Using B-Spline Expansions for Ionosphere Modeling

Michael Schmidt (), Denise Dettmering () and Florian Seitz ()
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Michael Schmidt: Deutsches Geodätisches Forschungsinstitut
Denise Dettmering: Deutsches Geodätisches Forschungsinstitut
Florian Seitz: Deutsches Geodätisches Forschungsinstitut

A chapter in Handbook of Geomathematics, 2015, pp 939-983 from Springer

Abstract: 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.

Date: 2015
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DOI: 10.1007/978-3-642-54551-1_80

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