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Comparison of GPS derived TEC with the TEC predicted by IRI 2012 model in the southern Equatorial Ionization Anomaly crest within the Eastern Africa region
Accepted Manuscript Comparison of GPS derived TEC with the TEC predicted by IRI 2012 model in the Southern Equatorial Ionization Anomaly crest within the Eastern Africa Region Emmanuel Daudi Sulungu, Christian B.S. Uiso, Patrick Sibanda PII: DOI: Reference:
S0273-1177(17)30550-1 http://dx.doi.org/10.1016/j.asr.2017.07.040 JASR 13350
To appear in:
Advances in Space Research
Received Date: Revised Date: Accepted Date:
27 January 2017 22 July 2017 29 July 2017
Please cite this article as: Daudi Sulungu, E., Uiso, C.B.S., Sibanda, P., Comparison of GPS derived TEC with the TEC predicted by IRI 2012 model in the Southern Equatorial Ionization Anomaly crest within the Eastern Africa Region, Advances in Space Research (2017), doi: http://dx.doi.org/10.1016/j.asr.2017.07.040
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Comparison of GPS derived TEC with the TEC predicted by IRI 2012 model in the Southern Equatorial Ionization Anomaly crest within the Eastern Africa Region Emmanuel Daudi Sulungu1,2, Christian B.S.Uiso1 and Patrick Sibanda3 1 Department of Physics, College of Natural and Applied Sciences, University of Dar es Salaam, P.O. Box 35063, Dar es salaam, Tanzania. 2 Department of Physics, College of Natural and Mathematical Sciences, The University of Dodoma, P.O. Box 338, Dodoma, Tanzania. 3 Department of Physics, School of Natural Sciences, University of Zambia, P. O. Box 32379, Lusaka, Zambia. Authors’ emails: Uiso: [email protected] Sulungu:[email protected] Sibanda: [email protected]
Abstract We have compared the TEC obtained from the IRI-2012 model with the GPS derived TEC data recorded within southern crest of the EIA in the Eastern Africa region using the monthly means of the 5 international quiet days for equinoxes and solstices months for the period of 2012 – 2013. GPS-derived TEC data have been obtained from the Africa array and IGS network of ground based dual-frequency GPS receivers from four stations (Kigali (1.95oS, 30.09oE; Geom. Lat. 11.63oS), Malindi (2.99oS, 40.19oE; Geom. Lat. 12.42oS), Mbarara (0.60oS, 30.74oE; Geom. Lat. 10.22oS) and Nairobi (1.22oS, 36.89oE; Geom. Lat. 10.69oS)) located within the EIA crest in this region. All the three options for topside Ne of IRI-2012 model and ABT-2009 for bottomside thickness have been used to compute the IRI TEC. Also URSI coefficients were considered in this study. These results are compared with the TEC estimated from GPS measurements. Correlation Coefficients between the two sets of data, the Root-Mean Square Errors (RMSE) of the IRI-TEC from the GPS-TEC, and the percentage RMSE of the IRI-TEC from the GPS-TEC have been computed. Our general results show that IRI-2012 model with all three options overestimates the GPS-TEC for all seasons and at all stations, and IRI-2001 overestimates GPSTEC more compared with other options. IRI-Neq and IRI-01-corr are closely matching in most of the time. The observation also shows that, GPS TEC are underestimated by TEC from IRI model during noon hours, especially during equinoctial months. Further, GPS-TEC values and IRI-TEC values using all the three topside Ne options show very good correlation (above 0.8). On the other hand, the TEC using IRI-Neq and IRI-01- corr had smaller deviations from the GPS-TEC compared to the IRI-2001. Keywords: Global Positioning System (GPS), Total Electron Content (TEC), IRI model 1. Introduction The equatorial and low-latitude ionosphere is highly dynamic due to various processes like Equatorial Ionization Anomaly (EIA), Equatorial Electrojet (EEJ), and equatorial spread-F (ESF) irregularities (Abdu, 2005). The EIA occurs when the daytime eastward electric field close to the geomagnetic equatorial ionosphere produces an upward E x B drift of plasma at great heights. This plasma diffuses downwards and outwards along geomagnetic field lines towards Corresponding author: Emmanuel D. Sulungu, Email: [email protected], Phone: +255767472247 1
north and south leaving a depletion (trough) at the equator and two peaks located at approximately 15o either side from the magnetic equator (Aggarwal, 2011; Appleton, 1946; Bhuyan and Bhuyan, 2009; Martyn, 1947). The dynamic nature of low latitude ionosphere affects radio signals for navigation and communication and thus makes it challenging in modeling variability of the ionosphere. The total electron content (TEC) is an important ionospheric parameter for satellite navigation, and it is the total number of electrons between the satellite and the receiver in a column of unit cross-section area (Kumar et al., 2015). The variations of TEC aid to reveal the variations of the ionosphere which in turn affect the navigation/positioning capability of Global Positioning System (GPS) and UHF/HF communication. The measurements of TEC using the GPS are impossible from all the locations on the Earth. In order to understand how the TEC is globally distributed, it is important to have some models that will help to get data from the locations with no data. Considering this, many ionospheric models have been developed during the last several decades. Empirical models are among the types of ionospheric models that have been developed. They provide an average behavior of the ionosphere based on observational data and they are limited by the amount of the spatial and temporal coverage of the data that were used in their construction (Shim, 2009). Examples include: the NeQuick model (Radicella and Leitinger, 2001; Nigussie et al., 2012) and the International Reference Ionosphere (IRI) model (Bilitza, 1986). Despite these limitations, empirical models are widely used because of their simplicity in use. Nigussie et al. (2013) validated the NeQuick 2 and IRI-2007 models in East-African equatorial region using three GPS receivers located in Ethiopia. The IRI model is based on experimental measurements using all available ground and space data sources (Aggarwal, 2011; Bilitza et al., 2014; Chakraborty et al., 2014; Kumar et al., 2015). The IRI model is continually upgraded as new data and new modeling approaches become available, and this process has resulted in improved editions of IRI. Several studies have been done worldwide to compare the results from GPS TEC measurements and that from IRI model. These include: Akala et al. (2013) at Lagos, Nigeria and Pucallpa, Chakraborty et al. (2014), Kenpankho et al. (2011) at the equatorial latitude station in Chumphon, Thailand, Kumar et al. (2014) for a station in Singapore, Okoh et al. (2012) at Nsukka, Nigeria, Olwendo et al. (2012) at Kenyan region, Mosert et al. (2007) at Ebro in Spain, Nigussie et al. (2013) at equatorial latitudes that lie in northern part of East African region, Rathore et al. (2015) at Varanasi, India and Tariku (2015) at Ethiopia. However, comparisons between TEC based on observation and that from the models over the southern crest of the EIA lying within the Eastern Africa region are scarce. Therefore, the objective of this study was to test the applicability of the IRI-2012 model over the EIA crest lying within the Eastern Africa region by comparing it with the GPS derived TEC data recorded at four stations within the region. 2. Data source and Methods of analysis 2.1. TEC from GPS receivers GPS-derived TEC data has been obtained from the Africa array and IGS network of ground based dual-frequency GPS receivers within the southern crest of the EIA in the Eastern Africa region. Stations used are as presented in figure 1 and table 1. The data from these stations were obtained from the UNAVCO website (http://www.unavco.org/). The data from two years, (2012 -2013) which is the period of solar maximum (Figure 2 illustrates this) for the solar cycle 2
24 were used in this study. TEC is measured along the ray path from the satellite to the receiver at differing elevation angles because different GPS satellites are observed at arbitrary elevation angles, and it is known as slant TEC (TECs) (eq. 1) (Klobuchar, 1996). 1 f12 f 22 P2 P1 (1) 40.3 f12 f 22 where P1 and P2 are pseudoranges observable on L1 and L2 signals, f1 and f2 are the corresponding high and low GPS frequency respectively, derived from the fundamental frequency as; TEC
fo = 10.23 MHz: f1 = 154.fo = 1575.42 MHz and f2 = 120.fo= 1227.60 MHz To compare the electron contents for paths with different elevation angles, the TECs provided at a sampling rate of 30 s are transformed into equivalent vertical TEC (TECv) using a mapping function which takes the curvature of the Earth into account according to Klobuchar (1986) as follows: TECv M e TECS bs br brx (2) where bs is satellite bias, br is a receiver bias, brx is a receiver interchannel bias, and 1 2
2 cose M e 1 (3) 1 h RE here e is an elevation angle of a satellite, h is ionospheric shell height, taken as 400 km in this study, and RE is the Earth's mean radius. To calculate TECv, the GPS-TEC processing software developed at the Institute for Scientific Research, Boston College, U.S.A. by S. G. Krishna was used. This software reads raw data, processes cycle slips in phase data, reads satellite biases from International GNSS Service (IGS) code file (if not available, it calculates them), calculates receiver bias, and calculates the interchannel biases for different satellites in the receiver. To neglect unwanted errors due to the effect of multipath, a cut off elevation angle of 30° was used. Since many values of TECv are obtained at a time from different satellites, a running average is done to get a single curve for a day. Since the IRI model predictions are best during the geomagnetic quiet days (Chakraborty et al., 2014; Kumar et al., 2015), in this study, an hourly mean of TECv data for the international geomagnetic quiets days only from equinoxes and solstices months have been taken. In order to get the monthly mean, we have taken the mean of TECv during 5 international geomagnetic quiet days from each month considered. The international geomagnetic quiet days are given by World Data Center for Geomagnetism, Kyoto (http://wdc.kugi.kyoto-u.ac.jp/cgi-bin/qddays-cgi. TEC from IRI 2012 model To obtain TEC from the IRI model, the particular location, date, and time were used as inputs to the model. The IRI-2012 model is accessible from the IRI homepage (http://IRI.gsfc.nasa.gov). The IRI-2012 model provides three different options for the topside electron density (Ne) (IRI-Neq, IRI-2001, and IRI-01-Corr) and three options for bottomside thicknesses (Bil-2000, Gul-1987, and ABT-2009). In this study, all the three options for topside 3
Ne and ABT-2009 for bottomside thickness have been used to compute the IRI TEC. The ABT2009 model has been opted based on its improvement of up to 32% in predicting B 0 over the Bil2000 model and up to 40% over the Gul-1987 model. It has also an improvement of up to 20% for the B1 values (Bilitza et al., 2014). Further, TECv data from IRI model using URSI coefficients were considered in this study because the URSI option performs better over the areas with sparse data measurements like oceans and the southern hemisphere region ( Aggarwal, 2011). Correlation Coefficients (r) between the two sets of data, the Root-Mean Square Errors (RMSE) of the IRI-TEC from the GPS-TEC, and the percentage RMSE (PRMSE) of the IRITEC from the GPS-TEC have been computed using the following equations; (4)
