Regional application of C1 finite element interpolation method in modeling of ionosphere total electron content over Europe.

• A novel approach for regional ionosphere grid model with high spatial-temporal resolution is suggested. • The results of the new model is analyzed at different disturb geomagnetic and solar conditions. • A comparative analysis between the results of new model, GIM, NeQuick and GPS-TEC is made. In this paper, a novel approach based on C1 finite element (FE) interpolation is used to construct a regional ionospheric grid model (RIGM) with high spatio-temporal resolution over Europe. The spatial resolution of the new model is 0.50 for a longitude and latitude and a temporal resolution is 15 min. Observations of 38 GPS stations at different days and seasons with different geomagnetic and solar activity conditions are used to evaluate the new method. All stations are used to discretize the whole domain of the problem into separate triangular patches using a Delaunay triangulation algorithm. In this case, GPS stations would be the vertices of the triangular patches. Also, the position of stations in sun-fixed coordinate system with coordinates of latitude and longitude are chosen in order to consider the temporal variations of vertical total electron content (VTEC). To model the behavior of VTEC in each triangular patch, a particular shape function is defined which is fitted to VTEC values at three vertices of each triangle while it satisfies C1 continuity of VTEC at the common edges of the adjacent triangles. The results of the new model are compared with the VTEC of GPS at 4 control stations as well as global ionosphere map (GIM) and NeQuick models. Statistical parameters, including correlation coefficient, root mean square error (RMSE), standard deviation and dVTEC = |VTEC GPS - VTEC model | have been used to evaluate the error of the models. In low geomagnetic activity (KP < 4), the average RMSE at 4 control stations for FE, GIM and NeQuick models are 0.89, 1.05 and 6.42 TECU, respectively, while in the high geomagnetic activity (KP > 4), they are 1.24, 1.68 and 7.62 TECU, respectively. For further analysis, the accuracy of three models in precise point positioning (PPP) has been also evaluated. In PPP method, there is an improvement of about 1–16 mm compared to GIM and NeQuick models at coordinate components of control stations in high geomagnetic activity. The results of the analysis performed in this paper show that the FE model has a very high capability and accuracy in regional VTEC modeling in high and low geomagnetic conditions. The regional accuracy of this model is higher than GIM and NeQuick models and therefore can be considered as a new model for the ionosphere. [ABSTRACT FROM AUTHOR]