Corresponding author: M. Nigussie, Washera Geospace and Radar Science Laboratory, Bahir Dar University, PO Box, 79, Bahir Dar, Gojjam, Ethiopia. (email@example.com)
 NeQuick 2 ionospheric empirical model depends on global ionospheric coefficients that are estimated from unevenly distributed ionosonde measurements. In regions, like Africa, where very few observational data were available until recently, the model estimated the ionospheric peak parameters by interpolation. When one wants to employ the model to specify the ionosphere where very few data have been used for model development, the performances of the model need careful validation. This study investigates the performances of NeQuick 2 in the East African region by assisting the model with measurements from a single Global Positioning System (GPS) receiver, which has been deployed recently. This can be done by first calculating an effective ionization level that drives NeQuick 2 to compute slant total electron content (sTEC) which fits, in the least square sense, with the measurements taken from a single GPS receiver. We then quantify the performances of NeQuick 2 in reproducing the measured TEC by running the model at four other locations, where GPS stations are available, using the same effective ionization level that we calculated from a single GPS station as a driver of the model. Finally, the performances of the model before and after data ingestion have been investigated by comparing the model results with the experimental sTEC and vertical TEC (vTEC) obtained from the four test stations. Three months data during low solar activity conditions have been used for this study. We have shown that the capability of NeQuick 2, in describing the East African region of the ionosphere, can be improved substantially by data ingestion. We found that the model after ingestion reproduces the experimental TEC better as far as about 620 km away from the reference station than that before adaptation. The statistical comparisons of the performances of the model in reproducing sTEC before and after ingestion are also discussed in this study.
 It is well known that trans-ionospheric propagating radio waves are highly affected by the Earth's ionosphere [Davies, 1990]. Understanding the spatial and temporal characterization of the ionosphere is very essential to mitigate its impact on radio signal. Ionospheric modeling has been taken as an alternative approach to capture the global, regional, or local characteristics of the ionosphere. For example, physics based models such as Ionospheric Forecast Model (IFM) [Schunk et al., 1997] provides the global distribution of the dominant molecular densities and also electron and ion temperatures at different ionospheric regions. Similarly, the physics based data driven model of the ionosphere and neutral atmosphere called Global Assimilation Ionospheric Measurements (GAIM) [Schunk et al., 2004] provides three dimensional electron density profile, the ionospheric layers peak parameters, and vertical TEC (vTEC). Angling and Jackson-Booth also developed the Electron Density Assimilative Model (EDAM), which can provide real-time ionospheric characteristics by assimilating diverse data sets into a background model. Other regional and global models such as a family of Neustrelitz TEC Models (NTCM) have been developed to reconstruct and forecast TEC based on Global Navigation Satellite System (GNSS) measurements [Jakowski et al., 2011]. Similarly, there are empirical models such as NeQuick, which has been developed to estimate the three-dimensional ionospheric electron density in space and time. NeQuick is based on the ionospheric electron density profiler proposed byDi Giovanni and Radicella . It reproduces the ionospheric electron density profile using the ionospheric layers peak parameter values as an anchor points [Radicella and Leitinger, 2001]. The model, for example, uses the Consultative Committee for International Radio (CCIR) maps for ionospheric peak parameters (example, foF2) modeling. The CCIR maps are developed based on long-term ionosonde measurements mainly collected in the midlatitude region of the Northern Hemisphere [Jones and Gallet, 1962].