(5) (6) where (7) where GPSi are GPS-TEC data, GPS is their mean, IRIi are IRI-TEC data, IRI is their mean, and n is the number of them. RMSGPS is the root-mean square value for the GPS-TEC data, and the subscripts ‘i’ denote numerical positions in the data, having integral values from 1 to n. 3. Results 3.1. Comparison of TEC from IRI-2012 Model with GPS TEC Comparison of IRI 2012 model at four stations located over the southern crest of the EIA within the Eastern Africa region has been carried out by analyzing GPS TEC and compare with the TEC obtained from IRI 2012 model for the equinoxes and solstices months of the years 2012 and 2013. Figures 3 – 6 show the comparison between the diurnal values of GPS TEC and IRI2012 TEC with three different options for topside Ne; IRI-Neq, IRI 2001, and IRI-01-Corr for the specified period. We also computed correlation coefficients between the two sets of data (Figure 7), the Root-Mean Square Errors (RMSE) of the IRI-TEC from the GPS-TEC (Figure 8), and the percentage RMSE of the IRI-TEC from the GPS-TEC (Figure 9) using equations (4), (5) and (6) respectively. From the figures 3 – 6, it can be observed that, the shape of the daily variations curves from GPS TEC and from all the three options of the IRI-2012 model are quite similar. The TEC increases gradually from sunrise, 3:00 to 4:00 UT (6:00 to 7:00 LT) in all the seasons reaching maximum values around midday, and at sunset, 15:00 to 16:00 UT (18:00 to 19:00 LT) the TEC values begin to decrease reaching minimum values around midnight. In all the cases studied, it was observed that IRI 2001 topside Ne option overestimates the GPS-TEC and also it gives the highest prediction values than other options. Figure 3(a) shows the comparison of GPS TEC and the IRI-2012 model at Kigali station using monthly means of the 5 quietest days of the equinoxes and solstices months for the year 4
2012. From the figure, it is observed that, during March equinox all the three options of the IRI model overestimated the GPS TEC in most times of the day, except during noon times where GPS TEC and TEC from IRI-Neq option were closely matching. Further, during June Solstice of the same year, GPS TEC was observed to have approximately equal values with the IRI-Neq and IRI-01-corr options especially during night times. From around 4:00 UT to 14:00 UT, all the three options of the IRI model were observed to overestimate the GPS TEC, and from around 14:00 UT to 15:00 UT, IRI-Neq had approximately equal values to GPS TEC, while IRI-2001 and IRI-01-corr had overestimations. In addition, during September equinox, there was a notable underestimation of GPS TEC by IRI-Neq and IRI-01-corr from around 11:00 UT to 17:00 UT. From around 21:00 UT, IRI-Neq and IRI-01-corr options were observed to have equal values with the GPS TEC. At other times of the day, all the three options of the IRI model were observed to overestimate the GPS TEC. During December solstice, all the three options of the IRI model showed an overestimation of GPS TEC for the entire 24 hours, except between around 13:00 UT and 16:00 UT where GPS TEC and IRI-neq have approximately equal values. For the year 2013 (figure 3(b)), during March equinox the GPS TEC are overestimated by all the three options of IRI model during night times, while an underestimations of GPS TEC by IRI-Neq was observed from around 12:00 UT to 16:00 UT and between 17:00 UT and 20:00 UT there was an overestimation. It was further noted that, during June solstice, all the three options of the IRI-2012 model were observed to have higher values than the GPS TEC throughout the day. During September equinox, an overestimation of GPS TEC by IRI model TEC was observed throughout the day. However, from about 12:00 UT to 16:00 UT, GPS TEC had close values to those of IRI-Neq option. On the other hand, during December solstice, there was an underestimation of GPS TEC by IRI-neq from about 8:00 UT to 16:00 UT, while IRI-01corr had close values to those of GPS TEC during this time. IRI-2001 options showed an overestimation during this month for the entire 24 hours. For Malindi station (figure 4(a) and 4(b)), the general observations show that, IRI-2012 model overestimated the GPS TEC, and that IRI-2001 option overestimated more than the other two options as in the previous cases. However, during March equinox of the year 2012 (figure 4(a)), IRI-Neq and IRI-01-corr options were observed to underestimate the GPS TEC during noon hours, and between 13:00 UT and 16:00 UT there was a close matching between GPS TEC and IRI-01-corr option. At other times of the day, all the three options of the IRI-2012 model were observed to overestimate the GPS TEC. The observations for June solstice show that, a good agreement between GPS TEC and IRI-Neq and IRI-01-corr options was observed during the night, i.e. between 22:00 UT and 3:00 UT. Similarly, the observations for September solstice show that, all the three options underestimate the GPS TEC between around 11:00 UT and 16:00 UT, and also there was a close consistence between GPS TEC and the IRI-Neq and IRI-01-corr options between 20:00 UT and 22:00 UT. On the other hand, December showed an overestimation of GPS TEC by all the three options of the IRI-2012 model throughout the day. Figure 4(b) shows the comparison between GPS TEC and the TEC from IRI-2012 model at Malindi station for the year 2013. From the figure it is observed that, an underestimation of GPS TEC by IRI-Neq and IRI-01-corr was observed during March equinox between 11:00 UT and 23:00 UT. However, around 12:00 UT and 16:00 UT, larger underestimations were noted compared to other periods. On the other hand, during this period of time, there was a close matching between GPS TEC and the IRI-2001 option especially from 12:00 UT to 16:00 UT, and also from 20:00 UT to 22:00 UT. Good agreement was observed between GPS TEC and the IRI-Neq and IRI-01-corr options during June solstice especially during evening and night hours. 5
All the three options of the IRI-2012 model were observed to overestimate the GPS TEC during September equinox at most of the time except around 11:00 UT and 16:00 UT where a close agreement between GPS TEC and IRI-neq TEC was observed. During December solstice, IRIneq and IRI-01.corr were observed to underestimate GPS TEC at around noon hours, and overestimate from around 0:00 UT to 7:00 UT and from 16:00 UT to 24:00 UT. IRI-2001 overestimated GPS TEC throughout the time of observation during this month. The results from Mbarara station (figure 5(a) and 5(b)) show that, there was a significant overestimation of GPS TEC by all options of the IRI-2012 model in most of the time during all seasons. For the year 2012 (figure 5(a)), there was no data for March equinox which might be due to either instrumental or power problems during this month. During June solstice, a good agreement between GPS TEC and IRI-Neq and IRI-01-corr TEC was observed during the night period, 0:00 UT to 4:00 UT. Further, the results show that, from 4:00 UT to 24:00 UT, all the three options of IRI-2012 model significantly overestimated the GPS TEC. For September equinox, the GPS TEC was observed to be higher than IRI-Neq and IRI-01-corr options, and almost equal to IRI-2001 option during the midday, whereas during the rest of time the entire three IRI-2012 model options overestimated GPS TEC. The observation from December solstice show that, from 1:00 UT to 3:00 UT, GPS TEC had higher values compared to IRI-Neq and IRI01-corr options, but less than IRI-2001 option. During the rest of time, IRI-2012 model TEC with all the three options has higher values than the GPS TEC. During March equinox of the year 2013 (figure 5(b)), GPS TEC values at Mbarara were observed to be higher than the values from IRI-Neq and IRI-01-corr options of the IRI-2012 model during the midday. For the rest of time, GPS TEC values remained to be less than the values from all options of the IRI-2012 model. During June solstice, all the three options of the IRI-2012 model overestimated the GPS TEC. An overestimation of GPS TEC by all the three options of the IRI-2012 model was noted during September equinox, and it was almost throughout the 24 hours. For December solstice, there was a close matching between the GPS TEC and the IRI-01-corr option between 8:00 UT and 16:00 UT, whereas the IRI-neq underestimated the GPS TEC during this time. At other times of the day, IRI-2012 model overestimated the GPS TEC. For Nairobi station (figure 6(a) and 6(b)), general observations show that, IRI-2012 model with all three options overestimated the GPS-TEC for all seasons and for both years, and that IRI-2001 overestimates GPS-TEC more compared with other options. During March equinox of 2012, all the three options of the IRI-2012 model overestimated GPS TEC between 0:00 UT and 12:00 UT. From approximately 12:00 UT to around 22:00 UT, IRI-Neq and IRI-01corr options are close to the GPS TEC. It was further noted that, during June solstice of the same year, IRI-Neq and IRI-01-corr closely match the GPS TEC at all time of the day, except between around 4:00 UT and 13:00 UT where an overestimation was observed. IRI-2001 was observed to overestimate the GPS TEC more than the other two options. Similar results were observed during September equinox, but IRI-Neq and IRI-01-corr were observed to underestimate the GPS TEC during the midday and during this period of time, IRI-2001 matched the GPS TEC. During December solstice, all the three options of the IRI-2012 model were observed to overestimate the GPS at most of the time, but IRI-neq closely agrees with GPS TEC values during the midday. For the year 2013 (figure 6(b)), an overestimation of the GPS TEC by all options of the IRI-2012 model was observed at most of the time during all seasons. However, during March equinox for this year, IRI-Neq and IRI-01-corr were observed to underestimate the GPS TEC 6
during the midday, while IRI-2001 option closely matched with GPS TEC during this time. During June solstice, a good agreement was observed between IRI-Neq and IRI-01-corr options and the GPS TEC. A good agreement was also noted during September equinox between GPS TEC and the IRI-Neq option during the midday. On the other hand, an overestimation of GPS TEC by all the three options of the IRI-2012 was observed at other time of the day. During December solstice, IRI-neq and IRI-01-corr were observed to underestimate GPS TEC during the midday. But, at most of the time, all the three options of the IRI-2012 model were noted to overestimate GPS TEC. Generally, from the results presented above, IRI-2012 model with all three options overestimated the GPS-TEC for all seasons and at all stations, and IRI-2001 overestimated GPSTEC more compared with other options, except for few cases as it is explained above. 3.2. Correlation coefficients, RMSE and PRMSE Correlation coefficients between the IRI-TEC values and the GPS-TEC values using the 5 quietest days’ monthly means for equinoxes and solstices months of the year 2012 and 2013 at four stations in the southern crest of the EIA within the Eastern Africa region are presented in figure 7. The RMSE of the IRI-TEC values from GPS derived TEC values are presented in figure 8, and figure 9 presents information on the PRMSE of the IRI-TEC values from GPS-TEC values for the same stations. From figure 7, it is observed that, for the year 2012, GPS-TEC values and IRI-TEC values using all the three topside Ne options show very good correlation. At most of the stations and during all seasons, it is above 0.9 which is quite strong. However, correlation coefficients at other locations are below 0.9, but above 0.7 which are also good. For example, during September equinox at Nairobi, correlation coefficients are below 0.9 but above 0.8. At Mbarara station, during December solstice, it was observed that, IRI-neq had small correlation coefficient compared to other options, and it was observed to be below 0.8. During this month, the other IRI-2001 and IRI-01-corr options had correlation coefficients less than 0.85 but above 0.8. For the year 2013, the TEC from all the three options of the IRI-2012 model and GPS TEC were observed to have correlation coefficients of above 0.9 at all locations and during all seasons. On the other hand, from figure 8 and 9 which show the RMSE and PRMSE respectively, the TEC using IRI-Neq and IRI-01- corr had small deviations from the GPS derived TEC which ranges from about 20 - 50% at most of stations compared to the IRI-2001 which goes above 100% at other stations. The maximum PRMSE for IRI-Neq option for the year 2012 was observed to be above 50%, while that given by IRI-01-corr was above 65%. Both were observed during December solstice at Nairobi. On the other hand, IRI-2001 was observed to have larger RMSE for 2012 with PRMSE of above100% and occurred during June solstice at Mbarara and during December solstice at Nairobi. However, for the year 2013, maximum PRMSE were observed to occur during September equinox at Nairobi, Mbarara and Kigali for all the three topside Ne options, as well as during June solstice at Kigali. During this period, the maximum PRMSE of both IRI-Neq TEC and IRI-01-corr TEC values from GPS-TEC values was above 40%. The IRI-2001 which was observed to have the largest deviations had the PRMSE of above 65%. Our results are in good agreement with the results from other scholars. Okoh et al. (2012) obtained that the IRI TEC values generally compared well with the GPS TEC values, with correlation coefficients as good as about 0.9, and root-mean square deviations generally around 20–50% for diurnal comparisons. This scenario of IRI-Neq and IRI-01-corr to have the least 7
