NeQuick Ionospheric Model

Fundamentals
Title	NeQuick Ionospheric Model
Author(s)	J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
Level	Intermediate
Year of Publication	2011

The NeQuick is the ionospheric model proposed to be used by the Galileo single frequency receiver to compute ionospheric corrections. It is based on the original profiler proposed by [Di Giovanni and Radicella, 1990].

NeQuick is a tridimensional and time-dependent ionospheric electron density model, which provides electron density in the ionosphere as a function of the position and time. Thence, it allows to compute ionospheric delays (TEC or STEC), as the integrated electron density along any ray path.

NeQuick FORTRAN 77 code was accepted by the International Telecommunication Union Radiocommunication Sector (ITU-R) in 2000 and revised in 2002. It is freely available from the ITU. It is referred to either as version 1 or ITU-R. This package includes a comprehensive description of the implementation as well as numerical integration subroutines allowing to compute Vertical and Slant TEC.

The input parameters of the model are the position (longitude, latitude and height), the epoch (month and UT) and the solar activity (either expressed as F10.7 or R12). Other internal parameters are the foF2 and M(3000)F2 values, which can be defined according to the ITU-R, amongst other options depending on the purpose.

The NeQuick model running in the Galileo single frequency receivers will be driven by the Effective Ionisation Level, [math]\displaystyle{ Az }[/math] parameter (replacing the solar flux), that is a function of the receiver location.

[math]\displaystyle{ Az=a_0+a_1\mu + a_2 \mu^2 \qquad\mbox{(1)} }[/math]

where [math]\displaystyle{ \mu }[/math] is the modified dip latitude, or MODIP:

[math]\displaystyle{ \tan \mu=\displaystyle \frac{I}{\sqrt{\cos \phi}}\qquad\mbox{(2)} }[/math]

being [math]\displaystyle{ I }[/math] the true magnetic inclination, or dip in the ionosphere (usually at 300 km), and [math]\displaystyle{ \Phi }[/math] the geographic latitude of the receiver [Rawer, 1963].

The coefficients [math]\displaystyle{ a_0 }[/math], [math]\displaystyle{ a_1 }[/math],[math]\displaystyle{ a_2 }[/math] will be broadcasted to the users in the Galileo navigation message and updated at least once a day . Ionospheric Disturbance Flag alerts for five predefined regions (see Figure 1) will be also broadcasted to aware the users when the ionospheric correction coming from the Galileo broadcast message might not meet the specified performance. These disturbance flags will be transmitted continuously and updated with the update rate of the Navigation Message (every [math]\displaystyle{ 100 }[/math] minutes).

Figure 1: The 5 Regions defined for the Disturbance Flags (in degrees MODIP) -90 to -60, -60 to -30, -30 to 30, 30-60, 60-90. (courtesy of [Arbesser-Rastburg, B., 2006]).

The Galileo single frequency receiver algorithm will be based in the following steps (the next paragraph is taken from [Arbesser-Rastburg, B., 2006]):

1. [math]\displaystyle{ Az }[/math] is evaluated using [math]\displaystyle{ a_0 }[/math], [math]\displaystyle{ a_1 }[/math],[math]\displaystyle{ a_2 }[/math] (from navigation message) and MODIP from the NeQuick model (which depends on estimated receiver position).

2. Electron density is calculated for a point along the satellite to receiver path, using the NeQuick model with [math]\displaystyle{ Az }[/math] in place of [math]\displaystyle{ F10.7 }[/math].

3. Steps 1 and 2 are repeated for many discrete points along the satellite receiver path. The number and spacing of the points will depend on the height and they will be a trade-off between integration error and computational time and power.

4. All electron density values along the ray are integrated in order to obtain Slant TEC (STEC).

5. Slant TEC, in TECUs, is converted to meters of L1 slant delay for correcting pseudo-ranges, by

[math]\displaystyle{ I_f = \frac{40.3\cdot 10^{16}}{f^2}TEC \qquad\mbox{(where f is in Hz)} \quad\mbox{(3)} }[/math]

Notice that, as with the Klobuchar model, the ionospheric corrections computed by the NeQuick can be used for any GNSS signal (GPS, GLONASS, Galileo…) simply by setting the corresponding frequency in the equation (3).