Radio Science

Are models predicting a realistic picture of vertical total electron content?



[1] The present work analyzes results coming from global maps of ionospheric total electron content (TEC) obtained from observations and from different empirical models like the International Reference Ionosphere (IRI), the model family developed at Trieste and Graz (NeQuick, COSTprof, and NeUoG-plas), and the GPS operational model (formulation by J. A. Klobuchar). Since they still appear in the context of assessment studies we have also included “old” models like the Bent model. The attention is focused on situations which occurred in the present period of high solar activity, pointing out features like the equatorial anomaly and polar regions, which are crucial test regions for ionospheric TEC models. Experimental estimates of slant TEC from International GPS Service (IGS) stations have been compared particularly with the predictions of the NeQuick and GPS models. A very simple picture of the ionosphere like the one given by the GPS operational model appears to be insufficient to reproduce the global complex behavior of the ionosphere, as it is needed for assessment studies or for modern operational real-time corrections of transionospheric propagation errors. The IRI estimates of TEC still present serious problems, essentially owing to the topside under high solar activity conditions, and the model cannot be integrated to heights above 2000 km. With processing resources suitable for real-time operation, it seems that the NeQuick model can give a more widely reliable picture of the TEC estimated from GPS measurements. Computing times for this model are considerably smaller than for more complex models like NeUoG-plas.

1. Introduction

[2] The study was carried out using global ionosphere maps (GIMs) of vertical total electron content (TEC) produced by the European Center for Orbit Determination (CODE); as reference, we refer to these as “experimental” maps. Those maps are made available through the Internet ( in Ionosphere Map Exchange (IONEX) format files containing global maps computed every 2 hours during 1 day. In particular, a spherical harmonics expansion is used at CODE to produce GIMs on the basis of vertical TEC estimated from the receiver independent exchange (RINEX) format files obtained at IGS stations distributed all around the world [Schaer et al., 1996]. As a consequence of the inhomogeneous concentration of IGS stations on the surface of Earth, there are wide regions where only few measurements are available (e.g., over oceans, Africa, and Antarctica). The estimated vertical TECs over those areas are affected by a greater uncertainty. In particular, no stations are located under the crests of the equatorial anomaly over Africa. For the purpose of this work, GIMs of CODE are assumed to give the “experimental” global picture of the ionosphere, with the limitations introduced by the limited coverage of the observing stations.

2. Models Analyzed

[3] Different kinds of ionospheric models, briefly described below have been used.

2.1. International Reference Ionosphere 2001 (IRI-2001)

[4] IRI is a well-known empirical model of the ionosphere that is widely used [Bilitza, 1990]. For given location, time, and date, IRI describes the electron concentration, electron temperature, ion temperature, and ion composition in the altitude range from about 50 km to about 2000 km, as well as the total electron content. IRI provides monthly medians in the nonauroral ionosphere for magnetically quiet conditions. IRI electron density profiles sources are the coefficients (foF2 and M(3000)) produced by the radiocommunications sector of the International Telecommunication Union (ITU-R), incoherent scatter radars (Jicamarca, Arecibo, Millstone Hill, Malvern, and St. Santin), ISIS and Alouette topside sounders, and in situ instruments on several satellites and rockets. It can also use experimental values of F2 peak electron concentration (i.e., foF2) and height as inputs. IRI is updated periodically and has evolved over a number of years.

2.2. Bent

[5] Bent et al. [1972] model was developed for transionospheric propagation uses. The model describes the ionospheric electron density as a function of latitude, longitude, time, season, and solar radio flux. The topside is represented by a parabola and three exponential profile segments, and the bottomside by a biparabola. The model is based on about 50,000 Alouette topside ionograms (1962–1966), 6000 Ariel 3 in situ measurements (1967–1968), and 400,000 bottomside ionograms (1962–1969). For the F2 peak, the Comite Consultatif International des Radiocommunications (CCIR) maps are used. The model has been widely used for ionospheric refraction corrections in satellite tracking. It does not include the lower layers (D, E, and F1) and uses a simple quadratic relationship between CCIR's M(3000)F2 factor and the height of the F2 peak.

2.3. GPS Klobuchar

[6] The model implemented in the Global Positioning System for single-frequency users, which is based on the Bent model [Klobuchar, 1987]. It reproduces the mean behavior of the vertical TEC on a location in time as a half cosine function centered at 1400 LT plus a constant bias. During the nighttime, only the constant bias is present. A series of eight coefficients (four Alpha and four Beta) is transmitted by the GPS system to control the amplitude and period of the cosine as function of the geomagnetic latitude.

