Journal of Geophysical Research: Space Physics

1 Introduction

Knowledge of the ionospheric variation is important to understand its effects on the operations of high‐frequency communications as well as space‐based positioning and navigation applications. Over the years, research efforts have been toward understanding the complexity and variability of the ionosphere, many of which have been documented. Several parameters have been used in these research efforts. Among these parameters, total electron content (TEC) is considered as the key parameter used in many ionospheric model applications [Bilitza and Reinisch, 2008]. GPS technology has made the estimation of TEC possible and thus provides a means of near‐real‐time ionospheric monitoring and hence has improved our understanding of the ionosphere.

For many years, the sparsity of GPS receivers has been a barrier to TEC investigation in the African region. The Africa region is located in the tropical region and has the largest tropical landmass in the world (https://www2.bc.edu). However, ionospheric effects on trans‐ionospheric signals have been reported to be more severe in tropical latitudes [Kintner et al., 2009]. Thus, the African region is located in an advantageous position for monitoring ionospheric dynamics. Ionospheric parameters derived from empirical models such as the International Reference Ionosphere (IRI) model, NeQuick, and many others, can serve as an alternative data set to specify the state of the ionosphere in regions like Africa that has limited number of continuous data sources. The performance of these models may largely depend on the techniques or the volume of ionospheric observations used in their development. Historically, the African region has remained under study due to fewer numbers of monitoring equipment. Consequently, discrepancies between the modeled and the observed ionospheric parameters are bound to exist in the region where there is no long‐term measurement for model development.

Among the empirical models, the IRI model has been recognized as the de facto standard for the climatological specification of ionospheric parameters such as electron density, electron temperature, TEC, and many more [Bilitza and Reinisch, 2008; Bilitza, 2009]. TEC is calculated in the IRI model by integrating through the entire ionospheric electron density profiles, i.e., the bottomside (region below the F₂ peak) and topside (region above the F₂ peak) electron density profiles. Although the bottomside portion contributes significantly to TEC, however, the main contribution comes from the topside portion. The need to improve the representation of the topside electron density profile has led to the development of several topside models [e.g., Bilitza, 1985; Rawer, 1990; Gulyaeva et al., 2002]. For the prediction of TEC, IRI model offers three options for the topside electron density model. They are the IRI 2001 (IRI‐01) option developed by Bilitza [2001], correction factor for the IRI‐2001 (IRI‐01 Corr) developed by Bilitza [2004], and the NeQuick option (NeQ) developed by Radicella and Leitinger [2001] and Coïsson et al. [2006].

The IRI model provides the monthly averages of ionospheric parameters in the altitude ranging from 60 to 2000 km [Bilitza et al., 2014]. In this case, the model may underestimate the true value of TEC since it does not account for electron contents between 2000 km and 20,200 km, which is the GPS orbital height. However, several models have been listed by the International Standardization Organization to extend the IRI model to plasmaspheric heights. The IRI Extended to Plasmasphere (IRI‐Plas) model is an acceptable international standard model for specifying ionospheric observables up to the plasmasphere region [Gulyaeva and Bilitza, 2012]. The plasmaspheric height limitation of IRI is overcome in the IRI‐Plas model; i.e., it provides a structural model of the ionosphere up to plasmasphere [Gulyaeva, 2010]. In IRI‐Plas model, the Russian Standard Model of the Ionosphere and Plasmasphere is combined with the IRI model [Chasovitin et al., 1998]. Both models used the International Radio Consultative Committee option for the prediction of the F₂ layer peak parameters [Zakharenkova et al., 2015]. However, the IRI‐Plas model introduces scale height parameter to determine the shape of the IRI topside electron density profile [Maltseva et al., 2013]. Apart from the fact that the IRI‐Plas model specifies the ionosphere up to the plasmaspheric height, the model also has the advantage of integrating ionospheric dynamics into it for a better representation of the temporal variation in the ionosphere. This is achieved by ingestion of experimental values of TEC into the model [Gulyaeva, 2003].

