Towards a GPS-based TEC prediction model for Southern Africa with feed forward networks

In this paper, first results from a national Global Positioning System (GPS) based total electron content (TEC) prediction model over South Africa are presented. Data for 10 GPS receiver stations distributed through out the country were used to train a feed forward neural network (NN) over an interval of at most five years. In the NN training, validating and testing processes, five factors which are well known to influence TEC variability namely diurnal variation, seasonal variation, magnetic activity, solar activity and the geographic position of the GPS receivers were included in the NN model. The database consisted of 1-min data and therefore the NN model developed can be used to forecast TEC values 1 min in advance. Results from the NN national model (NM) were compared with hourly TEC values generated by the earlier developed NN single station models (SSMs) at Sutherland (32.38°S, 20.81°E) and Springbok (29.67°S, 17.88°E), to predict TEC variations over the Cape Town (33.95°S, 18.47°E) and Upington (28.41°S, 21.26°E) stations, respectively, during equinoxes and solstices. This revealed that, on average, the NM led to an improvement in TEC prediction accuracy compared to the SSMs for the considered testing periods.     

TEC derived from some GPS stations in Nigeria and comparison with the IRI and NeQuick models

Total electron content (TEC) measured simultaneously using Global Positioning System (GPS) ionospheric monitors installed at some locations in Nigeria during the year 2011 (Rz = 55.7) was used to study the diurnal, seasonal, and annual TEC variations. The TEC exhibits daytime maximum, seasonal variation and semiannual variations. Measured TEC were compared with those predicted by the improved versions of the International Reference Ionosphere (IRI) and NeQuick models. The models followed the diurnal and seasonal variation patterns of the observed values of TEC. However, IRI model produced better estimates of TEC than NeQuick at all locations.     

Assessment of improvement of the IRI model over Ethiopia for the modeling of the variability of TEC during the period 2013–2016

This paper discusses the monthly and seasonal variation of the total electron content (TEC) and the improvement of performance of the IRI model in estimating TEC over Ethiopia during the solar maximum (2013–2016) phase employing as reference the GPS derived TEC data inferred from four GPS receivers installed in different regions of Ethiopia; Assosa (geog 10.05°N, 34.55°E, Geom. 7.01°N), Ambo (8.97°N, 37.86°E, Geom. 5.42°N), Nazret (8.57°N, 39.29°E, Geom. 4.81°N) and Arba Minch (6.06°N, 37.56°E, Geom. 2.62°N). The results reveal that, in the years 2013–2016, the highest peak GPS-derived diurnal VTEC is observed in the March equinox in 2015 over Arba Minch station. Moreover, both the arithmetic mean GPS-derived and modelled VTEC values, generally, show maximum and minimum values in the equinoctial and June solstice months, respectively in 2014–2015. However, in 2013, the minimum and maximum arithmetic mean GPS-derived values are observed in the March equinox and December solstice, respectively. The results also show that, even though overestimation of the modelled VTEC has been observed on most of the hours, all versions of the model are generally good to estimate both the monthly and seasonal diurnal hourly VTEC values, especially in the early morning hours (00:00–03:00?UT or 03:00–06:00?LT). However, it has also been shown that the IRI 2007 and IRI 2012 versions generally perform best in matching the diurnal GPS derived TEC values as compared to that of the IRI 2016 version. In addition, the IRI 2012 version with IRI2001 option for the topside electron density shows the highest overestimation of the VTEC as compared to the other options. None of the versions of the IRI model are proved to be able to capture the effects of geomagnetic storms.     

Low solar activity variability and IRI 2007 predictability of equatorial Africa GPS TEC

Diurnal, seasonal and latitudinal variations of Vertical Total Electron Content (VTEC) over the equatorial region of the African continent and a comparison with IRI-2007 derived TEC (IRI-TEC), using all three options (namely; NeQuick, IRI01-corr and IRI-2001), are presented in this paper. The variability and comparison are presented for 2009, a year of low solar activity, using data from thirteen Global Positioning System (GPS) receivers. VTEC values were grouped into four seasons namely March Equinox (February, March, April), June Solstice (May, June, July), September Equinox (August, September, October), and December Solstice (November, December, January). VTEC generally increases from 06h00 LT and reaches its maximum value at approximately 15h00–17h00 LT during all seasons and at all locations. The NeQuick and IRI01-corr options of the IRI model predict reasonably well the observed diurnal and seasonal variation patterns of VTEC values. However, the IRI-2001 option gave a relatively poor prediction when compared with the other options. The post-midnight and post-sunset deviations between modeled and observed VTEC could arise because NmF2 or the shape of the electron density profile, or both, are not well predicted by the model; hence some improvements are still required in order to obtain improved predictions of TEC over the equatorial region of the Africa sector.     

