The impact of spherical symmetry assumption on radio occultation data inversion in the ionosphere: An assessment study

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ScienceDirect Advances in Space Research 53 (2014) 599–608 www.elsevier.com/locate/asr

The impact of spherical symmetry assumption on radio occultation data inversion in the ionosphere: An assessment study M.M. Shaikh a,⇑, R. Notarpietro a, B. Nava b a

Department of Electronics and Telecommunications, Politecnico of Turin, Torino, Italy b The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy

Received 23 April 2013; received in revised form 14 October 2013; accepted 17 October 2013 Available online 31 October 2013

Abstract ‘Onion-peeling’ is a very common technique used to invert Radio Occultation (RO) data in the ionosphere. Because of the implicit assumption of spherical symmetry for the electron density (N(e)) distribution in the ionosphere, the standard Onion-peeling algorithm could give erroneous concentration values in the retrieved electron density profile. In particular, this happens when strong horizontal ionospheric electron density gradients are present, like for example in the Equatorial Ionization Anomaly (EIA) region during high solar activity periods. In this work, using simulated RO Total Electron Content (TEC) data computed by means of the NeQuick2 ionospheric electron density model and ideal RO geometries, we tried to formulate and evaluate an asymmetry level index for quasi-horizontal TEC observations. The asymmetry index is based on the electron density variation that a signal may experience along its path (satellite to satellite link) in a RO event and is strictly dependent on the occultation geometry (e.g. azimuth of the occultation plane). A very good correlation has been found between the asymmetry index and errors related to the inversion products, in particular those concerning the peak electron density NmF2 estimate and the Vertical TEC (VTEC) evaluation. Ó 2013 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Ionospheric asymmetry; Radio occultation; Onion-peeling; NeQuick2

1. Introduction RO missions such as GPS/MET (Global Positioning System/Meteorology), CHAMP (CHAllenging Minisatellite Payload), COSMIC (Constellation Observing System for Meteorology, Ionosphere, and Climate) and MetOP (Meteorological Operational) (Anthes et al., 2008; Gorbunov, 2001; Hajj et al., 2002; Healy et al., 2002; Luntama et al., 2008) have been designed to sound the Earth’s neutral atmosphere and ionosphere via radio links between a GPS navigation satellite and GPS receiver on-board Low Earth Orbit (LEO) satellites (Gorbunov, 1996). The US GPS/ MET experiment was the first mission which successfully applied RO technique to the Earth atmosphere monitoring, using GPS signals. Since then, RO technique has become a ⇑ Corresponding author. Tel.: +39 3802424640.

E-mail address: [email protected] (M.M. Shaikh).

powerful tool to study ionosphere (Kulikov et al., 2011; Liu et al., 2010). In neutral atmosphere, using RO technique, the bending of the signal is extracted and inverted into refractivity profiles through the Abel inversion (Kursinsky, 1997; Ware et al., 1996). In the ionosphere, where bending is negligible, carrier phase measurement and corresponding limb-TEC observations (LTEC in what follows) are used to extract electron density profiles, Ne(h), defined in terms of ray perigee’s location of each ray path between LEO and GPS (see Fig 1 for reference). The retrieval algorithm considers the internal orbit LTEC time-series (from points A1 to A2 in Fig. 1) observed from the same GPS satellite during an occultation event. Therefore the external LTEC (TEC from GPS-to-B or GPS-to-A2 in Fig. 1) should be removed before starting the inversion procedure. With older RO missions (GPSMET, CHAMP etc.) data, it was only possible to perform TEC measurements at the highest

0273-1177/$36.00 Ó 2013 COSPAR. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.asr.2013.10.025

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Fig. 1. Limb TEC (LTEC) measurement in the ionosphere using radio occultation technique. A1 and A2 are two sides of the LEO orbit determining the ray perigees (black dots). The TEC calculated between sides A1 and A2 are defined as internal orbit LTEC.

