NeQuick is a three-dimensional and time-dependent quick run electron density model specifically designed for transionospheric propagation applications. It allows calculation of electron concentration values at any location in the ionosphere and the total electron content (TEC) along any ground station–to–satellite ray path. After specific adaptations, the model has been used to develop a near-real-time nontomographic electron density retrieval technique able to provide the electron density of the ionosphere above the geographic area of interest. The technique relies on the knowledge of the model driving parameter Az (ionization level) for the location considered. In the present study, the necessary Az values have been obtained through direct ingestion of Global Positioning System (GPS)–derived slant TEC data in two different ways: using data from a single GPS receiver and using data from multiple ground stations. Statistical comparisons between experimental and reconstructed slant TEC values and between experimental and retrieved maximum electron concentration values are shown.
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 Empirical electron density models, like the International Reference Ionosphere (IRI) [Bilitza, 2001] and NeQuick [Radicella and Leitinger, 2001] have been conceived to reproduce median values of the electron density in the ionosphere. In order to achieve better results in describing the three dimensional electron density of the ionosphere for actual conditions with NeQuick, a technique based on vertical total electron content (TEC) data ingestion into the model has already been developed [Nava et al., 2005]. This technique relies on precalculated global vertical TEC maps to determine the corresponding global grids of the NeQuick driving parameter Az. Because of the preliminary computation needed to obtain the vertical TEC maps, the retrieval technique described in the work of Nava et al.  cannot be considered a real-time procedure. For this reason a different approach based on NeQuick adaptation through direct slant TEC data ingestion has been adopted and two techniques to retrieve the electron concentration of the ionosphere have been developed using the model driven by its local ionization parameter Az. The first is a retrieval method that considers the slant TEC at a single ground station to determine the Az, and thus the electron density of the ionosphere, above the area surrounding the station. The second is a near-real-time retrieval technique able to reproduce the electron density of the ionosphere at a wider geographic scale being based on the calculation of regional grids of the NeQuick driving parameter Az. In this case, at any given epoch, the Az grid is computed from the slant TEC data obtained from a network of several ground stations. When an Az grid is computed, it is possible to reconstruct the three dimensional electron density of the ionosphere with the NeQuick model and therefore the TEC value for any given ray path above the area under investigation can be calculated by means of numerical integration.
 It must be noted that several ionosphere electron density reconstruction techniques have been developed. They are of different complexity and rely on several kinds of models. The Global Assimilative Ionospheric Model [Wang et al., 2004], for example, is based on assimilation of data originating from different sources and implies the use of first principle models. The proposed retrieval methods aim to be simpler, being based on an empirical electron density model adaptation through the ingestion of TEC data only.
2. NeQuick Model
 The NeQuick model is an ionospheric electron density model developed at the Aeronomy and Radiopropagation Laboratory of The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy, and at the Institute for Geophysics, Astrophysics and Meteorology (IGAM) of the University of Graz, Austria, originally in the framework of the European Commission Co-operation in the field of Scientific and Technical Research (COST) Action 251. It is based on the DGR “profiler” proposed by Di Giovanni and Radicella  and subsequently modified by Radicella and Zhang . NeQuick is able to give the electron concentration distribution in both the bottomside and topside of the ionosphere and it is a quick run model particularly tailored for transionospheric applications. The model has been used by the European Space Agency (ESA) European Geostationary Navigation Overlay Service (EGNOS) project for assessment analysis and has been proposed for single-frequency positioning operations in the framework of the European Galileo project. It has been adopted by the International Telecommunication Union, Radiocommunication Sector (ITU-R) Recommendation P.531-6 (now superseded by P.531-7) [International Telecommunication Union, 2001] as a suitable method for TEC modeling. To describe the electron density of the ionosphere above 100 km and up to the F2 layer peak this model uses a modified DGR profile formulation [Radicella and Leitinger, 2001] which includes five semi-Epstein layers [Rawer, 1983] with modeled thickness parameters. The NeQuick is based on three profile anchor points: the E layer peak, the F1 peak and the F2 peak, that are modeled in terms of the “ionosonde parameters” foE, foF1, foF2 and M(3000)F2. The model topside is represented by a semi-Epstein layer with a height-dependent thickness parameter empirically determined [Hochegger et al., 2000; Leitinger et al., 2005]. The basic inputs of the NeQuick model are: position, time and solar flux (or sunspot number); the output is the electron concentration at the given location and time. In addition the NeQuick package includes specific routines to evaluate the electron density along any ray path and the corresponding TEC by numerical integration. NeQuick (FORTRAN 77) source code is available at http://www.itu.int/ITU-R/asp/documents.asp?link = rsg3&doctype = rsg3-soft-iono.