Seasonal variation of total electron content at crest of equatorial anomaly station during low solar activity conditions

The variability of total electron content (TEC) over the crest of equatorial anomaly station Bhopal has been studied during the low solar activity period (2005–2006) using global positioning system (GPS) data. Diurnal variation of TEC is studied for different seasons. Interesting features like the winter anomaly, semiannual anomaly and noon bite out in TEC have been reported. GPS derived TEC is then compared with International Reference Ionosphere (IRI) 2001 model and the difference between predictions and observation is being studied. Using the variability index we have also studied the TEC variability for different seasons and also during quiet and disturbed conditions. A higher variability is observed on quiet days as compared to disturbed days during daytime and nighttime hours.     

Equatorial total electron content (TEC) at low and high solar activity

Total electron content (TEC) derived from ionosonde data recorded at the station of Korhogo (Lat = 9.33°N, Long = 5.43°W, Dip = 0.67°S) are compared to the International Reference Ionosphere (IRI) model predicted TEC for high (1999) and low (1994) solar activity conditions. The results show that the model represents the diurnal variation of the TEC as well as a solar activity and seasonal dependence. This variation is closer to that of the ionosonde-inferred TEC at high solar activity. However, at low solar activity the IRI overestimates the ionosonde-inferred TEC. The relative deviation ΔTEC is more prominent in the equinoctial seasons during nighttime hours where it is as high as 70%. At daytime hours, the relative deviation is estimated to 0–30%.     

Performance evaluation of IRI-2007 at equatorial latitudes and its Matlab version for GNSS applications

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.     

Comparison of observed TEC values with IRI-2007 TEC and IRI-2007 TEC with optional foF2 measurements predictions at an equatorial region,Chumphon, Thailand

In this research, as part of working towards improving the IRI over equatorial region, the total electron content (TEC) derived from GPS measurements and IRI-2007 TEC predictions at Chumphon station (10.72°N, 99.37°E), Thailand, during 2004–2006 is analyzed. The seasonal variation of the IRI-2007 TEC predictions is compared with the TEC from the IRI-2007 TEC model with the option of the actual F2 plasma frequency (foF2) measurements as well as the TEC from the GPS and International GNSS service (IGS). The Chumphon station is located at the equatorial region and the low latitude of 3.22°N. For a declining phase of the solar cycle (2004–2006), the study shows that the IRI-2007 TEC underestimates the IRI-2007 TEC with the foF2 observation at the nighttime by about 5 TECU. The maximum differences are about 15 TECU during daytime and 5 TECU during nighttime. The overestimation is more evident at daytime than at nighttime. When compared in terms of the root-mean square error (RMSE), we find that the highest RMSE between GPS TEC and IRI 2007 TEC is 14.840 TECU at 1230 LT in 2004 and the lowest average between them is 1.318 TECU at 0630 LT in 2006. The noon bite-out phenomena are clearly seen in the IRI-2007 TEC with and without optional foF2 measurements, but not on the GPS TEC and IGS TEC. The IRI TEC with optional foF2 measurements gives the lowest RMSE values between IRI TEC predicted and TEC measurement. However, the TEC measurements (GPS TEC and IGS TEC) are more correct to use at Chumphon station.     

Global validation of IRI TEC for high and medium solar activity conditions

The IRI model offers a choice of options for the computation of the electron density profile and electron content (TEC). Recently new options for the topside electron density profile have been developed, which have a strong impact on TEC. Therefore it is important to test massively the IRI and the new options with experimental data. A large number of permanent stations record dual frequency GPS data from which it is possible to obtain TEC values. Thirty-one worldwide distributed stations have been selected to investigate the capabilities of the IRI to reproduce experimental TEC. Data for years 2000 (high solar activity) and 2004 (medium solar activity) have been analyzed computing modeled values with the IRI-2001 and the IRI-2007-NeQuick topside options. It is found that IRI-2007-NeQuick option generally improves the estimate of the slant TEC, especially in the case of high latitudes stations during high solar activity.     

