Maps of the total electron content (TEC) of the ionosphere can be reconstructed using data extracted from global positioning system (GPS) signals. For historic and other sparse data sets, the reconstruction of TEC images is often performed using multivariate interpolation techniques. In this paper, a quantitative comparison of the ability of artificial neural networks (ANN), polynomial fitting and kriging interpolation was carried out in order to model the spatial variations of TEC using GPS data over Iran. These methods are suitable for handling multi-scale phenomena and unevenly distributed data. The observations collected at 25 GPS stations from Iranian permanent GPS network (uniformly spread all over Iran with sampling rate of 30-seconds). Dual frequency carrier phase and code GPS observations were used. A smoothed TEC approach was used for absolute TEC recovery. Evaluation of the methods has been applied with single GPS station in Tehran equipped with ionosonde instrument. The minimum relative error for ANN, polynomial and kriging are 4.37, 6.35, 9.13 % and the maximum relative error are 8.61, 29.06, and 20.14 % respectively. Also root mean square error (RMSE) of 3.7 TECU is computed for ANN method which is less than RMSE of other mentioned methods. The results show that ANN method has higher accuracy and compiles speed than kriging and polynomial. As well as, it is found that polynomial and kriging methods required many computational points in adjustment step.

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The ionosphere is the ionized part of the upper region of the atmosphere extending from 60 to 1500 km above the earth's surface. In this layer, free electrons are produced during the interaction of extreme ultra violet and x-ray radiation with the upper neutral atmosphere. Knowledge of the ionospheric electron density distribution is important for scientific studies and practical applications. In this paper, a new computerized ionospheric tomography reconstruction technique is developed to estimate electron density profiles over Iran. In this method, a functional based model is used to represent the electron density in space. The functional based model uses empirical orthogonal functions and spherical cap harmonics to describe the vertical and horizontal distribution of the electron density, respectively. The degree and the number of basis functions are chosen so that, the relative error of results is minimized. For this purpose, ionosonde observations (Lat. = 35.73°, Lon. = 51.38°) at 2007.04.03 is used. To apply the method for constructing a 3D-image of the electron density, GPS measurements of the Iranian permanent GPS network (at 2012/08/11) has been used. The modeling region is between 24 to 40 N and 44 to 64 W. The result of 3D-model has been compared to that of the international reference ionosphere model 2012 (IRI-2012). The analysis conducted in this paper indicates that the choice of spherical cap harmonics to 3 (K max = 3) and empirical orthogonal function in 3 (Q = 3), the regional reconstructed error is less than 36 %. The results show the advantages of this method in modeling of the ionosphere electron density on local and regional scales.Keywords Ionosphere electron density Á Spherical cap harmonics Á Empirical orthogonal functions Á GPS Á IRI2012