point of LEO orbit (point B in Fig. 1) so the external TEC had to be modeled or considered constant all over the occultation. For the COSMIC mission, such external LTEC measurements are generally available (i.e. from GPS-to-A2 in Fig. 1) and can be removed before the inversion. A widely used method to invert LTEC measurements to obtain vertical electron density profile is the Onion-peeling inversion algorithm (Leitinger et al., 1997). The Onionpeeling algorithm is based on the assumption of spherical symmetry of Ne distribution in the ionosphere (Ne depends only on height). It is a very effective tool for RO data inversion in case of small horizontal gradients present in the ionosphere (particularly during low solar activity periods). But, for high solar activity conditions, for example under the EIA region, large electron density gradients may be experienced which could lead to the failure of Onion-peeling algorithm producing erroneous Ne(h) profiles as output. In the present work a simulation study to assess the effects of the spherical symmetry assumption for the ionospheric electron density on the Onion-peeling retrieved profiles has been performed. In order to produce synthetic electron density data and to simulate corresponding LTEC values for Onion-peeling assessment the NeQuick2 (Nava et al.) electron density model has been used throughout this study. NeQuick2 is an ionospheric electron density model developed at the Abdus Salam International Centre for Theoretical Physics (ICTP) and University of Graz. It is able to characterize the electron concentration distribution in the ionosphere, and it is a quick-run model particularly tailored for trans-ionospheric propagation applications. The basic inputs of the NeQuick2 model are position, time (UT) and solar flux (F10.7); the output is the electron concentration at the given location and time. Based on ITU

recommendations, NeQuick2 has a limit for the F10.7 solar flux input at 193 sfu1 to allow the corresponding saturation of the FoF2 parameter (ITU-R Recommendations P.12393, 2012). The first release of the model has been used by the European Space Agency (ESA) European Geostationary Navigation Overlay Service (EGNOS) project for single frequency assessment analysis and has been adopted in support to single-frequency positioning applications in the framework of the European Galileo project (Arbessor-Rastburg, 2006). It has been adopted by the International Telecommunication Union, Radio-communication Sector (ITU-R), as a suitable method for Total Electron Content (TEC) modeling (ITU-R Recommendations P.531-11, 2012). In addition, it has been implemented in GNSS Simulation Toolkit (GST) developed in Australia with the aim to qualitatively assess the performance of the future GNSS infrastructure (Seynat et al., 2004). Rutherford-Appleton Laboratory of the UK has adopted NeQuick to forecast vertical TEC from forecasted values of the critical frequency in F2 layer (namely, foF2) and of the Maximum Usable Frequency in F2 (MUF(3000)F2) (Cander, 2003). More recent uses of NeQuick includes the SPENVIS simulator of ESA (http://www.spenvis.oma.be). In the next sections, we will present how we assess the problem of asymmetry in the ionosphere both qualitatively and quantitatively. In Section 2, we will briefly introduce Onion-peeling algorithm and its implementation in our work. In Section 3 we will define a mathematical relationship helpful to assess ionospheric asymmetry. In Section 4, a discussion on the simulation results will be presented. In Section 5, we will summarize the work by drawing the main conclusions and discussing prospects for the future work. 2. Formulation of the problem In this work, we applied the standard Onion-peeling algorithm to invert simulated radio occultation data under a constraint of using ideal geometries: we have considered only internal orbit ray paths, namely the part of the LEOto-GPS ray-path below the LEO orbit (line between points A1 and A2 shown in Fig. 1), fixed occultation planes and vertically distributed ray perigees positions. The rationale behind the use of this so called ‘ideal geometry’ is to focus the dependency of retrieval errors on the inversion approach only, avoiding taking into account inaccuracies due to geometry. The possibility to use external data, like vertical TEC maps (Herna`ndez-Pajares et al., 2000) to improve the solution, has therefore not been considered in the present work. In our analysis, we considered a LEO satellite orbiting at 800 km of height. The background ionosphere has been computed using NeQuick2 with F10.7 = 190 sfu to reproduce high solar activity conditions. It is important to mention here that, in a real radio occultation scenario, the word ‘event’ is used to define 1

Solar Flux Unit (sfu) = 1022 watt/m2/Hz.