2.4. Trieste-Graz Family of “Profilers”

[7] A new family of electron concentration “profilers” which differ in complexity and which have different but related application areas has been developed, based on the DGR “profiler” concept [Di Giovanni and Radicella, 1990]. A sum of Epstein layers [Rawer, 1983] is used to reproduce analytically the electron density distribution in the ionosphere below the peak of the F2 layer. The topside electron density is based on a semi-Epstein layer controlled by a shape parameter [Radicella and Zhang, 1995]. Radicella and Leitinger [2001] describe the evolution of this series of models, which have an identical bottomside formulation but different, in complexity and computational time required, topsides. The three models are:

[8] 1. NeQuick, a quick-run model for ionospheric applications, which takes into account the plasmasphere electron density in a simplified manner. This model has been adopted in the ionospheric specifications for the European Space Agency European Geostationary Navigation Overlay System (EGNOS) project and recently by the ITU-R recommendation (recommendation P.531-6) as a suitable method for TEC modeling.

[9] 2. COSTprof, a model that can be used for ionospheric and plasmaspheric satellite to ground applications, which takes into account the change of gradients in the topside profile associated to the O+H+ transition. It has been adopted by the Cooperation in Scientific and Technological Research (COST) 251 action of the European Commission as the profiler for its electron density distribution model.

[10] 3. NeUoG-plas, a model that can be used particularly in assessment studies involving satellite to satellite propagation of radio waves, in which a precise estimate of the electron density distribution in the plasmasphere is required. It uses a magnetic field aligned formulation for an H+ diffusive equilibrium for heights above 2000 km.

[11] All of these models can use as input either measured ionospheric parameters (foF2, M3000) or the ITU-R coefficients driven by the solar activity level. They also allow the use of median or instantaneous ionospheric parameters values, or maps based on regional or global experimental data [Hochegger et al., 2000]. These values are used as anchor points for the vertical profile modelization. The output of these models is the electron concentration in the ionosphere as a function of height, geographic latitude, and longitude; solar activity (given by sunspot number or by 10.7 cm solar radio flux); and season (month) and time (UT or LT). The models also calculate electron concentration along arbitrarily chosen ray paths, and slant, or vertical, total electron content up to heights in the plasmasphere as those of GPS satellites. The profiles are continuous in all spatial first derivatives (a necessity in applications like ray tracing and location finding). Since most of the analyzed models are based on the ITU-R monthly median coefficients foF2 and M3000, it was necessary to compute monthly median GIMs using all the daily maps provided by CODE to deal with comparable quantities.

3. GIM Comparisons

[12] The study was focused on the period from January to September 2001. As already indicated, CODE maps can be obtained via anonymous ftp from The GPS model was calculated using the broadcasted coefficients alpha and beta as they are provided on the NOAA National Geodetic Survey (NGS) Continuously Operating Reference Stations (CORS) Web site ( The comparison was computed between GIM of a particular day and hour with the corresponding map obtained from the GPS model calculation using the alpha and beta coefficients broadcasted the same day. January and February months were discarded because the coefficients found for the analyzed day were not reliable. To compare with the other models, median monthly maps of the GIMs at a given UT were computed on the basis of the median TEC value at every map grid point. The grid width of the used maps is 2.5° in latitude and 5° in longitude. Such median maps were computed for different UTs. Each model was run to produce similar global maps using the value of R12 for each month as solar activity driving parameter. It has to be noted that IRI model can only be integrated up to 2000 km.

[13] In Figure 1, global maps computed for each model are presented as an example to show their main features. All the maps and computations shown are in TEC units (1016m−2). It can be see that while all models try to reproduce the main features of the ionosphere, the computed TEC values can be quite different, particularly at low latitudes, where the equatorial anomaly representation differ substantially from one model to the other. Only the GPS model does not present the equatorial anomaly behavior and gives a very rough representation of the global TEC, as it is designed mostly for a middle latitude use.

Figure 1.

Examples of global ionosphere maps for each model on 15 May 2001 at 2100 UT.

