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The interaction of trans-ionospheric radio waves with the ionospheric plasma causes a first-order propagation delay which is proportional to the inverse of the squared radio frequency (1/ f2) and the integrated electron density (Total Electron Content – TEC) along the ray path.
Hence, TEC describing the first-order ionospheric range error is of particular interest in GNSS applications. Consequently, TEC maps can be used to correct single frequency GNSS measurements.
The slant TEC is defined as the integral of the electron density ne along the ray path s between a satellite S and a receiver R according to:
Due to the dispersive nature of the ionosphere the slant TEC may be derived from dual frequency GNSS measurements after calibrating instrumental biases. To remove the dependency from the elevation angle µ of the ray path, slant TEC is converted to the vertical TEC by applying a mapping function M(µ).
Assuming a single layer spherical ionosphere, the corresponding mapping function M(µ) converting slant TEC (TECs) to vertical TEC (TECv) and vice versa is given by:
With Re: Earth radius, µ: elevation angle, hsp: height of ionospheric layer (hsp= 400 km).
To generate a TEC map, TECv data located at the pierce point coordinates are mapped into a background TEC model [e.g. Jakowski et al. 2011a, b] which is representative for the mapping area. The achievable absolute accuracy of the vertical TEC is in the order of a few TEC units (1 TECU = 1x1016 electrons / m2). For each grid value 27 days medians of vertical TEC are calculated which serve as reference for actual measurements and forecasts.
The construction of regional (e.g. European) and global maps of vertical TEC follows the same principle [Jakowski et al., 2011b].