B-spline modeling of VTEC over Turkey using GPS observations

In this study we propose two approaches to model the Vertical Total Electron Content (VTEC) of the ionosphere with quadratic B-spline functions. For the 2-D case, VTEC is modeled in a Sun-fixed reference frame. In the 3-D approach, the 2-D model is extended to represent the temporal variations in an Earth-fixed reference frame. The localizing features of B-splines allow resolving finer structures for the regions with a sufficient number of observations by increasing the level of functions. To reduce the effects of outliers, Iteratively Re-weighted Least Squares (IRLS) with a bi-square weighting function as a robust regression algorithm is applied for parameter estimation. Another iterative method LSQR is performed for the solution of the linear systems providing a regularization effect for ill-conditioned problems. B-spline approaches are applied to real data obtained from the ground-based GPS observations over Turkey. Results are compared with the solutions of the Bernese GPS Software.