Scientific- Research Quarterly of Geographical Data (SEPEHR)

Scientific- Research Quarterly of Geographical Data (SEPEHR)

Efficiency of Fourier transformation in studying of ionosphere time series

Document Type : Research Paper

Authors
Ramin Ali ramei 1
Mohammad Reza Seif 2
Seyyed Reza Ghaffari Razin 3
1 MSc ,Department of surveying engineering, Islamic Azad University of North Tehran, Tehran, Iran.
2 Assistant professor, Imam Hussein Comprehensive University, Tehran, Iran
3 Associate professor, Department of geoscience engineering, Arak University of Technology, Arak, Iran
10.22131/sepehr.2025.2019229.3048
Abstract
Extended Abstract
Introduction:
The ionosphere is a layer of the earth's atmosphere that extends from an altitude of 80 km to more than 1000 km above the earth. Due to its electrical properties, this layer of the atmosphere has very important and fundamental effects on the waves passing through it. The ionosphere exhibits temporary and intermittent variations such as daily, 27-day, seasonal, six-monthly, annual and 11-year changes. Ionosphere disturbances can cause distance error, cycle slips and phase fluctuations of satellite systems signals, which leads to degradation of the performance, accuracy and reliability of these systems. A parameter that can be used to study the ionosphere is the total electron content (TEC). This parameter is the sum of free electrons in a cylinder with a cross section of one square meter between the satellite and the receiver in the ground and its unit is ele./m2. If the TEC is along the vertical (zenith direction), it is called VTEC. Usually, TEC is expressed in terms of TECU, which is equal to 1016 ele/m2. Various methods have been developed to model the TEC. The simplest and at the same time the most practical method is to use observations of two-frequency receivers. If there is a proper station distribution, it is possible to obtain accurate TEC and model the ionosphere.
Materials & Methods
The main purpose of this paper is to use the Fourier transform method to model and predict the value of TEC and to examine the variations in the time series of the ionosphere in 2018. Fourier transform in mathematics is the study of the representation or estimation of general functions by sum of trigonometric functions. In engineering science, decomposition of a function into simpler parts is usually called Fourier analysis and the process of reconstructing the function from these simpler parts is called Fourier combination. Every transformation used for analysis also has an inverse transformation that is used as a composition. Using the Fourier transform, the main frequencies in the behavior of the ionosphere for the period 2007 to 2017 have been identified, and then using these frequencies, the value of the time series of TEC is predicted for 2018. All observations are related to the GPS station of Tehran, which is one of the stations of the international GNSS service (IGS) network. In order to evaluate the accuracy and correctness of the model presented in this paper, the statistical indicators of relative error and correlation coefficient are used. All the results obtained from the Fourier model are compared and evaluated with the results obtained from the outputs of the IGS network (TECGIM) and the ordinary Kriging (TECOK) model.
Results & Discussion
In the analysis of the results related to 2018, the correlation coefficient of FT, GIM and OK models with TEC obtained from GPS was obtained as 0.81, 0.71 and 0.77, respectively. Also, the averaged relative error of three models in 2018 was 13.18%, 27.75% and 15.18%, respectively. The comparison of the results of the correlation coefficient and the relative error indicated the higher accuracy and precision of the FT model than the GIM and OK models in predicting the TEC for quiet conditions of solar activities. Also, the RMSE parameter was investigated, which was lower for the FT model than the GIM and OK models.
Conclusion
In this paper, the total electron content (TEC) of the ionosphere is evaluated using the Fourier transform (FT). For this purpose, the observations of Tehran GPS station (35.690 N, 51.330 E), which is one of the stations of the IGS network, are used between 2007 and 2018. Using observations from 2007 to 2017, the coefficients of the Fourier series are calculated and the dominant frequencies in it are extracted. Then, using the obtained Fourier series coefficients, the amount of TEC is predicted daily, monthly and annually for 2018. The results of this paper showed that the Fourier transform model has the ability to know the behavioral frequencies of the ionosphere and also predict the TEC variations in the period of quiet solar activity. As a suggestion for the continuation of this research, the Fourier transform model for the state of severe solar activities can be investigated and evaluated and compared with other models. Also, with the availability of data from more stations, temporal and spatial variations of the ionosphere can be modeled with Fourier transform and then predicted.