In this present study, we evaluate the performance of the IRI 2012 and IRI‐Plas 2015 models over eight stations located in the southern hemisphere of the African region. To the best of our knowledge, this is the first time such validation of the IRI model and the latest version of the IRI‐Plas (IRI‐Plas 2015) in terms of TEC prediction is being done in the region simultaneously.

2 Data and Method of Analysis

In order to validate the two models over the region, TEC derived from GPS observations are compared to TEC predicted by the IRI‐Plas 2015 and the three topside options of the IRI 2012 models. The GPS data used are from eight GPS receivers stationed at different locations in the southern hemisphere of the African region as shown in Figure 1. Table 1 shows the geographic and geomagnetic coordinates of the locations of the stations used. The GPS data used for the study were recorded in the year 2014.

The estimation of TEC using the GPS technology is made possible because ionosphere introduces a frequency‐dependent delay on radio signals that propagate through it. The total number of electrons encountered by the signal along the satellite receiver path, known as the slant TEC (TEC_s) can be estimated from the combination of carrier phase and pseudorange of the GPS measurement. TEC_s, which is a function of the elevation angle of the satellite, passes and the spacing of the satellites in orbit may, however, pose a number of challenges due to spatiotemporal electron density gradient. To overcome this, the TEC_s is verticalized (converted to TEC that is independent of the satellite geometry) by dividing it by a factor, known as the obliquity or slant factor after the satellite and receiver biases have been removed, given by the expression in equation 1

where TEC_v is the verticalized TEC, b_R and b_S are the receiver (station) and satellite biases, respectively, and S(E) is the obliquity factor defined as a function of the zenith angle z and is modeled as given by the expression in equation 2 where R_E is the radius of the Earth, E is the elevation angle, and h_S is the effective height of the centroid of mass of the ionosphere, as known as the Ionospheric Pierce Point (IPP). In this study, the GPS‐TEC analysis software that was developed at the Institute of Scientific Research, Boston College, USA, was used to derive TEC_v from the GPS measurements based on equation 1. In converting the TEC_s to TEC_v, the conversion algorithm assumes an IPP altitude of 350 km, and only TEC data recorded by satellite pass whose elevation mask angle is greater than 30^o are selected to avoid error due to multipath and troposcatter effects [Rama Rao et al., 2006]. The satellite bias (b_S) is offset by using the P1C1 and P1P2 values provided by the Center for Orbit Determination in Europe (CODE) through their online database available at ftp://ftp.unibe.ch/aiub/CODE/, while the receiver bias (b_R) is calculated from the 2 sigma (2σ) iterated average of the observed diurnal minimum value of all the satellite passes at each of the stations. The output of the software is written in American Standard Code for Information Interchange (ASCII) format, where the diurnal values of TEC_v were obtained. The hourly average of diurnal variation of TEC for five quietest days was used to represent the diurnal monthly average values. The five international quietest days, which depict days when the geomagnetic variations are minima in each month, were selected based on the information supplied by the Helmholtz Centre Potsdam, GFZ German Research Centre for Geoscience and is available at http://www.gfz‐potsdam.de/en/section/earths‐magnetic‐field/data‐products‐services/kp‐index/qd‐days/. Readers are referred to the website for details of the selection criteria.

The corresponding values of TEC from IRI 2012 and IRI‐Plas models were also computed for the same period. The three available topside options (NeQuick (NeQ), IRI 2001 corrected (IRI‐01 Corr), and IRI 2001 (IRI‐01)) of the IRI 2012 model were used. The online version of the model available at the National Space Science Data Center (NSSDC) website: (http://modelweb.gsfc.nasa.gov/ionos/iri.html) was used. Just like the IRI model, the IRI‐Plas also provides the monthly average value of ionospheric parameters. In this study, the recently released version of the IRI‐Plas model (i.e., IRI‐Plas 2015) was used to compute TEC. The latest version, which was implemented by the IONOLAB group, can be accessed through the online database of the Hacettepe University, Ankara, Turkey (www.ionolab.org). To provide the same level playing ground for both models, the “no extra input option” of the IRI‐Plas model was used to compute TEC_v, since the IRI‐Plas model has the option of incorporating GPS‐TEC whereas the IRI model does not.