3. Retrieval Techniques
3.1. Effective Solar Indices
 During past years several solar indices based on solar observations have been developed to relate the response of the ionosphere to solar EUV output. Indices like sunspot number (SSN), the 10.7 cm solar radio noise flux (F10.7) or the smoothed sunspot numbers (R12) became standard inputs for many ionosphere models for the electron density distribution in the ionosphere. However, it is well known that these solar indices are far from ideal proxies for the solar activity in the EUV part of the solar radiation spectrum which is responsible for the production of ionization.
 The difficulties found when applying these solar-based indices, led to the development of a number of “effective” indices based on the use of models and experimental ionospheric data. For example, the “effective sunspot number” (SSNe) parameter valid for a set of foF2 observations has been defined as the SSN value that, when used as input to the URSI foF2 model, gives a weighted zero-mean difference between the observed and the modeled foF2 values [Secan and Wilkinson, 1997].
 Following the same approach, in recent times, other effective solar indices have been developed using electron density or electron content models and TEC observations. An example related to the use of electron density models is given by Komjathy et al. , where IRI is used to infer an IG12 index using GPS-derived measurements, whereas an example related to the use of TEC models is given by the Northwest Research Associates (see http://www.nwra-az.com/spawx/spawx.html), where a GPS-derived F10.7 index is inferred from the ionospheric model coefficients transmitted in the GPS navigation signal. In the present work the concept of an effective F10.7 has been developed further to implement different electron density retrieval techniques on the basis of the adaptation of the NeQuick model by means of electron content data ingestion.
3.2. Basic Concepts
 At a given time and for a fixed ray path, the TEC obtained by integration of the NeQuick electron density profile along the given ray path is a monotonic function of the 10.7 cm radio flux input that in this context has to be regarded as a formal “ionization level” input parameter. Applying this concept, it is possible to use the NeQuick model to define an instantaneous local effective 10.7 cm radio flux (symbol Az) valid at a given time and for a given location where an “experimental” electron content is available: Az is the value of the “ionization level” parameter that minimizes the difference between the experimental and the corresponding modeled TEC computed by means of NeQuick (integrating the electron density profile).
 The concept of Az can be used in different ways: for example in the paper of Nava et al. Az has been defined through vertical TEC values and Az grids have been computed from vertical TEC maps. In the following paragraphs, the concept of Az is also applied either to a single or to a set of slant TEC values.
3.3. Single-Station Technique
 At a given epoch, one ground station tracking n GPS satellites determines n ray paths and the corresponding experimental slant TEC values. Being the TEC mismodeling the difference between a modeled slant TEC and the related experimental slant TEC, we define as Az the ionization level value that input into NeQuick minimizes the root-mean-square of the n mismodelings. In this case it is assumed that Az is constant for all the geographic area identified by the projection of all the ray paths on the surface of the Earth.
 Once the Az is computed, the NeQuick model can be used to retrieve the electron density of the ionosphere above the area surrounding the ground station. In particular, foF2 values can be estimated at the given location or TEC along any ray path above the area of interest can be calculated.
