Total electron content modeling in terms of spherical radial basis functions over Iran

Document Type : Research Paper


1 M.Sc. Student, Department of Geodesy, Faculty of Geodesy and Geomatics Engineering, K. N. Toosi University of Technology, Tehran, Iran

2 Assistant Professor, Department of Geodesy, Faculty of Geodesy and Geomatics Engineering, K. N. Toosi University of Technology, Tehran, Iran

3 Ph.D. Student, Department of Geodesy, Faculty of Geodesy and Geomatics Engineering, K. N. Toosi University of Technology, Tehran, Iran


Satellite positioning using single frequency receivers and space technologies such as radar and communication systems all demand a precise knowledge of the ionosphere. Ionosphere is the upper layer of atmosphere which is ionized and affects the transmission of electromagnetic waves depending on their frequencies. Parameters that characterize this layer of the atmosphere are the Ionospheric Electron Density (IED) and the Total Electron Content (TEC). Hence, modeling and understanding of TEC in a precise way is an undeniable necessity. International Reference Ionosphere (IRI) and Global Ionospheric Maps (GIMs) are the sources of information that provide TEC values globally for all users. It could be expected that the accuracy of such global models in some regions like Iran are not suitable since these models are obtained from the global data sources which they lack a good density in Iran plateau. Thus, regional TEC modeling over Iran needs more attention. In this study, the total electron content obtained from the permanent dual-frequency GPS receivers are utilized in regional TEC modeling. Estimation of TEC requires satellites and receivers Differential Code Biases (DCB) to be known. DCB values for satellites and the International GNSS Service (IGS) receivers can be observed from IGS analysis centers e.g. the Center for Orbit Determination in Europe (CODE). However, for local dual frequency receivers to be used for the purpose of TEC monitoring, their DCB should be estimated. In this research, the DCB value of each station is computed from observations which their corresponding elevation angles are more than 60 degrees. The DCB computation process consists of 3 steps. First, Vertical Total Electron Content (VTEC) is obtained from the spatial and temporal interpolation of (IGS-IONEX) files. Second, each interpolated VTEC is multiplied by a mapping function. After that, the difference of the observed pseudo-range of the two frequencies is denoised via a moving average filter. Eventually utilizing the interpolated VTEC and smoothed difference of the observed pseudo-ranges and the mapping function, DCB values of all stations are estimated. Thereafter, a parameterization of the estimated VTEC over the study area is implemented. For this purpose, the Spherical Radial Basis Function (SRBF) method is used. These functions are compact support and more practical for interpolation of observations on a regional scale. It is necessary to mention that the optimization of the depth of SRBFs plays an important role in increasing the accuracy of the regression. The coefficients of the expansion are computed by least squares estimation, and the Tikhonov regularization method is used in which the regularization parameter is obtained from L-curve. Some of the observations are excluded from the dataset as check points for evaluation of the constructed model. In this research, once the modeling process is conducted over Iran and also the north-western region of Iran which has a more proper distribution of data, is parameterized on the 124th day of 2016. The height of the ionosphere layer is assumed 450 km above the earth's surface. Then aregular grid of point-mass functions that has the simplest form of SRBFs is constructed. Then, by changing the depth of the grid, an optimal depth is estimated at which the best accuracy is obtained at the check points. The results reveal that the parameterization of TEC with a regular grid of SRBFs in which the number of grid points are approximately 10% of the number of data, leads to the construction of a model whose accuracy in the check points is significantly enhanced comparing to GIMs. In addition, the accuracy of the modeling is better in areas where data density and distribution are more appropriate. The results of this research show that the accuracy of VTEC modeling in the whole region of Iran in 0 to 1 Universal Time (UT) and 10 to 11 UT are 0.87 and 1.30 TECU respectively. According to the GIMs VTEC accuracy of 1.91 and 1.97 TECU in the same periods of time, it is concluded that the accuracy of VTEC modeling in this research is improved by 1.04 and 0.67 TECU with respect to GIM. In addition, with increasing the density of data distribution and limiting the study region to the north west of Iran, the accuracy of the proposed model is equal to 0.33 and 1.66 TECU. With respect to the GIMs accuracy this is equal to 1.87 and 1.92 TECU, the proposed method has an improvement of about 1.54 and 0.86 TECU comparing to the GIMs model.