TEC variability near northern EIA crest and comparison with IRI model

Monthly median values of hourly total electron content (TEC) is obtained with GPS at a station near northern anomaly crest, Rajkot (geog. 22.29°N, 70.74°E; geomag. 14.21°N, 144.9°E) to study the variability of low latitude ionospheric behavior during low solar activity period (April 2005 to March 2006). The TEC exhibit characteristic features like day-to-day variability, semiannual anomaly and noon bite out. The observed TEC is compared with latest International Reference Ionosphere (IRI) – 2007 model using options of topside electron density, NeQuick, IRI01-corr and IRI-2001 by using both URSI and CCIR coefficients. A good agreement of observed and predicted TEC is found during the daytime with underestimation at other times. The predicted TEC by NeQuick and IRI01-corr is closer to the observed TEC during the daytime whereas during nighttime and morning hours, IRI-2001 shows lesser discrepancy in all seasons by both URSI and CCIR coefficients.     

NeQuick 2 and IRI Plas VTEC predictions for low latitude and South American sector

Using vertical total electron content (VTEC) measurements obtained from GPS satellite signals the capability of the NeQuick 2 and IRI Plas models to predict VTEC over the low latitude and South American sector is analyzed. In the present work both models were used to calculate VTEC up to the height of GPS satellites. Also, comparisons between the performance of IRI Plas and IRI 2007 have been done. The data correspond to June solstice and September equinox 1999 (high solar activity) and they were obtained at nine stations. The considered latitude range extends from 18.4°N to ?64.7°N and the longitude ranges from 281.3°E to 295.9°E in the South American sector. The greatest discrepancies among model predictions and the measured VTEC are obtained at low latitudes stations placed in the equatorial anomaly region. Underestimations as strong as 40?TECU [1?TECU?=?10¹⁶?m^?2] can be observed at BOGT station for September equinox, when NeQuick2 model is used. The obtained results also show that: (a) for June solstice, in general the performance of IRI Plas for low latitude stations is better than that of NeQuick2 and, vice versa, for highest latitudes the performance of NeQuick2 is better than that of IRI Plas. For the stations TUCU and SANT both models have good performance; (b) for September equinox the performances of the models do not follow a clearly defined pattern as in the other season. However, it can be seen that for the region placed between the Northern peak and the valley of the equatorial anomaly, in general, the performance of IRI Plas is better than that of NeQuick2 for hours of maximum ionization. From TUCU to the South, the best TEC predictions are given by NeQuick2.The source of the observed deviations of the models has been explored in terms of CCIR foF2 determination in the available ionosonde stations in the region. Discrepancies can be also related to an unrealistic shape of the vertical electron density profile and or an erroneous prediction of the plasmaspheric contribution to the vertical total electron content. Moreover, the results of this study could be suggesting that in the case of NeQuick, the underestimation trend could be due to the lack of a proper plasmaspheric model in its topside representation. In contrast, the plasmaspheric model included in IRI, leads to clear overestimations of GPS derived TEC.     

Solar flux effects on equatorial ionization anomaly and total electron content over Brazil: Observational results versus IRI representations

The F layer critical frequency (foF2) as measured by Digisondes in the equatorial and low latitude locations in Brazil is analyzed to investigate the seasonal and solar flux controls of the intensity of the equatorial ionization anomaly (EIA) in the equinoctial month of March. The analysis also included the total electron content (TEC) as measured by a GPS receiver operated at the EIA crest location. The foF2 data set covered a period of large solar flux variation from 1996 to 2003, while the GPS TEC data was for a period in 2002–2003 when the solar flux parameter F10.7 underwent large variations, permitting in both cases an examination of the solar flux effects on these parameters. The seasonal variation pattern in TEC shows a maximum in equinoctial months and a minimum in June solstice, with similar variations for foF2. The solar flux dependence of the TEC is a maximum during equinoxes, especially for post-sunset TEC values at times when the latitudinal distribution is controlled by the equatorial evening plasma fountain processes. Significant variations with local time are found in the degree of solar flux dependence for both the TEC and EIA. The EIA intensity shows large dependence on F10.7 during post-sunset to midnight hours. These results are discussed in comparison with their corresponding IRI representations.     

Estimation and analysis of GPS receiver differential code biases using KGN in Korean Peninsula

The total electron content (TEC) estimation by the Global Positioning System (GPS) can be seriously affected by the differential code biases (DCB), referred to as inter-frequency biases (IFB), of the satellite and receiver so that an accuracy of GPS–TEC value is dependent on the error of DCBs estimation. In this paper, we proposed the singular value decomposition (SVD) method to estimate the DCB of GPS satellites and receivers using the Korean GPS network (KGN) in South Korea. The receiver DCBs of about 49 GPS reference stations in KGN were determined for the accurate estimation of the regional ionospheric TEC. They obtained from the daily solution have large biases ranging from +5 to +27 ns for geomagnetic quiet days. The receiver DCB of SUWN reference station was compared with the estimates of IGS and JPL global ionosphere map (GIM). The results have shown comparatively good agreement at the level within 0.2 ns. After correction of receiver DCBs and knowing the satellite DCBs, the comparison between the behavior of the estimated TEC and that of GIMs was performed for consecutive three days. We showed that there is a good agreement between KASI model and GIMs.     