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the scenario between LEO and GPS satellites for slant TEC measurement. In this assessment study, as the whole work is based on simulated data, we will use the word ‘event’ with reference to our simulated radio occultation scenarios including the above mentioned ideal geometries. For a given occultation event, the LTEC related to the internal orbit ray path ‘i’ can be evaluated considering a set of spherical shells (identified by peel ‘j’) like ‘onion shells’ (Leitinger et al., 1997; Herna`ndez-Pajares et al., 2000), characterized by a constant electron density (the radius of each shell is the impact parameter of the ray). Analytically, the LTEC associated to the ith ray can be defined as: LTEC i

N X

2Lij Nej þ Lij Nei ;

ð1Þ

j¼iþ1

where, ‘ Lij ’ ‘ Nej ’ ‘ LTECi ’ ‘N’

is the length of the segment ‘i’ related to the electron density characterizing shell ‘j’ is the electron density charactering shell ‘j’ is the limb-TEC value related to the ‘ith’ internal orbit ray path crossing all the shells is total number of shells

Considering this definition, the LTEC may be easily inverted to extract the Ne characterizing each shell ‘Nej’, starting from the most external ray path. The matrix (Eq. (1)) describing the linear system of equations is triangular, and therefore it can be solved from top to bottom for LTEC inversion to extract the Ne(h) profile. But this approach faces two major issues. Firstly, having defined ‘spherical’ shells, this technique is based on spherical symmetry hypothesis, i.e., the Ne depends only on height. Secondly, as it is clear from the mathematical expression given in Eq. (1), the electron density in each shell is evaluated from electron densities characterizing all the layers above it. That is, if the calculation of Ne for one shell (at a particular height) is wrong because of any reason, the computed value, other than affecting electron density of that shell, adds an error contribution to the calculation of the electron densities for all the layers below it. Both these causes may impact the Ne profile retrieval, in particular when cases of large horizontal Ne gradients are considered which imply the Ne distributions to depart from the spherical symmetry assumption. With the current Onion-peeling implementation (without the help of external information like e.g. ground-based TEC data as suggested by Herna`ndez-Pajares et al., 2000), there is no simple way to predict or compensate for this error. In this paper our attention has been primarily devoted to test how much the ionospheric asymmetry may impact electron density retrieval considering high solar activity conditions. Using NeQuick2 as background ionospheric model, we inverted simulated LTEC data using Onion-peeling technique and compared it with geographically co-located

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‘truth’ data. With this approach the results produced by the standard Onion-peeling inversion can be quantitatively assessed in a simulated environment. Results are given both considering mid and low latitude ionospheric regions with particular attention given to the Equatorial Ionospheric Anomaly (EIA), in order to understand the effects of strong electron density gradients usually present in this region. 3. Ionospheric asymmetry assessment Shaikh et al. (2012) have shown that the Onion-peeling algorithm can be successfully applied where GNSS signals cross ionospheric regions characterized by small horizontal electron density gradients. In some cases, where the ionospheric conditions along the ray path differ greatly from the spherical symmetry assumptions like in the EIA region, the algorithm may lead to erroneous electron density profiles. As an example, two simulated occultation events are illustrated in Fig. 2. Fig 2(a) shows a global VTEC map computed using NeQuick2 (F10.7 = 190 sfu, month = 07, UT = 1:00). Superimposed are the A1 (white) and A2 (magenta) points characterizing the evaluated RO ray paths (see Fig. 1) at two different longitudinal planes, 170°W (day time occultation) and 20°W (night time occultation), projected on the ground. In both cases, the azimuth of the occultation plane is 0° (i.e. occultation plane is aligned with the Meridian plane). Fig. 2(b) and (c) describe the internal orbit ray path plotted against the background ionosphere (electron density values) simulated using NeQuick2. In Fig. 2(d) and (e), a qualitative comparisons between Ne(h) profiles obtained from Onion-peeling inversion (blue) and their corresponding truth (red) are shown. The two simulated events are experiencing different horizontal gradients along their ray paths. In fact, the event at 170°W cross a well-developed EIA region in contrast to what is happening at 20°W. Analysing their corresponding ray paths (Fig. 2(b) and 2(c)) and inverted profiles (Fig. 2(d) and 2(e)), it is evident that, in extreme cases, remarkable departures from the spherical symmetry assumption (in terms of electron density) may lead to large inversion errors. This, in turn, may also produce negative electron densities as can be seen in Fig. 2(e). In order to better analyse the effects of spherical symmetry assumptions, each ideal RO event was simulated by shifting perigee positions in latitude (60°N, 20°N, 20°S and 60°S), at the same longitudinal planes 170°W and 20°W, as shown in Fig. 3(a). The electron density profiles’ differences (errors) between inverted profile values and the corresponding true profile values are plotted in Fig. 3(b) (for 170°W longitude) and 3c (for 20°W longitude), considering all the RO events shown in Fig. 3(a). For both longitudinal lines we observed the largest errors when the ray perigees are placed around 0°N to 20°N latitudes. In our previous work, the analysis was presented following a qualitative approach. In the present paper, we have