Main Subjects

قلی‌پور، ن. و عامریان، ی.، 1398، برآورد مقادیر اریب تفاضلی کد گیرنده‌های شبکه دائم GPS ایران با استفاده از نقشه‌های یونسفری جهانی، نشریه علمی پژوهشی علوم و فنون نقشه‌برداری، 8(4)، 177-186.
Al-Fanek, O.J.S., 2013, Ionospheric imaging for Canadian polar regions, University of Calgary.
Amerian, Y., 2013, Regional modeling of the ionospheric electron density using wavelet analysis and GPS observations. Faculty of Geodesy and Geomatics Engineering, PhD Thesis, KN Toosi University of Technology.
Amerian, Y., Hossainali, M.M. and Voosoghi, B., 2013a, Regional improvement of IRI extracted ionospheric electron density by compactly supported base functions using GPS observations. Journal of Atmospheric and Solar-Terrestrial Physics, 92, pp.23-30.
Amerian, Y., Voosoghi, B. and Hossainali, M.M., 2013b, Regional ionosphere modeling in support of IRI and wavelet using GPS observations. Acta Geophysica, 61(5), 1246-1261.
Arikan, F., Deviren, M., Lenk, O., Sezen, U. and Arikan, O., 2012, Observed ionospheric effects of 23 October 2011 Van, Turkey earthquake. Geomatics, Natural Hazards and Risk, 3(1), 1-8.
Arikan, F., Erol, C. and Arikan, O., 2003, Regularized estimation of vertical total electron content from Global Positioning System data. Journal of Geophysical Research: Space Physics, 108(A12).
Arikan, F., Nayir, H., Sezen, U. and Arikan, O., 2008, Estimation of single station interfrequency receiver bias using GPS‐TEC. Radio Science, 43(4).
Bilitza, D. and Reinisch, B. W., 2008, International reference ionosphere 2007: improvements and new parameters. Advances in space research, 42(4), 599-609.
Bucha, B., Bezděk, A., Sebera, J. and Janák, J., 2015, Global and regional gravity field determination from GOCE kinematic orbit by means of spherical radial basis functions. Surveys in Geophysics, 36(6), 773-801.
Bucha, B., Janák, J., Papčo, J. and Bezděk, A., 2016, High-resolution regional gravity field modelling in a mountainous area from terrestrial gravity data. Geophysical Supplements to the Monthly Notices of the Royal Astronomical Society, 207(2), 949-966.
Calais, E. and Minster, J. B., 1998, GPS, earthquakes, the ionosphere, and the Space Shuttle. Physics of the Earth and Planetary Interiors, 105(3-4), 167-181.
Etemadfard, H. and Hossainali, M. M., 2016, Application of Slepian theory for improving the accuracy of SH‐based global ionosphere models in the Arctic region. Journal of Geophysical Research: Space Physics, 121(3), 2583-2594.
Etemadfard, H. and Hossainali, M. M., 2017, Vector ionosphere modeling by vector spherical Slepian base functions. GPS solutions, 21(2), 675-684.
Farzaneh, S. and Forootan, E., 2018, Reconstructing regional ionospheric electron density: a combined spherical slepian function and empirical orthogonal function approach. Surveys in Geophysics, 39(2), 289-309.
Hansen, P. C., 1994, Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems. Numerical algorithms, 6(1), 1-35.
Heikkinen, M., 1981, Solving the shape of the earth by using digital density models. Rep. Finnish Geod. Inst., 81(2), 69-81.
Jin, S., Cho, J.-H. and Park, J.-U., 2007, Ionospheric slab thickness and its seasonal variations observed by GPS. Journal of Atmospheric and Solar-Terrestrial Physics, 69(15), 1864-1870.
Klees, R., Slobbe, D. and Farahani, H., 2018, A methodology for least-squares local quasi-geoid modelling using a noisy satellite-only gravity field model. Journal of Geodesy, 92(4), 431-442.
Komjathy, A., 1997, Global ionospheric total electron content mapping using the Global Positioning System, University of New Brunswick Fredericton.