 By integrating the electron density NeQuick can also be used to obtain slant total electron content (sTEC) along a raypath between the receiver and Global Positioning System (GPS) satellite. The user inputs of the model are receiver and satellite coordinates, month and universal time, and daily solar flux (F10.7). The model has been used not only for basic research but also for different applications including simulation and validation for the European Geostationary Navigation Overlay System (EGNOS) [European Space Agency, 2006] and TEC prediction [Cander, 2003]. The International Telecommunication Union, Radio communication sector (ITU-R) has also adopted it for TEC prediction to improve their communication quality [International Telecommunication Union, 2003]. It has also been proposed for single frequency ionospheric error correction in the framework of GALILEO [Arbesser-Rastburg, 2006] (or see the Web site http://navipedia.org/index.php/NeQuick_Ionospheric_Model). The model used by ITU and proposed to be used by the Galileo single frequency receiver is NeQuick 1. The FORTRAN 77 code of this model can be downloaded from the Web site http://www.itu.int/oth/R0A04000018/en. NeQuick 1 has been upgraded to NeQuick 2 [Nava et al., 2008] after remodeling the topside shape parameter of the model [Coïsson et al., 2006]. Alongside its applications the performances of the model have been tested in different regions from time to time. It has been shown that both versions of the model, compared to other model, are well suited for GALILEO single frequency ionospheric error correction [Bidaine and Warnant, 2011; Radicella et al., 2008; Farah, 2008]. Jodogne et al.  compared the modeled vTEC (using NeQuick 1) with measurements at midlatitude regions and found good agreement. Similarly, Bidaine and Warnant  assisted the model (both versions) with ionosonde measurements at midlatitude region and found a good improvement of the model in computing vTEC. On the other hand, Coïsson et al.  have investigated that at low latitude regions NeQuick with new topside formulation (NeQuick 2) does not show improvements in reproducing the sTEC.
 In order to use the model for different purposes, it is very essential to investigate the performance of the model for different solar activity periods at different regions. Particularly, it is very important to improve the performances of NeQuick 2 at low-latitude regions where very few data have been used for model development [Jones and Gallet, 1962; Coïsson et al., 2006]. The performances of empirical models can be improved by assisting the models with ionosphere measurements. The technique on how to assist empirical models with measurements has been discussed in details by Komjathy et al.  and Nava et al. . The performances of NeQuick in reproducing the experimental sTEC can be improved by assisting the model with ionosphere measurements, which can be done by means of sTEC data ingestion using single or multistations measurements [Nava et al., 2006]. The basic idea of the data ingestion is to determine the local effective solar radio flux (Az) or effective ionization level, which minimizes the difference between the modeled and the experimental sTEC values. This has been demonstrated for a daylong data obtained for the North America region during high solar activity period using NeQuick 1 and the results have showed significant improvement in the model performances.
 In the present study we investigate the performances of NeQuick 2 in describing the low-latitude ionosphere in East African region during low solar activity periods. We first ingested into the model various sTEC values measured by a single GPS receiver located in the region to find the optimal value of the effective ionization level (Az), which minimizes the difference between the modeled and the experimental sTEC values. The performances of the model in reproducing the measurements are then tested by using the same effective ionization level (Az) values as a driver of NeQuick 2 to reproduce experimental TEC at the location of four other GPS stations available in the region. The results obtained have been used to investigate the potential of the method for regional ionospheric mapping.
2. Data and Analysis Method
 Instruments available in Ethiopia for the purpose of ionospheric studies have been very few and most of them became operational since 2006. One International GNSS System (IGS) and one Scintillation Network Decision Aid (SCINDA) stations are located in Addis Ababa, Ethiopia. One other SCINDA station is also located at the main campus of Bahir Dar University, Ethiopia [Amory-Mazaudier et al., 2009]. The GPS receivers, deployed by the tectonic group (UNAVCO and Africa Array) to study the Earth's plate movement in the East African region, also provide TEC values. We used these opportunity and utilized the data which is publicly available at the University of NAVSTAR Consortium (UNAVCO) website (www.unavco.org). About 88% of these stations started functioning since 2006 but most of them do not have continuously recorded data. This indicates that we do not have data for high solar activity period and thereby our study is limited only to low solar activity periods.