3.4. Multiple-Station Technique
 At a given epoch a given configuration of ground stations and GPS satellites determines m ray paths and the corresponding experimental slant TEC values. Applying the basic concepts expressed in the previous paragraphs, for each ray path it is possible to define Az as the ionization level value that minimizes the difference between the experimental and the corresponding modeled slant TEC computed by means of NeQuick (integrating the slant electron density profile along the given ray path). Unlike the case of an Az inferred from a vertical path, where the coordinates of the Az are the same as the location where the vertical TEC is evaluated, in the case of a slant path it is not obvious how to define the location for which the Az is valid. Nevertheless, it has to be considered that most of the contribution to a total electron content comes from the part of the electron density profile lying around the electron density maximum. For this reason, assuming a reference height of 350 km, the coordinates of an Az inferred from a slant TEC have been defined as the coordinates of the point of the slant ray path having a height of 350 km. Consequently a set of m Az values can be computed.
 If a suitable number of satellite links is available at a given epoch, it is possible to interpolate the scattered Az values to obtain a regularly spaced Az grid. Once an Az grid is computed, it can be used to drive NeQuick to generate a three-dimensional (3-D) representation of the ionosphere electron density over the area of interest and thus the total electron content value for any given ray path can be calculated by means of numerical integration. It is understood that ionosphere peak parameters, like foF2, can also be computed at any wanted location.
 For the present work a grid with a spacing of 2.5° in latitude and 5° in longitude has been used. Then the Az value at each grid node has been computed as a weighted average of the m scattered Azi values, where each weight is the inverse of the square of the distance node-Azi point. The implementation of the described reconstruction procedures needed adaptations of some of the NeQuick model computation routines.
4. Test of the Techniques
4.1. Data Used
 In order to compare the proposed techniques, the day 5 April 2000 has been chosen for the test. As can be seen from the World Data Center for Geomagnetism, Kyoto (http://swdcwww.kugi.kyoto-u.ac.jp), and the Space Environment Center (SEC) (http://www.sec.noaa.gov) Web sites, it is a geomagnetically undisturbed day during a high solar activity period. Therefore 24 hours of “ground truth” data obtained from 25 GPS receivers and foF2 values obtained from 6 ionosondes located in the vicinity of some “truth” receivers, as shown in Figure 1, have been used. “Ground truth” data are high-precision GPS-derived slant TEC measurements obtained at 1 s time interval from 25 Wide Area Augmentation System (WAAS) reference site locations, mainly situated in continental United States [Komjathy et al., 2005]. These data were made available by the WAAS project, whereas foF2 values have been obtained from the ionograms available in the digital ionogram database (DIDBase) of the Center for Atmospheric Research of University of Massachusetts at Lowell [Reinisch et al., 2004].
 For the present study, the sampling interval of “ground truth” data has been reduced to 15 min and foF2 values have been manually scaled, when possible, at 15 min time interval. Only slant TEC data corresponding to satellite links with an elevation greater than 10° have been considered. Hence 16,753 slant TEC data and 424 foF2 values have been used for the statistical analysis.
4.2. Evaluation Criteria
 To estimate the effectiveness of the two retrieval techniques on the basis of the computation of suitable Az values, the following approach has been used. The performance of the retrieval techniques has been evaluated through the statistical comparison between experimental and reconstructed slant TEC data and through the statistical comparison between experimental and retrieved foF2 data. More in detail, for each retrieval technique, the statistics has been based on scatterplot of the retrieved against experimental values and on relative frequencies distribution of the errors, where the differences between retrieved and experimental values are defined as errors.
 For comparison purposes the performance of the NeQuick model used in a standard way, namely driven by the 10.7 cm solar radio flux of the day, has been chosen as reference. It is understood that in all cases the same sets of experimental data have been used for the analysis.