deviations of IRI-TEC values from GPS TEC values compared to IRI-2001 was also observed by Rathore et al. (2015) at Varanasi, India. 4. Discussion Comparison of TEC from IRI-2012 model with all the three topside Ne options (IRI2001, IRI-Neq and IRI-01-corr) with GPS derived TEC from ground measurements at four stations in the southern crest of the EIA within Eastern Africa region has been presented. Our results show that, IRI-2012 model with all three options overestimated the GPS-TEC for all seasons and at all stations, and IRI-2001 overestimated GPS-TEC more compared with other options. In addition, an overestimation of GPS TEC by IRI-2012 model is higher during December solstice in most of the locations than other seasons for the year 2012, while for 2013, an overestimation was mostly observed during September equinox. The observation also showed that, during noon hours of equinoctial months, GPS TEC values are higher than the TEC values from IRI-neq and IRI-01-corr options. For example; during September equinox for Kigali 2012, March equinox for Kigali 2013, March and September equinoxes for Malindi 2012, March equinox for Malindi 2013, September and March equinoxes for Mbarara 2012 and 2013 respectively, March and September equinoxes for Nairobi 2012 and March equinox for Nairobi 2013. An underestimation of GPS TECv by IRI-TECv is contributed by the fact that, IRI-TECv does not include plasmasphere TEC. It is well known that, the percentage of plasmaspheric contribution to GPS TECv is much larger during the nighttime hours than the daytime hours (Kumar et al., 2015; Yizengaw et al., 2008). Therefore, it was expected for the IRI model to underestimate the GPS-TEC during the nighttime than the daytime. However, in this study, the IRI TECv from IRI-neq and IRI-01-corr options exhibited an underestimation from the derived GPS-TEC during the day. This high plasmaspheric contribution to GPS TEC during the day might have been caused by the equatorial electrodynamics that governs the density distribution, including the plasma exchange between the ionosphere and plasmasphere (Yizengaw et al., 2008). Our results agree with the previous studies. For example: Chakraborty et al. (2014) compared the GPS TEC and IRI-2012 TEC using four stations from equatorial to mid-latitudes and found that the TEC with topside option IRI-2001 overestimates the observed GPS TEC in low latitude regions in most of the times and the TEC from other two options of IRI are in consistent with the observed TEC data. Kumar et al. (2014) on their study on validation of the IRI-2012 model with GPS-based ground observations over a low-latitude Singapore station found that, for the year 2010, the IRI-2001 model overestimates, while IRI-Neq and IRI-01-corr underestimates the GPS-TEC and for the year 2011, the IRI-2012 model with all three options IRI-neq, IRI-2001, and IRI-01-corr underestimates the GPS-TEC. Their results further revealed that, the IRI-neq and IRI-01-corr options agree well with GPS-TEC at all times during the summer season only, while during the winter season and equinox, these two options show agreement with GPS only at nighttime for the year 2011. However, the IRI-2001 model overestimates the GPS-TEC during all seasons and also does not show agreement with GPS TEC. The results by Kenpankho et al. (2011) using IRI 2007 model at Chumphon, Thailand, showed that, the IRI-2007 model agrees well with the GPS TEC data mostly in the morning hours, but underestimates the GPS TEC at daytime than nighttime, particularly during the noon bite outs. Recently, Kumar et al. (2015) studied the TEC variation over an equatorial and anomaly crest region in India during 2012 and 2013 and found that, the IRI-2001 topside option overestimates the observed GPS-TEC at Lucknow most of the times during 2012–2013while the other two options (IRI-Neq and IRI01-corr) had close agreement with the GPS TEC.
8
The disagreements of the GPS TEC values and those estimated by IRI 2012 model is due to the relatively small amount of data from the region considered in developing the model (Adewale et al., 2011), in our case, the Eastern Africa region. Since the IRI model depends on the primary database, it’s accuracy in a specific region depends on the availability of reliable data for the region. Bilitza and Reinisch (2008) mentioned the inadequacy of ionospheric data over the African equatorial region as a factor that contributes to the diminished accuracies of the IRI predictions over this region. Additionally, the TEC from IRI model is calculated from foF2 by calculating the height profile of electron density based on the foF2, step by step. Then the density profile is integrated along the vertical line to obtain TEC. During all these procedures, the modeling of the topside electron density may not be done accurately. Therefore, an overestimation of TEC by the IRI model as observed in this study during the time of observation may be due to inaccurate prediction of foF2 by the IRI model (Chakraborty et al., 2014; Kumar et al., 2015; Rathore et al., 2015). Kumar et al. (2015) on their study on TEC variation over an equatorial and anomaly crest region in India during 2012 and 2013, proposed the discrepancies in the F2 peak parameters estimated by the IRI model, which are larger at lower latitudes regions as the sources of the large discrepancies in estimating the GPS TEC by IRI model. They further suggested that, an inaccuracy in estimation of slab thickness which is related to foF2 or equivalent NmF2 from the coefficients of the IRI models may contribute to the largest discrepancies in the TEC predicted by the IRI-model with the measured GPS-TEC observed during the December solstice. On the other hand, an underestimation of GPS TEC by IRI-model during noon hours is suggested to be due to the ionization contribution from the equator which affects the ionosphere over the equatorial anomaly region producing an electron density profile broader during noon time than those presumed by the model (Ezquer et al., 1995). Another likely reason for the daytime discrepancy in the IRI-2012 model as suggested by Kenpankho et al. (2011) and Kumar et al. (2015) is the daytime ionospheric expansion which causes a larger slab thickness to be covered at around noon time as compared to other times. Similarly, the reason for an underestimation of GPS TEC during equinoctial months might be due to the fact that, the IRI model does not take into consideration the actual ionisation rate of equatorial ionosphere during these seasons (Leong et al., 2014). 5. Conclusions We have analyzed the results of TECv variations from IRI-2012 model using all the three topside Ne option (IRI-neq, IRI-2001 and IRI-01-corr) at four stations located within the southern crest of the EIA in Eastern Africa region. The analysis has been done by comparing the IRI TECv with the ground based GPS TECv measurements using monthly means of the 5 international quiet days for equinoxes and solstices months for 2012-2013. We also computed Correlation Coefficients between the two sets of data, the Root-Mean Square Errors (RMSE) of the IRI-TECv from the GPS-TECv and the percentage RMSE of the IRI-TECv from the GPSTECv. The general results show that, IRI-2012 model with all three topside options overestimates the GPS-TECv for all seasons and at all stations, and IRI-2001 overestimates GPSTECv more compared with other options, except for few cases as it is explained above. On the other hand, IRI-neq and IRI-01-corr are closely matching in most of the time. Further, during noon hours of equinoctial months, GPS TECv values are higher than the TECv values from IRIneq and IRI-01-corr options. It was further observed that, GPS-TECv values and IRI-TECv values using all the three topside Ne options show very good correlation (above 0.8) at most of 9
time. On the other hand, the TECv using IRI-neq and IRI-01- corr had small PRMSE from the GPS measured TECv compared to the IRI-2001. The discrepancy of IRI TECv from GPS TECv could be attributed mainly to the relative small amount of data within the eastern Africa region. In addition, an overestimation of TECv by the IRI model as observed in this study might be contributed by an inaccurate prediction of foF2 by the IRI model. Similarly, an underestimation of GPS TECv by IRI-model during noon hours is suggested to be due to the ionization contribution from the equator which affects the ionosphere over the equatorial anomaly region producing an electron density profile broader during noon time than those presumed by the model. Likewise, an underestimation in IRI-TECv is contributed by the fact that, IRI-TECv does not include plasmasphere TECv as GPS TECv does. This high plasmaspheric contribution to GPS TECv during the day might have been caused by the equatorial electrodynamics that governs the density distribution, including the plasma exchange between the ionosphere and plasmasphere. In addition to that, an underestimation of GPS TECv observed during equinoctial months implies that the IRI model does not take into consideration the actual ionisation rate of equatorial ionosphere during these seasons. Acknowledgement: We express our thanks to the University of Dodoma for funding this study. The authors are also thankful to the International GNSS Service (IGS) for providing the access to the GPS data. We finally acknowledge Dr. Gopi Seemala for providing access to the GPS-TEC analysis software used in this work. References Abdu, M. A., Batista, I. S., Carrasco, A. J., and Brum, C. G. M., 2005. South Atlantic magnetic anomaly ionization: A review and a new focus on electrodynamic effects in the equatorial ionosphere, Journal of Atmospheric and Solar Terrestrial Physics 67, 1643–1657. Adewale A.O., Oyeyemi E.O., Adeniyi J.O., Adeloye A.B. and Oladipo O.A., 2011. Comparison of total eletcron content predicted using the IRI-2007 model with GPS observations over lagos, Nigeria. Indian Journal of Radio and Space Physics 40, 21-25. Aggarwal, M., 2011. TEC variability near northern EIA crest and comparison with IRI model. Advances in Space Research 48, 1221–1231. Akala, A.O., Seemala, G. K., Doherty, P.H., Valladares, C.E., Carrano, C.S., Espinoza, J. and Oluyo, S., 2013. Comparison of Equatorial GPS-TEC observations over an African station and an American station during the minimum and ascending phases of solar cycle 24. Annals of Geophysics 31, 2085–2096. Appleton E.V., 1946. Two anomalies in ionosphere. Nature 157, 691–693. Bilitza, B. and Reinisch, B.W., 2008. International Reference Ionosphere 2007: Improvements and new parameters. Advances in Space Research 42, 599–609. Bilitza, D., Altadill, D., Zhang, Y., Mertens, C., Truhlik, V., Richards, P., McKinnell, L. and Reinisch, B., 2014. The International Reference Ionosphere 2012 – a Model of International collaboration. Journal of Space Weather and Space Climate 4, A07.
