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Methodology and consistency of slant and vertical assessments for ionospheric electron content models

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A Correction to this article was published on 16 March 2020

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A summary of the main concepts on global ionospheric map(s) [hereinafter GIM(s)] of vertical total electron content (VTEC), with special emphasis on their assessment, is presented in this paper. It is based on the experience accumulated during almost two decades of collaborative work in the context of the international global navigation satellite systems (GNSS) service (IGS) ionosphere working group. A representative comparison of the two main assessments of ionospheric electron content models (VTEC-altimeter and difference of Slant TEC, based on independent global positioning system data GPS, dSTEC-GPS) is performed. It is based on 26 GPS receivers worldwide distributed and mostly placed on islands, from the last quarter of 2010 to the end of 2016. The consistency between dSTEC-GPS and VTEC-altimeter assessments for one of the most accurate IGS GIMs (the tomographic-kriging GIM ‘UQRG’ computed by UPC) is shown. Typical error RMS values of 2 TECU for VTEC-altimeter and 0.5 TECU for dSTEC-GPS assessments are found. And, as expected by following a simple random model, there is a significant correlation between both RMS and specially relative errors, mainly evident when large enough number of observations per pass is considered. The authors expect that this manuscript will be useful for new analysis contributor centres and in general for the scientific and technical community interested in simple and truly external ways of validating electron content models of the ionosphere.

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Change history

  • 16 March 2020

    In the original publication of the articles, ���Methodology and consistency of slant and vertical assessments for ionospheric electron content models��� and ���Consistency of seven different GNSS global ionospheric mapping techniques during one solar cycle���, a common typo affecting the text only (not the computations) has been recently noticed. It compromised the definition of the scaling factor from Global Navigation Satellite Systems ionospheric delay to electron content is clarified in this erratum.


  1. This typical maximum error can be deduced from the 2 mm of nominal carrier phase measurement noise (see page 4.15 in Wells et al. 1987), the definition of geometry-free combination of both carrier phases L1-L2, and the two STEC measurements involved in dSTEC, after taking into account that the carrier phase multipath is typically very small.

  2. Being \(M=1/\sqrt{1-r^2\cos ^2 E/r^2_{I}}\) the mapping function, where r and \(r_I\) are the geocentric distances of the receiver and the ionospheric pierce point (in our case the Earth radius plus 450 km) respectively, and E is the elevation angle of the satellite above the receiver spherical horizon (see, for instance, Equation 32 in Hernández-Pajares et al. 2011).


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The authors acknowledge the contribution of the four active IGS ionospheric analysis centres, in particular CODE, ESA-ESOC and JPL, for their continuous effort and improvement in their support of the combined IGS GIMs as far as the new analysis centres, NRCAN, CAS and WHU, contributing to IIWG. The English improvements suggested by Mr. Kacper Kotulak are very appreciated as well.

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Correspondence to Manuel Hernández-Pajares.

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Hernández-Pajares, M., Roma-Dollase, D., Krankowski, A. et al. Methodology and consistency of slant and vertical assessments for ionospheric electron content models. J Geod 91, 1405–1414 (2017).

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