Study of Ionospheric Variability Using GNSS Observations

With the increasing number of applications of Global navigation satellite system, the modeling of the ionosphere is a crucial element for precise positioning. Indeed, the ionosphere delays the electromagnetic waves which pass through it and induces a delay of propagation related to the electronic density (TEC) Total Electronic Content and to the frequency of the wave. The impact of this ionospheric error often results in a poor determination of the station’s position, particularly in strong solar activity. The first part of this paper focuses on a bibliographic study oriented first of all on the study of the ionosphere in relation to solar activity and secondly on the determination of the total electron content using GNSS measurements from the IGS network reference stations. Measurements were made on two permanent stations “RABT”, “TETN”. We selected years of GNSS measurements to evaluate the geomagnetic impact on the ionosphere, 2001, 2009 and 2013. A description of the ionospheric disturbances and geomagnetic storms was analyzed by determination of TEC, especially in high solar activity. The results show a strong dependence of the ionospheric activity with the geomagnetic activity.


Introduction
Ionosphere is a reflective and refractive medium for electromagnetic waves.It is important to monitor and model the ionosphere since it affects communication systems, space based navigation systems and space weather, among others.Using geometry-free linear combination of code and phase observables from dual trons/m 2 ).STEC is a quantity which is dependent on the ray path geometry through the ionosphere.The user can easily obtain the absolute TEC by using mapping function.The single layer thin-shell model was employed to compute the absolute vertical TEC (VTEC).Diurnal and seasonal variations were analyzed with TEC data derived from GNSS dual-frequency observations along with the solar activity dependence of TEC at the RABT and TETN stations.Data interpolated with information from IGS Global Ionosphere Maps (GIMs) were also used in the analysis [2].TEC data from GIMs and GNSS observations are used to illustrate the variation of VTEC at the RABT (33.99˚N, 6.85˚W) and TETN (35.56˚N, 5.36˚W) station.The comparison with VTEC of GIMs map and GNSS observation has validated our results and demonstrates strong correlation between these two models.
In this paper, estimation of ionospheric effect from dual frequency measurements is discussed.In Section 2, equations of observations of dual frequency are described briefly.This study contains a description of diurnal and seasonal variations of TEC, and the influence of geomagnetic activity on the VTEC values, especially during the low and high solar activity period 2001, 2009.

Dual-Frequency Model of Ionosphere
The use of two-frequency GNSS stations allow to calculate the STEC (Slant Tec) which is the integral of the electronic density along the path of the signal between satellite and receiver.
There are three techniques for measuring total electronic content (TEC): ionospheric soundings, radar and GNSS.There are two main approaches: Smith's 1987 single-frequency method [3] and Warrant's 1996 dual-frequency method [4].In this article, we used the two-frequency method using two GPS signals of frequencies 1 f and 2 f .The two-frequency method is the most efficient to de- terminate the TEC.GPS satellites currently transmit two signals in the L-band called 1 L and 2 L radio frequencies 1 f = 1575.42Mhz and 1 f = 1227.60 Mhz and wavelength 1 λ = 19 cm and 2 λ = 24.4cm respectively.

Code and Carrier Phase Observation Equation
The two-frequency method is based on the "geometry free" combination named

4
L .This combination eliminates all terms relating to geometry (distances) and clocks.However, it depends mainly on ionospheric refraction and differential phase delays [4].
The general form of the pseudo-distance and carrier phase observation equations are: The geometric distance is expressed by: N is related to lack of knowledge of the number of the whole cycles traveled by the phase on each of the frequencies at the first moment when the signal of the satellite is received by the receiver.
The code measurement is noisy.The method of phase smoothing of the code allows to separate the measurement noise from the signal and to have a significant precision in the ionospheric delay measurement [5] [6] [7].This method is not developed as part of this article.We used observations of the code to calculate the TEC.By using the equation for the code pseudo range for two different frequencies f 1 and f 2 , it can be written as follows: ( ) ( ) However, receiver DCBs is generally unknown and should be estimated within ionosphere modeling process.Replacing the ionospheric term with the equation: ( ) Schaer found that in practice the SLM mapping function is mainly the most used [8].In the single-layer model, it is assumed that all the electrons of the ionosphere are contained in a shell of infinitesimal thickness.The height of this layer located approximately at an altitude between 350 and 450 km where the electronic density is maximum.In fact, this hypothesis is only an approximation of the real physical truth since the ionosphere is situated approximately at an altitude of 50 km to 1000 km above the surface of the Earth.
The intersection between the line of sight of the satellite and this spherical shell is called the ionospheric point (Ionospheric Point IP).The projection of the ionospheric point on the surface of the Earth is called the subionospheric point (Sub-ionospheric point SIP).In Figure 1, Zand I Z respectively represent the zenith angles of the GPS satellite as viewed by the receiver at a given site and at the ionospheric point.R symbolizes the terrestrial ray.
Since the satellite is not upright, the total electronic content measured along this line of sight is returned to the vertical via the projection function ( ) also named mapping function [10].Then, we model the total vertical electron content VTEC Using the law of secant: et sin sin cos According to Equation (5), we derive the expression of the vertical VTEC such that: The zenith angle Z can be calculated in case we know the coordinates of the observation site and the position of the observed satellite.R is the average half-diameter of the Earth, iono H is the average height of the ionosphere above the Earth.The usual value of iono H is between 300 km and 400 km.[11], reported that Hionovaries between 300 and 450 km.Most of the research is limited to a height between 300 and 400 km.These values correspond approximately to the altitude of the region F in the ionosphere.In our study we chose a height of 400 km.
Expression of ionospheric delay is given by the following formula: with E is the satellite elevation.Hence the relationship: In the following we note iono ∆ by iono I .

