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Tomographic reconstruction of the ionosphere using ground-based GPS data in the Australian region E. Yizengaw, P.L. Dyson & E. A. Essex CRC for Satellite Systems Department of Physics La Trobe University, VIC 3086 G P S T E C

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(Knowledge of the electron density distribution in the Earths ionosphere and plasmasphere is important for several purposes, such as: estimation and correction of propagation delays in the Global Positioning System (GPS); improving the accuracy of satellite navigation; predicting changes due to ionospheric storms; predicting space weather effects on telecommunications, and many more. Introduction (During the past decades, the scientific community has developed and used different ground based observing instruments to gather information on the ionosphere and plasmasphere, such as vertical incidence sounders (ionosondes), incoherent scatter radars, etc. However, measurements by these methods are restricted to either the bottomside ionosphere or the lower part of the topside ionosphere (usually below about 800 km) Tomographic imaging provides a powerful technique for obtaining images of the ionospheric and plasmaspheric electron density distribution, using reception at the ground of signals from satellite radio beacons, such as GPS satellites [1]. It has promising features to supplement the above mentioned ground-based instruments.

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(One of the advantages of tomography is that, because of satellite motion, large segments of the ionosphere can be investigated in a comparatively short time interval and it is possible to observe variations in the satellite signals caused by irregularities of various dimensions. Introduction (cont.) (In satellite radio tomography the Total Electron Content (TEC) measurements are inverted and reconstructed to obtain a two- dimensional electron density profile. The TEC, which is the main input to radio tomography, is defined as the integral of the electron density from the ground height up to the ceiling height, i.e., the height of the transmitting satellite (GPS satellite in our case) and can be determined using the method described in [2]. This paper describes the experimental procedures of tomographic imaging techniques developed and used at La Trobe University. The reconstruction of the electron density distribution has been used to study important features in ionospheric structure such as ionization troughs and quasi-wave formations.

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Ionosphere Satellite Geometry 400 km GPS Satellite Zenith Sub-Ionospheric point S Ionospheric pierce point. R Where, STEC and VTEC, respectively, are slant and vertical TEC Figure 1 G P S

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For this study we used the ART (Algebraic Reconstruction Tomography) reconstruction method [1] and by assuming that the electron density distribution changes insignificantly during satellite passes, the reconstruction plane is discretized into two-dimensional pixels as shown in Figure 2. Reconstruction Methods (By assuming that the electron density is constant in each pixel, the TEC along the ray path can be represented as a finite sum of shorter integrals along segments of the ray path length [1]. where Y is a column of T measurements, N is a column of the M unknown electron densities, E is a column of T values representing the error due to data noise and discretization, D is a T M matrix with d ij being the length of link i within pixel j, and thus d ij is 1 if the i th ray traverses through the j th pixel and 0 otherwise. An inversion algorithm is required to determine the unknown electron densities from known Y and D, and the ART algorithm has been used.

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where D i is the i th row of D, k is iteration number, and k is the relaxation parameter. The relaxation parameter ensures that the correction remains stable, and it is a real number, usually confined to be between 0 and 2. (The ART algorithm, which requires an initial description of the ionosphere to start with (for which the combination of CHAMPMAN and IRI-2001 model profile has been used), uses the observed TEC data to improve on the initial description of the ionosphere be reconstructing the electron density distribution in an iterative fashion. It is implemented as described by the following equation [1]: Reconstruction Methods (cont.)

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The experimental setup showing ray path links between a GPS satellite and ground based GPS-receivers Figure 2

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Ionization trough observation (Examples of typical tomographic images of the dayside ionosphere, obtained during the magnetically active period on August 18, 2003. An apparent equatorward movement of the trough minimum (indicated by white arrow), from latitude of 35.0 S to 32.0 S is evident. Figure 3

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The electric potential pattern, from the Defence Meteorological Satellite Program (DMSP) ionospheric convection model. Plasma convects along the equipotentials and the model clearly indicates that convection flow could be expected to extend equatorward to the Australian south coast during local afternoon (indicated by red arrow) on 18 August 2003. Here the region of sunward return flow of the dusk convection cell may bring plasma that has been circulating in darkness into the higher density region of the dayside ionosphere [3], creating the ionization trough structure as shown in Figure 3. Figure 4 Ionization trough observation (cont.)

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Quasi-wave structure observation (Results obtained using tomographic reconstruction for an equinoctial geo- magnetically active period (31 March 2001). Quasi-wave structures perturbing the ionosphere are evident, demonstrating that tomography can be an important technique for studying ionospheric irregularities. Figure 5

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Ionospheric perturbation observation (cont.) Figure 6 (Variations of ionospheric density with time (top two panels) and the vertical TEC (bottom left), observed at 35.38 S and 42.80 S latitudes, indicate ionization enhancement corresponding to the locations of the finger-like formations shown in Figure 5. at 42.80 S latitude at 35.38 S latitude

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Figure 7 (The three panels at the left show the latitudinal variations of electron density at three altitudes, determined by subtracting background density values from the density values shown in the reconstruction images in Figure 5. Quasi-wave disturbance are clearly evident and their parameters are more readily determined from this type of plot. (The rates of change of TEC (dTEC) at 35.38 S and 42.80 S latitudes during the severe storm of 31 March 2001 (right two panels) also indicate that the TIDs were migrating quatorward. Ionospheric perturbation observation (cont.)

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Validation with other independent measurements and model profiles Figure 8 (Validation of the tomographic reconstructed technique. Tomographic electron density profiles (black dots), IRI-2001 model density profiles (blue dots) and density profiles (red dots) determined from ionosonde observati- ons at Hobart and Canberra are plotted. These three independent density profiles generally show excellent agreement.

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Conclusion (Excellent agreement between independently measured profiles and the reconstruction density profiles, as shown in the typical examples in Figure 8, confirms the capability of ionospheric tomography in detecting the different important features of the ionosphere. (Although the tomographic observations presented here are from a campaign of limited duration, they clearly show that the method can be used to identify and study important features of the ionosphere. The observations were obtained during a severe magnetic storm during which different features developed in the ionosphere. [1] Austen, J.R., S.J. Franke, and C.H. Liu, 1988. Ionospheric imaging using computerized tomography. Radio Science 23, 299-307. [2] Sardón, E., A. Rius, and N. Zarraoa, 1994. Estimation of the transmitter and receiver differential biases and the ionospheric total electron content from Global Positioning System observations. Radio Science 29, 577-586. [3] Whalen, J. A, 1989. The daytime F layer trough and its relation to ionospheric- magnetospheric convection. J. Geophys. Res., 94, 17169-17184. References

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