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Bilitza, D., 1986. International reference ionosphere: recent developments, Radio Science 21, 343–346, Doi: 10.1029/RS021i003p00343. Bhuyan, P. K. and Bhuyan, K., 2009. The equatorial ionization anomaly at the topside F region of the ionosphere along 75oE. Advances in Space Research 43, 1676–1682. Chakraborty, M., Kumar, S., Kumar, De B., Guha , A., 2014. Latitudinal characteristics of GPS derived ionospheric TEC: a comparative study with IRI 2012 model. Annals of Geophysics 57 (5) A0539; Doi: 10.4401/Ag-6438. Ezquer, R. G., Ortiz de Adler, N., Radicella, S. M. Mosert de Gonzalez, M. and Manzano, J. R., 1995. IRI and BPM Total Electron Content Predictions for Tucuman. Advances in Space Research 15 (2) 121-124. Kenpankho, P., Watthanasangmechai, K., Supnithi P., Tsugawa, T. and Maruyama, T., 2011. Comparison of GPS TEC measurements with IRI TEC prediction at the equatorial latitude station, Chumphon, Thailand. Earth Planets and Space 63, 365–370. Klobuchar, J., 1986. Design and characteristics of the GPS ionospheric time delay algorithm for single frequency users, in: Proceedings of PLANS’86 – Position Location and Navigation Symposium, Las Vegas, Nevada, 4–7 November, 280–286. Klobuchar, J. A., 1996. Ionospheric effects on GPS, in: Global Positioning System: Theory and application Vol. 1, edited by: Parkinson, B. W. and Spilker, J. J., American Institute of Aeronautics and Astronautics INC. Washington DC, 485–515. Kumar, S., Patel, K. and Singh, A.K., 2015. TEC variation over an equatorial and anomaly crest region in India during 2012 and 2013. GPS Solution 20 (4), 617-626 DOI 10.1007/s10291-0150470-4. Kumar, S., Tan, E. L., Razul, S. G., See, C. M. S. and Siingh, D., 2014. Validation of the IRI2012 model with GPS-based ground observation over a low-latitude Singapore station. Earth. Planets and Space 66 (17), 1-10. Leong, S. K, Musa, T. A., Omar, K., Subari, M. D., Pathy, N. B., and Asillam, M. F., 2015. Assessment of ionosphere models at Banting: Performance of IRI-2007, IRI-2012 and NeQuick 2 models during the ascending phase of Solar Cycle 24. Advances in Space Research, 55 (8), 1928-1940. Martyn, D.F., 1947. Atmospheric tides in the ionosphere. I. Solar tides in the F2 region. Proceedings of the Royal Society of London. A, Mathematical and Physical Sciences 189, 241– 260. Mosert, M., Gende, M., Brunini, C., Ezquer, R., Altadill, D., 2007. Comparisons of IRI TEC predictions with GPS and digisonde measurements at Ebro. Advances in Space Research 39, 841–847. Nigussie, M., Radicella, S.M., Damtie, B., Nava, B., Yizengaw, E. and Ciraolo, L., 2012. TEC ingestion into NeQuick 2 to model the East African equatorial ionosphere. Radio Science 47 (5) RS5002.
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Nigussie, M., Radicella, S. M., Damtie, B., Nava, B., Yizengaw, E. and Groves, K., 2013. Validation of the NeQuick 2 and IRI-2007 models in East-African equatorial region. Journal of Atmospheric and Solar Terrestrial Physics 102, 26–33. Okoh, D., Eze A., Adedoja, O., Okere, B. and Okeke, P.K., 2012. A comparison of IRI-TEC predictions with GPS-TEC measurements over Nsukka, Nigeria. Space Weather 10, S10002, Doi:10.1029/2012SW000830. Olwendo O. J., Baki P., Cilliers P.J., Mito C., Doherty P., 2012. Comparison of GPS TEC measurements with IRI-2007 TEC prediction over the Kenyan region during the descending phase of solar cycle 23. Advances in Space Research 49, 914–921. Radicella, S.M., Leitinger, R., 2001.The evolution of the DGR approach to model electron density profiles. Advances in Space Research 27, 35–40. Rathore, V.S., Kumar, S., Singh, A.K., 2015. A statistical comparison of IRI TEC prediction with GPS TEC measurement over Varanasi. Journal of Atmospheric and Solar Terrestrial Physics 124, 1–9 Shim, J. S., 2009. Analysis of Total Electron Content (TEC) variations in the low and middle latitude ionosphere. PhD Thesis, Department of Physics, Utah State University. Tariku Y. A., 2015. TEC prediction performance of the IRI-2012 model over Ethiopia during the rising phase of solar cycle 24 (2009–2011). Earth, Planets and Space 67, 140 Doi: 10.1186/s40623-015-0312-1. Yizengaw, E., Moldwin, M.B., Galvan, D., Iijima, B.A., Komjathy, A., Mannucci, A.J., 2008. Global plasmaspheric TEC and its relative contribution to GPS TEC. Journal of Atmospheric and Solar-Terrestrial Physics 70, 1541– 1548.
List of tables Table 1: Stations co-ordinates
Figure captions Figure 1: The map view of the locations of the stations used Figure 2: International SSN for the last five cycles (http://www.sidc.be/silso/datafiles) Figure 3: Comparison of GPS TEC and IRI-2012 model TEC from the monthly means of the 5 quietest days of the equinoxes and solstices months at Kigali for (a) 2012 (left panel) (b) 2013 (right panel) Figure 4: Comparison of GPS TEC and IRI-2012 model TEC from the monthly means of the 5 quietest days of the equinoxes and solstices months at Malindi for (a) 2012 (left panel) (b) 2013 (right panel)
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Figure 5: Comparison of GPS TEC and IRI-2012 model TEC from the monthly means of the 5 quietest days of the equinoxes and solstices months at Mbarara for (a) 2012 (left panel) (b) 2013 (right panel) Figure 6: Comparison of GPS TEC and IRI-2012 model TEC from the monthly means of the 5 quietest days of the equinoxes and solstices months at Nairobi for (a) 2012 (left panel) (b) 2013 (right panel) Figure 7: Correlation coefficients between the IRI-TEC values and the GPS-TEC values using monthly means of the 5 quietest days for equinoxes and solstices months of the year (a) 2012 (left panel) (b) 2013 (right panel) Figure 8: Root mean square errors of the IRI-TEC values from the GPS-TEC values using monthly means of the 5 quietest days for equinoxes and solstices months of the year (a) 2012 (left panel) (b) 2013 (right panel) Figure 9: Percentage root mean square errors of the IRI-TEC values from the GPS-TEC values using monthly means of the 5 quietest days for equinoxes and solstices months of the year (a) 2012 (left panel) (b) 2013 (right panel)
13
List of figures for web version
Figure 1
Figure 2
14
TECU
80 60 40 20 0
0 80 60 40 20 0 0 80
Kigali, March 2012
4
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Kigali, June 2012
4 8 12 16 20 Kigali, September 2012
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Kigali, March 2013
IRI-neq IRI-01-corr 0
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8 12 16 Time (Hours) UT (a)
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0 80 60
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Figure 3
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Figure 4
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Mbarara, June 2012
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Figure 5
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IRI-2001
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60
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Nairobi, March 2012
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8 12 16 20 Time (Hours) UT (a)
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IRI-01-corr 8 12 16 Nairobi, June 2013
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GPS IRI-neq
0 0 80
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Nairobi, March 2013
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Figure 6
18
8 12 16 20 Time (Hours) UT (b)
Correlation coefficients
IRI-2001 1.05 1 0.95 0.9 0.85 0.8 1 0.95
IRI-01-corr 1 0.95
Malindi, 2012
0.85 Mar
Jun Sep Nairobi, 2012
0.8 1 0.95
Dec
0.9
0.85
0.85 Mar
Jun Sep Mbarara, 2012
0.8 1 0.95
Dec
Mar
Jun Sep Nairobi, 2013
Dec
Mar
Jun Sep Mbarara, 2013
Dec
Mar
Jun Sep Kigali, 2013
Dec
0.9 0.85 Mar
Jun Sep Kigali, 2012
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Dec
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0.95
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Malindi, 2013
0.9
0.9 0.8 1 0.95 0.9 0.85 0.8 0.75 1
IRI-neq
0.8 Mar
Jun
Sep
Dec
(a)
Mar
Jun
Sep (b)
Figure 7
19
Dec
IRI-2001
RMSE (TECU)
20 15 10 5 0 25 20 15 10 5 0 25 20 15 10 5 0 25 20 15 10 5 0
Malindi, 2012
Mar Jun Sep Nairobi, 2012
Dec
Mar Jun Sep Mbarara, 2012
Dec
Mar
Dec
Mar
Jun Sep Kigali, 2012
Jun
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IRI-01-corr IRI-neq 20 Malindi, 2013 15 10 5 0 Mar Jun 25 Nairobi, 2013 20 15 10 5 0 Mar Jun 25 Mbarara, 2013 20 15 10 5 0 Mar Jun 25 Kigali, 2013 20 15 10 5 0 Mar Jun (b)
Figure 8
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Sep
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Dec
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100 80 60 40 20 0 120 100 80 60 40 20 0 120 100 80 60 40 20 0 100 80 60 40 20 0
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Malindi, 2012
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Jun (b)
Figure 9
21
List of tables
Table 1 Station
Code
Geographic co-ordinates Latitude Longitude
Magnetic co-ordinates Latitude Longitude
Kigali
NURK
1.95oS
30.09oE
11.63oS
101.66oE
Malindi
MAL2
2.99oS
40.19oE
12.42oS
111.86oE
Mbarara MBAR
0.60oS
30.74oE
10.22oS
102.36oE
Nairobi
1.22oS
36.89oE
10.69oS
108.59oE
RCMN
22
S0273-1177(17)30550-1 http://dx.doi.org/10.1016/j.asr.2017.07.040 JASR 13350
To appear in:
Advances in Space Research
Received Date: Revised Date: Accepted Date:
27 January 2017 22 July 2017 29 July 2017
Please cite this article as: Daudi Sulungu, E., Uiso, C.B.S., Sibanda, P., Comparison of GPS derived TEC with the TEC predicted by IRI 2012 model in the Southern Equatorial Ionization Anomaly crest within the Eastern Africa Region, Advances in Space Research (2017), doi: http://dx.doi.org/10.1016/j.asr.2017.07.040
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Comparison of GPS derived TEC with the TEC predicted by IRI 2012 model in the Southern Equatorial Ionization Anomaly crest within the Eastern Africa Region Emmanuel Daudi Sulungu1,2, Christian B.S.Uiso1 and Patrick Sibanda3 1 Department of Physics, College of Natural and Applied Sciences, University of Dar es Salaam, P.O. Box 35063, Dar es salaam, Tanzania. 2 Department of Physics, College of Natural and Mathematical Sciences, The University of Dodoma, P.O. Box 338, Dodoma, Tanzania. 3 Department of Physics, School of Natural Sciences, University of Zambia, P. O. Box 32379, Lusaka, Zambia. Authors’ emails: Uiso: [email protected] Sulungu:[email protected] Sibanda: [email protected]
Abstract We have compared the TEC obtained from the IRI-2012 model with the GPS derived TEC data recorded within southern crest of the EIA in the Eastern Africa region using the monthly means of the 5 international quiet days for equinoxes and solstices months for the period of 2012 – 2013. GPS-derived TEC data have been obtained from the Africa array and IGS network of ground based dual-frequency GPS receivers from four stations (Kigali (1.95oS, 30.09oE; Geom. Lat. 11.63oS), Malindi (2.99oS, 40.19oE; Geom. Lat. 12.42oS), Mbarara (0.60oS, 30.74oE; Geom. Lat. 10.22oS) and Nairobi (1.22oS, 36.89oE; Geom. Lat. 10.69oS)) located within the EIA crest in this region. All the three options for topside Ne of IRI-2012 model and ABT-2009 for bottomside thickness have been used to compute the IRI TEC. Also URSI coefficients were considered in this study. These results are compared with the TEC estimated from GPS measurements. Correlation Coefficients between the two sets of data, the Root-Mean Square Errors (RMSE) of the IRI-TEC from the GPS-TEC, and the percentage RMSE of the IRI-TEC from the GPS-TEC have been computed. Our general results show that IRI-2012 model with all three options overestimates the GPS-TEC for all seasons and at all stations, and IRI-2001 overestimates GPSTEC more compared with other options. IRI-Neq and IRI-01-corr are closely matching in most of the time. The observation also shows that, GPS TEC are underestimated by TEC from IRI model during noon hours, especially during equinoctial months. Further, GPS-TEC values and IRI-TEC values using all the three topside Ne options show very good correlation (above 0.8). On the other hand, the TEC using IRI-Neq and IRI-01- corr had smaller deviations from the GPS-TEC compared to the IRI-2001. Keywords: Global Positioning System (GPS), Total Electron Content (TEC), IRI model 1. Introduction The equatorial and low-latitude ionosphere is highly dynamic due to various processes like Equatorial Ionization Anomaly (EIA), Equatorial Electrojet (EEJ), and equatorial spread-F (ESF) irregularities (Abdu, 2005). The EIA occurs when the daytime eastward electric field close to the geomagnetic equatorial ionosphere produces an upward E x B drift of plasma at great heights. This plasma diffuses downwards and outwards along geomagnetic field lines towards Corresponding author: Emmanuel D. Sulungu, Email: [email protected], Phone: +255767472247 1
