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Performance evaluation of IRI-2007 at equatorial latitudes and its Matlab version for GNSS applications
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Advances in Space Research 52 (2013) 1845–1858 www.elsevier.com/locate/asr
Performance evaluation of IRI-2007 at equatorial latitudes and its Matlab version for GNSS applications V. Satya Srinivas a, A.D. Sarma a,⇑, K.C.T. Swamy a, K. Satyanarayana b a
R and T Unit for Navigational Electronics, Osmania University, Hyderabad 500 007, A.P, India b Department of Biomedical Engineering, Osmania University, Hyderabad 500 007, A.P, India Available online 27 December 2012
Abstract International Reference Ionosphere (IRI) model is the widely used empirical model for ionospheric predictions, especially TEC which is an important parameter for radio navigation and communication. The Fortran based IRI-2007 does not support real-time interactive visualization and debugging. Therefore, the source code is converted into Matlab and is validated for the purposes of this study. This facilitates easy representation of results and for near real-time implementation of IRI in the applications including spacecraft launching, now casting, pseudolite based navigation systems etc. In addition, the vertical delay results over the equatorial region derived from IRI and GPS data of three IGS stations namely Libreville (Garbon, Africa), Brasilia (Brazil, South America) and Hyderabad (India, Asia) are compared. As the IRI model does not account for plasmasphere TEC, the vertical delays are underestimated compared to vertical delays of GPS signals. Therefore, the model should be modified accordingly for precise TEC estimation. Ó 2012 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: IRI-2007; GNSS; Ionospheric vertical delay; Equatorial latitudes
1. Introduction An effort to better characterize nominal and disturbed/ storm ionospheric conditions has resulted in IRI model (Bilitza, 1990). Data due to several instruments such as ionosonde, incoherent scatter radar, alouette satellites etc., are used to model the behavior of ionosphere with respect to seasonal and solar cycle variations. For satellite based navigation the L-band frequencies are being used. The Global Navigation Satellite System (GNSS) signals travel through the oxygen dominated plasma of the ionosphere (up to approx. 1000 km) and hydrogen-dominated plasmasphere (approx. 1000–20,500 km) (Kersley and Klobuchar, 1980). The two ionized regions form a dispersive medium, which introduce frequency dependent path delay proportional to Total Electron Content (TEC). The TEC is combination of both ionospheric electron content (IEC) and plasmaspheric electron content (PEC). The plasama⇑ Corresponding author.
E-mail address: [email protected] (A.D. Sarma).
sphere’s electron density is several orders of magnitude less than ionosphere. However, as a result of longer distance traveled by the GNSS signals through plasmasphere, the plasmasphere can have a significant effect on the signals (Lunt et al., 1999a; Balan et al., 2002). And when the GNSS signals pass through ionosphere they are subjected to various effects. One is bending due to the refractive index of the ionosphere. The refraction continuously changes along the propagation path. However, the refraction or bending becomes negligible for satellites with elevation angles greater than 5° (Parkinson and Spilker, 1996). And also the speed of propagation of signals will vary as they pass through different layers of ionosphere before reaching the user’s receiver. When the GNSS signal propagates through the ionosphere the carrier phase is advanced and code is delayed resulting in the distance between transmitter and receiver too short and too big respectively (Misra and Enge, 2001). The resulting time delay is inversely proportional to the square of the transmission frequency. As the plasmasphere and ionosphere are dispersive in nature, a dual frequency GNSS receiver can
0273-1177/$36.00 Ó 2012 COSPAR. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.asr.2012.12.002
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be used to estimate the time delay effects on the propagating signals. But for most of the critical applications such as aircraft navigation, vehicle tracking etc., only single frequency receivers are being employed. Therefore, global, regional and local Total Electron Content (TEC) models are being developed for supporting Global Navigation Satellite Systems (GNSS) systems worldwide. The Klobuchar (1987) and IRI are the widely used global models. Klobuchar time delay model is the official broad cast model in GPS systems to mitigate effect of ionosphere for single frequency GPS users. The major limitations are, model assumes only ideal smooth behavior of ionosphere with constant delay during night time and the transmitted coefficients remain same for about 10 days (Klobuchar,1987). Another major limitation is that, the model is a single layer model and thus not applicable in strategic applications like missile tracking etc., where the signal propagates only part of the ionosphere. But, in the IRI model the ionosphere is well defined at the abstraction level when compared to the other models such as Klobuchar model etc. IRI gives altitude versus electron densities from 60 to 2000 kms. The integration of electron densities between the low and upper boundary altitudes provides TEC for desired region of ionosphere. Thus, with necessary modifications, the model can be used in several strategic applications of GNSS. The IRI2007 is developed in Fortran. In view of the software flexibility and compatibility of Matlab, an attempt is made to convert the Fortran coded IRI-2007 into Matlab. The whys and wherefores regarding this aspect are discussed in detail in subsequent sections. In this paper, the electron density profiles due to Matlab source code are compared with that due to IRI-web and validated for the purposes of this study. The electron densities at Toro (Lat: 10.05° N, Long: 9.11° E), Nigeria in Africa region and at Hyderabad (Lat: 17.30° N, Long: 78.55° E) in Indian region are considered to analyze the reliability of the developed Matlab based IRI-2007. Further, diurnal variations of vertical delays over the equatorial region derived from GPS measurements are compared with the vertical delays due to IRI derived TEC values. The GPS data corresponding to Libreville (0.35° N, 9.67° E), Brasilia (15.94° S, 47.88° W) and Hyderabad (17.30° N, 78.55° E) are considered. The analysis is carried out with the quiet and disturbed days data pertaining to period 2003–2009.
larities in electron density distributions. The high latitude region is the one covering above 60° dip around the magnetic poles. This region also has more disturbances such as phase scintillations and these are mostly depending on the magnetic activity (Das Gupta et al., 2007). The visual auroral or ‘northern and southern lights’ effect is generally observed in the polar cap and auroral latitudes, within the high latitude region. Auroral effect causes the strong scintillation fading on operating GPS receivers in these regions. And the mid- latitude region is one which covers the region in between the equatorial and high latitude regions. This region exhibits the fewest disturbances and those can be easily predicted, when compared to the other regions (Das Gupta et al., 2007). 3. MatLab based IRI 2007 The model is basically developed in Fortran and can be accessible through website (http://ccmc.gsfc.nasa.gov/ modelweb/models/iri_vitmo.php). The Fortran based IRI-2007 is not convenient for near real-time and real-time applications. The reasons in this regard are; (i) Fortran has extremely limited support for real-time interactive visualization and debugging, (ii) generally Fortran users write intermediate and final results to text files and post-process them using other software (e.g., Excel, Matlab) (Thyer et al., 2011), and (iii) when compared to modern languages the I/O facilities are limited, inflexible and primitive in Fortran. In order to handle interrupts and scheduling, and communication with external devices, assembly language coding is indispensable, which is time-consuming and tedious in large scale embedded applications (Matjaz et al., 2007). Compared to Fortran, MATLAB is a highlevel computer programming language that can be used
2. Significance of latitudinal variations of TEC Basically the earth’s ionosphere consists of three major geographic regions; they are the equatorial region, the Mid-latitude region, and the high latitude region. The equatorial region is one which extends to 20° on either side of the earth’s magnetic equator and it covers 50% of earth’s surface. It is observed that highest TEC values, strongest large scale gradients of TEC and worst disturbances occur in this region (Wanninger, 1993). The ionosphere in this region is characterized by two prominent features, the Equatorial Ionization Anomaly (EIA) and intense irregu-
Fig. 1. IRI electron density profile.