Highlights about the performances of storm-time TEC modelling techniques for low/equatorial and mid-latitude locations

A statistical evaluation of storm-time total electron content (TEC) modelling techniques over various latitudes of the African sector and surrounding areas is presented. The source of observational TEC data used in this study is the Global Navigation Satellite Systems (GNSS), specifically the Global Positioning Systems (GPS) receiver networks. For each selected receiver station, three different storm-time models based on empirical orthogonal functions (EOF) analysis, non-linear regression analysis (NLRA) and Artificial neural networks (ANN), were implemented. Storm-time GPS TEC data used for both development and validation of the models was selected based on the storm criterion of $\mathit{Dst}?-50$ nT or $K_p?4$ to take into account both coronal mass ejections (CMEs) and co-rotating interaction regions (CIRs) driven storms, respectively. To make an independent test of the models, storm periods considered for validation were excluded from datasets used during the implementation of the models and results are compared with observations, monthly median values, and International Reference Ionosphere (IRI-2016) predictions. Considering GPS TEC as reference, a statistical analysis performed over six storm periods reserved for validation revealed that ANN model is about 10%, 26%, and 58% more accurate than EOF, NLRA, and IRI models, respectively. It was further found that, EOF model performs 15%, and 44% better than NLRA, and IRI models, respectively, while NLRA is 25% better than IRI. On the other hand, results are also discussed referring to the background ionosphere represented by monthly median TEC (MM TEC) and statistics are provided. Moreover, strengths and weaknesses of each model are highlighted.     

An investigation of ionospheric disturbances over South Africa during the magnetic storm on 15 May 2005

The effects of the 15 May 2005 severe geomagnetic storm on the South African ionosphere are studied using ground-based and satellite observations. Ionospheric disturbances have less frequently been investigated over mid-latitude regions. Recently, a number of studies investigated their evolution and generation over these regions. This paper reports on the first investigation of travelling ionospheric disturbances (TIDs) over mid-latitude South Africa. Using global positioning system (GPS)-derived total electron content (TEC) variations from the South African network of dual frequency GPS receivers, we were able to examine the effects of the disturbance on the TEC. During this storm, two TEC enhancements were observed at low- and mid-latitudes: the first enhancement was observed between 30–45°S geomagnetic latitudes associated with equatorward neutral winds and the passage of a TID, while the second TEC enhancement is associated with a second TID. In addition, the F-region critical frequency (foF2) values observed at two ionosonde stations show response features that differ from those of the TEC during the disturbance period. The dissimilarity between the TEC and the foF2 suggests that two competing drivers may have existed, i.e., the westward electric field and equatorward neutral wind effects.     

Total electron content at low latitudes and its comparison with the IRI90

We used total electron content (TEC) data measured by Faraday rotation technique over Cachoeira Paulista (22.5°S, 45°W), in Brazil, to study the TEC variations with the solar flux at 10.7 cm (F10.7) and to compare the results with the IRI90 predictions. The data were divided into summer, equinox and winter. During the analysed period F10.7 varied from 66 up to 330. Our data shows that the observed TEC at 1600 LT (around the diurnal maximum) and at 0500 LT (around the diurnal minimum) increases with F10.7 until saturation is reached which occurs at F10.7≈210 to 220 for equinox and summer, and at F10.7≈180 for winter months. Comparison with the IRI90 predictions shows that IRI overestimates the TEC at 0500 LT for all solar flux values. At 1600 LT, IRI overestimates the observed TEC for low solar flux but underestimates it for high solar flux values.     