north and south leaving a depletion (trough) at the equator and two peaks located at approximately 15o either side from the magnetic equator (Aggarwal, 2011; Appleton, 1946; Bhuyan and Bhuyan, 2009; Martyn, 1947). The dynamic nature of low latitude ionosphere affects radio signals for navigation and communication and thus makes it challenging in modeling variability of the ionosphere. The total electron content (TEC) is an important ionospheric parameter for satellite navigation, and it is the total number of electrons between the satellite and the receiver in a column of unit cross-section area (Kumar et al., 2015). The variations of TEC aid to reveal the variations of the ionosphere which in turn affect the navigation/positioning capability of Global Positioning System (GPS) and UHF/HF communication. The measurements of TEC using the GPS are impossible from all the locations on the Earth. In order to understand how the TEC is globally distributed, it is important to have some models that will help to get data from the locations with no data. Considering this, many ionospheric models have been developed during the last several decades. Empirical models are among the types of ionospheric models that have been developed. They provide an average behavior of the ionosphere based on observational data and they are limited by the amount of the spatial and temporal coverage of the data that were used in their construction (Shim, 2009). Examples include: the NeQuick model (Radicella and Leitinger, 2001; Nigussie et al., 2012) and the International Reference Ionosphere (IRI) model (Bilitza, 1986). Despite these limitations, empirical models are widely used because of their simplicity in use. Nigussie et al. (2013) validated the NeQuick 2 and IRI-2007 models in East-African equatorial region using three GPS receivers located in Ethiopia. The IRI model is based on experimental measurements using all available ground and space data sources (Aggarwal, 2011; Bilitza et al., 2014; Chakraborty et al., 2014; Kumar et al., 2015). The IRI model is continually upgraded as new data and new modeling approaches become available, and this process has resulted in improved editions of IRI. Several studies have been done worldwide to compare the results from GPS TEC measurements and that from IRI model. These include: Akala et al. (2013) at Lagos, Nigeria and Pucallpa, Chakraborty et al. (2014), Kenpankho et al. (2011) at the equatorial latitude station in Chumphon, Thailand, Kumar et al. (2014) for a station in Singapore, Okoh et al. (2012) at Nsukka, Nigeria, Olwendo et al. (2012) at Kenyan region, Mosert et al. (2007) at Ebro in Spain, Nigussie et al. (2013) at equatorial latitudes that lie in northern part of East African region, Rathore et al. (2015) at Varanasi, India and Tariku (2015) at Ethiopia. However, comparisons between TEC based on observation and that from the models over the southern crest of the EIA lying within the Eastern Africa region are scarce. Therefore, the objective of this study was to test the applicability of the IRI-2012 model over the EIA crest lying within the Eastern Africa region by comparing it with the GPS derived TEC data recorded at four stations within the region. 2. Data source and Methods of analysis 2.1. TEC from GPS receivers GPS-derived TEC data has been obtained from the Africa array and IGS network of ground based dual-frequency GPS receivers within the southern crest of the EIA in the Eastern Africa region. Stations used are as presented in figure 1 and table 1. The data from these stations were obtained from the UNAVCO website (http://www.unavco.org/). The data from two years, (2012 -2013) which is the period of solar maximum (Figure 2 illustrates this) for the solar cycle 2
24 were used in this study. TEC is measured along the ray path from the satellite to the receiver at differing elevation angles because different GPS satellites are observed at arbitrary elevation angles, and it is known as slant TEC (TECs) (eq. 1) (Klobuchar, 1996). 1 f12 f 22 P2 P1 (1) 40.3 f12 f 22 where P1 and P2 are pseudoranges observable on L1 and L2 signals, f1 and f2 are the corresponding high and low GPS frequency respectively, derived from the fundamental frequency as; TEC
fo = 10.23 MHz: f1 = 154.fo = 1575.42 MHz and f2 = 120.fo= 1227.60 MHz To compare the electron contents for paths with different elevation angles, the TECs provided at a sampling rate of 30 s are transformed into equivalent vertical TEC (TECv) using a mapping function which takes the curvature of the Earth into account according to Klobuchar (1986) as follows: TECv M e TECS bs br brx (2) where bs is satellite bias, br is a receiver bias, brx is a receiver interchannel bias, and 1 2
2 cose M e 1 (3) 1 h RE here e is an elevation angle of a satellite, h is ionospheric shell height, taken as 400 km in this study, and RE is the Earth's mean radius. To calculate TECv, the GPS-TEC processing software developed at the Institute for Scientific Research, Boston College, U.S.A. by S. G. Krishna was used. This software reads raw data, processes cycle slips in phase data, reads satellite biases from International GNSS Service (IGS) code file (if not available, it calculates them), calculates receiver bias, and calculates the interchannel biases for different satellites in the receiver. To neglect unwanted errors due to the effect of multipath, a cut off elevation angle of 30° was used. Since many values of TECv are obtained at a time from different satellites, a running average is done to get a single curve for a day. Since the IRI model predictions are best during the geomagnetic quiet days (Chakraborty et al., 2014; Kumar et al., 2015), in this study, an hourly mean of TECv data for the international geomagnetic quiets days only from equinoxes and solstices months have been taken. In order to get the monthly mean, we have taken the mean of TECv during 5 international geomagnetic quiet days from each month considered. The international geomagnetic quiet days are given by World Data Center for Geomagnetism, Kyoto (http://wdc.kugi.kyoto-u.ac.jp/cgi-bin/qddays-cgi. TEC from IRI 2012 model To obtain TEC from the IRI model, the particular location, date, and time were used as inputs to the model. The IRI-2012 model is accessible from the IRI homepage (http://IRI.gsfc.nasa.gov). The IRI-2012 model provides three different options for the topside electron density (Ne) (IRI-Neq, IRI-2001, and IRI-01-Corr) and three options for bottomside thicknesses (Bil-2000, Gul-1987, and ABT-2009). In this study, all the three options for topside 3
Ne and ABT-2009 for bottomside thickness have been used to compute the IRI TEC. The ABT2009 model has been opted based on its improvement of up to 32% in predicting B 0 over the Bil2000 model and up to 40% over the Gul-1987 model. It has also an improvement of up to 20% for the B1 values (Bilitza et al., 2014). Further, TECv data from IRI model using URSI coefficients were considered in this study because the URSI option performs better over the areas with sparse data measurements like oceans and the southern hemisphere region ( Aggarwal, 2011). Correlation Coefficients (r) between the two sets of data, the Root-Mean Square Errors (RMSE) of the IRI-TEC from the GPS-TEC, and the percentage RMSE (PRMSE) of the IRITEC from the GPS-TEC have been computed using the following equations; (4)
(5) (6) where (7) where GPSi are GPS-TEC data, GPS is their mean, IRIi are IRI-TEC data, IRI is their mean, and n is the number of them. RMSGPS is the root-mean square value for the GPS-TEC data, and the subscripts ‘i’ denote numerical positions in the data, having integral values from 1 to n. 3. Results 3.1. Comparison of TEC from IRI-2012 Model with GPS TEC Comparison of IRI 2012 model at four stations located over the southern crest of the EIA within the Eastern Africa region has been carried out by analyzing GPS TEC and compare with the TEC obtained from IRI 2012 model for the equinoxes and solstices months of the years 2012 and 2013. Figures 3 – 6 show the comparison between the diurnal values of GPS TEC and IRI2012 TEC with three different options for topside Ne; IRI-Neq, IRI 2001, and IRI-01-Corr for the specified period. We also computed correlation coefficients between the two sets of data (Figure 7), the Root-Mean Square Errors (RMSE) of the IRI-TEC from the GPS-TEC (Figure 8), and the percentage RMSE of the IRI-TEC from the GPS-TEC (Figure 9) using equations (4), (5) and (6) respectively. From the figures 3 – 6, it can be observed that, the shape of the daily variations curves from GPS TEC and from all the three options of the IRI-2012 model are quite similar. The TEC increases gradually from sunrise, 3:00 to 4:00 UT (6:00 to 7:00 LT) in all the seasons reaching maximum values around midday, and at sunset, 15:00 to 16:00 UT (18:00 to 19:00 LT) the TEC values begin to decrease reaching minimum values around midnight. In all the cases studied, it was observed that IRI 2001 topside Ne option overestimates the GPS-TEC and also it gives the highest prediction values than other options. Figure 3(a) shows the comparison of GPS TEC and the IRI-2012 model at Kigali station using monthly means of the 5 quietest days of the equinoxes and solstices months for the year 4
2012. From the figure, it is observed that, during March equinox all the three options of the IRI model overestimated the GPS TEC in most times of the day, except during noon times where GPS TEC and TEC from IRI-Neq option were closely matching. Further, during June Solstice of the same year, GPS TEC was observed to have approximately equal values with the IRI-Neq and IRI-01-corr options especially during night times. From around 4:00 UT to 14:00 UT, all the three options of the IRI model were observed to overestimate the GPS TEC, and from around 14:00 UT to 15:00 UT, IRI-Neq had approximately equal values to GPS TEC, while IRI-2001 and IRI-01-corr had overestimations. In addition, during September equinox, there was a notable underestimation of GPS TEC by IRI-Neq and IRI-01-corr from around 11:00 UT to 17:00 UT. From around 21:00 UT, IRI-Neq and IRI-01-corr options were observed to have equal values with the GPS TEC. At other times of the day, all the three options of the IRI model were observed to overestimate the GPS TEC. During December solstice, all the three options of the IRI model showed an overestimation of GPS TEC for the entire 24 hours, except between around 13:00 UT and 16:00 UT where GPS TEC and IRI-neq have approximately equal values. For the year 2013 (figure 3(b)), during March equinox the GPS TEC are overestimated by all the three options of IRI model during night times, while an underestimations of GPS TEC by IRI-Neq was observed from around 12:00 UT to 16:00 UT and between 17:00 UT and 20:00 UT there was an overestimation. It was further noted that, during June solstice, all the three options of the IRI-2012 model were observed to have higher values than the GPS TEC throughout the day. During September equinox, an overestimation of GPS TEC by IRI model TEC was observed throughout the day. However, from about 12:00 UT to 16:00 UT, GPS TEC had close values to those of IRI-Neq option. On the other hand, during December solstice, there was an underestimation of GPS TEC by IRI-neq from about 8:00 UT to 16:00 UT, while IRI-01corr had close values to those of GPS TEC during this time. IRI-2001 options showed an overestimation during this month for the entire 24 hours. For Malindi station (figure 4(a) and 4(b)), the general observations show that, IRI-2012 model overestimated the GPS TEC, and that IRI-2001 option overestimated more than the other two options as in the previous cases. However, during March equinox of the year 2012 (figure 4(a)), IRI-Neq and IRI-01-corr options were observed to underestimate the GPS TEC during noon hours, and between 13:00 UT and 16:00 UT there was a close matching between GPS TEC and IRI-01-corr option. At other times of the day, all the three options of the IRI-2012 model were observed to overestimate the GPS TEC. The observations for June solstice show that, a good agreement between GPS TEC and IRI-Neq and IRI-01-corr options was observed during the night, i.e. between 22:00 UT and 3:00 UT. Similarly, the observations for September solstice show that, all the three options underestimate the GPS TEC between around 11:00 UT and 16:00 UT, and also there was a close consistence between GPS TEC and the IRI-Neq and IRI-01-corr options between 20:00 UT and 22:00 UT. On the other hand, December showed an overestimation of GPS TEC by all the three options of the IRI-2012 model throughout the day. Figure 4(b) shows the comparison between GPS TEC and the TEC from IRI-2012 model at Malindi station for the year 2013. From the figure it is observed that, an underestimation of GPS TEC by IRI-Neq and IRI-01-corr was observed during March equinox between 11:00 UT and 23:00 UT. However, around 12:00 UT and 16:00 UT, larger underestimations were noted compared to other periods. On the other hand, during this period of time, there was a close matching between GPS TEC and the IRI-2001 option especially from 12:00 UT to 16:00 UT, and also from 20:00 UT to 22:00 UT. Good agreement was observed between GPS TEC and the IRI-Neq and IRI-01-corr options during June solstice especially during evening and night hours. 5