 Five stations have been selected for this study. One station, Nazret (NAZR) located nearly at the center of the Ethiopian region has been selected as a reference station to obtain the driver of NeQuick 2. The four other stations Asab (ASAB), Bahir Dar (BDAR), Robe (ROBE), and Arba Minch (ARMI) are selected to demonstrate the spatial validity of the driver of NeQuick 2 in reproducing TEC. Figure 1 shows the locations of these stations, their geographic and geomagnetic coordinates of the stations are shown in Table 1. To select data, possibilities of getting reasonable TEC order of magnitude and simultaneous availability of data across the selected stations have been taken into account. Hence, we did not consider data during the years 2008 and 2009 since these years were during the extremely low solar activity conditions. The year 2006 also was not considered since there were no simultaneous observations across all the stations. Again, based on simultaneous availability of data in each of these five stations two equinoctial months (April and October 2007) have been selected for the declining phase of solar activity period. However, since we had no simultaneous observations in the equinoctial months of rising phase of the 24th solar cycle February 2010 (which is near to March equinoctial months) has been selected. During this month we had no data for ROBE station.
Table 1. Locations of GPS Receivers
Geographic (Lat., Long.)
Geomagnetic (Lat., Long.)
Arba Minch Unv
 The GPS is a constellation of about 32 satellites, orbiting the Earth at 20, 200 km altitude with an inclination of 55 degree in six distinct orbital planes. Each satellite transmits two L-band signals at frequencies f1 = 1.5754 GHz and f2 = 1.2276 GHz. The satellite signals are separated by modulating each carrier with a pseudorandom noise (PRN) code unique to each satellite. By receiving on two frequencies, TEC along the raypath between a GPS receiver and a GPS satellite can be derived from the combination of GPS pseudo-ranges (P1–P2) and carrier phases (L1–L2) [Mannucci et al., 1998; Ciraolo et al., 2007]. The TEC that we calculated from the available GPS RINEX data has been calibrated using the technique described in Ciraolo et al.  and Ciraolo . The software distributed during the Second Workshop on Satellite Navigation Science and Technology for Africa has been used to estimate the calibrated experimental sTEC. Simulation results of the calibration technique have shown satisfactory results with uncertainties about very few TECu even though larger uncertainties occur at low latitudes [Ciraolo, 2009].
 As described by Nava et al.  and the references therein, NeQuick 2 has been developed for median ionospheric electron density or TEC computation. The NeQuick 2 performance test during the geomagnetically active periods is beyond the scope of this study. Therefore, the calibrated sTEC corresponding to geomagnetic active (Ap greater than 20) days are filtered out from model adaptation. Finally, 25 days data for April 2007, 28 days data for October 2007, and 24 days data for February 2010 are used in this study.
 The sTEC observed at the reference station (NAZR) has been used for NeQuick 2 adaptation. All the sTEC in an epoch has been ingested into NeQuick 2 for each hour to compute hourly Az values. The local effective ionization level Az that produces the possible minimum root-mean square-error between the experimental and the corresponding modeled sTEC is then estimated. This means that Az is calculated by minimizing
where sTECm and sTECo represent the modeled and experimental sTEC, respectively; and N is the number of satellites visible to the GPS receiver in an epoch. Using this procedure we have determined 24 Az values for each day.
 The modeled sTEC along the raypath between the locations of the receivers and visible satellites is computed before and after ingestion. NeQuick 2 input parameters used for this computation are receivers and satellites coordinates, time, solar radio flux (before ingestion), and effective ionization level (after ingestion). The effective ionization levels computed only from the NAZR data are used to reproduce the sTEC observed by the test stations (ASAB, BDAR, ROBE, and ARMI). The test stations air distance (in km) and azimuth (in degrees) relative to the reference station (NAZR) are given in Table 2.