Leick, A., Rapoport, L. and Tatarnikov, D., 2015, GPS satellite surveying. John Wiley & Sons.
Leigh, R., Robinson, T. and Lester, M., 1988, Ionospheric corrections for radar altimetry, International Geoscience and Remote Sensing Symposium,'Remote Sensing: Moving Toward the 21st Century'. IEEE, 989-992.
Liu, Z., 2004, Ionosphere tomographic modeling and applications using Global Positioning System (GPS) measurements. Calgary.
Liu, Q., Kikuchi, F., Goossens, S., Matsumoto, K., Hanada, H., Ping, J., Shi, X., Tamura, Y., Harada, Y., Asari, K., Tsuruta, S., Ishikawa, T., Kawano, N., Ishihara, Y., Noda, H., Sasaki, Sh., Iwata, T. and Namiki, N., 2009, S-band same-beam VLBI observations in SELENE (Kaguya) and correction of atmospheric and ionospheric delay. J. Geod. Soc. Japan, 55, 243-254.
Nohutcu, M., Karslioglu, M. and Schmidt, M., 2010, B-spline modeling of VTEC over Turkey using GPS observations. Journal of Atmospheric and Solar-Terrestrial Physics, 72(7-8), 617-624.
Safari, A., Sharifi, M. and Foroughi, I., 2013, Local gravity field modeling using radial basis functions, case study: coastal area of the Persian Gulf. Journal of the EARTH and SPACE PHYSICS, 39, 33-48.
Schaer, S., 1999, Mapping and predicting the Earth’s ionosphere using the Global Positioning System. PhD thesis, Bern University, Switzerland.
Schmidt, M., Karslioglu, M.O. and Zeilhofer, C., 2008, Regional multi-dimensional modeling of the ionosphere from satellite data. Proceedings of the TUJK Annual Scientific Meeting, Ankara.
Schmidt, M., Dettmering, D., Mößmer, M., Wang, Y. and Zhang, J., 2011, Comparison of spherical harmonic and B spline models for the vertical total electron content. Radio Science, 46(6).
Schreiner, W. S., Markin, R. E. and Born, G. H., 1997, Correction of single frequency altimeter measurements for ionosphere delay. IEEE transactions on geoscience and remote sensing, 35(2), 271-277.
Sezen, U., Arikan, F., Arikan, O., Ugurlu, O. and Sadeghimorad, A., 2013, Online, automatic, near-real time estimation of GPS-TEC: IONOLAB-TEC. Space Weather, 11(5), 297-305.
Sharifi, M. A. and Farzaneh, S., 2014, The spatio-spectral localization approach to modeling VTEC over the western part of the USA using GPS observations. Advances in Space Research, 54(6), 908-916.
Sharifi, M. A. and Farzaneh, S., 2016, Local Ionospheric Modeling Using the Localized Global Ionospheric Map and Terrestrial GPS. Acta Geophysica, 64(1), 237-252.
Sharifi, M. A. and Farzaneh, S., 2017, The ionosphere electron density spatio-temporal modeling based on the Slepian basis functions. Acta Geodaetica et Geophysica, 52(1), 5-18.
Steigenberger, P., Rothacher, M., Dietrich, R., Fritsche, M., Rulke, A. and Vey, S., 2006, Geodesy and Gravity Tectonophysics-B05402-Reprocessing of a global GPS network (DOI 10.1029/2005JB003747). Journal of Geophysical Research-Part B-Solid Earth, 111(5).
Tenzer, R. and Klees, R., 2008, The choice of the spherical radial basis functions in local gravity field modeling. Studia Geophysica et Geodaetica, 52(3), 287.
Tenzer, R., Klees, R. and Wittwer, T., 2012, Local gravity field modelling in rugged terrain using spherical radial basis functions: case study for the Canadian rocky mountains, Geodesy for Planet Earth. Springer, 401-409.
Wittwer, T., 2009, Regional gravity field modelling with radial basis functions.
Zeilhofer, C., 2008, Multi-dimensional B-spline modeling of spatio-temporal ionospheric signals. 123, A, DGK, Mänchen.