Physics
Scientific paper
Dec 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011agufmsa13b1898b&link_type=abstract
American Geophysical Union, Fall Meeting 2011, abstract #SA13B-1898
Physics
[0394] Atmospheric Composition And Structure / Instruments And Techniques
Scientific paper
In tomography, the region to be imaged is divided into a grid and knowledge of the values of a parameter as measured along known paths through the region is used to reconstruct the interior of the region by assigning a value to each voxel of the grid. In the ionospheric case, slant Total Electron Content (sTEC) values for rays passing through the ionosphere can be used. The principle source of such data is recordings from Global Positioning System (GPS) ground receiver stations. Each ray is broken down into pieces, according to the path length within each voxel traversed. Each voxel is assigned an unknown value of electron concentration. A set of simultaneous equations in electron concentration and path length can then be constructed for each ray. In ideal circumstances enough rays from sufficient broadcast points to different receiver points exist so that a unique solution to the set of simultaneous equations can be determined. In practice the solution with the minimum error (usually in a least-squares sense) is found because there is always some error in the input measurements. In the case of the ionosphere and the set of broadcasting GPS satellites and ground based receivers, it is in principle impossible to determine a unique solution even in terms of a minimum error. The geometry is such that the set of simultaneous equations has more unknowns than equations. Hence it is necessary to constrain the solution by some additional method or methods [Bust and Mitchell, 2008]. The solution to this inverse problem is re-calculated for each epoch of interest. The Multi-Instrument Data Assimilation System algorithm developed at the University of Bath, UK, and used at the University of New Brunswick under licence uses empirical Orthogonal Functions (EOFs) to constrain the vertical dimension and spherical harmonics to constrain the locally horizontal dimensions. Two different grid boundaries are tested, using MIDAS. The larger of the two includes two ground receiver stations within it that are excluded from the smaller. (The larger there-by including all northern-hemisphere International Global Navigation Satellite System Service (IGS) permanent stations operating at the time.) It is not clear without testing whether the extra voxels necessary to include these two extra stations offset the benefits of their extra input-data or not, when the MIDAS reconstruction is made. For each grid boundary, runs with 2x2, 3x3 and 4x4, latitude x longitude (in degrees), divisions of the grid are compared with Incoherent Scatter Radar (ISR) data the NmF2 parameter. The results shown demonstrate that in each case tested the extra data improves the results despite the increase in number of grid voxels. Further results show that accuracy in the vertical dimension is worse affected than in the locally horizontal dimensions.
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