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for scientific computing and data visualization. The major advantage in this is that the programs can be tested and debugged quickly. There is no necessity to compile, link and execute after each correction (Kiusalaas, 2005). Therefore, it is possible to develop MATLAB programs in much shorter time than equivalent Fortran programs. And also like Fortran, Matlab is equally fast with the advancement of high speed processors. Though Matlab facilitates execution of compiled Fortran and C programs through Matlab External (MEX) interface files, MEX files are not appropriate for all applications. The general features of Matlab are found elsewhere in open literature (Davis and Sigmon, 2005). Further, many applications of GNSS technology such as GNSS Software Defined Radio (SDR) – a real time software GNSS receiver are being developed in Matlab. Even customized Matlab based tools are being developed around the world for data acquisition, analysis and modeling. As Matlab is more flexible and robust, Fortran coded IRI-2007 is converted into Matlab. The software can be widely used for academic, research and industrial purposes. The IRI-2007 web model is often compared and validated by several users worldwide with the developed regional/
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local TEC models. The major disadvantage here is that the data has to be manually processed when accessed through the web. The developed MATLAB source code will aid in reducing the human efforts in this perspective and also provides a lot of scope for customization for navigation applications. 3.1. Data source The electron density profile from 60 to 2000 km is divided into six regions (Fig. 1). The region wise automation of IRI 2007 in MatLab is done for TEC estimation. The code is translated into 33 subroutines/programs. These programs provide electron density at a particular range of altitudes. The necessary data files for the development of software are downloaded from the website (ftp://hanna. ccmc.gsfc.nasa.gov/pub/modelweb/Ionospheric/iri). The developed programs make use of the data files corresponding to solar, ionospheric and geomagnetic indices, CCIR (1966) and URSI coefficients (Perrone and de Franceschi, 1998; Rush, 1992). The CCIR and URSI coefficients are used for continental and for oceanic applications
Fig. 2. Comparison of electron density profiles due to Matlab and web versions of IRI-2007 at local time (a) 0100 h, (b) 0700 h, (c) 1300 h and (d) 1900 h on 28th Dec. 2008 at Toro.
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Fig. 3. Comparison of electron density profiles due to Matlab and web versions of IRI-2007 at local time (a) 0100 h, (b) 0700 h, (c) 1300 h and (d) 1900 h on 29th Oct. 2003 at Toro.
respectively. The 11th generation of IGRF coefficients is incorporated in Matlab based IRI-2007, where web based IRI-2007 contains 10th generation of IGRF coefficients (Finlay et al., 2010).
delay experienced by GPS signals due to the presence of electrons, is measured in terms of TEC units (TECu). In the developed MatLab code the TEC is calculated by estimating the area under the electron density profile using the following equation, (see Fig. 5)
4. Comparison of electron density profiles using IRI-2007 web and Matlab based versions
TEC ¼
As the web based IRI model supports TEC estimation for the period 1958–2009, two typical days corresponding to low solar activity (2009) and moderate solar activity (2003) years are considered. The analysis is carried out by observing electron density values for every six hours (0100 h, 0700 h, 1300 h and 1900 h), at Toro (Bauchi state, Nigeria) (Lat:10.05° N, Long:9.11° E) for 28th Dec. 2008 (Kp 6 1) and 29th Oct. 2003 (5 P Kp 6 9). Also at Hyderabad station (Lat:17.40° N, Long:78.47° E) for 30th Dec. 2009 (Kp < 1) and 29th Oct. 2003 (5 < Kp < 9). Figs. 2–5 show that, the developed Matlab model of IRI-2007 is reliable and compares well. Usually, the ionospheric time
where, x: electron density values (el/m3), Dy: Height resolution with which electron density is estimated (km), i = 1 and n corresponds to initial and final height of electron density profile. The values due to both codes compare well. In addition, a cross validation procedure is included to quantify the performance of IRI-2007 Matlab with mathematical relevance using ionospheric slab thickness as key parameter. The slab thickness parameter as given in Eq. (3), is a very useful parameter as it allows a simple conversion between foF2 and TEC. Therefore, this equation is used for cross validation. Beside this, slab thickness can be related to a variety
n1 X
ð0:5 ðxi þ xiþ1 ÞÞ Dy ðTECuÞ
ð1Þ
i¼1
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Fig. 4. Comparison of electron density profiles due to Matlab and web versions of IRI-2007 at local time (a) 0100 h, (b) 0700 h, (c) 1300 h and (d) 1900 h on 29th Dec. 2009 at Hyderabad.
of quantities of interest that affect the overall profile shape (Stankov and Warnant, 2009; Kouris et al., 2004; Fox and Mendillo, 1989). As the maximum ionization takes place in F2-layer, TEC has correlation and can be directly predicted from F2-layer critical frequency (foF2 (MHz)). Therefore, Eq. (2) is used to find out the difference in estimation of ionospheric delay as a result of IRI-2007 Matlab and web models (Kouris et al., 2004). TEC ¼ 1:24 106 sf 2 ðfoF 2Þ2
ð2Þ
where, sf2 is the slab thickness (meters) of F2 layer estimated from IRI-2007 web model. This is defined as, sf 2 ¼ TEC=NMF 2
ð3Þ
where, NMF2 is the F2-layer peak electron density and is given as, NmF 2 ¼ 1:24 1010 foF 2 foF 2
ð4Þ
The sf2 estimated from IRI web is considered as reference for the Matlab model to estimate TEC for crossvalidation. The slab thickness is derived from the NmF2 and TEC of IRI web (Eq. (3)), then it is used in Eq. (2) with the value of foF2 of Matlab IRI to estimate TEC.
Table 1 gives the difference in TEC (TEC) estimation in TECu (1016 el/m2) due to these methods at Toro station. The example estimations are carried out for 28th Dec. 2008. The TEC, is given as, DTEC ¼ jTECMatlab TECweb j
ð5Þ
The maximum TEC is observed to be 0.27 TECu. Table 2 give the difference in TEC (TEC) estimation on 29th Oct. 2003 (storm day). The maximum difference in TEC estimation is 0.39 TECu. Tables 3 and 4 gives the difference in TEC (TEC) estimation on 29th Dec. 2009 (quiet day) and 29th Oct. 2003 (storm day) at Hyderabad station. The maximum TEC observed for respective days is observed to be 0.27 TECu. Therefore, it is clear that the developed software code is producing reliable results and even the error or difference in estimates is within the limits. It can be noted that 1 TECu is equal to 0.163 m of range delay on GPS L1 frequency. 5. IGS stations data acquisition and processing In general most of the ionospheric time delay models including IRI give vertical delays. Therefore, it is necessary to convert the GPS slant delays to vertical delays.
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Fig. 5. Comparison of electron density profiles due to Matlab and web versions of IRI-2007 at local time (a) 0100 h, (b) 0700 h, (c) 1300 h and (d) 1900 h on 29th Oct. 2003 at Hyderabad.
Table 1 Difference in TEC estimation due to Matlab and web versions of IRI models for quiet (Kp 6 1) day (28th Dec. 2008) at Toro station. S.No.
1. 2. 3. 4.
Local time (Hours)
0100 h 0700 h 1300 h 1900 h
sf2 (meters) 112222.94 139586.82 128350.79 91816.43
foF2 (MHz)
TEC (TECU)
DTEC
Matlab
Web
Matlab
Web
3.03 4.21 6.22 7.06
2.93 4.16 6.19 6.89
1.27 3.06 6.15 5.67
1.20 3.00 6.10 5.40
0.07 0.06 0.05 0.27
Table 2 Difference in TEC estimation due to Matlab and web versions of IRI models for storm (5 P Kp 6 9) day (29th Oct. 2003) at Toro station. S.No.
1. 2. 3. 4.