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Fig. 3. (a) Global VTEC grid evaluated using NeQuick2 superimposed with five different occultation events simulated along longitudinal planes 170°W and 20°W. Curves shown in (b) and (c) are the difference between the Onion-peeling derived and the corresponding true profile having their ray perigees at lat = 60°N, 20°N, 0°N, 20°S and 60°S along longitudinal lines 170°W and 20°W respectively (for true background in color, please refer to Fig. 2(a)).

Fig. 2. Comparison between Onion-peeling-derived inversion and true profiles for high solar activity period (solar flux = 190 sfu). (a) global VTEC map evaluated using NeQuick2 with superimposed RO events having an ideal geometry: ray prigees at lat = 0°N, long = 170°W/20°W. (b) and (c) A1 to A2 occulted ray paths plotted against Ne background at 170°W and 20°W respectively. (d) and (e) Ne(h) profiles obtained from Onion-peeling inversion (blue) and their corresponding truth (red) at 170°W and 20°W respectively.

defined, mathematically, an asymmetry level index in order to quantify the impact of asymmetry on Onion-peeling retrieval errors considering N(e) variation along the limbsounding ray path. Moreover, to study asymmetry effects in detail, electron density variations have also been analysed by varying the azimuth of occultation plane, i.e. by rotating the occultation plane along the vertical axis where the Ne(h) profiles are reconstructed, at different locations on Earth. We performed our analysis considering five occultation events (A to E, shown in Fig. 4) which are selected

considering different background ionosphere as modeled using NeQuick2. A brief summary of each RO event considered in Fig. 4 is given in Table 1. For each RO event, we have rotated the azimuth of the RO plane (i.e. rotation of RO plane around the vertical axis) by 180° with a 10° step. For each azimuth of the occultation plane, errors between the Onion-peeling inversion and the co-located true ones have been evaluated. Errors taken into account

Fig. 4. Global VTEC Distribution evaluated using NeQuick2 with superimposed RO events for five considered positions around the globe as defined in Table 1 (a) (for true background in color, please refer to Fig. 2(a)).

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Table 1 A summary of various parameters for the five simulated radio occultation events considered in this study as shown in Fig 4. (a) parameters which are specific to each event while (b) parameters which are generally applied to all simulations throughout this assessment study. RO event

Region

Perigee position (Lat/Long)

Time

VTEC along ray path Max

Min

49 TECU 64 TECU 76 TECU 3 TECU 33 TECU

3 TECU 35 TECU 42 TECU 2 TECU 12 TECU

(a) A B C D E Solar activity

Equatorial Equatorial Equatorial Mid-High Mid-High

0°N/20°W 0°N/140°E 0°N/140°W 50°S/20°W 60°N/40°W

(b) Solar Flux value Month UT Azimuth of RO plane

are Vertical TEC (VTEC), the peak electron density value (NmF2) and the slab thickness () (see Section 3.2 for their definition). 3.1. Mathematical formulation for asymmetry assessment We define the asymmetry level of the ionosphere considering the degree of dissimilarity of electron density distribution along the two- halves of a given internal orbit ray path (as defined in Section 2) crossing the ionosphere from LEO satellite height down to a given height. We chose two internal orbit ray paths; one with the ray perigee at 126 km (defined as Low Ray Height (LRH)) and the other one at the peak electron density height (i.e. hmF2). Electron density at each point along the ray path has been computed with NeQuick2 knowing the geographical position of that point (latitude, longitude and height) and solar flux value. Latitude and longitude values used in following equations depend on the spatial sampling of the ray path. For simplicity, we divided the complete ray path in 100 equal segments and then the electron density along the ray path was evaluated at the end point of each ray segment. Considering internal orbit ray path:

