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 (TEC_GIM) and the ordinary Kriging (TEC_OK) 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.