Using B-Spline Expansions for Ionosphere Modeling

  • Michael SchmidtEmail author
  • Denise Dettmering
  • Florian Seitz
Reference work entry


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Michael Schmidt
    • 1
    Email author
  • Denise Dettmering
    • 1
  • Florian Seitz
    • 1
  1. 1.Deutsches Geodätisches ForschungsinstitutMunichGermany

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