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Annales Geophysicae An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/angeo-2019-32
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/angeo-2019-32
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Regular paper 04 Mar 2019

Regular paper | 04 Mar 2019

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This discussion paper is a preprint. It is a manuscript under review for the journal Annales Geophysicae (ANGEO).

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

Andreas Goss1, Michael Schmidt1, Eren Erdogan1, Barbara Görres2, and Florian Seitz1 Andreas Goss et al.
  • 1Deutsches Geodätisches Forschungsinstitut der Technischen Universität München, Arcisstraße 21, 80333 Munich
  • 2Bundeswehr GeoInformation Centre (BGIC), Euskirchen, Germany

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.

Andreas Goss et al.
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Short summary
The paper describes an approach to model VTEC from NRT GNSS observations only by generating a Multi-Scale-Representation (MSR) based on B-splines. The unknown model parameters are estimated by means of a Kalman-Filter. A number of products have been created which differ both in their spectral and temporal resolution. The validation studies show that the product of highest resolution, based on NRT input data is of higher accuracy than other used within the selected time span of investigation.
The paper describes an approach to model VTEC from NRT GNSS observations only by generating a...
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