Table 2. Distance and Azimuth of Test Stations Relative to NAZR Station
 The performances of the model are evaluated by subtracting the experimental sTEC from the modeled sTEC. This difference is defined as mismodeling. The mismodeling statistics is used as a measure of the effectiveness of the model in reproducing the experimental sTEC. The difference between the experimental and modeled sTEC by using daily observed solar radio flux (F10.7) as an input to the model, is defined as the mismodeling before ingestion. The difference between the experimental and modeled sTEC using local effective ionization level (Az) as an input to the model, is defined as mismodeling after ingestion. The performances of NeQuick 2 after and before ingestion in reproducing the vTEC over the station are also compared. The technique of estimating vTEC over the station is found in Ciraolo .
 sTEC has been converted to vTEC at Ionosphere Pierce Point (IPP) by applying the ionospheric thin shell model [Mannucci et al., 1998]. The conversion can be done using the relation given by
where χ is the zenith angle of a GPS satellite at IPP. Mathematically it is defined as
where ς is the zenith angle of a GPS satellite raypath at the user position, Re is the radius of the Earth and h (=400 km) is the thin shell height from Earth surface.
3. Results and Discussions
3.1. The sTEC Mismodeling Distribution With 10° Mask Angle
 We first consider TEC measurements corresponding to satellites with an elevation mask above 10°. The sTEC observed by the GPS receiver at NAZR during April 2007, October 2007, and February 2010 is ingested into the model, which allows us to estimate the corresponding effective ionization levels on an hourly basis. The model then uses these ionization levels to compute the sTEC along a raypath between ground GPS receivers stationed at ARMI, ROBE, NAZR, BDAR, and ASAB and the corresponding visible GPS satellites. The sTEC before ingestion is obtained by using the daily solar radio flux, F10.7 as a driver of the model. The results are shown in the Figures 2 and 3.
 The frequency distribution of the mismodelings for April 2007 is shown in Figure 2. Figure 2 (top) depicts the frequency distribution of the mismodelings of NeQuick 2 before data ingestion. Each panel depicts for different stations, specified at the top of each panel. Figure 2 (bottom) illustrates the frequency distribution of the mismodelings after data ingestion. The corresponding means and standard deviations (designated by μ and σ respectively) of these mismodelings of NeQuick 2 are also shown in each panel. The means of the mismodelings before data ingestion are almost similar for all stations (of the order of 9–10 TECu) as for the standard deviations (again of the order of 8–10 TECu). As it is clearly seen in Figure 2 (bottom), mismodelings after data ingestion have significantly decreased compared to the values obtained before data ingestion. For example, the means of the mismodelings have decreased from 9.79 to −0.09, 9.63 to −0.17, 9.32 to −0.47, 9.61 to −0.80 and 9.83 to 0.36 TECu for ARMI, ROBE, NAZR, BDAR, and ASAB stations, respectively. The corresponding standard deviations have also decreased from 8.62 to 4.88, 8.65 to 4.40, 8.73 to 4.52, 8.78 to 5.72, and 9.64 to 7.14 TECu. In addition, data ingestion into the model leads the frequency distributions of the mismodelings to be more symmetric about a peak than the distribution of the mismodelings before ingestion (see Figure 2).
 The standard deviations of the mismodelings for ASAB appear to be the largest even after data ingestion. This may be due to the fact that ASAB is the farthest from the reference station (NAZR), indicating that the ionosphere has significant spatial variation between ASAB and the reference station. However, it is interesting to note that these values are still smaller than the corresponding means and standard deviations obtained before ingestion.
 The means and standard deviations of the mismodelings before and after sTEC ingestion into NeQuick 2 for October 2007 and February 2010 are shown in Figures 3 (left) and 3 (right) respectively. Figures 3 (top) and 3 (bottom), respectively, show the means and the standard deviations of the mismodelings (before and after ingestion) for test and reference stations. Station ROBE is not included due to the lack of data for February 2010 (Figure 3, right). Similarly, for October 2007 and February 2010 the means and standard deviations of the mismodelings have decreased significantly after ingestion. This indicates that under quiet geomagnetic and solar conditions NeQuick 2 reproduce observed sTEC better using the effective ionization level obtained from a single station as a driver of the model than the daily observed solar radio flux. This has been demonstrated in the geographic area at least within a radius of about 620 km (see Table 2) relative to the station used for model adaptation. In general, as far as the standard deviations of the mismodelings after data ingestion are less than or equal to the standard deviations of the mismodelings before data ingestion, the effective ionization level can be used in the model to reproduce sTEC for distant locations.