All the three options of the IRI-2012 model were observed to overestimate the GPS TEC during September equinox at most of the time except around 11:00 UT and 16:00 UT where a close agreement between GPS TEC and IRI-neq TEC was observed. During December solstice, IRIneq and IRI-01.corr were observed to underestimate GPS TEC at around noon hours, and overestimate from around 0:00 UT to 7:00 UT and from 16:00 UT to 24:00 UT. IRI-2001 overestimated GPS TEC throughout the time of observation during this month. The results from Mbarara station (figure 5(a) and 5(b)) show that, there was a significant overestimation of GPS TEC by all options of the IRI-2012 model in most of the time during all seasons. For the year 2012 (figure 5(a)), there was no data for March equinox which might be due to either instrumental or power problems during this month. During June solstice, a good agreement between GPS TEC and IRI-Neq and IRI-01-corr TEC was observed during the night period, 0:00 UT to 4:00 UT. Further, the results show that, from 4:00 UT to 24:00 UT, all the three options of IRI-2012 model significantly overestimated the GPS TEC. For September equinox, the GPS TEC was observed to be higher than IRI-Neq and IRI-01-corr options, and almost equal to IRI-2001 option during the midday, whereas during the rest of time the entire three IRI-2012 model options overestimated GPS TEC. The observation from December solstice show that, from 1:00 UT to 3:00 UT, GPS TEC had higher values compared to IRI-Neq and IRI01-corr options, but less than IRI-2001 option. During the rest of time, IRI-2012 model TEC with all the three options has higher values than the GPS TEC. During March equinox of the year 2013 (figure 5(b)), GPS TEC values at Mbarara were observed to be higher than the values from IRI-Neq and IRI-01-corr options of the IRI-2012 model during the midday. For the rest of time, GPS TEC values remained to be less than the values from all options of the IRI-2012 model. During June solstice, all the three options of the IRI-2012 model overestimated the GPS TEC. An overestimation of GPS TEC by all the three options of the IRI-2012 model was noted during September equinox, and it was almost throughout the 24 hours. For December solstice, there was a close matching between the GPS TEC and the IRI-01-corr option between 8:00 UT and 16:00 UT, whereas the IRI-neq underestimated the GPS TEC during this time. At other times of the day, IRI-2012 model overestimated the GPS TEC. For Nairobi station (figure 6(a) and 6(b)), general observations show that, IRI-2012 model with all three options overestimated the GPS-TEC for all seasons and for both years, and that IRI-2001 overestimates GPS-TEC more compared with other options. During March equinox of 2012, all the three options of the IRI-2012 model overestimated GPS TEC between 0:00 UT and 12:00 UT. From approximately 12:00 UT to around 22:00 UT, IRI-Neq and IRI-01corr options are close to the GPS TEC. It was further noted that, during June solstice of the same year, IRI-Neq and IRI-01-corr closely match the GPS TEC at all time of the day, except between around 4:00 UT and 13:00 UT where an overestimation was observed. IRI-2001 was observed to overestimate the GPS TEC more than the other two options. Similar results were observed during September equinox, but IRI-Neq and IRI-01-corr were observed to underestimate the GPS TEC during the midday and during this period of time, IRI-2001 matched the GPS TEC. During December solstice, all the three options of the IRI-2012 model were observed to overestimate the GPS at most of the time, but IRI-neq closely agrees with GPS TEC values during the midday. For the year 2013 (figure 6(b)), an overestimation of the GPS TEC by all options of the IRI-2012 model was observed at most of the time during all seasons. However, during March equinox for this year, IRI-Neq and IRI-01-corr were observed to underestimate the GPS TEC 6
during the midday, while IRI-2001 option closely matched with GPS TEC during this time. During June solstice, a good agreement was observed between IRI-Neq and IRI-01-corr options and the GPS TEC. A good agreement was also noted during September equinox between GPS TEC and the IRI-Neq option during the midday. On the other hand, an overestimation of GPS TEC by all the three options of the IRI-2012 was observed at other time of the day. During December solstice, IRI-neq and IRI-01-corr were observed to underestimate GPS TEC during the midday. But, at most of the time, all the three options of the IRI-2012 model were noted to overestimate GPS TEC. Generally, from the results presented above, IRI-2012 model with all three options overestimated the GPS-TEC for all seasons and at all stations, and IRI-2001 overestimated GPSTEC more compared with other options, except for few cases as it is explained above. 3.2. Correlation coefficients, RMSE and PRMSE Correlation coefficients between the IRI-TEC values and the GPS-TEC values using the 5 quietest days’ monthly means for equinoxes and solstices months of the year 2012 and 2013 at four stations in the southern crest of the EIA within the Eastern Africa region are presented in figure 7. The RMSE of the IRI-TEC values from GPS derived TEC values are presented in figure 8, and figure 9 presents information on the PRMSE of the IRI-TEC values from GPS-TEC values for the same stations. From figure 7, it is observed that, for the year 2012, GPS-TEC values and IRI-TEC values using all the three topside Ne options show very good correlation. At most of the stations and during all seasons, it is above 0.9 which is quite strong. However, correlation coefficients at other locations are below 0.9, but above 0.7 which are also good. For example, during September equinox at Nairobi, correlation coefficients are below 0.9 but above 0.8. At Mbarara station, during December solstice, it was observed that, IRI-neq had small correlation coefficient compared to other options, and it was observed to be below 0.8. During this month, the other IRI-2001 and IRI-01-corr options had correlation coefficients less than 0.85 but above 0.8. For the year 2013, the TEC from all the three options of the IRI-2012 model and GPS TEC were observed to have correlation coefficients of above 0.9 at all locations and during all seasons. On the other hand, from figure 8 and 9 which show the RMSE and PRMSE respectively, the TEC using IRI-Neq and IRI-01- corr had small deviations from the GPS derived TEC which ranges from about 20 - 50% at most of stations compared to the IRI-2001 which goes above 100% at other stations. The maximum PRMSE for IRI-Neq option for the year 2012 was observed to be above 50%, while that given by IRI-01-corr was above 65%. Both were observed during December solstice at Nairobi. On the other hand, IRI-2001 was observed to have larger RMSE for 2012 with PRMSE of above100% and occurred during June solstice at Mbarara and during December solstice at Nairobi. However, for the year 2013, maximum PRMSE were observed to occur during September equinox at Nairobi, Mbarara and Kigali for all the three topside Ne options, as well as during June solstice at Kigali. During this period, the maximum PRMSE of both IRI-Neq TEC and IRI-01-corr TEC values from GPS-TEC values was above 40%. The IRI-2001 which was observed to have the largest deviations had the PRMSE of above 65%. Our results are in good agreement with the results from other scholars. Okoh et al. (2012) obtained that the IRI TEC values generally compared well with the GPS TEC values, with correlation coefficients as good as about 0.9, and root-mean square deviations generally around 20–50% for diurnal comparisons. This scenario of IRI-Neq and IRI-01-corr to have the least 7
deviations of IRI-TEC values from GPS TEC values compared to IRI-2001 was also observed by Rathore et al. (2015) at Varanasi, India. 4. Discussion Comparison of TEC from IRI-2012 model with all the three topside Ne options (IRI2001, IRI-Neq and IRI-01-corr) with GPS derived TEC from ground measurements at four stations in the southern crest of the EIA within Eastern Africa region has been presented. Our results show that, IRI-2012 model with all three options overestimated the GPS-TEC for all seasons and at all stations, and IRI-2001 overestimated GPS-TEC more compared with other options. In addition, an overestimation of GPS TEC by IRI-2012 model is higher during December solstice in most of the locations than other seasons for the year 2012, while for 2013, an overestimation was mostly observed during September equinox. The observation also showed that, during noon hours of equinoctial months, GPS TEC values are higher than the TEC values from IRI-neq and IRI-01-corr options. For example; during September equinox for Kigali 2012, March equinox for Kigali 2013, March and September equinoxes for Malindi 2012, March equinox for Malindi 2013, September and March equinoxes for Mbarara 2012 and 2013 respectively, March and September equinoxes for Nairobi 2012 and March equinox for Nairobi 2013. An underestimation of GPS TECv by IRI-TECv is contributed by the fact that, IRI-TECv does not include plasmasphere TEC. It is well known that, the percentage of plasmaspheric contribution to GPS TECv is much larger during the nighttime hours than the daytime hours (Kumar et al., 2015; Yizengaw et al., 2008). Therefore, it was expected for the IRI model to underestimate the GPS-TEC during the nighttime than the daytime. However, in this study, the IRI TECv from IRI-neq and IRI-01-corr options exhibited an underestimation from the derived GPS-TEC during the day. This high plasmaspheric contribution to GPS TEC during the day might have been caused by the equatorial electrodynamics that governs the density distribution, including the plasma exchange between the ionosphere and plasmasphere (Yizengaw et al., 2008). Our results agree with the previous studies. For example: Chakraborty et al. (2014) compared the GPS TEC and IRI-2012 TEC using four stations from equatorial to mid-latitudes and found that the TEC with topside option IRI-2001 overestimates the observed GPS TEC in low latitude regions in most of the times and the TEC from other two options of IRI are in consistent with the observed TEC data. Kumar et al. (2014) on their study on validation of the IRI-2012 model with GPS-based ground observations over a low-latitude Singapore station found that, for the year 2010, the IRI-2001 model overestimates, while IRI-Neq and IRI-01-corr underestimates the GPS-TEC and for the year 2011, the IRI-2012 model with all three options IRI-neq, IRI-2001, and IRI-01-corr underestimates the GPS-TEC. Their results further revealed that, the IRI-neq and IRI-01-corr options agree well with GPS-TEC at all times during the summer season only, while during the winter season and equinox, these two options show agreement with GPS only at nighttime for the year 2011. However, the IRI-2001 model overestimates the GPS-TEC during all seasons and also does not show agreement with GPS TEC. The results by Kenpankho et al. (2011) using IRI 2007 model at Chumphon, Thailand, showed that, the IRI-2007 model agrees well with the GPS TEC data mostly in the morning hours, but underestimates the GPS TEC at daytime than nighttime, particularly during the noon bite outs. Recently, Kumar et al. (2015) studied the TEC variation over an equatorial and anomaly crest region in India during 2012 and 2013 and found that, the IRI-2001 topside option overestimates the observed GPS-TEC at Lucknow most of the times during 2012–2013while the other two options (IRI-Neq and IRI01-corr) had close agreement with the GPS TEC.