Local time (Hours)
0100 h 0700 h 1300 h 1900 h
sf2 (meters) 106497.96 133934.55 93591.37 41623.30
foF2 (MHz)
TEC (TECU)
DTEC
Matlab
Web
Matlab
Web
7.32 7.52 10.17 9.78
7.12 7.36 10.08 9.64
7.07 9.39 12.00 4.93
6.70 9.00 11.80 4.80
The data due to three International GNSS Service (IGS) network stations namely Libreville (Africa), Brasilia (Brazil) and Hyderabad (India) are considered to analyze the delay variations over equatorial region. The slant ionospheric delay (Sd) is estimated using the
0.37 0.39 0.20 0.13
measured pseudoranges on both L1 and L2 frequencies and is given as (Seeber, 2003), 2 fL2 ð6Þ Sd ¼ ðqL2 qL1 Þ 2 2 fL1 fL2
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Table 3 Difference in TEC estimation due to Matlab and web versions of IRI models for quiet (Kp 6 1) day (29th Dec. 2009) at Hyderabad station. S.No.
Local time (Hours)
sf2 (meters)
foF2 (MHz)
TEC (TECU)
Matlab
Web
Matlab
Web
1. 2. 3. 4.
0100 h 0700 h 1300 h 1900 h
238995.35 259386.11 110273.32 126884.15
4.35 5.01 9.33 7.34
4.30 4.92 9.25 7.26
5.61 8.07 11.90 8.47
5.50 7.80 11.70 8.30
DTEC
0.11 0.27 0.20 0.17
Table 4 Difference in TEC estimation due to Matlab and web versions of IRI models for storm (5 P Kp 6 9) day (29th Oct. 2003) at Hyderabad station. S.No.
Local time (Hours)
sf2 (meters)
1. 2. 3. 4.
0100 h 0700 h 1300 h 1900 h
121365.58 153543.30 96515.08 90426.87
foF2 (MHz)
TEC (TECU)
DTEC
Matlab
Web
Matlab
Web
9.69 9.13 14.12 12.70
9.61 9.05 13.88 12.63
14.13 15.87 23.86 18.11
13.90 15.60 23.70 17.90
Fig. 6. Comparison IRI-2007 with experimental data (a) vertica delay (b) IPP latitude and (c) IPP longitude at Libreville station on quiet day (8th Nov. 2003).
where, fL1: L1 carrier frequency (1575.42 MHz), fL2: L2 carrier frequency (1227.60 MHz), qL1, qL2: Pseudorange on L1and L2 (m). The slant delay is converted to vertical delay (Vd) at a mean height of 350 km from the surface of the earth where
0.23 0.27 0.16 0.21
Fig. 7. Comparison IRI-2007 with experimental data (a) vertica delay (b) IPP latitude and (c) IPP longitude at Brasilia station on quiet day (8th Nov. 2003).
peak electron density is assumed to be present (Klobuchar, 1987) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi Re COSðhÞ V d ¼ Sd 1 ðRe þ hi Þ
ð7Þ
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Fig. 8. Comparison IRI-2007 with experimental data (a) vertica delay (b) IPP latitude and (c) IPP longitude at Hyderabad station on quiet day (8th Nov. 2003).
Fig. 9. Comparison IRI-2007 with experimental data (a) vertica delay (b) IPP latitude and (c) IPP longitude at Libreville station on storm day (29th Oct. 2003).
where, Re: Effective radius of the earth, h: Elevation angle, hi : Height of ionospheric shell (350 km). The parameters such as satellite elevation angle (h), azimuth (AZ), user latitude (uu) and longitude (ku) are used to calculate Ionospheric Pierce Point (IPP) latitude and longitude. 6. Performance evaluation of IRI-2007 for equatorial latitudes The IRI model is continuously updated with the contributions from worldwide scientists (Bilitza and Reinisch, 2008). Several newly discovered phenomena are incorporated in the model and also there is a lot of scope for the further development. TEC maps due to the model are provided to North America, Japan, and Australia. Even efforts are in progress to provide TEC maps over India and Brazil by including suitable models (Bilitza, 2006). In order to investigate the performance of IRI-2007 at equatorial region, three IGS stations that are within ±20° of latitude Libreville (0.35° N, 9.67° E), Brasilia (15.94° S, 47.88° W) and Hyderabad (17.30° N, 78.55° E) are considered. The diurnal variation analysis is done for two typical days data corresponding to both quiet and disturbed ionospheric conditions in each year from 2003 to 2009. The duration corresponds to moderately high (2003–2004) and low (2005–2009) solar activity periods. The delay estimates due to IRI-2007 and the experimental data are compared.
Fig. 10. Comparison IRI-2007 with experimental data (a) vertica delay (b) IPP latitude and (c) IPP longitude at Brasilia station on storm day (29th Oct. 2003).
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due to IRI-2007 is considered for comparison. The data with sampling interval of 5 min is used. The results are plotted for the duration of 0–24 h to understand the diurnal behavior of ionosphere at equatorial latitudes. The diurnal vertical delay variation plots due to GPS data and that derived from IRI-2007 corresponding to the three IGS stations for both quiet and storm days are shown in Figs. 6–23. In Figs. 6–11, the IPP latitude and longitudes of the respective satellites along with the vertical delays are depicted. However, from Fig. 12 onwards only vertical delay variations at three stations are presented. It is noticed that the IRI underestimates delays mostly. Table 5 depicts the Root Mean Square Error (RMSE) between the GPS and IRI derived vertical delays for all considered days. The following are the observations, The vertical delays are large for moderately high solar activity period (2003–2004) compared to low solar activity period (2005–2009).
Fig. 11. Comparison IRI-2007 with experimental data (a) vertica delay (b) IPP latitude and (c) IPP longitude at Hyderabad station on storm day (29th Oct. 2003).
Satellite and receiver instrumental biases are removed from dual frequency GPS data for precise estimation of vertical delays. The satellite and receiver specific instrumental bias are acquired through ftp (ftp.unibe.ch/aiub/BSWUSER50/ ORB/). At any particular instant of time a minimum of four or more GPS satellites are visible. The vertical delays are calculated at the corresponding IPP locations. Among them the vertical delay of the satellite with maximum elevation is considered, so that, the slant to vertical conversion error is less. At the same IPP location the delay estimate
(a) The minimum RMSE observed at three stations namely Hyderabad, Libreville and Brasilia on 2nd Dec. 2008 (Kp < 1) are 1.99 m, 0.71 m and 2.21 m. (b) The maximum RMSE observed at the respective stations on 29th Oct. 2003 (6 6 Kp 6 9) are 8.90 m, 9.34 m, and 14.28 m respectively. (c) Compared to other two stations the RMSE for both quiet and disturbed days is less at Libreville station. (d) From the observations and figures it is apparent that for low solar activity period IRI-2007 estimates are quite closer with the experimental data during quiet days. However, the difference or underestimation due to IRI model could be due to the upper boundary limitation of 2000 km in contrast to 20,200 km of the GPS signals. As the GPS TEC is combination of IEC and PEC the vertical delays are expected to be larger compared to IRI model. It was also reported that, The TEC contribution of plasmasphere at equatorial latitudes is approximately 30% (http://www.ips.gov.au/IPSHosted/STSP/meetings/ aip/phil/phil.htm). The PEC is often 3 TEC units (TECU)
Fig. 12. Comparison of IRI-2007 with experimental data on storm day (22nd Jan. 2004) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
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Fig. 13. Comparison of IRI-2007 with experimental data on quiet day (20th Jun. 2004) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Fig. 14. Comparison of IRI-2007 with experimental data on storm day (18th Jan. 2005) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Fig. 15. Comparison of IRI-2007 with experimental data on quiet day (13th Oct. 2005) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
or more (Ciraolo and Spalla, 1997; Lunt et al., 1999b). The PEC can be as high as 10% during the day and 40% at night time (Davies, 1980). The percentage contribution of PEC to the GPS-TEC over Japan changes about 12% in day and even up to 60% in night (Balan et al., 2002). Any GNSS receiver at a particular geographic location has its own geometry with the visible satellites. Thus, the
contribution of plasmasphere TEC to GNSS-TEC varies accordingly. Further it is understood that to take into account the effect of plasmasphere on GPS signals thorough investigations are required using the modified mapping functions with effective thickness of ionosphere and plasmasphere (Mazzella, 2009). Usually the ionospheric time delay derived from GPS measurements are slant delay
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Fig. 16. Comparison of IRI-2007 with experimental data on quiet day (26th Jul. 2006) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Fig. 17. Comparison of IRI-2007 with experimental data on storm day (15th Dec. 2006) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Fig. 18. Comparison of IRI-2007 with experimental data on quiet day (1st Apr. 2007) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
measurements. A standard mapping function is used to convert to ionospheric vertical delay (Eq. (7)). In thin shell approximation of ionosphere, peak electron density is assumed at an altitude of 350 km and the same is used in the mapping function. As a result there will be some
amount of error in vertical delay estimation. However, it is also noticed that the vertical delays due to GPS satellites at lower elevation and as well due to satellites at or near to zenith (where slant to vertical conversion error is minimal or insignificant) are not matching with the vertical delays
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Fig. 19. Comparison of IRI-2007 with experimental data on storm day (8th Nov. 2007) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Fig. 20. Comparison of IRI-2007 with experimental data on storm day (27th Mar. 2008) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Fig. 21. Comparison of IRI-2007 with experimental data on quiet day (2nd Dec. 2008) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Fig. 22. Comparison of IRI-2007 with experimental data on storm day (13th Mar. 2009) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
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Fig. 23. Comparison of IRI-2007 with experimental data on quiet day (6th Nov. 2009) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Table 5 The RMSE of delays between experimental data and IRI-2007 for quiet and disturbed days. S.No.
