The effects of Ionospheric layers on TEC values using continuous satellite tracking data

Wan Aziz W A and Md Nor K
Department of Geomatic Engineering
Faculty of Geoinformation Science & Engineering
University Technology Malaysia,
[email protected]
The Global Positioning System (GPS) is the satellite-based method of collecting 3D data for various scientific applications. For most of its trips from the satellite to the receiver antenna, the GPS signals ‘enjoys’ a trip through the virtual vaccum of ‘empty space’. When it gets to the earth’s atmosphere, however, the speed drops by an amount that varies somewhat randomly. Of course, since the calculation of the range to the satellite depends on the speed of the signal, a change in signal speed implies an error in distance, which produces an error in position finding. Significant changes in signal speed occur through the atmosphere is known as atmospheric effects. One of this effect is the ionospheric delays.

The ionising action of the sun’s radiation on the earth’s upper atmosphere produces free electrons which affect the propagation of electromagnetic waves. The ‘ionised’ region of the atmosphere is a plasma and its referred as the ionosphere. Shorter wavelength signals (30 MHz), such as GPS signals, pass through the ionosphere but are affected by it. The ionospheric refraction is one of the major error sources in GPS, which causes signal propagation delays. The major effects the ionospheric can have on GPS are the followings, see Klobuchar, (1996) :

• group delay of the signal modulation, or absolute range error;
• carrier phase advance, or relative range error,
• Doppler shift, or range-rate errors
• refraction or bending of the radio wave,
• distortion of pulse waveforms,
• signal amplitude fading or amplitude scintillation, and phase scintillation

The ionospheric delay is a function of the Total Electron Content (TEC) along the signal path and the frequency of the propagated signals. Since the ionosphere is a dispersive medium for radio waves, a dual-frequency GPS receiver can minimise ionospheric delay through a linear combination of L1 and L2 observables (Lao, 1998). Nowadays, with the decreasing cost of GPS equipment, permanent GPS tracking stations have been installed at a rapid pace over almost all the worlds. The permanent GPS tracking stations are normally set to operate 24 hours a day, all year round, and one of these, is the Malaysian Active Satellite System (MASS). The MASS network is used in a variety of applications in Malaysia involving the determination of precise positions, unified datum, earth rotation parameters and crustal studies as well as for atmospheric (tropospheric and ionospheric) modelling. This paper describes the potential of the dual-frequency GPS observations collected by MASS network in modelling the TEC values with respect to ionospheric layers.

Fig. 1: Illustrates the ionospheric refraction, which causes the GPS signal propagation delays.
The Mass Network and Ionospheric TEC
Current trend indicates that for the most precise, effective, economical and fast applications, some form of permanent GPS network should be established. Therefore, a large number of permanent GPS tracking stations has been built up in the past few years that allows for many scientific researches. In order to realise such requirements, the Directorate of Surveying and Mapping, Malaysia (DSMM) has started establishing permanent GPS tracking stations namely MASS network, at the end of 1998. Currently, the MASS network consists of seventeen (17) permanent GPS stations over the country. This network is also known as the Zero Order Geodetic Network and it complies with international standards to provide the highest precision for positioning in Malaysia. Thus, GPS data of the MASS network seemed to be a very reliable sources for ionospheric studies, particularly in the Equatorial regions. The network is set to operate 24 hours a day, all year round, so that the daily variations of the electron density in the ionosphere can be studied. The continuous GPS data can be collected on a daily basis, centrally archieved at data centers, and are available via the internet to users.

The ionosphere is a shell of electrons and electrically charged atoms and molecules that surrounds the earth, streching from a height of about 50 km to more than 1000 km above the earth’s surface. The existence of the ionosphere is primarily due to the extreme ultraviolet radiation and X-rays from the sun. Different regions of the ionosphere are produced by different chemical species. The ionosphere is composed of the D, E, F1 and F2 regions. Figure 2 illustrates the different regions of the ionosphere.

Fig. 2: The different regions of the ionosphere

The parameter of the ionosphere that produces most of the effect on GPS signals is the total number of electrons in the ionosphere called total electron content, which is characterised by the number of electrons in a vertical column with a cross-sectional area of one square metre, and extending all the way from the GPS satellites to the observer (Klobuchar, 1996). Mathematically, TEC is expressed as the integrated electron content along the radio signal path, i.e (Lao, 1998):

where ne is the electron density in the units of electron/m3 and ds is the infinitesimal line element. The electron density is a function of the amount of incident solar radiation. Throughout the day, TEC at a location is dependent on the local time, reaching a maximum between 12:00 and 16:00. TEC is measured in units of 1016 electrons per m2. The ionospheric delay can be expressed in unit of seconds as:

where c is the speed of light in m/s
The major characteristics and importance of each region of the ionosphere for potential effects on GPS signals are summarised as follows:

• D-region, 50 – 90 km: This region, produced by ionisation of several molecular species from hard x-rays and solar Lyman a radiations, causes absorption of radio signals at frequencies up to low VHF band.
• E-Region, 90-140 km: The normal E region, produced by solar soft x-rays, has a minimal effect on GPS. An intense E region, with irregular structure, produced by solar particle precipitation in the auroral region, might cause minor scintillation effects.
• F1-region, 140-210 km: In this F1 region, it can account for up to 10% of the ionospheric delay encounted by GPS. It has a highly predictable density of molecular species, and its electron density merges into the bottom-side of the F2 region.
• F2-region, 210-1000km: The F2 region is the most dense and also has the highest variability, causing most of the observed effects on GPS receivers. The height of the peak of the electron density of the F2 region generally varies from 250 to 400 km.