8
The disagreements of the GPS TEC values and those estimated by IRI 2012 model is due to the relatively small amount of data from the region considered in developing the model (Adewale et al., 2011), in our case, the Eastern Africa region. Since the IRI model depends on the primary database, it’s accuracy in a specific region depends on the availability of reliable data for the region. Bilitza and Reinisch (2008) mentioned the inadequacy of ionospheric data over the African equatorial region as a factor that contributes to the diminished accuracies of the IRI predictions over this region. Additionally, the TEC from IRI model is calculated from foF2 by calculating the height profile of electron density based on the foF2, step by step. Then the density profile is integrated along the vertical line to obtain TEC. During all these procedures, the modeling of the topside electron density may not be done accurately. Therefore, an overestimation of TEC by the IRI model as observed in this study during the time of observation may be due to inaccurate prediction of foF2 by the IRI model (Chakraborty et al., 2014; Kumar et al., 2015; Rathore et al., 2015). Kumar et al. (2015) on their study on TEC variation over an equatorial and anomaly crest region in India during 2012 and 2013, proposed the discrepancies in the F2 peak parameters estimated by the IRI model, which are larger at lower latitudes regions as the sources of the large discrepancies in estimating the GPS TEC by IRI model. They further suggested that, an inaccuracy in estimation of slab thickness which is related to foF2 or equivalent NmF2 from the coefficients of the IRI models may contribute to the largest discrepancies in the TEC predicted by the IRI-model with the measured GPS-TEC observed during the December solstice. On the other hand, an underestimation of GPS TEC by IRI-model during noon hours is suggested to be due to the ionization contribution from the equator which affects the ionosphere over the equatorial anomaly region producing an electron density profile broader during noon time than those presumed by the model (Ezquer et al., 1995). Another likely reason for the daytime discrepancy in the IRI-2012 model as suggested by Kenpankho et al. (2011) and Kumar et al. (2015) is the daytime ionospheric expansion which causes a larger slab thickness to be covered at around noon time as compared to other times. Similarly, the reason for an underestimation of GPS TEC during equinoctial months might be due to the fact that, the IRI model does not take into consideration the actual ionisation rate of equatorial ionosphere during these seasons (Leong et al., 2014). 5. Conclusions We have analyzed the results of TECv variations from IRI-2012 model using all the three topside Ne option (IRI-neq, IRI-2001 and IRI-01-corr) at four stations located within the southern crest of the EIA in Eastern Africa region. The analysis has been done by comparing the IRI TECv with the ground based GPS TECv measurements using monthly means of the 5 international quiet days for equinoxes and solstices months for 2012-2013. We also computed Correlation Coefficients between the two sets of data, the Root-Mean Square Errors (RMSE) of the IRI-TECv from the GPS-TECv and the percentage RMSE of the IRI-TECv from the GPSTECv. The general results show that, IRI-2012 model with all three topside options overestimates the GPS-TECv for all seasons and at all stations, and IRI-2001 overestimates GPSTECv more compared with other options, except for few cases as it is explained above. On the other hand, IRI-neq and IRI-01-corr are closely matching in most of the time. Further, during noon hours of equinoctial months, GPS TECv values are higher than the TECv values from IRIneq and IRI-01-corr options. It was further observed that, GPS-TECv values and IRI-TECv values using all the three topside Ne options show very good correlation (above 0.8) at most of 9
time. On the other hand, the TECv using IRI-neq and IRI-01- corr had small PRMSE from the GPS measured TECv compared to the IRI-2001. The discrepancy of IRI TECv from GPS TECv could be attributed mainly to the relative small amount of data within the eastern Africa region. In addition, an overestimation of TECv by the IRI model as observed in this study might be contributed by an inaccurate prediction of foF2 by the IRI model. Similarly, an underestimation of GPS TECv by IRI-model during noon hours is suggested to be due to the ionization contribution from the equator which affects the ionosphere over the equatorial anomaly region producing an electron density profile broader during noon time than those presumed by the model. Likewise, an underestimation in IRI-TECv is contributed by the fact that, IRI-TECv does not include plasmasphere TECv as GPS TECv does. This high plasmaspheric contribution to GPS TECv during the day might have been caused by the equatorial electrodynamics that governs the density distribution, including the plasma exchange between the ionosphere and plasmasphere. In addition to that, an underestimation of GPS TECv observed during equinoctial months implies that the IRI model does not take into consideration the actual ionisation rate of equatorial ionosphere during these seasons. Acknowledgement: We express our thanks to the University of Dodoma for funding this study. The authors are also thankful to the International GNSS Service (IGS) for providing the access to the GPS data. We finally acknowledge Dr. Gopi Seemala for providing access to the GPS-TEC analysis software used in this work. References Abdu, M. A., Batista, I. S., Carrasco, A. J., and Brum, C. G. M., 2005. South Atlantic magnetic anomaly ionization: A review and a new focus on electrodynamic effects in the equatorial ionosphere, Journal of Atmospheric and Solar Terrestrial Physics 67, 1643–1657. Adewale A.O., Oyeyemi E.O., Adeniyi J.O., Adeloye A.B. and Oladipo O.A., 2011. Comparison of total eletcron content predicted using the IRI-2007 model with GPS observations over lagos, Nigeria. Indian Journal of Radio and Space Physics 40, 21-25. Aggarwal, M., 2011. TEC variability near northern EIA crest and comparison with IRI model. Advances in Space Research 48, 1221–1231. Akala, A.O., Seemala, G. K., Doherty, P.H., Valladares, C.E., Carrano, C.S., Espinoza, J. and Oluyo, S., 2013. Comparison of Equatorial GPS-TEC observations over an African station and an American station during the minimum and ascending phases of solar cycle 24. Annals of Geophysics 31, 2085–2096. Appleton E.V., 1946. Two anomalies in ionosphere. Nature 157, 691–693. Bilitza, B. and Reinisch, B.W., 2008. International Reference Ionosphere 2007: Improvements and new parameters. Advances in Space Research 42, 599–609. Bilitza, D., Altadill, D., Zhang, Y., Mertens, C., Truhlik, V., Richards, P., McKinnell, L. and Reinisch, B., 2014. The International Reference Ionosphere 2012 – a Model of International collaboration. Journal of Space Weather and Space Climate 4, A07.
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Bilitza, D., 1986. International reference ionosphere: recent developments, Radio Science 21, 343–346, Doi: 10.1029/RS021i003p00343. Bhuyan, P. K. and Bhuyan, K., 2009. The equatorial ionization anomaly at the topside F region of the ionosphere along 75oE. Advances in Space Research 43, 1676–1682. Chakraborty, M., Kumar, S., Kumar, De B., Guha , A., 2014. Latitudinal characteristics of GPS derived ionospheric TEC: a comparative study with IRI 2012 model. Annals of Geophysics 57 (5) A0539; Doi: 10.4401/Ag-6438. Ezquer, R. G., Ortiz de Adler, N., Radicella, S. M. Mosert de Gonzalez, M. and Manzano, J. R., 1995. IRI and BPM Total Electron Content Predictions for Tucuman. Advances in Space Research 15 (2) 121-124. Kenpankho, P., Watthanasangmechai, K., Supnithi P., Tsugawa, T. and Maruyama, T., 2011. Comparison of GPS TEC measurements with IRI TEC prediction at the equatorial latitude station, Chumphon, Thailand. Earth Planets and Space 63, 365–370. Klobuchar, J., 1986. Design and characteristics of the GPS ionospheric time delay algorithm for single frequency users, in: Proceedings of PLANS’86 – Position Location and Navigation Symposium, Las Vegas, Nevada, 4–7 November, 280–286. Klobuchar, J. A., 1996. Ionospheric effects on GPS, in: Global Positioning System: Theory and application Vol. 1, edited by: Parkinson, B. W. and Spilker, J. J., American Institute of Aeronautics and Astronautics INC. Washington DC, 485–515. Kumar, S., Patel, K. and Singh, A.K., 2015. TEC variation over an equatorial and anomaly crest region in India during 2012 and 2013. GPS Solution 20 (4), 617-626 DOI 10.1007/s10291-0150470-4. Kumar, S., Tan, E. L., Razul, S. G., See, C. M. S. and Siingh, D., 2014. Validation of the IRI2012 model with GPS-based ground observation over a low-latitude Singapore station. Earth. Planets and Space 66 (17), 1-10. Leong, S. K, Musa, T. A., Omar, K., Subari, M. D., Pathy, N. B., and Asillam, M. F., 2015. Assessment of ionosphere models at Banting: Performance of IRI-2007, IRI-2012 and NeQuick 2 models during the ascending phase of Solar Cycle 24. Advances in Space Research, 55 (8), 1928-1940. Martyn, D.F., 1947. Atmospheric tides in the ionosphere. I. Solar tides in the F2 region. Proceedings of the Royal Society of London. A, Mathematical and Physical Sciences 189, 241– 260. Mosert, M., Gende, M., Brunini, C., Ezquer, R., Altadill, D., 2007. Comparisons of IRI TEC predictions with GPS and digisonde measurements at Ebro. Advances in Space Research 39, 841–847. Nigussie, M., Radicella, S.M., Damtie, B., Nava, B., Yizengaw, E. and Ciraolo, L., 2012. TEC ingestion into NeQuick 2 to model the East African equatorial ionosphere. Radio Science 47 (5) RS5002.