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Date
29th Oct. 2003 8th Nov. 2003 22nd Jan. 2004 20th Jun. 2004 18th Jan. 2005 13th Oct. 2005 26th Jul. 2006 15th Dec. 2006 1st Apr. 2007 8th Nov. 2007 27th Mar. 2008 2nd Dec. 2008 13th Mar. 2009 6th Nov. 2009
Kp value
6 6 Kp 6 9 1 6 Kp 6 3 5 < Kp < 7 Kp 6 1 5 < Kp < 7 1 6 Kp 6 2 0 6 Kp 6 3 4 6 Kp 6 8 3 6 Kp 6 5 Kp 6 1 3 6 Kp 6 5 Kp < 1 2 6 Kp 6 5 Kp < 1
Stations Hyderabad (17.30° N, 78.55° E)
Libreville (0.35° N, 9.67° E)
Brasilia (15.94° S, 47.88° W)
8.90 m 7.27 m 4.07 m 2.91 m 5.25 m 4.04 m 4.36 m 4.38 m 3.46 m 2.99 m 3.71 m 1.99 m 4.20 m 2.10 m
9.34 m 6.45 m 3.39 m 2.18 m 3.31 m 1.72 m 2.54 m 1.78 m 2.80 m 1.99 m 2.67 m 0.71 m 1.83 m 1.47 m
14.28 m 13.9 m 10.53 m 8.07 m 11.83 m 7.75 m 8.77 m 8.59 m 2.79 m 2.96 m 3.03 m 2.21 m 2.66 m 2.73 m
calculated from IRI-2007. Therefore, improvements to the IRI model are necessary to match the actual atmospheric conditions over equatorial latitudes. 7. Conclusions The Fortran has got limited real-time interactive visualization and debugging capabilities. Also for an embedded application using Fortran requires huge assembly language programming for supporting I/O operations. Therefore, the Fortran coded IRI-2007 is converted into Matlab. The electron density profiles are generated at Toro, Nigeria for quiet and disturbed days, for Web and Matlab versions of IRI-2007 and are compared. The TEC values are calculated for the electron density profiles for web and Matlab versions of IRI-2007 using basic principle of area under curve. Further a cross validation procedure is carried out to validate the TEC from IRI Matlab using ionospheric slab thickness. It is confirmed; the developed software code is producing reliable results and compares well with Web model. Further several days of data is analyzed to comprehend the IRI model performance at equatorial latitudes. The vertical delays of GPS signals at three IGS stations
for two typical days corresponding to both quiet and disturbed days in each year from 2003 to 2009 are compared with the results due to IRI-2007. The IRI predictions are not in full agreement for both quiet and storm days with the delay variation derived from GPS data. This could be due to the effect of plasmasphere on GPS signals and requires further analysis. The best performance of IRI is noticed at low solar activity period. The minimum and maximum RMSE observed at the stations (within ±20° latitudes of equator) Libreville, Hyderabad and Brasilia are 1.99 m, 0.71 m and 2.21 m (2nd Dec. 2008, Kp < 1) and 8.90 m, 9.34 m, and 14.28 m (29th Oct. 2003, 6 6 Kp 6 9) respectively (Table 3). Therefore, to implement IRI for strategic GNSS applications, the model should be modified to take into account the effects of plasmasphere for precise TEC estimation. Acknowledgments The research work presented in this paper has been carried out under the project entitled “Investigation of Statistical Behavior of Ionosphere Over the Indian Region using GNSS data for Navigation Applications” funded by ISRO,
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Vide Order No. CAWSES-10, Dated: 19th Mar. 2010. Thanks are due to CSIR, New Delhi for providing SRF fellowship to Mr. V. Satya Srinivas. Thanks are also due to the anonymous reviewers for their valuable comments for improving the quality of this paper. References Balan, N., Otsuka, Y., Tsugawa, T., Miyazaki, S., Ogawa, T., Shiokawa, K. Plasmaspheric electron content in the GPS ray paths over Japan under magnetically quiet conditions at high solar activity. Earth Planets Space 54, 71–79, 2002. Bilitza, D. The international reference ionosphere – climatological standard for the ionosphere in characterizing the ionosphere, in: Meeting Proceedings RTO-MP-IST-056. Paper 32, Neuilly-sur-Seine, France, pp. 1–12, 2006. Bilitza, D., Reinisch, B.W. International reference ionosphere 2007: improvements and new parameters. Advances in Space Research 42, 599–609, 2008. Bilitza, D. International Reference Ionosphere 1990. National Space Science Data Center. Report 90–22. Greenbelt, MD, USA, 1990. CCIR. Committee Consultative International Radio Communications. Report 340. Switzerland, pp. 1–6, 1966. Ciraolo, L., Spalla, P. Comparison of ionospheric total electron content from the navy navigation satellite system and the GPS. Radio Sciences 32, 1071–1080, 1997. Das Gupta, A., Paul, A., Das, A. I¨onospheric TEC studies with GPS in the equatorial region. IJRSP 36, 278–292, 2007. Davies, K. Recent progress in satellite radio beacon studies with particular emphasis on the ATS-6 radio beacon experiment. Space Science Reviews 25, 357–430, 1980. Davis, T.A., Sigmon, K. Matlab Primer, seventh ed Chapman and Hall/ CRC Publisher, New York, 2005. Finlay, C.C., Maus, S., Beggan, C.D., Bondar, T.N., Chambodut, A., Chernova, T.A., Chulliat, A., Golovkov, V.P., Hamilton, B., Hamoudi, M., Holme, R., Hulot6, G., Kuang, W., Langlais, B., Lesur, V., Lowes, F.J., Lu¨hr, H., Macmillan, S., Mandea1, M., McLean, S., Manoj, C., Menvielle, M., Michaelis, I., Olsen, N., Rauberg, J., Rother, M., Sabaka, T.J., Tangborn, A., Tøffner-Clausen, L., Thebault, E., Thomson, A.W.T., Wardinski, I., Wei1, Z., Zvereva, T.I. International geomagnetic reference field: the 11th generation. International Journal of Geophysics 183 (3), 1216–1230, 2010.
