 in the southern EIA region at 21:00 LT.The difference between the two electron densities N 500 -N 800 generally agrees with the above comparisons and also reveals that N 500 is greater than N 800 in the northern EIA at 21:00 LT.The F2 peak electron density NmF2 observed from 500 and 800 km altitude (NmF2 500 and NmF2 800 ) displays that the two NmF2s yield similar patterns and NmF2 800 is generally greater than NmF2 500 in the northern EIA area.However, due to the data locations being different, the difference of NmF2 500 -NmF2 800 is difficult to identify.The F2 peak height hmF2 probed from 500 and 800 km satellite altitude (hmF2 500 and hmF2 800 ) as well as their difference illustrated that the two hmF2s are general similar in the low and mid-latitudes.In short, the F3/C electron densities observed from 500 and 800 km satellite altitude are qualitatively similar.

Abel OSSE
To carry out Abel OSSEs, we first insert realistic F3/C RO ray path geometries into the corresponding ionosphere computed by the International Reference Ionosphere (IRI)-2007 (Bilitza and Reinisch, 2008) to simulate the total electron content (TEC), and then apply the Abel inversion routine of CDAAC (COSMIC Data Analysis and Archival Center) to derive electron density profiles.Figure 3 displays the truth of the electron density, the NmF2, and hmF2 computed by IRI.The truth electron density shows that the EIA is greater in the Northern Hemisphere than that in the Southern Hemisphere, which can be found in NmF2 distributions.The daytime hmF2 reaches the highest altitude in the EIA region, while hmF2 at mid-and high latitudes in nighttime is higher than those in daytime.Figure 4 depicts OSSE electron density, NmF2, and hmF2 observed by satellites at 500 and 800 km altitude, and their difference.It can be seen that N 500 is slightly weaker than N 800 in the South Pole region at 09:00 LT; N 500 is greater than N 800 in the EIA region at 1300 and 17:00 LT; and N 500 is weaker than N 800 in the southern EIA region at 21:00 LT.Note that both N 500 and N 800 in EIA are greater in the north than those in the south obtained by the Abel OSSE, which agree with the truth, respectively.It should be mentioned that the difference between N 500 and N 800 of the F3/C observation and that of the Abel OSSE yield similar features.The OSSE reveals that the NmF2 500 is slightly less  than NmF2 800 in the northern EIA region; however the corresponding difference of NmF2 500 -NmF2 800 is rather complex.
On the other hand, hmF2 500 and hmF2 800 in the low and midlatitudes are generally similar.
We further find whether there is any systematic error due to the different satellite altitudes of 500 and 800 km by subtracting the results of the Abel OSSE from the IRI truth.Similar patterns shown in Fig. 5a and 5b suggest the Abel inversion could result in systematic error in the EIA region, where both N 500 and N 800 underestimate the electron density in the EIA crests but overestimate in the magnetic equator and/or poleward sides of the EIA crests.Again, we examine the differences of the topside ionosphere retrieved between satellites at 500 and 800 km altitudes (Fig. 5c).The underestimation of N 500 is more severe than that of N 800 above F2 peak in the EIA region at 1300 LT and N 500 is not as severe as N 800 above F2 peak in the EIA region at 09:00 and 17:00 LT.On the other hand, the error patterns of NmF2 500 and NmF2 800 are similar, which underestimate in the two EIA crests but overestimate in their poleward sides.It is interesting to find that the errors of both hmF2 500 and hmF2 800 are similar, which show error of hmF2 being small globally.