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Nigussie, M., Radicella, S. M., Damtie, B., Nava, B., Yizengaw, E. and Groves, K., 2013. Validation of the NeQuick 2 and IRI-2007 models in East-African equatorial region. Journal of Atmospheric and Solar Terrestrial Physics 102, 26–33. Okoh, D., Eze A., Adedoja, O., Okere, B. and Okeke, P.K., 2012. A comparison of IRI-TEC predictions with GPS-TEC measurements over Nsukka, Nigeria. Space Weather 10, S10002, Doi:10.1029/2012SW000830. Olwendo O. J., Baki P., Cilliers P.J., Mito C., Doherty P., 2012. Comparison of GPS TEC measurements with IRI-2007 TEC prediction over the Kenyan region during the descending phase of solar cycle 23. Advances in Space Research 49, 914–921. Radicella, S.M., Leitinger, R., 2001.The evolution of the DGR approach to model electron density profiles. Advances in Space Research 27, 35–40. Rathore, V.S., Kumar, S., Singh, A.K., 2015. A statistical comparison of IRI TEC prediction with GPS TEC measurement over Varanasi. Journal of Atmospheric and Solar Terrestrial Physics 124, 1–9 Shim, J. S., 2009. Analysis of Total Electron Content (TEC) variations in the low and middle latitude ionosphere. PhD Thesis, Department of Physics, Utah State University. Tariku Y. A., 2015. TEC prediction performance of the IRI-2012 model over Ethiopia during the rising phase of solar cycle 24 (2009–2011). Earth, Planets and Space 67, 140 Doi: 10.1186/s40623-015-0312-1. Yizengaw, E., Moldwin, M.B., Galvan, D., Iijima, B.A., Komjathy, A., Mannucci, A.J., 2008. Global plasmaspheric TEC and its relative contribution to GPS TEC. Journal of Atmospheric and Solar-Terrestrial Physics 70, 1541– 1548.
List of tables Table 1: Stations co-ordinates
Figure captions Figure 1: The map view of the locations of the stations used Figure 2: International SSN for the last five cycles (http://www.sidc.be/silso/datafiles) Figure 3: Comparison of GPS TEC and IRI-2012 model TEC from the monthly means of the 5 quietest days of the equinoxes and solstices months at Kigali for (a) 2012 (left panel) (b) 2013 (right panel) Figure 4: Comparison of GPS TEC and IRI-2012 model TEC from the monthly means of the 5 quietest days of the equinoxes and solstices months at Malindi for (a) 2012 (left panel) (b) 2013 (right panel)
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Figure 5: Comparison of GPS TEC and IRI-2012 model TEC from the monthly means of the 5 quietest days of the equinoxes and solstices months at Mbarara for (a) 2012 (left panel) (b) 2013 (right panel) Figure 6: Comparison of GPS TEC and IRI-2012 model TEC from the monthly means of the 5 quietest days of the equinoxes and solstices months at Nairobi for (a) 2012 (left panel) (b) 2013 (right panel) Figure 7: Correlation coefficients between the IRI-TEC values and the GPS-TEC values using monthly means of the 5 quietest days for equinoxes and solstices months of the year (a) 2012 (left panel) (b) 2013 (right panel) Figure 8: Root mean square errors of the IRI-TEC values from the GPS-TEC values using monthly means of the 5 quietest days for equinoxes and solstices months of the year (a) 2012 (left panel) (b) 2013 (right panel) Figure 9: Percentage root mean square errors of the IRI-TEC values from the GPS-TEC values using monthly means of the 5 quietest days for equinoxes and solstices months of the year (a) 2012 (left panel) (b) 2013 (right panel)
13
List of figures for web version
Figure 1
Figure 2
14
TECU
80 60 40 20 0
0 80 60 40 20 0 0 80
Kigali, March 2012
4
8
12
16
20
24
Kigali, June 2012
4 8 12 16 20 Kigali, September 2012
24
80 60 40 20 0
Kigali, March 2013
IRI-neq IRI-01-corr 0
40
40
20
20 4 8 12 16 20 Kigali, December 2012
4
8 12 16 Time (Hours) UT (a)
20
24
8
12
16
20
24
4
8 12 16 20 Kigali, September 2013
24
4
8 12 16 20 Kigali, December 2013
24
4
8 12 16 20 Time (Hours) UT (b)
24
Kigali, June 2013
0 80 60
0 80 60 40 20 0 0
4
80 60 40 20 0
60
0
GPS
0
0 80 60 40 20 24 00
Figure 3
15
IRI-2001
80 60
60
40
40
20
20
0
0
0 80 60
TECU
80
Malindi, March 2012
4
8
12
16
20
24
Malindi, June 2012
40
20
20
80
0
4
8
12
16
20
Malindi, September 2012
60
IRI-01-corr IRI-2001
24 00 80 40
20
20 0
80 60 40 20 0
4
8
12
16
20
24
20
24
Malindi, June 2013
4
8
12
16
Malindi, September 2013
60
40 0
GPS IRI-neq
0 80 60
40 0
Malindi, March 2013
4
8
12
16
20
24
Malindi, December 2012
0
4
8 12 16 20 Time (Hours) UT (a)
24
0 80 60 40 20 0
0
4 8 12 16 20 Malindi, December 2013
24
0
4
24
Figure 4
16
8 12 16 20 Time (Hours) UT (b)
80 60
Mbarara, March 2013
40
IRI-neq
20
IRI-01-corr
0
0 80
80
Mbarara, June 2012
TECU
60
20
24
0
4 8 12 16 20 Mbarara, September 2013
24
0
4
24
40
20
20 4 8 12 16 20 Mbarara, September 2012
24
0 80
60
60
40
40
20
20
0 80 60 40 20 0
0
0
4 8 12 16 20 Mbarara, December 2012
24
4
24
8 12 16 20 Time (Hours) UT (a)
4
8 12 16 Mbarara, June 2013
60
40 0 0 80
GPS
0 80 60 40 20 0
8
12
16
20
Mbarara, December 2013
0
4
8 12 16 Time (Hours) UT (b)
Figure 5
17
20
24
IRI-2001
80 60
60
40
40
20
20
0 0 80
4
8
12
16
20
24
Nairobi, June 2012
60
TECU
80
Nairobi, March 2012
20
20 24
60
40
40
20
20 4 8 12 16 20 Nairobi, December 2012
4
8 12 16 20 Time (Hours) UT (a)
IRI-2001 4
0 0 80
60
0 0 80 60 40 20 0 0
IRI-01-corr 8 12 16 Nairobi, June 2013
20
24
4 8 12 16 20 Nairobi, September 2013
24
4 8 12 16 20 Nairobi, December 2013
24
4
24
60 40
4 8 12 16 20 Nairobi, September 2012
GPS IRI-neq
0 0 80
40 0 0 80
Nairobi, March 2013
0 0 80 60 40 20 0 24 0 24
Figure 6
18
8 12 16 20 Time (Hours) UT (b)
Correlation coefficients
IRI-2001 1.05 1 0.95 0.9 0.85 0.8 1 0.95
IRI-01-corr 1 0.95
Malindi, 2012
0.85 Mar
Jun Sep Nairobi, 2012
0.8 1 0.95
Dec
0.9
0.85
0.85 Mar
Jun Sep Mbarara, 2012
0.8 1 0.95
Dec
Mar
Jun Sep Nairobi, 2013
Dec
Mar
Jun Sep Mbarara, 2013
Dec
Mar
Jun Sep Kigali, 2013
Dec
0.9 0.85 Mar
Jun Sep Kigali, 2012
0.8 1
Dec
0.95
0.95
0.9
0.9
0.85
0.85
0.8
Malindi, 2013
0.9
0.9 0.8 1 0.95 0.9 0.85 0.8 0.75 1
IRI-neq
0.8 Mar
Jun
Sep
Dec
(a)
Mar
Jun
Sep (b)
Figure 7
19
Dec
IRI-2001
RMSE (TECU)
20 15 10 5 0 25 20 15 10 5 0 25 20 15 10 5 0 25 20 15 10 5 0
Malindi, 2012
Mar Jun Sep Nairobi, 2012
Dec
Mar Jun Sep Mbarara, 2012
Dec
Mar
Dec
Mar
Jun Sep Kigali, 2012
Jun
Sep (a)
Dec
IRI-01-corr IRI-neq 20 Malindi, 2013 15 10 5 0 Mar Jun 25 Nairobi, 2013 20 15 10 5 0 Mar Jun 25 Mbarara, 2013 20 15 10 5 0 Mar Jun 25 Kigali, 2013 20 15 10 5 0 Mar Jun (b)
Figure 8
20
Sep
Dec
Sep
Dec
Sep
Dec
Sep
Dec
IRI-2001
PRMSE (%)
100 80 60 40 20 0 120 100 80 60 40 20 0 120 100 80 60 40 20 0 100 80 60 40 20 0
IRI-01-corr 80 60 40 20 0
Malindi, 2012
Mar Jun Nairobi, 2012
Sep
Dec
Mar Jun Mbarara, 2012
Sep
Dec
Mar
Sep
Jun
100 80 60 40 20 0 100 80 60 40 20 0
Dec
100 80 60 40 20 0
Kigali, 2012
Mar
Jun
Sep
Dec
(a)
IRI-neq
Malindi, 2013
Mar Jun Nairobi, 2013
Sep
Dec
Mar Jun Sep Mbarara, 2013
Dec
Mar
Sep
Dec
Sep
Dec
Jun
Kigali, 2013
Mar
Jun (b)
Figure 9
21
List of tables
Table 1 Station
Code
Geographic co-ordinates Latitude Longitude
Magnetic co-ordinates Latitude Longitude
Kigali
NURK
1.95oS
30.09oE
11.63oS
101.66oE
Malindi
MAL2
2.99oS
40.19oE
12.42oS
111.86oE
Mbarara MBAR
0.60oS
30.74oE
10.22oS
102.36oE
Nairobi
1.22oS
36.89oE
10.69oS
108.59oE
RCMN
22