Fox, M., Mendillo, M. Ionospheric equivalent slab thickness and its modelling applications. Scientific Report No. 2. Center for Space Physics. Boston University, Boston, Massachusetts, November, 1989. Kersley, L., Klobuchar, J.A. Storm associated protonospheric depletion and recovery. Planetary and Space Sciences 28, 453–458, 1980. Kiusalaas, J. Numerical Methods in Engineering with Matlab. Cambridge University Press, NY, USA, 2005. Klobuchar, J.A. Ionospheric time delay algorithm for single frequency GPS users. IEEE Transactions on Aerospace Electronic system AES23 (3), 325–331, 1987. Kouris, S.S., Xenos, T.D., Polimeris, K.V., Stergiou, D. TEC and foF2 variations: preliminary results. Annals of Geophysics 47 (4), 1325– 1332, 2004. Lunt, N., Kersley, L., Bailey, G.J. The influence of the protonosphere on GPS observations: model simulations. Radio Sciences 34 (3), 725–732, 1999a. Lunt, N., Kersley, L., Bishop, G.J., Mazzella, A.J. The contribution of protonosphere to GPS total electron content: experimental measurements. Radio Sciences 34, 1273–1280, 1999b. Matjaz, C., Verber, D., Halang, V.A. Distributed Embedded Control Systems: Improving Dependability with Coherent Design. SpringerVerlag, London, 2007. Mazzella, A.J. Plasmasphere effects on GPS measurements in North America. American Geophysical Union 44 (RS5014), 1–15, 2009. Misra, P., Enge, Per (Global Positioning System). Ganga–Jamuna Press, Lincoln, MA, USA, 2001. Parkinson, B.W., Spilker, J.J.. Global Positioning System: Theory and Applications, vol. 1. American Institute of Aeronautics and Astronautics, Washington, 1996. Perrone, L., de Franceschi, G. Solar, Ionospheric, and Geomagnetic Indices. Annali di Geofisica 41, 843–855, 1998. Rush, C.M. URSI foF2 model maps. Journal of Planetary and Space Science 40 (4), 546–547, 1992. Seeber, G. Satellite Geodesy. Walter de Gruyter, Berlin, New York, 2003. Stankov, S.M., Warnant, R. Ionospheric slab thickness – analysis, modelling and monitoring. Advances in Space Research 44, 1295– 1303, 2009. Thyer, M., Leonard, M., Kavetski, D., Need, S., Renard, B. The open source RFortran library for accessing R from Fortran with applications in environmental modeling. Enivronmental Modelling and Software 26, 219–234, 2011. Wanninger, L. Effects of the equatorial ionosphere on GPS. GPS World 4 (7), 48–54, 1993.
Advances in Space Research 52 (2013) 1845–1858 www.elsevier.com/locate/asr
Performance evaluation of IRI-2007 at equatorial latitudes and its Matlab version for GNSS applications V. Satya Srinivas a, A.D. Sarma a,⇑, K.C.T. Swamy a, K. Satyanarayana b a
R and T Unit for Navigational Electronics, Osmania University, Hyderabad 500 007, A.P, India b Department of Biomedical Engineering, Osmania University, Hyderabad 500 007, A.P, India Available online 27 December 2012
Abstract International Reference Ionosphere (IRI) model is the widely used empirical model for ionospheric predictions, especially TEC which is an important parameter for radio navigation and communication. The Fortran based IRI-2007 does not support real-time interactive visualization and debugging. Therefore, the source code is converted into Matlab and is validated for the purposes of this study. This facilitates easy representation of results and for near real-time implementation of IRI in the applications including spacecraft launching, now casting, pseudolite based navigation systems etc. In addition, the vertical delay results over the equatorial region derived from IRI and GPS data of three IGS stations namely Libreville (Garbon, Africa), Brasilia (Brazil, South America) and Hyderabad (India, Asia) are compared. As the IRI model does not account for plasmasphere TEC, the vertical delays are underestimated compared to vertical delays of GPS signals. Therefore, the model should be modified accordingly for precise TEC estimation. Ó 2012 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: IRI-2007; GNSS; Ionospheric vertical delay; Equatorial latitudes
1. Introduction An effort to better characterize nominal and disturbed/ storm ionospheric conditions has resulted in IRI model (Bilitza, 1990). Data due to several instruments such as ionosonde, incoherent scatter radar, alouette satellites etc., are used to model the behavior of ionosphere with respect to seasonal and solar cycle variations. For satellite based navigation the L-band frequencies are being used. The Global Navigation Satellite System (GNSS) signals travel through the oxygen dominated plasma of the ionosphere (up to approx. 1000 km) and hydrogen-dominated plasmasphere (approx. 1000–20,500 km) (Kersley and Klobuchar, 1980). The two ionized regions form a dispersive medium, which introduce frequency dependent path delay proportional to Total Electron Content (TEC). The TEC is combination of both ionospheric electron content (IEC) and plasmaspheric electron content (PEC). The plasama⇑ Corresponding author.
E-mail address: [email protected] (A.D. Sarma).
sphere’s electron density is several orders of magnitude less than ionosphere. However, as a result of longer distance traveled by the GNSS signals through plasmasphere, the plasmasphere can have a significant effect on the signals (Lunt et al., 1999a; Balan et al., 2002). And when the GNSS signals pass through ionosphere they are subjected to various effects. One is bending due to the refractive index of the ionosphere. The refraction continuously changes along the propagation path. However, the refraction or bending becomes negligible for satellites with elevation angles greater than 5° (Parkinson and Spilker, 1996). And also the speed of propagation of signals will vary as they pass through different layers of ionosphere before reaching the user’s receiver. When the GNSS signal propagates through the ionosphere the carrier phase is advanced and code is delayed resulting in the distance between transmitter and receiver too short and too big respectively (Misra and Enge, 2001). The resulting time delay is inversely proportional to the square of the transmission frequency. As the plasmasphere and ionosphere are dispersive in nature, a dual frequency GNSS receiver can
0273-1177/$36.00 Ó 2012 COSPAR. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.asr.2012.12.002
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be used to estimate the time delay effects on the propagating signals. But for most of the critical applications such as aircraft navigation, vehicle tracking etc., only single frequency receivers are being employed. Therefore, global, regional and local Total Electron Content (TEC) models are being developed for supporting Global Navigation Satellite Systems (GNSS) systems worldwide. The Klobuchar (1987) and IRI are the widely used global models. Klobuchar time delay model is the official broad cast model in GPS systems to mitigate effect of ionosphere for single frequency GPS users. The major limitations are, model assumes only ideal smooth behavior of ionosphere with constant delay during night time and the transmitted coefficients remain same for about 10 days (Klobuchar,1987). Another major limitation is that, the model is a single layer model and thus not applicable in strategic applications like missile tracking etc., where the signal propagates only part of the ionosphere. But, in the IRI model the ionosphere is well defined at the abstraction level when compared to the other models such as Klobuchar model etc. IRI gives altitude versus electron densities from 60 to 2000 kms. The integration of electron densities between the low and upper boundary altitudes provides TEC for desired region of ionosphere. Thus, with necessary modifications, the model can be used in several strategic applications of GNSS. The IRI2007 is developed in Fortran. In view of the software flexibility and compatibility of Matlab, an attempt is made to convert the Fortran coded IRI-2007 into Matlab. The whys and wherefores regarding this aspect are discussed in detail in subsequent sections. In this paper, the electron density profiles due to Matlab source code are compared with that due to IRI-web and validated for the purposes of this study. The electron densities at Toro (Lat: 10.05° N, Long: 9.11° E), Nigeria in Africa region and at Hyderabad (Lat: 17.30° N, Long: 78.55° E) in Indian region are considered to analyze the reliability of the developed Matlab based IRI-2007. Further, diurnal variations of vertical delays over the equatorial region derived from GPS measurements are compared with the vertical delays due to IRI derived TEC values. The GPS data corresponding to Libreville (0.35° N, 9.67° E), Brasilia (15.94° S, 47.88° W) and Hyderabad (17.30° N, 78.55° E) are considered. The analysis is carried out with the quiet and disturbed days data pertaining to period 2003–2009.