The variability and predictability of the IRI B0, B1 parameters over Grahamstown,South Africa

The International Reference Ionosphere (IRI) parameters B₀ and B₁ provide a representation of the thickness and shape, respectively, of the F2 layer of the bottomside ionosphere. These parameters can be derived from electron density profiles that are determined from vertical incidence ionograms. This paper aims to illustrate the variability of these parameters for a single mid latitude station and demonstrate the ability of the Neural Network (NN) modeling technique for developing a predictive model for these parameters. Grahamstown, South Africa (33.3°S, 26.5°E) was chosen as the mid latitude station used in this study and the B₀ and B₁ parameters for an 11 year period were determined from electron density profiles recorded at that station with a University of Massachusetts Lowell Center for Atmospheric Research (UMLCAR) Digisonde. A preliminary single station NN model was then developed using the Grahamstown data from 1996 to 2005 as a training database, and input parameters known to affect the behaviour of the F2 layer, such as day number, hour, solar and magnetic indices. An analysis of the diurnal, seasonal and solar variations of these parameters was undertaken for the years 2000, 2005 and 2006 using hourly monthly median values. Comparisons between the values derived from measured data and those predicted using the two available IRI-2001 methods (IRI tables and Gulyaeva, T. Progress in ionospheric informatics based on electron density profile analysis of ionograms. Adv. Space Res. 7(6), 39–48, 1987.) and the newly developed NN model are also shown in this paper. The preliminary NN model showed that it is feasible to use the NN technique to develop a prediction tool for the IRI thickness and shape parameters and first results from this model reveal that for the mid latitude location used in this study the NN model provides a more accurate prediction than the current IRI model options.     

GPS derived TEC and foF2 variability at an equatorial station and the performance of IRI-model

The ionosphere induces a time delay in transionospheric radio signals such as the Global Positioning System (GPS) signal. The Total Electron Content (TEC) is a key parameter in the mitigation of ionospheric effects on transionospheric signals. The delay in GPS signal induced by the ionosphere is proportional to TEC along the path from the GPS satellite to a receiver. The diurnal monthly and seasonal variations of ionospheric electron content were studied during the year 2010, a year of extreme solar minimum (F10.7 = 81 solar flux unit), with data from the GPS receiver and the Digisonde Portable Sounder (DPS) collocated at Ilorin (Geog. Lat. 8.50°N, Long. 4.50°E, dip −7.9°). The diurnal monthly variation shows steady increases in TEC and F2-layer critical frequency (foF2) from pre-dawn minimum to afternoon maximum and then decreases after sunset. TEC show significant seasonal variation during the daytime between 0900 and 1900 UT (LT = UT + 1 h) with a maximum during the March equinox (about 35 TECU) and minimum during the June solstice (about 24 TECU). The GPS-TEC and foF2 values reveal a weak seasonal anomaly and equinoctial asymmetry during the daytime. The variations observed find their explanations in the amount of solar radiation and neutral gas composition. The measured TEC and foF2 values were compared with last two versions of the International Reference Ionosphere (IRI-2007 and IRI-2012) model predictions using the NeQuick and CCIR (International Radio Consultative Committee) options respectively in the model. In general, the two models give foF2 close to the experimental values, whereas significant discrepancies are found in the predictions of TEC from the models especially during the daytime. The error in height dependent thickness parameter, daytime underestimation of equatorial drift and contributions of electrons from altitudes above 2000 km have been suggested as the possible causes.     

武汉地区电离层电子浓度总含量的统计经验模式研究

由武汉电离层观象台一个太阳黑子周期（1980-1990年）的实测电离层电子浓度总含量（TEC）资料，统计分析得出了武汉地区的一个TEC经验模式，模式很好地再现了武汉地区的TEC观测值，其预测误差在太阳活动高年稍太，低年较小；在春秋两季稍大，冬夏两季较小；在当地时间白天和傍晚稍大，夜间和早晨较小。此外，与国际参考电离层模式IRI的计算结果比较，本模式预测的TEC值更接近于实际观测结果，同时，本文也初步探讨了TEC的半年变化特征和冬季异常现象。     

Evaluating the IRI topside model for the South African region: An overview of the modelling techniques

The representation of the topside ionosphere (the region above the F2 peak) is critical because of the limited experimental data available. Over the years, a wide range of models have been developed in an effort to represent the behaviour and the shape of the electron density (Ne) profile of the topside ionosphere. Various studies have been centred around calculating the vertical scale height (VSH) and have included (a) obtaining VSH from Global Positioning System (GPS) derived total electron content (TEC), (b) calculating the VSH from ground-based ionosonde measurements, (c) using topside sounder vertical Ne profiles to obtain the VSH. One or a combination of the topside profilers (Chapman function, exponential function, sech-squared (Epstein) function, and/or parabolic function) is then used to reconstruct the topside Ne profile. The different approaches and the modelling techniques are discussed with a view to identifying the most adequate approach to apply to the South African region’s topside modelling efforts. The IRI-2001 topside model is evaluated based on how well it reproduces measured topside profiles over the South African region. This study is a first step in the process of developing a South African topside ionosphere model.