High Resolution Vertical Total Electron Content Maps Based on Multi-Scale B-spline Representations

Abstract

Abstract. For more than two decades the IGS (International GNSS Service) Ionosphere Associated Analysis Centers (IAAC) provide global maps of the vertical total electron content (VTEC). In general, the representation of a two- or three-dimensional function can be performed by means of a series expansion or by using a discretization technique. Whereas in the latter case for a spherical function such as VTEC usually pixels or voxels are chosen, in case of a series expansion mostly spherical harmonics (SH) are used as basis functions. The selection of the best suited approach for ionosphere modelling means a trade-off between the distribution of available data and their possibility to represent ionospheric variations with high resolution and high accuracy. Most of the IAACs generate Global Ionosphere Maps (GIMs) based on SH expansions up to the spectral degree n = 15 and provide them with a spatial resolution of 2.5° × 5° with respect to latitude and longitude direction, and a temporal sampling of two hours. In the recent years it was frequently claimed to improve the spatial sampling of the VTEC GIMs to a spatial resolution of 1° × 1° and to a temporal sampling of about 15 minutes. Enhancing the grid resolution means a interpolation of VTEC values for intermediate points but with no further information about variations in the signal. A degree 15 in the SH case for instance corresponds to a spatial sampling of 12° × 12°. Consequently, increasing the grid resolution requires at the same time an extension of the spectral content, i.e. to choose a higher SH degree value than 15. Unlike most of the IAACs, the VTEC modelling approach at DGFI-TUM is based on localizing basis functions, namely tensor products of polynomial and trigonometric B-splines. This way, not only data gaps can be handled appropriately and sparse normal equation systems are established for the parameters estimation procedure, also a multi-scale-representation (MSR) can be set up, to determine GIMs of different spectral content directly by applying the so-called pyramid algorithm and to perform highly effective data compression techniques. The estimation of the MSR model parameters is finally performed by a Kalman-Filter driven by near real-time (NRT) GNSS data. Within this paper we realize the MSR and create multi-scale products based on B-spline scaling and wavelet coefficients and VTEC grid values. We compare these products with different final and rapid products of the IAACs, e.g., the SH model from CODE (Berne) and the voxel solution from UPC (Barcelona). In opposite to that, DGFI-TUM's products are solely based on NRT GNSS observations and ultra-rapid orbits. Nevertheless, we can conclude that DGFI-TUMs high-resolution product (`othg') outperforms all products used within the selected time span of investigation, namely September 2017.

Intercalibration of the Plasma Density Measurements in Earth's Topside Ionosphere

“…Unlike the neutral atmosphere, which can cause errors in navigation and positioning in the order of several meters, ionospheric effects can yield uncertainties of up to 100 m (e.g., Hernández‐Pajares et al., 2011; Petit & Luzum, 2010). Ionospheric delays are inversely related to the square of carrier frequency, and directly proportional to electron density integrated along the ray path (e.g., Goss et al., 2019; Hobiger & Jakowski, 2017).…”

Influence of temporal resolution on the performance of global ionospheric maps

“…However, there are few studies about which GIM time resolution is most suitable for its application. Preliminary studies of different GIM temporal resolutions, based on spherical harmonic model and multi-scale representation as well as products from B-spline function, were performed by using GNSS data of one month ( [26,5]). It was found that 30-minutes or 10-minute GIM can obtain a noticeable improvement of the GIM accuracy compared with 2-hour GIM.…”

Operational Multi‐GNSS Global Ionosphere Maps at GFZ Derived From Uncombined Code and Phase Observations

“…In order to obtain estimates of the unbiased TEC, the ionospheric delays ( ) (2011). We use the common single-layer model (Azpilicueta et al, 2006;, 2010Davies & Hartmann, 1997;Goss et al, 2019;Mannucci et al, 1998;Schaer, 1999), in which the TEC is assumed to be contained within an infinitesimal thin shell at a constant height, which we assume at 450km E above the mean Earth radius in agreement with the solutions provided within the IGS. The slant ionospheric delays ( ) s r E i t are assumed to be related to the vertical ionospheric delays ( )…”