Estimating Electron Density of the Ionosphere from Radio Occultation TEC Data using Abel Inversion

Scientific Study, 2016

17 Pages, Grade: excellent



1. Introduction ... 3
Objective ... 4

2. Methodology ... 5

3. Results and discussion ... 8
Observation ... 10

4. Conclusion and recommendation ... 15
Conclusion ... 15
Recommendations ... 15
Acknowledgements ... 15

1. Introduction

Ionosphere is the ionized part of the Earth’s upper atmosphere which contains free electrons and positive ions. It is formed when solar radiation strikes the upper atmosphere in such a way that the incoming radiation with sufficient energy takes away electrons from the neutral atom and hence ionized medium is formed. The electrons formed as a result of the ionization process in general and Total Electron Content (TEC) in particular are the main characterizing features of the ionosphere. TEC is defined as the integration of the free electron distribution in a 1m2 column along the signal path from the satellite to the receiver. The variation of these parameters describes the variations of the ionosphere. Some of the determinants of ionosphere variation are solar radiation variation, thermospheric wind, deposition of energetic particles at higher latitudes and variation in neutral composition of the atmosphere [2].

The variation of the ionosphere affects trans-ionospheric radio wave users, for example, communication and GPS (Global Positioning System) applications such as positioning and navigation. A proper way of understanding the ionospheric variability can help us to use the appropriate signals that are used for communication purposes.

Ionospheric effects on the radio waves can be mitigated in many ways. Linear combinations of signals with different frequencies can be used for mitigating the effect of ionosphere on global navigation satellite system (GNSS) measurements. On the other hand, the integration of free electrons that are on the radio path, TEC estimation can be used to reduce the effects of the dispersive medium (ionosphere) on communication and navigation technology [7]. It is also used to study about the properties of the ionospheric regions for ionospheric research. Ionospheric TEC can be estimated from ground and space-based GPS measurements. The space-based GPS receivers are carried by the LEO (Low Earth Orbit) satellites. The measurement system using GPS receivers carried by LEO satellites is called radio occultation (RO). RO is a remote sensing technique which is used to study the atmosphere of planets from an appropriate transmitter (GPS) - receiver (LEO) combination. The receivers carried by the LEO track signals from the constellation of GPS satellites at 20,000km altitude.

Incoherent Scatter Radar (ISR) techniques and Ionosonds can be used for ionospheric measurements. ISR is based on sending radio signals to probe the ionosphere and helps us to get information from the reflected echo. When a radio wave is sent in to the ionosphere, free electrons can scatter the waves. The strength of the echo received from the ionosphere can be used to estimate the number of electrons in the scattering volume; hence electron density can be determined this way. Ionosonde can be used to estimate ionospheric electron density and is based on sending radio signals to the ionospheric region and studying the properties of the reflected signals. From the heights of the reflective ionospheric region, vertical profiles of electron density can be found. From ground-based GPS measurement of TEC data, electron density profile can be estimated using Tomographic inversion method (Endawoke et al., 2007). Tomographic inversion is based on dividing the ionosphere into separate boxes (voxels), and estimating one value of electron density for each box. Also, Abel inversion can be used to retrieve ionospheric electron density profile from space based TEC measurement data. Starting from the upper part of the ionospheric layer, we ingest TEC data in to the Abel inversion algorithm and go inward until the integrated sum of free electrons on the radio path is computed. This algorithm is called onion peeling algorithm as it seems peeling an onion (Nava, 2012). As compared to Abel inversion method, Tomographic inversion takes relatively longer computational time and there is sacristy of data in ground based measurement as receivers can’t be deployed everywhere (Skone, 2010).

While a lot of work is done on estimating TEC for the East African ionosphere from ground based GPS measurement (Melessew et al., 2013), electron density retrieval from radio occultation TEC data is not yet done here in our country. Therefore, in this paper, electron density of the ionosphere is going to be estimated from radio occultation COSMIC TEC data using Abel inversion method.


- Retrieving electron density profile from radio occultation TEC data using onion peeling algorithm.
- Comparing radio occultation electron density profiles with electron density profiles estimated by standard model (international reference ionosphere, IRI).

The main contribution of this work is the Matlab code developed to implement the Abel inversion onion peeling algorithm.

Also, the outputs of the Abel inversion algorithm can be used to validate others work that will be carried out in the future. Moreover, it can be utilized as springboard for further study related to radio occultation observations.

2. Methodology

As ionosphere is a dispersive medium, radio waves propagating through it may take relatively longer times to arrive at the receiver end than the normal straight line trajectory. This ionospheric delay is directly proportional to the slant total electron content (sTEC) along the radio path and inversely related to the radio frequency. As the 6-COSMIC satellites rotate in a low earth orbit, they acquire radio signals from GPS satellites which are at 20,000km altitude so; ionospheric effect is contained in the radio signals that are measured in the receiver. The basic observable for each occultation is the phase change between the transmitter and the receiver as the signal propagates through the ionosphere and the neutral atmosphere. sTEC can then be extracted from phase observations of the radio occultation measurements on the LEO receiver. This sTEC data is then feed to the Abel inversion onion peeling algorithm to get electron density profiles of the ionosphere.

The methodology of this study is based on Abel inversion of sTEC data under the assumption of spherical symmetry. Ionospheric electron density profile retrieval using Abel inversion is based on spherical symmetry of electron density in the occultation plane. Spherical symmetry means that the retrieved electron density depends only on height. The LEO satellites are rotating in nearly circular orbits and radio signals propagate in a straight line from the transmitter to the receiver. First order estimation of electron density is done up to the LEO satellites altitude (Schreiner et al., 2009). Abel inversion algorithm for electron density of the ionosphere to be:

[Equations are not displayed in this preview]

Where p is the impact parameter, r is the radial distance and N is ionospheric electron density and TEC is the total electron content on the radio path.

For practical applications, the above Abelian inversion for the electron density of the ionosphere (Equation 2.1) can be formulated in another way by using the discretized value of the TEC along the signal path.

[Figures are not displayed in this preview]

Figure 2.1: RO geometry and divided ionospheric layers (Adapted from Ouyang, 2008b).

The assumption is that electron density in each layer has a uniform distribution.

Having the COSMIC height to be approximately 800km, we can divide the ionosphere in to n layers as shown in figure 2.1 above. Also, it is assumed that the electron density is nearly zero below 50km and above 1000km since there is no significant number of free electrons in these regions.

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Estimating Electron Density of the Ionosphere from Radio Occultation TEC Data using Abel Inversion
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estimating, electron, density, ionosphere, radio, occultation, data, abel, inversion
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Bizuayehu Adisie Beyene (Author), 2016, Estimating Electron Density of the Ionosphere from Radio Occultation TEC Data using Abel Inversion, Munich, GRIN Verlag,


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