Using B-Spline expansions for ionosphere modeling

Michael Schmidt, Denise Dettmering, Florian Seitz

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

11 Scopus citations


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.

Original languageEnglish
Title of host publicationHandbook of Geomathematics
Subtitle of host publicationSecond Edition
PublisherSpringer Berlin Heidelberg
Number of pages45
ISBN (Electronic)9783642545511
ISBN (Print)9783642545504
StatePublished - 15 Sep 2015
Externally publishedYes


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