Regional 4-D modeling of the ionospheric electron density

The knowledge of the electron density is the key point in correcting ionospheric delays of electromagnetic measurements and in studying the ionosphere. During the last decade GNSS, in particular GPS, has 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 informations on the electron density, which is basically a four-dimensional function depending on spatial position and time. In addition, these GNSS measurements can be combined with other available data including nadir, over-ocean TEC observations from dual-frequency radar altimetry (T/P, JASON, ENVISAT), and TECs from GPS-LEO occultation systems (e.g., FORMOSAT-3/COSMIC, CHAMP) with heterogeneous sampling and accuracy.In this paper, we present different multi-dimensional approaches for modeling spatio-temporal variations of the ionospheric electron density. To be more specific, we split the target function into a reference part, computed from the International Reference Ionosphere (IRI), and an unknown correction term. Due to the localizing feature of B-spline functions we apply tensor-product spline expansions to model the correction term in a certain multi-dimensional region either completely or partly. Furthermore, the multi-resolution representation derived from wavelet analysis allows monitoring the ionosphere at different resolutions levels. For demonstration we apply three approaches to electron density data over South America.