larities in electron density distributions. The high latitude region is the one covering above 60° dip around the magnetic poles. This region also has more disturbances such as phase scintillations and these are mostly depending on the magnetic activity (Das Gupta et al., 2007). The visual auroral or ‘northern and southern lights’ effect is generally observed in the polar cap and auroral latitudes, within the high latitude region. Auroral effect causes the strong scintillation fading on operating GPS receivers in these regions. And the mid- latitude region is one which covers the region in between the equatorial and high latitude regions. This region exhibits the fewest disturbances and those can be easily predicted, when compared to the other regions (Das Gupta et al., 2007). 3. MatLab based IRI 2007 The model is basically developed in Fortran and can be accessible through website (http://ccmc.gsfc.nasa.gov/ modelweb/models/iri_vitmo.php). The Fortran based IRI-2007 is not convenient for near real-time and real-time applications. The reasons in this regard are; (i) Fortran has extremely limited support for real-time interactive visualization and debugging, (ii) generally Fortran users write intermediate and final results to text files and post-process them using other software (e.g., Excel, Matlab) (Thyer et al., 2011), and (iii) when compared to modern languages the I/O facilities are limited, inflexible and primitive in Fortran. In order to handle interrupts and scheduling, and communication with external devices, assembly language coding is indispensable, which is time-consuming and tedious in large scale embedded applications (Matjaz et al., 2007). Compared to Fortran, MATLAB is a highlevel computer programming language that can be used
2. Significance of latitudinal variations of TEC Basically the earth’s ionosphere consists of three major geographic regions; they are the equatorial region, the Mid-latitude region, and the high latitude region. The equatorial region is one which extends to 20° on either side of the earth’s magnetic equator and it covers 50% of earth’s surface. It is observed that highest TEC values, strongest large scale gradients of TEC and worst disturbances occur in this region (Wanninger, 1993). The ionosphere in this region is characterized by two prominent features, the Equatorial Ionization Anomaly (EIA) and intense irregu-
Fig. 1. IRI electron density profile.
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for scientific computing and data visualization. The major advantage in this is that the programs can be tested and debugged quickly. There is no necessity to compile, link and execute after each correction (Kiusalaas, 2005). Therefore, it is possible to develop MATLAB programs in much shorter time than equivalent Fortran programs. And also like Fortran, Matlab is equally fast with the advancement of high speed processors. Though Matlab facilitates execution of compiled Fortran and C programs through Matlab External (MEX) interface files, MEX files are not appropriate for all applications. The general features of Matlab are found elsewhere in open literature (Davis and Sigmon, 2005). Further, many applications of GNSS technology such as GNSS Software Defined Radio (SDR) – a real time software GNSS receiver are being developed in Matlab. Even customized Matlab based tools are being developed around the world for data acquisition, analysis and modeling. As Matlab is more flexible and robust, Fortran coded IRI-2007 is converted into Matlab. The software can be widely used for academic, research and industrial purposes. The IRI-2007 web model is often compared and validated by several users worldwide with the developed regional/
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local TEC models. The major disadvantage here is that the data has to be manually processed when accessed through the web. The developed MATLAB source code will aid in reducing the human efforts in this perspective and also provides a lot of scope for customization for navigation applications. 3.1. Data source The electron density profile from 60 to 2000 km is divided into six regions (Fig. 1). The region wise automation of IRI 2007 in MatLab is done for TEC estimation. The code is translated into 33 subroutines/programs. These programs provide electron density at a particular range of altitudes. The necessary data files for the development of software are downloaded from the website (ftp://hanna. ccmc.gsfc.nasa.gov/pub/modelweb/Ionospheric/iri). The developed programs make use of the data files corresponding to solar, ionospheric and geomagnetic indices, CCIR (1966) and URSI coefficients (Perrone and de Franceschi, 1998; Rush, 1992). The CCIR and URSI coefficients are used for continental and for oceanic applications
Fig. 2. Comparison of electron density profiles due to Matlab and web versions of IRI-2007 at local time (a) 0100 h, (b) 0700 h, (c) 1300 h and (d) 1900 h on 28th Dec. 2008 at Toro.
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Fig. 3. Comparison of electron density profiles due to Matlab and web versions of IRI-2007 at local time (a) 0100 h, (b) 0700 h, (c) 1300 h and (d) 1900 h on 29th Oct. 2003 at Toro.
respectively. The 11th generation of IGRF coefficients is incorporated in Matlab based IRI-2007, where web based IRI-2007 contains 10th generation of IGRF coefficients (Finlay et al., 2010).
delay experienced by GPS signals due to the presence of electrons, is measured in terms of TEC units (TECu). In the developed MatLab code the TEC is calculated by estimating the area under the electron density profile using the following equation, (see Fig. 5)
4. Comparison of electron density profiles using IRI-2007 web and Matlab based versions
TEC ¼
As the web based IRI model supports TEC estimation for the period 1958–2009, two typical days corresponding to low solar activity (2009) and moderate solar activity (2003) years are considered. The analysis is carried out by observing electron density values for every six hours (0100 h, 0700 h, 1300 h and 1900 h), at Toro (Bauchi state, Nigeria) (Lat:10.05° N, Long:9.11° E) for 28th Dec. 2008 (Kp 6 1) and 29th Oct. 2003 (5 P Kp 6 9). Also at Hyderabad station (Lat:17.40° N, Long:78.47° E) for 30th Dec. 2009 (Kp < 1) and 29th Oct. 2003 (5 < Kp < 9). Figs. 2–5 show that, the developed Matlab model of IRI-2007 is reliable and compares well. Usually, the ionospheric time
where, x: electron density values (el/m3), Dy: Height resolution with which electron density is estimated (km), i = 1 and n corresponds to initial and final height of electron density profile. The values due to both codes compare well. In addition, a cross validation procedure is included to quantify the performance of IRI-2007 Matlab with mathematical relevance using ionospheric slab thickness as key parameter. The slab thickness parameter as given in Eq. (3), is a very useful parameter as it allows a simple conversion between foF2 and TEC. Therefore, this equation is used for cross validation. Beside this, slab thickness can be related to a variety
n1 X
ð0:5 ðxi þ xiþ1 ÞÞ Dy ðTECuÞ
ð1Þ
i¼1
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Fig. 4. Comparison of electron density profiles due to Matlab and web versions of IRI-2007 at local time (a) 0100 h, (b) 0700 h, (c) 1300 h and (d) 1900 h on 29th Dec. 2009 at Hyderabad.
of quantities of interest that affect the overall profile shape (Stankov and Warnant, 2009; Kouris et al., 2004; Fox and Mendillo, 1989). As the maximum ionization takes place in F2-layer, TEC has correlation and can be directly predicted from F2-layer critical frequency (foF2 (MHz)). Therefore, Eq. (2) is used to find out the difference in estimation of ionospheric delay as a result of IRI-2007 Matlab and web models (Kouris et al., 2004). TEC ¼ 1:24 106 sf 2 ðfoF 2Þ2
ð2Þ
where, sf2 is the slab thickness (meters) of F2 layer estimated from IRI-2007 web model. This is defined as, sf 2 ¼ TEC=NMF 2
ð3Þ
where, NMF2 is the F2-layer peak electron density and is given as, NmF 2 ¼ 1:24 1010 foF 2 foF 2
ð4Þ
The sf2 estimated from IRI web is considered as reference for the Matlab model to estimate TEC for crossvalidation. The slab thickness is derived from the NmF2 and TEC of IRI web (Eq. (3)), then it is used in Eq. (2) with the value of foF2 of Matlab IRI to estimate TEC.