4.3. Data Analysis
 Using NeQuick driven by the F10.7 of 5 April 2000, all modeled slant TEC corresponding to all experimental slant TEC and all modeled foF2 corresponding to experimental foF2 have been calculated. The corresponding scatterplots illustrated in Figure 2 indicate a poor agreement between experimental and retrieved data and a general underestimation of modeled values, as confirmed by the best fit line coefficients, also indicated in the graphics. The relative frequencies distribution reported in Figure 3 allow us to better quantify the model underestimation and data spreading: the TEC error average and standard deviation are −16.50 TECU (1 TECU = 1016 el m−2) and 16.70 TECU, while the foF2 error average and standard deviation are −0.52 MHz and 0.94 MHz.
 Using the single-station technique, for each ground station 96 Az values (one every 15 min) have been computed for 5 April 2000. Consequently these 96 Az values have been input into NeQuick to compute all modeled slant TEC corresponding to all experimental slant TEC and all modeled foF2 corresponding to experimental foF2.
 This process has been applied to all 25 ground stations and the results have been gathered in single diagrams. The scatterplots illustrated in Figure 4 indicate a better agreement between experimental and retrieved data, if compared to the standard use of NeQuick. Only a small underestimation of modeled values in terms of TEC and a small overestimation in terms of foF2 are observed. The relative frequencies distribution reported in Figure 5 allow us to point out that the improvements due to the single-station retrieval technique are more noticeable in terms of TEC values than in terms of foF2 values reconstruction. In fact the TEC error average and standard deviation are −0.60 TECU and 9.14 TECU, while the foF2 error average and standard deviation are 0.52 MHz and 0.62 MHz.
 It should be remembered that the results shown in Figures 4 and 5 are the summary of the application of the single-station technique to several locations. Therefore they do not represent the performance of a possible regional retrieval technique based on the application of the single-station method.
 Using the multiple-station technique, 96 global Az grids (one every 15 min) have been computed for 5 April 2000. The 96 Az grids have been input into NeQuick to compute all modeled slant TEC corresponding to all experimental slant TEC and all modeled foF2 corresponding to experimental foF2.
 The scatterplots illustrated in Figure 6 underline that the multiple-station technique leads to a further improvement in terms of slant TEC reconstruction, but not in terms of foF2 retrieval, if compared with the case of single-station method. This conclusion is even more evident if the distributions illustrated in Figure 7 are considered: in this case the TEC error average and standard deviation are −0.13 TECU and 6.04 TECU, and the foF2 error average and standard deviation are 0.49 MHz and 0.60 MHz.
 Two ionosphere electron concentration retrieval techniques have been developed using the NeQuick electron density model, namely a single-station and a multiple-station retrieval techniques. They are able to provide in near real time a realistic 3-D representation of the electron density of the ionosphere under given conditions. They are based on NeQuick model adaptation through experimental slant TEC data ingestion to obtain single values (by single-station method) and grid values (in the case of the multiple-station method) of the model driving parameter Az. Considering the most evolved technique, the computation of an Az grid allows calculation with the NeQuick model of the electron density of the ionosphere over the region of interest. As a consequence it is possible to calculate the slant TEC and other radio wave propagation parameters along any ground-to-satellite ray path or to reconstruct foF2 values at any wanted location. The data analysis performed indicates that there is a remarkable improvement in terms of TEC reconstruction capabilities when passing from the single-station retrieval technique to the multiple-station retrieval technique. This behavior is expected since the multiple-station technique can take advantage of the higher density of the data used to adapt the model. The same analysis has shown that in terms of foF2 no substantial improvement can be observed when the multiple-station technique is used instead of the single-station method. Nevertheless the tests performed demonstrated the potentiality and the effectiveness of the retrieval techniques based on model adaptation by means of actual data and the results obtained in the present study encourage further developments of the proposed techniques.
 The authors are grateful to the United States Federal Aviation Administration's Wide Area Augmentation System (WAAS) community for providing us with the high-precision ionospheric “ground truth” measurements for the present study and to the Center for Atmospheric Research of University of Massachusetts at Lowell for providing access to the digital ionogram database (DIDBase).