Non-parametric regional VTEC modeling with Multivariate Adaptive Regression B-Splines Murat Durmaz a , Mahmut Onur Karsliog ˘lu a,b,⇑ a Middle East Technical University (METU), Institute of Applied and Natural Sciences, Department of Geodetic and Geographic Information Technologies (GGIT), 06800 Ankara, Turkey b Middle East Technical University (METU), Civil Engineering Department, Geomatics Engineering Division, 06800 Ankara, Turkey Received 26 February 2011; received in revised form 22 June 2011; accepted 28 June 2011 Available online 5 July 2011 Abstract In this work Multivariate Adaptive Regression B-Splines (BMARS) is applied to regional spatio-temporal mapping of the Vertical Total Electron Content (VTEC) using ground based Global Positioning System (GPS) observations. BMARS is a non-parametric regres- sion technique that utilizes compactly supported tensor product B-splines as basis functions, which are automatically obtained from the observations. The algorithm uses a scale-by-scale model building strategy that searches for B-splines at each scale fitting adequately to the data and provides smoother approximations than the original Multivariate Adaptive Regression Splines (MARS). It is capable to process high dimensional problems with large amounts of data and can easily be parallelized. The real test data is collected from 32 ground based GPS stations located in North America. The results are compared numerically and visually with both the regional VTEC modeling generated via original MARS using piecewise-linear basis functions and another regional VTEC modeling based on B-splines. Ó 2011 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Ionosphere; GPS; MARS; B-spline; BMARS; Regional modeling 1. Introduction Dual frequency GPS observations are widely used for the estimation of the Total Electron Content (TEC) of the ionosphere. The behavior of the TEC data plays a deci- sive role particularly in positioning and navigation, tele- communication systems and space weather studies (Liu and Gao, 2004). Slant Total Electron Content (STEC) is obtained by integrating the total number of free electrons in a column of one meter squared cross section along the signal path between the GPS satellite and the receiver. Since ground based GPS observations are not sensitive enough to the vertical structure of the ionosphere, a single spherical layer approach is often used (Dettmering, 2003; Jin et al., 2006, 2008). This approach assumes that all elec- trons are concentrated in a spherical layer of infinitesimal thickness at a certain height. Accordingly, STEC is trans- formed into the Vertical Total Electron Content (VTEC) which can be modeled by a three dimensional function depending on geographic latitude, geographic longitude and time. For the generation of VTEC maps many works have been done in the literature on the basis of GPS obser- vations (Mannucci et al., 1998; Hernandez-Pajares and Sanz, 1999; Schaer, 1999; Yuan and Ou, 2002; Brunini et al., 2004; Jin et al., 2004). Two dimensional distribution of VTEC is traditionally modeled by spherical harmonic expansions which work very efficiently as long as the data is regularly distributed over the globe. Irregular data distri- bution and data gaps lead to some drawbacks which can be overcome by two different gridded TEC approaches pre- sented by Yuan and Ou (2002) and Mautz et al. (2005). For regional and local modeling of both the electron 0273-1177/$36.00 Ó 2011 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2011.06.031 ⇑ Corresponding author at: Middle East Technical University (METU), Civil Engineering Department, Geomatics Engineering Division, 06800 Ankara, Turkey. Tel.: +90 3122102440; fax: +90 3122105401. E-mail addresses: muratd@bilgigis.com (M. Durmaz), karsliog@ metu.edu.tr (M.O. Karsliog ˘lu). www.elsevier.com/locate/asr Available online at www.sciencedirect.com Advances in Space Research 48 (2011) 1523–1530