Because of complicated nature of the ionosphere, there have been numerous approaches to ionospheric modelling over the years. These approaches include: (i) Empirical models based on extensive world-wide data sets, (ii) 3D, time-dependent physical models, (iii) Analytical model based on orthogonal function fits to the output obtained from numerical models, and (iv) Models driven by real-time ionospheric inputs. In our case, we adopted the empirical model as a standard ionospheric modelling. This ionospheric model is dependent on measurements whereby the data are collected over an extended period of time. However, the empirical model represents ‘average’ not ‘instantaneous’ conditions. One of the empirical models is Bent Model which was developed for ground-to-satellite communications. This global model provides the TEC in the altitude range from 150 – 2000 km as a function of position of the observer, time, solar flux and the sunspot number.

The Data Set
In this experiment, we processed the MASS GPS data in 1-hour segments. Once every hour our process transfers via ftp 1 hour of raw GPS data on which this 1-hour segments of raw data is translated to RINEX format. Consequently, these one-hour RINEX files are processed with Bernese software. It has been proven that the Bernese software is one of the most powerful programming source in estimating the total TEC values at regular time interval. The normal equations file from the 1-hour analysis is stored. Subsequently, we stack the normal equation files from the 24 hour solutions to obtain equivalent of a 24 hours GPS solution. The main reason to apply this stacking technique, rather than re-processing many hours of data is the significant saving in CPU time. The results in shorter latency with modest requirements in computing power. Thus, in our preliminary experiment, a set of data from the four (4) stations of the MASS network has been used and analysed. These permanent tracking stations are listed in Table: 1
Table 1: List of MASS stations used for data analysis

During the post-processing stages using Bernese GPS post-processing software, we have detected bad points and cycle slips. The next step is to repair cycle slips and then adjust the phase ambiguities.. The Bernese software supports two types of ionosphere models to represent the deterministic component of the ionosphere such as the local models based on two-dimensional Taylor series expansions and global models based on spherical harmonic expansions. The global ionospheric model (empirical) is used to estimate the TEC values, i.e.

where
nmax is the maximum degree of the spherical harmonic expansion

Pnm are the normalised associated Lagendre functions of degree n and order m based on the normalised function L(n,m) and Lagendre functions Pnm, and anm, bnm are the TEC coefficients of the spherical harmonics. All results are shown in the TIDs (Travelling Ionospheric Disturbances) Indicator and TEC values for the day of experiments. TIDs is a wavelike structures, which may imply variations in the ionospheric electron density of several percent of the TEC.

Results and Discussion
We investigated the effects of using different ionospheric shell height, which plays an important role in computing the coordinates of the sub-ionospheric points. The single layer ionospheric model assumes that a thin spherical shell can approximate the vertical TEC, which is located at a specified height above the surface of earth. This altitude is often assumed to correspond to the maximum electron density of the ionosphere. Futhermore, it is usually assumed that the ionospheric shell height has no temporal or geographical variation, and therefore it is set to a constant value regardless of the time or location of interest. In our investigation, we tried to estimate the TEC values at fixed heights of D-region 70 km, E-region 120 km, F1-region 180 km, F2-region 500 km and H+region 1500 km. The results for all ionospheric shell height are shown in Table 2.

From Table 2 it can be seen that the maximum TIDs Indicator values on the 12 December 1999 occurred at the D region 0.64 TECU and minimum values is F2 region 0.51 TECU. While the maximum TIDs Indicator values for the 13 December 1999 is at the D region 0.67 TECU and minimum values is at F2 region 0.58 TECU. These differences may be due to the solar activities, whereby the sunspots number for 12 December 1999 is 90 and the solar flux is 150 , and for 13 December 1999, the sunspots number is 105 and the solar flux is 163. Graphically its can be seen in Figure 3.
Table 2 : TIDs Indicator values for different ionospheric region and shell height

The result have shown that the TIDs Indicator values for both days at the F2-region is smaller than the D, E and F1 region, however, the electron contents at F2-region is greater than the others region – see Table 3.0.

Fig. 3 : Tids Indcator values for different region

Table 3 : TEC values for different ionospheric region and shell height

From the above table, it is shown that the results for the TEC values in Table 3.0 on 12 December 1999 vary from 7 to 24 TECU for D, E, F1 and F2-region. While for 13 December 1999 the TEC values vary from 8 to 51 TECU. Table 3 also shows that there is no significant differences between the TEC values for all regions on the 12 December 1999 compared to the TEC values on 13 December 1999. Perhaps, it may due to the minimum solar activities on the 12 December 1999 compared to 13 Desember 1999. The Total Electron Content map for the Malaysian region for 12 and 13 December 1999 have been plotted in Figures 4 to 11.
Conclusion
The ionosphere is the largest source of error in GPS positioning whereby the main ionospheric effects on GPS signals is a group delay. This ionospheric delay is a function of the TEC along the signal path and the frequency of the propagated signal. In this experiment, we have estimated TEC values with respect to the ionospheric shell heights using the continuous GPS tracking data, i.e. MASS GPS data. The GPS data is being processed by using the Bernese software. The ionospheric global model has been adopted as a standard model for estimating the TEC values. In our preliminary results, we have found that different ionospheric shell heights shall be used for studying the ionospheric TEC estimates. The results have shown that approximately 0.5 to 0.6 TECU in TIDs Indicator Value for Peninsular Malaysia. Finally, we strongly believed that when combined with other scientific data, the ionospheric information can be used for environmental studies (e.g. continuous weather monitoring and climatology), microwave communication signals and other geoscience applications.

Fig. 4 : Malaysian TEC maps at D-region on 12 December 1999

Fig. 6 : Malaysian TEC maps at F1-region on 12 December 1999

Fig. 7 : Malaysian TEC maps at F2-region on 12 December 1999

Fig. 11: Malaysian TEC maps at F2-region on 13 December 1999
References

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