3.2. The sTEC Mismodeling Distribution With 45° Mask Angle
 In order to avoid multipath impact in determining the Az value using data observed at the reference station, the data ingestion technique has been tested by taking only sTEC data with an elevation angle greater than 45°. Thus, for the cases of Figures 4 and 5, the hourly Az values have been obtained using the same technique described above but using only sTEC data with an elevation angle greater than 45°. Figure 4 presents the mismodeling frequency distribution for April 2007. Figures 4 (top) and 4 (bottom) show the distribution of the mismodelings before and after data ingestion into the model, respectively. The means and standard deviations of the mismodelings are shown in each panel. Figures 5 (left) and 5 (right) show the means and standard deviations of the mismodelings (before and after ingestion) for October 2007 and February 2010, respectively. The means and standard deviations of the mismodelings shown in these figures have decreased significantly after data ingestion. However, it is evidently shown that the decrease spread for ASAB is relatively small.
 It is clearly shown that the model shows different performances when it is adapted to sTEC corresponding to 10° and 45° elevation masks (Figures 2, 3, 4, and 5). This difference of performance may be due to the effect of the multipath, which usually occurs at lower elevation mask angles. An additional cause could be related to the fact that the Az parameter that drives NeQuick 2, calculated in the data ingestion process, could be affected by the variation of elevation mask angles. This is due to the effect of TEC horizontal gradients and the length of the signal's path through the ionosphere that would change by varying the elevation angle mask.
 Taking the ratio of standard deviations of the mismodelings after (σa) and before (σb) ingestion may be useful to see the relevance of the effective ionization levels in driving NeQuick 2 to reproduce sTEC at other stations. Figure 6 shows the ratio of the standard deviations of the mismodelings after and before ingestion (σa/σb) as a function of stations' distance from the reference station (NAZR). Figures 6 (left) and 6 (right), respectively, show the ratio of standard deviations as a function of distance corresponding to elevation angles above 10° and 45°. The minimum and maximum ratio values are obtained at NAZR (the reference station) and ASAB (the farthest station to the reference station), respectively. This indicates that the capability of the effective ionization levels, obtained from NAZR to drive the model and reproduce sTEC at far away station from the reference station is decreasing. The estimated ratio generally shows a linear increasing trend away from the reference station (dash dotted line). This trend is estimated by the linear equation, which is shown in each panel. These linear equations may be useful to predict the limit radius (relative to location of GPS station used for model adaptation) where the effective ionization levels drive NeQuick 2 better than the daily solar flux.