Discussion and conclusion
The F3/C observation and OSSE show that the electron density, NmF2, and hmF2 probed at 500 and 800 km altitude are similar (Figs.2a and b and 4a and b).Although the real and IRI ionospheres might be different, the differences N 500 -N 800 shown in Figs.2c and 4c are somewhat similar, especially in the topside ionosphere.Table 1 further reveals that the overall difference N 500 -N 800 of the F3/C observation and OSSE are 23.5 ± 35.1 and 18.6 ± 30.9 %.The overall difference N 500 -N 800 could result from the observation data  2d and e and 4d and e).Table 1 shows that during the solar minimum of 2007, the overall differences NmF2 500 -NmF2 800 (hmF2 500 -hmF2 800 ) of the F3/C observation and OSSE are 28.0 ± 39.1 and 14.1 ± 21.3 % (19.3 ± 27.3 and 7.4 ± 10.4 km), respectively.Nevertheless, the pattern similarities and the difference means being less than 20 % imply that the Abel inversion routine of CDAAC can be applied to reasonably derive electron density profiles by the RO TEC probed at 500 km satellite altitude.The OSSE error of the Abel inversion reveals that the topside ionospheric electron density at EIA region has been underestimated (Fig. 5).Moreover, we want to see whether the results hold true for the solar maximum when 500 km is much closer to the F region peak altitude.We also conduct OSSEs during the solar maximum of 2002.It is found that the standard deviation in the solar maximum is similar to the corresponding one in the solar minimum, which confirms that the results hold true even for the solar maximum.They also find that in comparing them to the retrieval error caused by the spherical symmetry assumption, the changes in solar activity and orbit altitude have a relatively small influence on the retrieval error of NmF2, hmF2, and TEC.To validate the above inference we conduct an OSSE by comparing the electron density profiles retrieved from satellites at 800 km altitude and those from satellites with identical sounding geometries but at 500 km altitude.Figure 6 shows that the electron density profiles retrieved by the satellite at 500 km tend to be smaller than those at 800 km altitude in the EIA region but are greater than those in the magnetic equator and/or poleward sides of the EIA crests.These discrepancies result from the spherical symmetry assumption of Abel inversion in the EIA region (Liu et al., 2010a).By contrast, Fig. 4 shows that the electron density profiles retrieved by the satellite at 500 km are very different from those at 800 km altitude, especially in the EIA region.This further indicates that differences of the sounding geometry at 500 and 800 km altitude satellites could significantly influence the retrieved electron density profiles by using Abel inversion.It is known that F7/C2 will be ultimately placed during the first launch of six satellites into orbits with 24-28.5 • inclination and 520-550 km altitude, and during the second launch of six satellites with 72 • inclination and 720-750 km altitude.Since the sounding geometries of the two launches are going to be very different, the electron density profiles probed by the two altitudes shall be different.Therefore, one must take care to construct the three-dimensional electron density structure by merging the retrieved electron density profiles of the two launches.
Table 1 displays the OSSE results: the means of the overall differences N 500 -N 800 , NmF2 500 -NmF2 800 , and hmF2 500 -hmF2 800 in the solar minimum (maximum) are 18.6 (19.1 %), 14.1 (11.9 %), and 7.4 (8.7 km), respectively.The associated values in the F3/C observations, 23.5, 28.0 %, and 19.3 km are greater than those in the OSSE results.The differences of the observations are constantly larger than those of the OSSEs, which might result from the true ionosphere being more structured than the IRI-simulated ionosphere during the study period.Nevertheless, this suggests that the Abel inversion routine of CDAAC can be employed to reasonably derive electron density profiles from the RO TEC sounded at 520 km F7/C2 satellite altitude.Therefore, the sounding geometry and the contour process are the major bias for constructing the global three-dimensional electron density structure by merging the retrieved electron density profiles probed by the two F7/C2 launches.

Figure 1 .
Figure 1.The altitude of each F3/C microsatellite from launch to middle of 2007.The red box indicates the time period of the study.

Figure 3 .
Figure 3.The OSSE truth.The median of IRI output obtained from 12:00-14:00 UT in March and April of 2007.The electron density distribution, NmF2, and hmF2 are shown from up to down.

Figure 4 .
Figure 4.The Abel inversion OSSE electron density, NmF2, and hmF2 observed from 500 and 800 km altitude satellites, and their difference during 12:00-14:00 UT in March and April of 2007.(a) OSSE electron density observed from 500 km altitude, (b) OSSE electron density observed from 800 km altitude, and (c) their difference.(d) OSSE NmF2 and hmF2 observed from 500 km altitude, (e) OSSE NmF2 and hmF2 observed from 800 km altitude, and (f) their difference.

Figure 5 .
Figure 5.The Abel inversion OSSE error (OSSE result-truth) electron density, NmF2, and hmF2 observed from 500 and 800 km altitude satellites, and their difference during 12:00-14:00 UT in March and April of 2007.(a) OSSE electron density error observed from 500 km altitude, (b) OSSE electron density error observed from 800 km altitude, and (c) their difference.(d) OSSE NmF2 and hmF2 error observed from 500 km altitude, (e) OSSE NmF2 and hmF2 error observed from 800 km altitude, and (f) their difference.

Figure 6 .
Figure 6.The Abel inversion OSSE electron density, NmF2, and hmF2 observed from 500 and 800 km altitude satellites, whose sounding geometries are identical, and their difference during 12:00-14:00 UT in March and April of 2007.(a) OSSE electron density observed from 800 shifted to 500 km altitude, (b) OSSE electron density observed from 800 km altitude, and (c) their difference.(d) OSSE NmF2 and hmF2 observed from 800 shifted to 500 km altitude, (e) OSSE NmF2 and hmF2 observed from 800 km altitude, and (f) their difference.

Table 1 .
The differences of N, NmF2, and hmF2 observed at 500 and 800 km altitude.