Keywords
Ionosphere
Fourier transformation
Prediction
GPS
GIM
Subjects
1- Abdi, N., Azmoudeh Ardalan, A., & Karimi, R. H. (2017). Integration of GPS observations and satellite altimetry for local ionospheric modeling in Iran. *Science and Technology of Surveying and Mapping, 7*(3), 109–125.
2- Abe, O. E., Rabiu, A. B., Bolaji, O. S., & Oyeyemi, E. O. (2018). Modeling African equatorial ionosphere using ordinary Kriging interpolation technique for GNSS applications. *Astrophysics and Space Science, 363*, 168.
3- Akhoondzadeh, M. (2014). Investigation of GPS-TEC measurements using ANN method indicating seismo-ionospheric anomalies around the time of the Chile (Mw = 8.2) earthquake of 01 April 2014. *Advances in Space Research, 54*(9), 1768–1772.
4- Amerian, Y., Vosoughi, B., & Mashhadi Hossainali, M. (2013). Regional ionosphere modeling in support of IRI and wavelet using GPS observations. *Acta Geophysica, 61*(5), 1246–1261. https://doi.org/10.2478/s11600-013-0121-5
5- Ansari, K., Kumar Panda, S., & Corumluoglu, O. (2018). Mathematical modelling of ionospheric TEC from Turkish permanent GNSS network (TPGN) observables during 2009–2017 and predictability of NeQuick and Kriging models. *Astrophysics and Space Science, 363*, 42.
6- Bilitza, D., & Reinisch, B. W. (2008). International Reference Ionosphere 2007: Improvements and new parameters. *Advances in Space Research, 42*, 599–609.
7- Burrus, C. S. (1995). Multiband least squares FIR filter design. *IEEE Transactions on Signal Processing, 43*(2), 412–421.
8- Ciraolo, L., Azpilicueta, F., Brunini, C., Meza, A., & Radicella, S. M. (2007). Calibration errors on experimental slant total electron content (TEC) determined with GPS. *Journal of Geodesy, 81*(2), 111–120. https://doi.org/10.1007/s00190-006-0093-1
9- Etemadfard, H., & Hossainali, M. M. (2016). Application of Slepian theory for improving the accuracy of global ionosphere models in the Arctic region. *Journal of Geophysical Research: Space Physics, 121*(3), 2583–2594.
10- Feizi, R., Vosoughi, B., & Ghaffari Razin, M. R. (2019). Regional modeling of the ionosphere using adaptive neuro-fuzzy inference system in Iran. *Advances in Space Research, 65*, 2515–2528.
11- Ghaffari Razin, M. R., & Vosoughi, B. (2016). Modeling and interpolation of total electron content of the ionosphere using artificial neural networks and GPS observations. *Earth and Space Physics, 42*(2), 419–437.
12- Ghaffari Razin, M. R., & Vosoughi, B. (2017). Wavelet neural networks using particle swarm optimization training in modeling regional ionospheric total electron content. *Journal of Atmospheric and Solar-Terrestrial Physics, 149*, 21–30. https://doi.org/10.1016/j.jastp.2016.09.005
13- Ghaffari Razin, M. R., & Vosoughi, B. (2020). Ionosphere time series modeling using adaptive neuro-fuzzy inference system and principal component analysis. *GPS Solutions, 24*, 51.
14- Ghaffari Razin, M. R., Moradi, A. R., & Inyurt, S. (2021). Spatio-temporal analysis of TEC during solar activity periods using support vector machine. *GPS Solutions, 25*, 121. https://doi.org/10.1007/s10291-021-01158-3
15- Han, Y., Wang, L., Fu, W., Zhou, H., Li, T., & Chen, R. (2022). Machine learning-based short-term GPS TEC forecasting during high solar activity and magnetic storm periods. *IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 15*, 115–126. https://doi.org/10.1109/JSTARS.2021.3132049
16- Harris, F. J. (1978). On the use of windows for harmonic analysis with the discrete Fourier transform. *Proceedings of the IEEE, 66*(1), 51–83.
