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Using B-Spline Expansions for Ionosphere Modeling

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Handbook of Geomathematics

Abstract

The knowledge of the electron density is the key point in correcting electromagnetic measurements for ionospheric disturbances. In the last 15 years, the space-geodetic observation techniques such as the Global Positioning System (GPS) or radar altimetry have become a promising tool for monitoring the electron distribution in the ionosphere.This chapter gives a detailed overview of the mathematical modeling of ionospheric parameters such as the electron density by means of B-spline expansions. B-splines – which are locally supported basis functions – allow for optimal handling of unevenly distributed observations and data gaps. By combining the one-dimensional basis functions by means of tensor products, multidimensional models can be constructed easily. The unknown model coefficients are estimated based on observations from a number of space-geodetic techniques. In addition to the mathematical model and the basis functions used, the estimation process including variance component estimation (VCE) and multi-scale representation (MSR) is introduced. The feasibility of the approach is shown for one example modeling the vertical total electron content (VTEC) for 24 h in South America.

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Authors and Affiliations

  1. Deutsches Geodätisches Forschungsinstitut, Munich, Germany

    Michael Schmidt, Denise Dettmering & Florian Seitz

Authors
  1. Michael Schmidt
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  2. Denise Dettmering
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  3. Florian Seitz
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Corresponding author

Correspondence to Michael Schmidt .

Editor information

Editors and Affiliations

  1. Geomathematics Group, University of Kaiserslautern, Kaiserslautern, Germany

    Willi Freeden

  2. Department of Mathematics, University of Central Florida, Orlando, Florida, USA

    M. Zuhair Nashed

  3. Computational Mathematics, Technische Universität Braunschweig, Braunschweig, Germany

    Thomas Sonar

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Schmidt, M., Dettmering, D., Seitz, F. (2015). Using B-Spline Expansions for Ionosphere Modeling. In: Freeden, W., Nashed, M., Sonar, T. (eds) Handbook of Geomathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54551-1_80

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