For seasonal evaluation of the models, the months of the year were divided into four to represent the seasons. They are the March equinox (February, March, and April), June Solstice (May, June, and July), September equinox (August, September, and October), and December solstice (November, December, and January). The mean seasonal values of TEC were obtained by averaging the diurnal monthly mean values of TEC of the months in each division. To quantify the prediction error or the deviation of modeled values from the observed values, we calculated the root‐mean‐square deviation (RMSD) using the expression in equation 3.

where n is the number of data points.

3 Results

4 Discussion

We examined the performances of the IRI and IRI‐Plas models in predicting TEC over the Southern African equatorial and low‐latitude stations. Some agreements as well as discrepancies between the measured and modeled TEC were observed. Discrepancy between the observed TEC and TEC predicted by the IRI model has been partly attributed to the height limitation of the model by several authors [e.g., Coisson et al., 2008; Venkatesh et al., 2011; Adebiyi et al., 2014, 2016; Satya Srinivas et al., 2013]. The IRI model estimates TEC by integrating the electron density profile between the path length of 60 and 2000 km, whereas the GPS derived TEC accounts for electron content up to the GPS orbital height (20,200 km). Since the IRI‐Plas model accounts for electron content up to the plasmaspheric altitude, therefore, the values of TEC predicted using the IRI‐Plas model are expected to be higher than the IRI model predictions. We observed from the diurnal monthly and seasonal plots of TEC values that all the options of the IRI model generally underestimate TEC in some periods in most of the stations, particularly in the months of February, March and during the MEQU, and also at stations outside the equatorial region in the DSOL. This corresponds to the period when the IRI‐Plas model performed better than the three options of the IRI model. This may suggest that the underestimation of TEC by the IRI model observed in the diurnal monthly and seasonal variation plots may be attributed to the failure of the IRI model to account for electron beyond the 2000 km height. Also, apart from the inclusion of the plasmaspheric contribution to TEC in the IRI‐Plas model, the offset between the IRI and IRI‐Plas models may also be due to the topside estimates in the two models. In the IRI‐Plas model, the topside basis scale height parameter was introduced to determine the shape of the topside profile [Maltseva et al., 2013]. We observed in some months that the IRI Plas predictions are lower than the IRI model. This may be due to the different approaches employed in the topside modeling between the two models.

Also, overestimation of TEC by both models was observed in some hours, particularly during the daytime, in the diurnal and seasonal variation plots. This may be attributed to the inaccurate prediction of the electron density profiles in the two models over the region. Electron density profile is a key parameter for modeling the ionosphere. TEC is calculated in both models by integrating the electron density profile from the D layer in the bottomside to the topside regions. In the IRI model, the bottomside electron density is modeled as a function of height and is described in terms of the thickness and the shape parameters. The bottomside region contributes 15%–40% of electron content to GPS‐TEC [Bilitza et al., 2012]. For the description of the thickness and shape parameters, the IRI model uses data from global ionosonde networks consisting mainly of data from the midlatitudes and other regions different from the African region. Unfortunately, since the African region is not well covered by ionosonde, this may contribute significantly to a less reliable IRI modeled‐thickness parameter in the region and with a consequent effect in the modeled TEC. On the other hand, the topside profile contributes the largest values to TEC and it is of great importance. It also serves as a foot point for plasmaspheric models [Gallagher et al., 2000; Gulyaeva and Bilitza, 2012]. The inaccurate representation of this part of the ionosphere in both models may also contribute significantly to TEC data‐model discrepancies. According to Bilitza et al. [2006], the truthful representation of fountain effect in the equatorial region in almost all the topside models is still a major challenge for topside modeling. This may contribute significantly to the poor performance of both models within the equatorial region. The result obtained showed that the IRI model, in particular, the NeQ and IRI‐01 Corr options, generally performed better than the IRI‐Plas at stations in the equatorial region. This may be attributed to whether the equatorial features like the high altitudes of the equatorial ionosphere and the equatorial ionospheric transport process have been adequately addressed in the two topside options.