Night Day Day Night Night High

190 sfu July 0100 0° to 180° 10°

Range Step size

presence of two peaks in LHR case, as compared to hmF2 case, is because the ray experiences peak electron density twice along its path, once before the perigee and once after. In the bottom subplots, the same electron density values are illustrated bisecting and overlapping the ray in two parts, from ray perigee ‘p’ to ‘A1’ (cyan) and from ‘p’ to ‘A2’ (magenta). A1, A2 and p are the points defined in Fig. 1. For simplicity, we will indicate the distance between ‘p and A1’ as ‘l’ and ‘p to A2’ as ‘l’ considering ‘0’ as ray perigee positions (see Fig. 5). Being, jpA1j ¼ jpA2j ¼ halfRayLength ðhRlÞ asymmetry is then calculated by considering the following integral which defines the area between cyan and magenta lines: Z hRL Asymmetry lono ¼ jNeðlÞ  NeðlÞjdl ð3Þ 0

In order to normalize the asymmetry values, we divided the AsymmetryIono value (Eq. (3)) by the TEC along ray path (Eq. (2)). The asymmetry index for the ionosphere is therefore defined as: Asymmetry lono LETC

jA1 A2j ¼ RayLength ðRLÞ

Asymmetryindexlono ¼

the corresponding LTEC value is obtained by using the trapezoidal rule, on the grid of 100 electron density points along the ray path as: Z RL LETC ¼ Ne dl ð2Þ

The asymmetry index ranges between 0 (perfectly symmetric ionosphere) to 1 (completely asymmetric ionosphere). The former may be experienced when the two half curves (cyan and magenta curves shown in Fig. 5) completely overlap each other exhibiting two sides of the ray around the ray perigee with identically the same Ne distribution. The latter may be experienced when one of the two half curves completely vanishes (Ne = 0) exhibiting largest possible difference in the Ne distribution present at the two sides of ray path with respect to the ray perigee. For a given occultation geometry (simulated or realistic) and background 3D Ne distribution derived from a model,

0

As an example the top plots in Fig. 5(a) and (b) show the electron density distributions along the ray path (RO sounding of event A at 0° azimuth of occultation plane) at hmF2 and LRH, respectively. The main difference between hmF2 case (Fig. 5(a)) from LHR case (Fig. 5(b)) is the shape of electron density along the ray path. The

ð4Þ

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Fig. 5. Ne along occulted ray paths at (a) hmF2 and (b) LRH for event A at 0° azimuth of RO plane. Top subplots show the Ne variation along internal orbit ray path. In bottom subplots, magenta curve shows Ne variation along the ray path from ray perigee ‘p to point A2’ as ‘Ne(l)’ and cyan curve shows Ne variation along the ray path from point ‘p to A1’ as ‘Ne(l)’ considering ‘0’ as ray perigee position. See Fig 1 for details of points A1, A2 and p (a complete overview is available as Figs. A1 and A2 of Appendix A).

this index could provide an indication of the asymmetry level expected for that particular occultation event, giving in advance an idea of how misleading the spherical symmetry assumption is.

In our case, the error we are evaluating is the difference (absolute error) between slab thickness evaluated for the inverted profiles and their corresponding truth profile values. Analytically: Ds ¼ jsOnion-peeling  sTrue j

ð8Þ

3.2. Onion-peeling related errors After having qualitatively shown the impact of ionospheric asymmetry on retrieved product, we will now demonstrate, quantitatively, the correlation between the observed errors and the asymmetry level. Therefore, the second step in our assessment study is the definition of the errors and observables we will use to evaluate the impact of ionospheric asymmetry. The retrieved electron density profiles are then compared with the collocated NeQuick2 ‘true’ vertical Ne(h) profile in terms of difference on VTEC, difference on the NmF2 and on the s values. The first two error indicators can be respectively defined as: Z hLEO Z hLEO DVTEC ¼ NeOnion-peeling dh  NeTrue dh ð5Þ h

h

DNmF 2 ¼ jNmF 2Onion-peeling  NmF 2True j

ð6Þ

Slab thickness ‘s’ is a measure of the width of vertical electron density profile. This parameter offers substantial information on the shape of the electron density profile, the neutral and ionospheric temperatures and gradients and on the ionospheric composition and dynamics (Titheridge, 1973; Davies, 1990, 1991). It is defined as the ratio of the Vertical TEC (VTEC) and the peak electron density (NmF2) of the local ionosphere as stated in Eq. (7): s¼

