Murat Durmaz

Regional vertical total electron content (VTEC) modeling together with satellite and receiver differential code biases (DCBs) using semi-parametric multivariate adaptive regression B-splines (SP-BMARS)

There are various global and regional methods that have been proposed for the modeling of ionospheric vertical total electron content (VTEC). Global distribution of VTEC is usually modeled by spherical harmonic expansions, while tensor products of compactly supported univariate B-splines can be used for regional modeling. In these empirical parametric models, the coefficients of the basis functions as well as differential code biases (DCBs) of satellites and receivers can be treated as unknown parameters which can be estimated from geometry-free linear combinations of global positioning system observables. In this work we propose a new semi-parametric multivariate adaptive regression B-splines (SP-BMARS) method for the regional modeling of VTEC together with satellite and receiver DCBs, where the parametric part of the model is related to the DCBs as fixed parameters and the non-parametric part adaptively models the spatio-temporal distribution of VTEC. The latter is based on multivariate adaptive regression B-splines which is a non-parametric modeling technique making use of compactly supported B-spline basis functions that are generated from the observations automatically. This algorithm takes advantage of an adaptive scale-by-scale model building strategy that searches for best-fitting B-splines to the data at each scale. The VTEC maps generated from the proposed method are compared numerically and visually with the global ionosphere maps (GIMs) which are provided by the Center for Orbit Determination in Europe (CODE). The VTEC values from SP-BMARS and CODE GIMs are also compared with VTEC values obtained through calibration using local ionospheric model. The estimated satellite and receiver DCBs from the SP-BMARS model are compared with the CODE distributed DCBs. The results show that the SP-BMARS algorithm can be used to estimate satellite and receiver DCBs while adaptively and flexibly modeling the daily regional VTEC.

Multi-scale ionosphere model with data-adapted spatial resolution

Space weather research and a wide range of applications in communication and navigation require high-resolution ionosphere models. Today, the global ionosphere maps (GIMs) provided by the International GNSS Service (IGS) are the widely-used global vertical total electron content (VTEC) products. However, their spatial resolution of 2.5° in latitude and 5° in longitude is not high enough for modeling small-scale structures of the ionosphere. Therefore, besides the GIMs some regional high-resolution ionosphere models were developed. The German Aerospace Center (DLR), for instance, provides a regional VTEC model over Europe with a spatial resolution of 2° in both latitude and longitude.

Regional spatio - temporal modeling of the ionospheric Vertical Total Electron Content (VTEC) using Multivariate Adaptive Regression B‒Splines (BMARS)

Spatio‒temporal Regional modeling of the ionosphere in terms of the vertical total electron content (VTEC) is accomplished using a non‒parametric Multivariate Adaptive Regression B‒ Spline (BMARS) algorithm on the basis of Global Positioning System (GPS) observations. The basis functions are constructed as compactly supported tensor products of quadratic B‒Splines which are derived from the observations automatically. A smooth approximation is achieved by scale‒by‒scale model building strategy which searches for best fitting B Spline to the data at each scale. The real data set processed is gathered from ground based GPS stations in Europe and falls within the time interval of the geomagnetic storm on 15 February, 2011. The result of BMARS modeling apparently demonstrates the efficiency and the potential of the method. It is also compared both numerically and visually with a well‒known global and regional VTEC modeling based on spherical harmonics and B‒Splines respectively.

Estimation of global VTEC in near real-time using B-splines in support of IRI

Summary form only given. Real-time measurement streams from GNSS are becoming a reality with the advancements in technology. Currently, IGS and many regional networks provide real-time data streams. To explore the possible use of these streams, (near) real-time ionosphere modeling has been the focus of research in recent years. Reliable and accurate algorithms are required in order to use the data streams or derived short RINEX patches to deliver accurate real-time or near real-time (NRT) products such as global ionospheric Vertical Total Electron Content (VTEC).