GNSS Data Processing
The first implemented function used for the TEC determination is the read_rinex_file function.It implements the algorithm used to extract information from the RINEX file (time, Prn, L1, L2, P1, P2, C1, S1, S2) and the almanacs file (YUMA.TXT), which contains measurements of the satellite position at a specific moment.
The RINEX file format is standard, but there may be changes from one receiver to another, the way optional fields may or not appear, or there may be changes in the position of certain items in the file of ASCII format.
Elevation and azimuth calculations, required to calculate the VTEC value, are computed by the matlabelevation_azimuth function.This function has an input as matrix which contains position of satellite in the Earth Centered Earth Fixed (ECEF) coordinates, the satellite identification number and the time in GPS format.The algorithm for calculating the TEC is given in Figure 2. Calculation of the TEC from measurements of a station goes through the following steps: 1) RINEX format file: the RINEX (Receiver Independent Exchange) file contains the observations that make it possible to determine the local TEC or experimental TEC denoted TEC GNSS.This data are downloads from the IGS website.
2) IONEX format file: the IONEX file (Ionosphere Exchange) contains the observations of the global TEC or theoretical TEC, denoted TEC GIM.This data are downloads from the website: ftp.unibe.ch[12].
3) Almanac file (yuma file): the almanac is the set of parameters allowing a priori the state, trajectory and clock bias of one or more satellites.Each almanac is linked to a GPS week number.It is valid for all GPS stations.It is retrieved from the website https://celestrak.com/GPS/almanac/Yuma/.
4) DCB file (Differential Code Biased): it gives all the satellite and receivers bias.It is valid for one month and for all GNSS stations, and is retrieved from the website: ftp.unibe.ch.
Above is an algorithmic diagram that illustrates methodology for computation of ionospheric delay: The process of extracting data from the RINEX file by using Matlab programming language.The program will analyze and extract the information needed to calculate the TEC. Figure 3 shows the main steps of extractions of raw data such as: observation Rinex file, ephemeris file, DCB file and Ionex file.

Results and Discussions
We calculated the monthly daily variation of the TEC of all data obtained during the days of the year.The months of a year are divided into four seasons: the  In order to interpret the geomagnetic effects in relation to the ionospheric activity, we began to study the behavior of the TEC according to the days classified in ascending order of geomagnetic activity (Table 1).

Monthly Variation of the Ionosphere
The diurnal variation of the TEC is attributed to daily rotation of the Earth.In order to determine the diurnal variation of the ionosphere, we calculated the TEC on the three specific years 2001-2009-2013.The results of a year with low solar activity year (2009) are presented in Figure 7, Figure 10, and Figure 11.
Similarly for a year with a high solar activity (2001/2013) are represented in Figure 6, Figure 8, Figure 9 and Figure 11.The results are expressed in ordinate for VTEC (tecu) between 0 and 100 tecu and in abscisshour UT between 00 and 24.The blue curve represents the median VTEC values of the GNSS model and the red curve shows the median VTEC values of the GIM model.Later we will note VTEC-GIM for the GIM model and VTEC-GNSS for GNSS model.Over the three years, the values of VTEC-GIM are in perfect agreement with those of VTEC-GNSS in all years studied.Both methods are on dual-frequency GPS observations.However, the TEC-GIM data was relatively smooth, whereas the TEC-GNSS values varied much faster in a short time.These results can be attributed to the different models used: the TEC-GNSS derived from a regional station (RABT/TETN), while the TEC-GIM was obtained from several global IGS stations.