VTEC NmF 2

ð7Þ

4. Simulation results and analysis 4.1. Asymmetry analysis For each geographical positions highlighted in Fig. 4, we have calculated asymmetry values as a function of the azimuth of the occultation plane. The results, illustrated in Fig. 6, indicate that in general the asymmetry level has a minimum about 80–100° and a maximum about 0–170° azimuth. The RO event A is producing the largest asymmetry variations since the asymmetry level goes from 0.1 to almost 0.7 (Fig. 6(b)). It can be observed that the asymmetry values are higher for the LRH rays than for the hmF2 rays. This is due to the coupling of the ray path geometry with the intrinsic shape of the ionosphere. Indeed a double peaked electron density structure (crest of the EIA) can be observed for lower heights, whereas for higher altitudes this double peak structure merges in a single peak one at the geomagnetic equator. Therefore as the height increases, the symmetry of the ionosphere electron density increases. The lower the height of the ray path from Earth’s surface, the larger the distance it crosses in the ionosphere inside the LEO orbit and consequently the higher the probability is to experience electron density gradients along the ray-path. It is important to observe the correlation between VTEC distributions and the asymmetry index. If we compare the

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Fig. 6. (a) and (b) show asymmetry calculations with respect to the azimuth of the occultation plane for (a) hmF2 and (b) LRH for all five considered events (a complete overview is available as Fig. A3 of Appendix A).

five RO events in the light of background TEC distribution shown in Fig. 4, we observe that the ionosphere exhibits bigger ionization (higher VTEC values) for the RO events B or C as compared to RO event A. The corresponding asymmetry index distributions shown in Fig. 6 are lower for these two RO events (B and C) compared to results obtained for RO event A. This leads us to conclude that the true analysis for the impact of asymmetry on RO ionospheric retrievals has to be done by evaluating the electron density values along the ray paths and therefore VTEC maps cannot be used as a unique mean to identify asymmetries in the ionosphere, which are fundamental for RO retrieval. As far as the case D is concerned, the asymmetry trend for this event does not follow the trend of the other RO events (Fig. 6). That is, for RO event D the asymmetry is highest at around 40° azimuth and lowest around 0° and 170° azimuth. This can be explained in accordance to the low VTEC (Table 1) and electron density values concerning the occultation event considered. In this case, weak electron density structures could have a remarkable relative importance in the calculation of the asymmetry index. In order to have a general overview about how asymmetry varies for a particular azimuth angle of the occultation plane, we have evaluated the asymmetry values around the globe with a grid spacing of 5°  10° (Lat  Long) at 01:00 UT in July using F10.7 of 190 sfu as NeQuick2 input. In the global asymmetry maps shown in Fig. 7 (for 0° azimuth of occultation plane), it is evident once again that the horizontal asymmetry in the ionosphere cannot be judged by just looking at the VTEC maps (evaluated using NeQuick2). The high asymmetric areas on the map shown in Fig. 7 consistently include those regions which were observed as low VTEC regions in the TEC maps shown in Fig. 4. Also, the variations shown in the global asymmetry maps (Fig. 7) are of significant value in particular for RO electron density retrievals performed under spherical symmetry assumption, due to the fact that these maps represent what