Table 1 gives the difference in TEC (TEC) estimation in TECu (1016 el/m2) due to these methods at Toro station. The example estimations are carried out for 28th Dec. 2008. The TEC, is given as, DTEC ¼ jTECMatlab TECweb j
ð5Þ
The maximum TEC is observed to be 0.27 TECu. Table 2 give the difference in TEC (TEC) estimation on 29th Oct. 2003 (storm day). The maximum difference in TEC estimation is 0.39 TECu. Tables 3 and 4 gives the difference in TEC (TEC) estimation on 29th Dec. 2009 (quiet day) and 29th Oct. 2003 (storm day) at Hyderabad station. The maximum TEC observed for respective days is observed to be 0.27 TECu. Therefore, it is clear that the developed software code is producing reliable results and even the error or difference in estimates is within the limits. It can be noted that 1 TECu is equal to 0.163 m of range delay on GPS L1 frequency. 5. IGS stations data acquisition and processing In general most of the ionospheric time delay models including IRI give vertical delays. Therefore, it is necessary to convert the GPS slant delays to vertical delays.
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Fig. 5. Comparison of electron density profiles due to Matlab and web versions of IRI-2007 at local time (a) 0100 h, (b) 0700 h, (c) 1300 h and (d) 1900 h on 29th Oct. 2003 at Hyderabad.
Table 1 Difference in TEC estimation due to Matlab and web versions of IRI models for quiet (Kp 6 1) day (28th Dec. 2008) at Toro station. S.No.
1. 2. 3. 4.
Local time (Hours)
0100 h 0700 h 1300 h 1900 h
sf2 (meters) 112222.94 139586.82 128350.79 91816.43
foF2 (MHz)
TEC (TECU)
DTEC
Matlab
Web
Matlab
Web
3.03 4.21 6.22 7.06
2.93 4.16 6.19 6.89
1.27 3.06 6.15 5.67
1.20 3.00 6.10 5.40
0.07 0.06 0.05 0.27
Table 2 Difference in TEC estimation due to Matlab and web versions of IRI models for storm (5 P Kp 6 9) day (29th Oct. 2003) at Toro station. S.No.
1. 2. 3. 4.
Local time (Hours)
0100 h 0700 h 1300 h 1900 h
sf2 (meters) 106497.96 133934.55 93591.37 41623.30
foF2 (MHz)
TEC (TECU)
DTEC
Matlab
Web
Matlab
Web
7.32 7.52 10.17 9.78
7.12 7.36 10.08 9.64
7.07 9.39 12.00 4.93
6.70 9.00 11.80 4.80
The data due to three International GNSS Service (IGS) network stations namely Libreville (Africa), Brasilia (Brazil) and Hyderabad (India) are considered to analyze the delay variations over equatorial region. The slant ionospheric delay (Sd) is estimated using the
0.37 0.39 0.20 0.13
measured pseudoranges on both L1 and L2 frequencies and is given as (Seeber, 2003), 2 fL2 ð6Þ Sd ¼ ðqL2 qL1 Þ 2 2 fL1 fL2
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Table 3 Difference in TEC estimation due to Matlab and web versions of IRI models for quiet (Kp 6 1) day (29th Dec. 2009) at Hyderabad station. S.No.
Local time (Hours)
sf2 (meters)
foF2 (MHz)
TEC (TECU)
Matlab
Web
Matlab
Web
1. 2. 3. 4.
0100 h 0700 h 1300 h 1900 h
238995.35 259386.11 110273.32 126884.15
4.35 5.01 9.33 7.34
4.30 4.92 9.25 7.26
5.61 8.07 11.90 8.47
5.50 7.80 11.70 8.30
DTEC
0.11 0.27 0.20 0.17
Table 4 Difference in TEC estimation due to Matlab and web versions of IRI models for storm (5 P Kp 6 9) day (29th Oct. 2003) at Hyderabad station. S.No.
Local time (Hours)
sf2 (meters)
1. 2. 3. 4.
0100 h 0700 h 1300 h 1900 h
121365.58 153543.30 96515.08 90426.87
foF2 (MHz)
TEC (TECU)
DTEC
Matlab
Web
Matlab
Web
9.69 9.13 14.12 12.70
9.61 9.05 13.88 12.63
14.13 15.87 23.86 18.11
13.90 15.60 23.70 17.90
Fig. 6. Comparison IRI-2007 with experimental data (a) vertica delay (b) IPP latitude and (c) IPP longitude at Libreville station on quiet day (8th Nov. 2003).
where, fL1: L1 carrier frequency (1575.42 MHz), fL2: L2 carrier frequency (1227.60 MHz), qL1, qL2: Pseudorange on L1and L2 (m). The slant delay is converted to vertical delay (Vd) at a mean height of 350 km from the surface of the earth where
0.23 0.27 0.16 0.21
Fig. 7. Comparison IRI-2007 with experimental data (a) vertica delay (b) IPP latitude and (c) IPP longitude at Brasilia station on quiet day (8th Nov. 2003).
peak electron density is assumed to be present (Klobuchar, 1987) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi Re COSðhÞ V d ¼ Sd 1 ðRe þ hi Þ
ð7Þ
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Fig. 8. Comparison IRI-2007 with experimental data (a) vertica delay (b) IPP latitude and (c) IPP longitude at Hyderabad station on quiet day (8th Nov. 2003).
Fig. 9. Comparison IRI-2007 with experimental data (a) vertica delay (b) IPP latitude and (c) IPP longitude at Libreville station on storm day (29th Oct. 2003).
where, Re: Effective radius of the earth, h: Elevation angle, hi : Height of ionospheric shell (350 km). The parameters such as satellite elevation angle (h), azimuth (AZ), user latitude (uu) and longitude (ku) are used to calculate Ionospheric Pierce Point (IPP) latitude and longitude. 6. Performance evaluation of IRI-2007 for equatorial latitudes The IRI model is continuously updated with the contributions from worldwide scientists (Bilitza and Reinisch, 2008). Several newly discovered phenomena are incorporated in the model and also there is a lot of scope for the further development. TEC maps due to the model are provided to North America, Japan, and Australia. Even efforts are in progress to provide TEC maps over India and Brazil by including suitable models (Bilitza, 2006). In order to investigate the performance of IRI-2007 at equatorial region, three IGS stations that are within ±20° of latitude Libreville (0.35° N, 9.67° E), Brasilia (15.94° S, 47.88° W) and Hyderabad (17.30° N, 78.55° E) are considered. The diurnal variation analysis is done for two typical days data corresponding to both quiet and disturbed ionospheric conditions in each year from 2003 to 2009. The duration corresponds to moderately high (2003–2004) and low (2005–2009) solar activity periods. The delay estimates due to IRI-2007 and the experimental data are compared.
Fig. 10. Comparison IRI-2007 with experimental data (a) vertica delay (b) IPP latitude and (c) IPP longitude at Brasilia station on storm day (29th Oct. 2003).
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due to IRI-2007 is considered for comparison. The data with sampling interval of 5 min is used. The results are plotted for the duration of 0–24 h to understand the diurnal behavior of ionosphere at equatorial latitudes. The diurnal vertical delay variation plots due to GPS data and that derived from IRI-2007 corresponding to the three IGS stations for both quiet and storm days are shown in Figs. 6–23. In Figs. 6–11, the IPP latitude and longitudes of the respective satellites along with the vertical delays are depicted. However, from Fig. 12 onwards only vertical delay variations at three stations are presented. It is noticed that the IRI underestimates delays mostly. Table 5 depicts the Root Mean Square Error (RMSE) between the GPS and IRI derived vertical delays for all considered days. The following are the observations, The vertical delays are large for moderately high solar activity period (2003–2004) compared to low solar activity period (2005–2009).