Seasonal Variation
In order to validate our results, the correlation coefficients are calculated between the data VTEC-GNSS and VTEC-GIM for the year 2001 and 2009.For Positioning The correlation technique is used to mount if there is a strong connection between the models and if this connection is strong.The results of the correlation of the RABT station are shown in Figure 13 and Figure 14

Geomagnetic Activity
From Figure 17, the calculation of VTEC is done for all days of the year.We opted to put a scale of comparison with the variation of the magnetic index to identify magnetic storms (Table 2).We took the average value of the VTEC for each day and plotted the result for the whole year.A large variation in the maximum values of the parameters of the geomagnetic activity is observed between the two periods 2001 and 2009.According to our results presented in Figure 17, the values of the VTEC confirm the same variation.This leads to the conclusion that the geomagnetic activity affects the TEC data largely during the period of high activity (2001) compared to the period of low activity (2009).Table 3 presents the result of calculation of the ionospheric error on the L1 band of the two GNSS stations during the two solar years 2001 and 2009.

Conclusions
In this study, we calculated the ionospheric TEC at the RABT and TETN station in year with high solar activity (2001) and year with low solar activity (2009).Then, we analyzed the diurnal variation, monthly variation, and solar dependence of the TEC.The main results are as follows: -TEC value generally increased in the period of 07:00 to 10:00 UT inall seasons and was maximized in the period of 12:00 to 16:00 h UT. -The maximum values of TEC were found during the equinox and winter for both measurement years 2001 and 2009.In the first period of 2001 the maximum values for RABT and TETN station ≈ 40 -50 TECU, during the equinox and the minimum was found in the winter ≈ 12 -17 TECU.-The comparison between VTEC-GNSS and VTEC-GIM allowed us to validate our methology for computing ionospheric VTEC.A strong correlation (≈0.99) between the VTEC-GNSS and VTEC-GIM has been found for all season except winter season (≈0.78) for RABT station in period 2009.Therefore, it maybe concluded that the TEC value will be maximum during equinox season which may be attributed to solar activity for each period.-The effect of geomagnetic storm on the ionosphere provides a positioning error ranging from 2.33 m to 15.17 m in period of low and high solar activity delay of the satellite for code measurement , i r f d : Instrumental code delay of the receiver for code measurement i s f b : Instrumental code delay of the satellite for phase measurement , i r f b : Instrumental code delay of the receiver for phase measurement ,

Equation ( 3 )
expresses the dual-frequency ionospheric model according to Positioning satellite and receiver-related instrumental biases, Satellite bias is published daily by the international organizations of Centers of Analysis which deal with positioning: Center for Orbit Determination in Europe (CODE), by the University of Bern (Switzerland); the Jet Propulsion Laboratory (JPL) and the Crustal Dynamics Data Information System (CDDIS) in the USA, the European Space Agency (ESA) in Germany and the Technical University of Catalonia (UPC) in Spain.The values are published under the acronym "DCB" for "Differential Code Biases".We decided to retain the one calculated by CODE.

Figure 3 .
Figure 3. Subroutine Matlab for computing the vertical TEC.

Figure 6 .
Figure 6.The monthly medians of the VTEC for the RABT station, during the year 2001 located at the maximum of solar cycle 3.Cycle with strong activity.

Figure 7 .Figure 8 .
Figure 7.The monthly medians of the VTEC for the RABT station, during the year 2009 located at least of the solar cycle 23.with the exception of February due to instrument failure.

Figure 9 .Figure 10 .
Figure 9.The monthly medians of Total Electron Content at TETN station during the year 2001 with the exception of February 2001 and October to December 2001 due to instrument failure.
Figure 12 shows the monthly average VTEC values obtained by different models at the RABT and TETN stations in 2001, 2009 and 2013.The values are calculated on average with all the TEC data collected during each month.In the three years, the monthly average TEC time series showed two peaks.In April-May and in September-October, The values of the TEC observed are greater at equinoxes, spring and winter, especially in the year of maximum solar 2001-2013.In 2009 solar minimum values of the TEC becomes more important at the summer solstice (June).The minimum values of the TEC observed during the three years are those attributed to the month of January.

Figure 11 .
Figure 11.The monthly medians of Total Electron Content at TETN station during the year 2013.

Figure 12 .
Figure 12.Monthly average values of VTEC for RABT and TETN stations in 2001, 2009 and 2013.

Figure 13 .
Figure 13.Correlation between the two models VTEC_GNSS and VTEC_GIM of the RABT station for the year 2001.

Figure 15 .
Figure 15.Correlation between the two models VTEC_GNSS and VTEC_GIM of the station TETN for the year 2001.

Figure 16 .
Figure 16.Correlation between the two models VTEC_GNSS and VTEC_GIM of the station TETN for the year 2009.

Figure 17 .
Figure 17.VTEC-GNSS, VTEC-GIM and AP index for the RABT and TETN station for the two years 2001 and 2009.

Table 1 .
Classification of geomagnetic activity according to the days of the year 2001-2009-2013.

Table 3 .
Effect of geomagnetic activity on ionospheric error.