the ray experience in terms of electron density variation along its path. Maps like those presented in Fig 7 can be useful to globally understand what level of asymmetry is expected. In the next section, we will show how these asymmetry values are correlated with the DVTEC, DNmF2 and Ds characterizing the onion peeling retrieval errors as defined in Section 3.2. 4.2. Correlation between asymmetry levels and retrieval errors Up to now we have shown how the asymmetry can be defined and evaluated in a deterministic way. In this section we will try to show how much the errors on inverted Ne(h) profile are correlated with such asymmetry indicators. For each geographical position, retrieval errors defined in terms of DVTEC, DNmF2 and Ds, as defined in Section 3.2, have been evaluated as a function of the azimuth of occultation plane and compared with the corresponding azimuthal distributions of asymmetry level. Fig. 8 shows the results for all the considered events (A to E). From Fig. 8 it is evident that a very good correlation exists between DVTEC (Fig. 8(a)), DNmF2 (Fig. 8(b)), Ds (Fig. 8(c)) and the asymmetry index calculation (shown previously in Fig. 6(a) and (b)) as a function of the azimuth of the occultation plane. The correlation coefficients between DVTEC, DNmF2, D and the asymmetry index are shown in Tables 1 and 2 for all five RO events (A to E) under consideration. The numbers present in Table 2 further confirm the qualitative assessment of asymmetry made above (Figs. 6 and 8). By looking at the high correlation coefficients, we can easily conclude that the asymmetry index we attempt to define is a good indicator of possible errors in the retrieval, when the standard Onion-peeling algorithm is used as RO data inversion algorithm. Stronger correlations are experienced, as expected, considering asymmetry index evaluated at hmF2 height.

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Fig. 7. Global asymmetry maps evaluated for (a) hmF2 and (b) LRH at 01:00 UT and 0° azimuth for occultation plane (a complete overview is available as Fig. A4 of Appendix A).

Fig. 8. Onion-peeling related errors for all five RO events (A to E) under consideration. Onion-peeling errors in the evaluation of (a) VTEC, (b) NmF2 and (c) , respectively (a complete overview is available as Fig. A3 of Appendix A).

Table 2 Correlation coefficients between DVTEC, DNmF2, D and asymmetry vales for hmF2 and LRH for all five RO events (A to E) under consideration. Asymmetry Event A

DVTEC DNmF2 Ds

Event B

Event C

Event D

Event E

hmF2

LRH

hmF2

LRH

hmF2

LRH

hmF2

LRH

hmF2

LRH

0.998 0.997 0.653

0.992 0.994 0.606

0.910 0.872 0.859

0.922 0.887 0.849

0.970 0.902 0.981

0.936 0.950 0.921

0.942 0.941 0.947

0.911 0.916 0.906

0.996 0.996 0.993

0.992 0.991 0.992

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5. Conclusion and future work Using the NeQuick2 model as a simulation tool, in this paper we have shown how the asymmetry of the ionospheric electron density may impact the Onion-peeling derived products in relation to Radio Occultation data inversion. In Section 3 we tried to evaluate, deterministically, an asymmetry indicator defined on a scale from 0 (perfectly symmetric ionosphere) to 1 (completely asymmetric ionosphere) with the help of a simple mathematical relationship. The asymmetry index is based on the electron density variation that may be experienced along a ray path characterizing typical radio occultation geometry. After evaluating the asymmetry index with a number of different simulated events, we found a very good level of correlation between the asymmetry index and the Onion-peeling related errors (on VTEC, NmF2 and s) evaluated comparing the Onion-peeling-derived vertical electron density profiles with the collocated ‘true’ ones. A high correlation between these errors and the asymmetry index (Table 2) indicates how well the index is performing in assessing the asymmetry of the ionosphere. It is also evident from our analysis that the ionospheric asymmetry and Onionpeeling related errors are function of the azimuth of the occultation plane. In general, the azimuthal angle between 80° to 100° may experience the lowest asymmetry index values and therefore in these cases the spherical symmetry assumption for the ionosphere electron density produces the least effects on the Onion-peeling derived electron density profiles. This assessment study has been totally based on simulated data. In particular idealized satellite orbits have been considered with fixed occultation planes formed by occulted (internal orbit) ray paths, LEO satellites and ray perigees all lying in the same plane. In addition a climatological ionospheric electron density model has been used which is not able to simulate a number of medium and small-scale ionospheric structures that are usually present in the actual ionosphere. For these reasons at this stage of the research it would be premature to define asymmetry index thresholds to ‘rank’ the level of asymmetry of the ionosphere. As a future work, the possibility to assess the effects of spherical symmetry assumption on the Onion-peeling derived electron density profile using real satellite and ionospheric data is foreseen. In this case data assimilation techniques to improve the NeQuick2 model capabilities to represent the current distribution of the ionospheric electron density will be considered.

Acknowledgements This research work is undertaken under the framework of the TRANSMIT ITN (www.transmitionosphere.net), funded by the Research Executive Agency within the 7th Framework Program of the European Commission, People

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