17- Inyurt, S., & Sekertekin, A. (2019). Modeling and predicting seasonal ionospheric variations in Turkey using artificial neural network (ANN). *Astrophysics and Space Science, 364*, 62.
18- Jakowski, N., Stankov, S., & Klaehn, D. (2005). Operational space weather service for GNSS precise positioning. *Annales Geophysicae, 23*(9), 3071–3079.
19- Klobuchar, J. A. (1996). Ionospheric effects on GPS. In B. W. Parkinson & J. J. Spilker Jr. (Eds.), *Global Positioning System: Theory and applications* (Vol. 1, pp. 485–510). American Institute of Aeronautics and Astronautics.
20- Liu, Z., & Gao, Y. (2003). Ionospheric TEC predictions over a local area GPS reference network. *GPS Solutions, 8*(1), 23–29.
21- Mallika, I. L., Ratnam, D. V., Raman, S., & Sivavaraprasad, G. (2020). A new ionospheric model for single frequency GNSS user applications using the Klobuchar model driven by auto regressive moving average (SAKARMA) method over the Indian region. *IEEE Access, 8*, 54535–54553. https://doi.org/10.1109/ACCESS.2020.2981365
22- Nava, B., Coisson, P., & Radicella, S. M. (2008). A new version of the NeQuick ionosphere electron density model. *Journal of Atmospheric and Solar-Terrestrial Physics.* https://doi.org/10.1016/j.jastp.2008.01.015
23- Nematipour, P., Raoofian-Naeeni, M., & Ghaffari Razin, M. R. (2021). Regional application of C1 finite element interpolation method in modeling of ionosphere total electron content over Europe. *Advances in Space Research.*
24- Osgood, B. (2004). *The Fourier transform and its applications*. Stanford University.
25- Ram, S., Gowtam, S., Mitra, V., & Reinisch, B. (2018). The improved two-dimensional artificial neural network-based ionospheric model (ANNIM). *Journal of Geophysical Research: Space Physics, 123*(7), 5807–5820.
26- Sabzehee, F., Farzaneh, S., Sharifi, M. A., & Akhoondzadeh, M. (2018). TEC regional modeling and prediction using ANN method and single frequency receiver over Iran. *Annals of Geophysics, 61*(1).
27- Schaer, S. (1999). Mapping and predicting the Earth’s ionosphere using the Global Positioning System (Ph.D. thesis). Astronomical Institute, University of Berne, Berne, Switzerland.
28- Schunk, R. W., & Nagy, A. F. (2000). *Ionospheres: Physics, Plasma Physics, and Chemistry*. Cambridge University Press.
29- Seeber, G. (2003). *Satellite geodesy: Foundations, methods, and applications*. Walter de Gruyter.
30- Sharifi, M. A., & Farzaneh, S. (2015). Regional TEC dynamic modeling based on Slepian functions. *Advances in Space Research, 56*(5), 907–915.
31- Stankov, S., Jakowski, N., Tsybulya, K., & Wilken, V. (2006). Monitoring the generation and propagation of ionospheric disturbances and effects on Global Navigation Satellite System positioning. *Radio Science, 41*, RS6S09. https://doi.org/10.1029/2005RS003327
32- Tebabal, A., Radicella, S. M., Damtie, B., Migoya-Orue, B., Nigussie, M., & Nava, B. (2019). Feed forward neural network-based ionospheric model for the East African region. *Journal of Atmospheric and Solar-Terrestrial Physics, 191*, 105052.
33- Wang, C., Xin, S., Liu, X., et al. (2018). Prediction of global ionospheric VTEC maps using an adaptive autoregressive model. *Earth Planets Space, 70*, 18. https://doi.org/10.1186/s40623-017-0762-8
34- Yilmaz, A., Akdogan, K. E., & Gurun, M. (2018). GPS ionospheric modeling over the Turkish region using Kriging interpolation and artificial neural networks. *Astrophysics and Space Science, 363*, 137