## 1. Introduction

[2] When traveling through the ionosphere, L band signals of Global Navigation Satellite Systems (GNSS) are delayed. The delay corresponds to range errors of up to 100 m. In a first-order approximation the range error *d*_{i} is proportional to the integral of the electron density along the raypath (total electron content (TEC)) and may be approximated by:

where *K* = 40.3 m^{3}s^{−2} and the integral of the electron density *n*_{e} along the raypath *s* defines the slant total electron content (TEC^{slnt}).

[3] Whereas this error can be corrected in dual-frequency measurements by a linear combination of L1 and L2 phases, in single-frequency measurements, additional information is needed to mitigate the ionospheric error. This information can be provided by TEC maps deduced from corresponding GNSS measurements or by model values. Hence, single-frequency systems used for example in positioning and in remote sensing radars rely on ionospheric models which provide a climatological estimation of the ionospheric impact. For estimating the transionospheric time delay or range error, several ionospheric models are currently available.

[4] Whereas single-frequency GPS users may correct ionospheric range errors by the broadcasted GPS correction or Klobuchar model [*ARINC Research Corporation*, 1993; *Klobuchar*, 1987], Galileo users will apply the NeQuick model [*Hochegger et al.*, 2000; *Radicella and Leitinger*, 2001; *Leitinger et al.*, 2005; *Nava et al.*, 2008]. The Klobuchar model describes the diurnal variation of vertical ionospheric delay by a cosine function with varying amplitude and period, depending on the geomagnetic latitude. For nighttime hours the vertical ionospheric delay is approximated to a constant value fixed at 5 ns. The related third-order polynomial is determined by eight coefficients which are broadcasted via the GPS navigation message. Thus, any GPS user, knowing the satellite geometry can reduce the link-related ionospheric range error easily by about 50% [*Klobuchar*, 1987]. Single-frequency users of the European global navigation satellite system ‘Galileo’ are offered to use the electron density model NeQuick for range error corrections.

[5] NeQuick, developed at the International Centre for Theoretical Physics in Trieste and at the University of Graz, is a quick run 3-D electron density model from which TEC can be determined along any ground-to-satellite or satellite-satellite raypath by means of numerical integration. Electron density models such as International Reference Ionosphere [*Bilitza*, 2001] or the Bent model [*Bent et al.*, 1972] may represent the peak density very well but may fail in estimating TEC [e.g., *Brown et al.*, 1991; *Batista et al.*, 1994; *Mazzella et al.*, 2002; *Coisson et al.*, 2006].

[6] The other option to correct ionospheric propagation errors relies on current monitoring data as demonstrated by Satellite Based Augmentation Systems (SBAS). The ionospheric correction information provided by SBAS systems such as the European Geostationary Navigation Overlay Service [*Ventura-Traveset and Flament*, 2006] and the Wide Area Augmentation System [*El-Arini et al.*, 2001] consists of vertical ionospheric delays and associated residual error bounds called grid ionospheric vertical errors at the nodes, or ionospheric grid points, of a predefined ionospheric grid with a grid spacing of 5° by 5° in latitude and longitude. As we will discuss in the subsequent chapters, also this type of TEC data provision to users may benefit from TEC modeling. Thus, TEC models may assist the calibration of TEC measurements, may help to generate operational TEC maps and finally may be used to forecast the ionospheric behavior. All these aspects are taken into account in the operational ionosphere data service provided by the Space Weather Application Center–Ionosphere (SWACI, http://swaciweb.dlr.de) and will be described in sections 2–4.