Fig. 11. Comparison IRI-2007 with experimental data (a) vertica delay (b) IPP latitude and (c) IPP longitude at Hyderabad station on storm day (29th Oct. 2003).
Satellite and receiver instrumental biases are removed from dual frequency GPS data for precise estimation of vertical delays. The satellite and receiver specific instrumental bias are acquired through ftp (ftp.unibe.ch/aiub/BSWUSER50/ ORB/). At any particular instant of time a minimum of four or more GPS satellites are visible. The vertical delays are calculated at the corresponding IPP locations. Among them the vertical delay of the satellite with maximum elevation is considered, so that, the slant to vertical conversion error is less. At the same IPP location the delay estimate
(a) The minimum RMSE observed at three stations namely Hyderabad, Libreville and Brasilia on 2nd Dec. 2008 (Kp < 1) are 1.99 m, 0.71 m and 2.21 m. (b) The maximum RMSE observed at the respective stations on 29th Oct. 2003 (6 6 Kp 6 9) are 8.90 m, 9.34 m, and 14.28 m respectively. (c) Compared to other two stations the RMSE for both quiet and disturbed days is less at Libreville station. (d) From the observations and figures it is apparent that for low solar activity period IRI-2007 estimates are quite closer with the experimental data during quiet days. However, the difference or underestimation due to IRI model could be due to the upper boundary limitation of 2000 km in contrast to 20,200 km of the GPS signals. As the GPS TEC is combination of IEC and PEC the vertical delays are expected to be larger compared to IRI model. It was also reported that, The TEC contribution of plasmasphere at equatorial latitudes is approximately 30% (http://www.ips.gov.au/IPSHosted/STSP/meetings/ aip/phil/phil.htm). The PEC is often 3 TEC units (TECU)
Fig. 12. Comparison of IRI-2007 with experimental data on storm day (22nd Jan. 2004) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
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Fig. 13. Comparison of IRI-2007 with experimental data on quiet day (20th Jun. 2004) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Fig. 14. Comparison of IRI-2007 with experimental data on storm day (18th Jan. 2005) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Fig. 15. Comparison of IRI-2007 with experimental data on quiet day (13th Oct. 2005) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
or more (Ciraolo and Spalla, 1997; Lunt et al., 1999b). The PEC can be as high as 10% during the day and 40% at night time (Davies, 1980). The percentage contribution of PEC to the GPS-TEC over Japan changes about 12% in day and even up to 60% in night (Balan et al., 2002). Any GNSS receiver at a particular geographic location has its own geometry with the visible satellites. Thus, the
contribution of plasmasphere TEC to GNSS-TEC varies accordingly. Further it is understood that to take into account the effect of plasmasphere on GPS signals thorough investigations are required using the modified mapping functions with effective thickness of ionosphere and plasmasphere (Mazzella, 2009). Usually the ionospheric time delay derived from GPS measurements are slant delay
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Fig. 16. Comparison of IRI-2007 with experimental data on quiet day (26th Jul. 2006) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Fig. 17. Comparison of IRI-2007 with experimental data on storm day (15th Dec. 2006) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Fig. 18. Comparison of IRI-2007 with experimental data on quiet day (1st Apr. 2007) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
measurements. A standard mapping function is used to convert to ionospheric vertical delay (Eq. (7)). In thin shell approximation of ionosphere, peak electron density is assumed at an altitude of 350 km and the same is used in the mapping function. As a result there will be some
amount of error in vertical delay estimation. However, it is also noticed that the vertical delays due to GPS satellites at lower elevation and as well due to satellites at or near to zenith (where slant to vertical conversion error is minimal or insignificant) are not matching with the vertical delays
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Fig. 19. Comparison of IRI-2007 with experimental data on storm day (8th Nov. 2007) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Fig. 20. Comparison of IRI-2007 with experimental data on storm day (27th Mar. 2008) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Fig. 21. Comparison of IRI-2007 with experimental data on quiet day (2nd Dec. 2008) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Fig. 22. Comparison of IRI-2007 with experimental data on storm day (13th Mar. 2009) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
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Fig. 23. Comparison of IRI-2007 with experimental data on quiet day (6th Nov. 2009) at (a) Hyderabad, (b) Libreville and (c) Brasilia.
Table 5 The RMSE of delays between experimental data and IRI-2007 for quiet and disturbed days. S.No.
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Date
29th Oct. 2003 8th Nov. 2003 22nd Jan. 2004 20th Jun. 2004 18th Jan. 2005 13th Oct. 2005 26th Jul. 2006 15th Dec. 2006 1st Apr. 2007 8th Nov. 2007 27th Mar. 2008 2nd Dec. 2008 13th Mar. 2009 6th Nov. 2009
Kp value
6 6 Kp 6 9 1 6 Kp 6 3 5 < Kp < 7 Kp 6 1 5 < Kp < 7 1 6 Kp 6 2 0 6 Kp 6 3 4 6 Kp 6 8 3 6 Kp 6 5 Kp 6 1 3 6 Kp 6 5 Kp < 1 2 6 Kp 6 5 Kp < 1
Stations Hyderabad (17.30° N, 78.55° E)
Libreville (0.35° N, 9.67° E)
Brasilia (15.94° S, 47.88° W)
8.90 m 7.27 m 4.07 m 2.91 m 5.25 m 4.04 m 4.36 m 4.38 m 3.46 m 2.99 m 3.71 m 1.99 m 4.20 m 2.10 m
9.34 m 6.45 m 3.39 m 2.18 m 3.31 m 1.72 m 2.54 m 1.78 m 2.80 m 1.99 m 2.67 m 0.71 m 1.83 m 1.47 m
14.28 m 13.9 m 10.53 m 8.07 m 11.83 m 7.75 m 8.77 m 8.59 m 2.79 m 2.96 m 3.03 m 2.21 m 2.66 m 2.73 m
calculated from IRI-2007. Therefore, improvements to the IRI model are necessary to match the actual atmospheric conditions over equatorial latitudes. 7. Conclusions The Fortran has got limited real-time interactive visualization and debugging capabilities. Also for an embedded application using Fortran requires huge assembly language programming for supporting I/O operations. Therefore, the Fortran coded IRI-2007 is converted into Matlab. The electron density profiles are generated at Toro, Nigeria for quiet and disturbed days, for Web and Matlab versions of IRI-2007 and are compared. The TEC values are calculated for the electron density profiles for web and Matlab versions of IRI-2007 using basic principle of area under curve. Further a cross validation procedure is carried out to validate the TEC from IRI Matlab using ionospheric slab thickness. It is confirmed; the developed software code is producing reliable results and compares well with Web model. Further several days of data is analyzed to comprehend the IRI model performance at equatorial latitudes. The vertical delays of GPS signals at three IGS stations
for two typical days corresponding to both quiet and disturbed days in each year from 2003 to 2009 are compared with the results due to IRI-2007. The IRI predictions are not in full agreement for both quiet and storm days with the delay variation derived from GPS data. This could be due to the effect of plasmasphere on GPS signals and requires further analysis. The best performance of IRI is noticed at low solar activity period. The minimum and maximum RMSE observed at the stations (within ±20° latitudes of equator) Libreville, Hyderabad and Brasilia are 1.99 m, 0.71 m and 2.21 m (2nd Dec. 2008, Kp < 1) and 8.90 m, 9.34 m, and 14.28 m (29th Oct. 2003, 6 6 Kp 6 9) respectively (Table 3). Therefore, to implement IRI for strategic GNSS applications, the model should be modified to take into account the effects of plasmasphere for precise TEC estimation. Acknowledgments The research work presented in this paper has been carried out under the project entitled “Investigation of Statistical Behavior of Ionosphere Over the Indian Region using GNSS data for Navigation Applications” funded by ISRO,
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