3.3. Percentage Error Distribution
 The percentage errors before and after data ingestion are computed. As a sample the frequency distribution of the percentage errors corresponding to Figures 2 and 4 are shown in Figures 7 and 8, respectively. The means and standard deviations of the percentage errors, which are shown at the top of each panel in Figures 7 and 8, are significantly decreased after data ingestion. For example, the means are decreased from 80.05% to 4.49%, 76.44% to 2.12%, 74.89% to −0.95%, 76.31% to −6.95%, and 85.81% to 0.62% for the stations ARMI, ROBE, NAZR, BDAR, and ASAB, respectively (see Figure 7). The corresponding standard deviations are decreased from 113.97% to 29.04%, 102.75% to 25.81%, 114.37% to 24.70%, 106.48% to 27.85%, and 132.46% to 40.94%. Figure 8 also shows similar scenario. The means are decreased from 64.15% to 10.38%, 58.03% to 5.17%, 54.71% to −0.27%, 64.26% to −4.14%, and 78.14% to 7.71% for the above stations, respectively. The corresponding standard deviations are decreased from 86.24% to 25.41%, 78.36% to 18.43%, 85.98% to 10.87%, 96.07% to 22.96%, and 124.78% to 34.87%. The means and standard deviations of the percentage errors estimated for October 2007 and February 2010 are displayed in Figures 9 (left) and 9 (right), respectively. Figures 9a, 9b, 9e, and 9f show the means of the mismodelings (before and after ingestion) computed corresponding to 10° and 45° elevation mask for each station. Figures 9c, 9d, 9g, and 9h show the standard deviations of the mismodelings corresponding to 10° and 45° elevation mask. In all of the panels of this figure, the means and standard deviations of the percentage errors estimated after data ingestion are less than the corresponding means and standard deviations of the percentage errors computed before data ingestion.
3.4. Diurnal Variations of vTEC
 The same effective ionization levels, corresponding to satellite elevation angles above 10° and 45°, are also used to calculate the modeled vTEC over the stations. The corresponding modeled vTEC before data ingestion are also estimated for each of these stations. Three-day sample results for the months of April 2007, October 2007, and February 2010 are shown in theFigures 10, 11, and 12, respectively. Each panel of these figures displays one-day diurnal variation of estimated vTEC for different stations. For example, the three panels ofFigure 10from top to bottom, respectively, depict the diurnal vTEC for day of year (DOY) 094, 095, and 096 estimated at five stations (ARMI, ROBE, NAZR, BDAR, and ASAB). The minimum modeled (denoted by F10.7, Az-45, and Az-10) and experimental (denoted by Expt.) vTEC values occur at around 0500 LT and then increase until it reaches a maximum. In general, the modeled vTEC (before ingestion) overestimate the experimental vTEC. However, for some cases in April and October 2007 the model tends to underestimates the measurements between around 1100 and 1700 LT. The diurnal variation of the modeled vTEC after data ingestion agrees with the experimental vTEC better than the modeled vTEC before data ingestion. However, the model after data ingestion corresponding to 45° and 10° elevation mask has shown different performances (Figures 10, 11, and 12). For example, the model after data ingestion corresponding to 45° elevation mask reproduces the experimental vTEC over the reference station (NAZR) better than after data ingestion corresponding to 10° elevation mask. The errors associated to the mapping function, which has higher values at lower elevation mask angle, may contribute for this variation. In general, the discrepancy between the experimental and modeled vTEC before data ingestion is significantly improved after the model is assisted with data ingestion both in the cases of 10° and 45° satellite elevation mask.
 We have shown that the capability of NeQuick 2 in describing the characteristics of the low-latitude ionosphere in the East African region can be improved substantially by assisting the model with data ingestion. This is done in practice by calculating the main input parameter of the model, which is the effective ionization levels Az that drives NeQuick 2 to compute modeled sTEC that fit with the observation values at the reference station in an optimal manner. The good results obtained at four test stations indicate that adapting NeQuick 2 with data from one reference station can improve the performance of the model to be able to provide a wider ionospheric specification on East African ionosphere. In general, the method can be easily developed to accommodate the requirements of different applications that need information about the ionosphere in the region. This may be done by creating maps of Az which in turn can be used to produce reasonably well estimated modeled TEC and electron density maps.
 M. Nigussie is grateful to the Abdus Salam International Centre for Theoretical Physics (ICTP), TWAS, Trieste, Italy, for their support and hospitality through the ICTP STEP program. E. Yizengaw's work has been supported by NASA LWS (NNX10AQ53G) and Geospace Science programs (NNX09AR84G) and AFOSR YIP grant (FA9550-10-1-0096). Also, the authors would like to thank University of NAVSTAR Consortium (UNAVCO) for GPS data available.