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