ION GNSS 2012
Session A4: Remote Sensing with GNSS & Integrated Systems

Title: Tomographic Imaging of Ionospheric Electron Density Over Ethiopia using GPS Satellites
Author(s): G. Kidanu Zewdie & G. Mengistu Tsidu, Addis Ababa University, Ethiopia
Room: 103/104 (NCC)

The ionosphere is the region of partially ionized plasma above the Earth´s atmosphere formed due to primarily photo-ionization of the neutral atoms and molecules. The increase in the density of the atmosphere as we go further down to the surface of the Earth and the decrease in the intensity of photons as it bombards the neutral atoms and the availability of different atoms and molecules at different heights from the Earth´s surface forms a large scale vertical layer of ionization with in the ionosphere. This makes the ionosphere to exist as vertically stratified partially ionized plasma state from at about 50km - 1000km from the surface of the Earth.

Signals from the Global Positioning System (GPS) satellites are dispersed by the ionosphere as they pass through the ionosphere. Using the dispersion effect of the ionosphere on the GPS signals we can derive the Total Electron Content (TEC) from a spatially distributed network of GPS stations along the signal path. TEC can show the temporal, seasonal, latitudinal and longitudinal variations of the ionospheric electron distribution. However, it does not convey any information about electron density structure along the vertical direction. Computerized Ionospheric Tomography(CIT) is a method to investigate vertical ionospheric electron density profile in two or three dimensions.

The primary objective of this study is to calculate TEC from GPS receivers spatially distributed over Ethiopia to the highest accuracy possible for a satellite to receiver pair and invert by the computerized tomography method to reconstruct ionospheric electron density distribution over Ethiopia in two and three dimensions (2D and 3D). In processing the TEC, corrections have been made for phase ambiguity, satellite and receiver hardware delays. However, the TEC calculated is subject to discretization and measurement errors.


In two dimensions (2D), a vertical plane (altitude versus latitude) along 40.02610E longitude is selected over Ethiopia. The altitude range of the plane is from 100km to 900km and, therefore, it essentially is with in the Earth´s ionosphere. The latitude range is limited with in the range 30 N ? 150 N . Subsequently, this plane is discretized into small rectangular planes called pixels of 83.486km by 100km. Near altitudes of high ionospheric concentration (200km ? 400km) pixels are made to have smaller size of 83.486km by 50km for better resolution. The distance traveled in each pixel crossed by GPS signals to four receivers located close to this vertical plane is calculated in a selected reference frame using the precise position of the satellites. The distances calculated make the coefficient matrix and the continuous non-linear inverse problem becomes discrete and linear. The discrete linear problem is then inverted for ionospheric electron density with in each pixel using TEC from these four stations for 10 epochs of 60 second intervals.

In three dimensions (3D), the volumetric region of space with latitude 30N ? 150N, longitude 330E to 480E and vertical height 100km to 1100km is divided into numerous small voxels. The 3D ionosphere over Ethiopia is discretized into large voxels with dimensions 128.26km to the East, 102.75km to the North and 100km along the vertical. Similar to the 2D ionospheric discretization, voxels with in ionospheric altitude range of 200km to 400km are made to have a vertical dimension of 50km for better resolution. The distance traveled by GPS signals in each voxel is calculated from the precise position of the GPS satellites setting up our algorithm in an appropriate coordinate system. So as to have enough measurement TEC data for inversion, we made an important assumption that the ionosphere does not substantially vary for consecutive 25 minutes and TEC from all GPS receivers located all over the country is taken for this time period at 30 seconds epoch. A 3D ionospheric electron density distribution is then inverted with in each voxel.

In both 2D and 3D tomographic reconstructions, damped least square inversion algorithm using Generalized Singular Value Decomposition (GSVD) based second order Tikhonov regularization has been employed. A comparative assessment among some of inversion algorithms has been made to select the damped least square inversion algorithm. The performance of the inversion algorithm has been numerically validated with a simulated TEC data. For 2D validation simulated TEC from IRI2007 model and a preprocessed simulated TEC from the algorithm itself for 3D validation have been used. We used the L-curve method to find the regularization parameter and the numerical validations show that the algorithm produced results efficiently with high accuracy.

Tomographic inversion results in both 2D and 3D cases indicate that the ionosphere over Ethiopia has been reconstructed well exhibiting spatial-temporal characteristics of the equatorial global ionosphere.

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