Enhanced TEC maps based on different space-geodetic observations

The ionosphere is defined as part of the upper earth’s atmosphere, where the density of free electrons and ions is high enough to influence the propagation of electromagnetic radio frequency waves. The ionisation process is primarily depending on the Sun’s activity and varies strongly with time, as well as with geographical location. The knowledge of the electron density is the critical point for many applications in positioning and navigation. During the last decade, dual-frequency Global Navigation Satellite Systems (GNSS), in particular the Global Positioning System (GPS) have become a promising tool for monitoring the Total Electron Content (TEC), i.e. the integral of the electron density along the ray-path between the transmitting satellite and the receiver. Hence, geometry-free GNSS measurements provide information on the electron density, which depends on spatial position and time, i.e. four-dimensional (4-D). At present the International GNSS Service (IGS) provides time dependent vertical TEC (VTEC) maps based on more than 100 permanent ground stations; however, these stations are mainly located on the continents and provide less accurate results over the oceans. New space-based observation techniques, especially various Low-Earth-Orbiting (LEO) satellite missions such as FORMOSAT-3/COSMIC and CHAMP, as well as dual-frequency radar altimetry missions such as Jason-1, Jason-2 and Envisat, can also contribute ionospheric evaluation on a global scale. The former get the TEC values from GPS-LEO occultation observations, whereas the latter provide VTEC observations from the on-board double-frequency radar altimeter. In order to enhance the IGS VTEC maps, i.e. balancing the insufficient GNSS coverage over the sea, efficient and inexpensive occultation observations and altimetry measurements can be collected and utilized. In this way the IGSVTEC products can benefit from additional data sources. In this paper, we combine both occultation and altimetry measurements to enhance the IGS VTEC maps. Our model consists of a given reference part (background model) computed from the IGS VTEC products, and also of an unknown correction term. In contrary to the traditional spherical harmonic approach, we use a global multi-dimensional B-spline approach for modelling the unknown correction term. We rely on normalized endpoint-interpolating B-splines for modelling the latitude- and the time-dependency and trigonometric B-splines for the dependency on the longitude. Several constraints, e.g. for the poles, for meridian, have to be considered carefully. Since B-splines are localizing functions, i.e. they are characterized by a compact support, data gaps can be handled appropriately. The unknown series coefficients of our multi-dimensional B-spline expansion are calculable from the LEO and the altimetry measurements applying parameter estimation. The relative weighting between the different data sources, the prior information, and the constraints will be performed by Variance Component Estimation (VCE). We compare the enhanced VTEC maps between the combined approach, which is based on VCE, and a second approach using FORMOSAT-3/COSMIC and Jason-1 data only within selected periods. It will be shown that an improvement from the additional data sources is visible in the areas with good data coverage. In regions with limited amount of observations the background model values from IGS will be conserved.