In addition, the poor performance of the IRI‐Plas model within the equatorial region may also be attributed to the inaccurate prediction of the plasmaspheric contribution to TEC in the region. The plasmaspheric contributions to the GPS‐TEC have been reported to vary spatially and temporally [Satya Srinivas et al., 2013; Balan et al., 2002; Klimenko et al., 2014]. For example, plasmaspheric contribution to TEC has been reported by Satya Srinivas et al. [2013] to reach up to 30% at the equatorial latitudes during the daytime, while Klimenko et al. [2014] reported a nighttime maximum contribution of 85% and a daytime contribution of 40% at the equator during the winter in the year 2009 (a period of extreme solar minimum condition). Balan et al. [2002] reported a contribution of about 12% during the daytime and 60% during the nighttime over Japan. The plasmaspheric contribution to TEC has also been found to decrease with increase in latitude and altitude [e.g., Lunt et al., 1999; Klimenko et al., 2014]. For example, Yizengaw et al. [2008] and Klimenko et al. [2014] reported a higher plasmaspheric contribution to TEC at the equatorial latitudes than in other latitudes. This was attributed to longer receiver satellite path length in the equatorial region compared to other latitudes. This may account for the improved performance of both models, particularly the IRI‐Plas model, outside the equatorial region. All these point to the fact that the plasmaspheric contribution to GPS‐TEC depends on several factors such as solar activity, season, latitude, altitude, and local time [Klimenko et al., 2014], and detailed knowledge of its variation over the region may be vital. It is therefore suggested that the structure and the dynamics of the plasmaspheric electron content should be investigated at different space weather conditions over the region. Results from such investigation will be useful to improve on the performance of existing plasmasphere models in the region or to develop new ones.

5 Conclusion

We have investigated the performance of the IRI and IRI‐Plas models in terms of TEC prediction over eight stations located in the Southern African equatorial and low‐latitude region. The diurnal and seasonal structures of TEC predicted by both models followed fairly well with the observed structure. Generally, both models overestimate and underestimate TEC during the daytime and the nighttime. In most cases, the IRI‐Plas performed better than the IRI model in the months and seasons at the time the three options of the IRI model underestimate TEC during the daytime. This has been attributed to the height limitation of the IRI model. Overall, the best predictions by both models were recorded during the September equinox (SEQU) at stations outside the equatorial region while the worst are obtained in June solstice, particularly in the equatorial region. The prediction errors of both models generally decrease with increasing latitudes, indicating that both models predict TEC better outside the equatorial region. In general, the data‐model divergence of TEC is most significant during the daytime and the nighttime at stations in the equatorial region. On the other hand, the data‐model convergence is most pronounced during the nighttime at stations outside the equatorial region in most of the months. The TEC data‐model offset has been attributed to the height limitation of the IRI model, the inaccurate predictions of the electron density profiles, and the plasmaspheric contribution to TEC in the region. More studies are required to determine the contributions of each of these factors to data‐model discrepancy.

Acknowledgments

The authors are grateful to the IRI working group for their efforts in improving the IRI model and for making it available freely to the international community from the link: http://modelweb.gsfc.nasa.gov/ionos/iri.html. The authors would also like to thank the International GNSS Service (IGS) team for the GPS data (available at ftp://garner.ucsd.edu.) and the IONOLAB group for implementing the IRI‐Plas model and making it available for public use and can be accessed at www.ionolab.org. One of the authors (Adebiyi, S. J.) thanks F. Arikan (Hacettepe University, Beytepe, Ankara, Turkey) for providing useful information on the online computation of IRI‐Plas 2015 model products.