[14] Comparisons were done for a given UT between each model and the corresponding CODE map, considering different bands of modified dip latitude (modip). Modip μ [Rawer, 1963] is a coordinate used in ionospheric modeling and it is defined by

equation image

with ψ being the magnetic dip in the ionosphere and ϕ the geographic latitude. Modip bands were chosen to have: polar regions (−90°, −60° and 60°, 90°), midlatitudes regions (−60°, −35° and 35°, 60°), equatorial anomaly crest regions (−35°, −5° and 5°, 35°), and equatorial anomaly trough region (−5°, 5°). The comparisons always showed a similar general trend at each UT analyzed, making evident that every model has a consistent behavior in terms of modip. As an example, we show in Figure 2 the absolute root mean square (RMS) values (a measure of model performance or mismodeling) computed in every bands for each model with respect to the CODE maps for 2100 UT. It appears evident that each model has a characteristic behavior. IRI RMS values are quite stable and low in midlatitudes, but in the other regions the behavior is different from month to month. At both polar regions, IRI shows unrealistic increase of TEC. It is the only model analyzed to have a general tendency to overestimate TEC, particularly at those latitudes, even if the integration limit is only 2000 km. The NeQuick model presents a more stable behavior in time during the analyzed period in most regions. Only in the trough of the equatorial anomaly is its performance sometimes considerably poorer. However, like the GPS and Bent models, NeQuick generally underestimates TEC. The other two models of the same family, NeUoG-plas and COSTprof, show a similar behavior at middle and high latitudes with better performances, but they have a tendency to strongly overestimate the equatorial anomaly, especially in the case of COSTprof. They present a strong development of the equatorial anomaly tails, which are very smoothed in the “experimental” maps. The Bent and GPS-Klobuchar models show both quite similar results, reflecting the fact that the latter one was derived from the Bent model, presenting worse performance in the equatorial anomaly region, where they both give much lower TEC values than the other models.

Figure 2.

RMS computed with respect to CODE median monthly GIM in different bands of modified dip latitude from January to September 2001. In the case of the GPS model, the RMS is computed on the day 15 GIM for each month.

[15] It has to be pointed out that CODE maps, used as “experimental” base maps, show areas with zero TEC over the southern part of Pacific and Indian Oceans. These conditions clearly affect the performance statistics computed for the models. On those areas the map values are almost completely artificial since they are based on very few observing stations. To overcome that problem, a series of longitudinal cross sections of vertical TEC was analyzed for areas where more IGS stations are found. The results of the comparisons for the 285°E meridian cross section at 1700 UT (local noon) are shown in Figure 3 as an example. From the figure the general trends indicated in Figure 2 are confirmed. At this latitude and UT, RMS values tend to be larger in the case of the IRI and Bent models, while NeUoG-plas and COSTprof show a very good behavior at all latitudes, showing that their representation of the equatorial anomaly region during daytime is closer to the one seen on CODE GIMs.

Figure 3.

RMS in the longitudinal cross section at 285°E at local noon.

4. Slant TEC Comparisons

[16] Slant TEC estimated from RINEX files of IGS and other stations have been used to compare experimental values with the operational GPS model and with NeQuick. Only the NeQuick model was chosen here because of its capability to quickly compute TEC on any given path. As an example we show a quiet day: 9 September 2001. The NeQuick model was driven by the value of sunspot number for that particular day (R = 166) and the GPS model by the coefficients broadcasted on that date. The attention was focused on stations over Europe and North America, as shown in Figure 4. Data every 10 min were analyzed, and an elevation cutoff angle of 10° was used. RMS of the TEC differences in TEC units and of the percent TEC difference were computed, as summarized in Table 1. In the American sector, both models show a better agreement with the experimental slant TEC than in the European sector. In the case of the NeQuick the differences are only few TEC units, and in any case it gives RMS values much lower than the GPS model. In such an example it appears that the technique used to compute slant TEC with the NeQuick model can give better results than the one of the GPS model.

Figure 4.

Stations used to compare 9 September 2001 slant TEC values with NeQuick and GPS models. Stations in Europe are: anka, geno, hers, lamp, and wtzr; stations in North America are: albh, aoml, cic1, and cro1.

Table 1. Comparison of the NeQuick and GPS Models With Slant TEC Estimated From Stations in Europe and North America as Shown in Figure 4
StationsDataRMSRMS %

5. Conclusions

[17] Global maps of TEC (GIMs) computed using different models have been compared with monthly median maps computed on the basis of CODE GIMs; in the case of GPS operational model the comparison was carried out with the maps of the corresponding day. Each model has shown regions in which its performances are poorer: IRI gives very high values of TEC at high latitudes, and the GPS model does not reproduce the equatorial anomaly, but the NeQuick seems to be the one with the more stable behavior in time and space. Comparisons of slant TEC estimated from the RINEX files of some North American and European stations have been performed to test the ability of NeQuick and GPS model to reproduce the slant TEC, and the NeQuick model has shown a remarkably better performance.