Regional VTEC modeling with multivariate adaptive regression splines Murat Durmaz a , Mahmut Onur Karslioglu a,b, * , Metin Nohutcu b a Middle East Technical University (METU), Institute of Applied and Natural Sciences, Department of Geodetic and Geographic Information Technologies, 06531 Ankara, Turkey b Middle East Technical University (METU), Civil Engineering Department, Geomatics Engineering Division, 06531 Ankara, Turkey Received 2 December 2009; received in revised form 19 February 2010; accepted 22 February 2010 Abstract Different algorithms have been proposed for the modeling of the ionosphere. The most frequently used method is based on the spher- ical harmonic functions achieving successful results for global modeling but not for the local and regional applications due to the bounded spherical harmonic representation. Irregular data distribution and data gaps cause also difficulties in the global modeling of the ionosphere. In this paper we propose an efficient algorithm with Multivariate Adaptive Regression Splines (MARS) to represent a new non-parametric approach for regional spatio-temporal mapping of the ionospheric electron density using ground-based GPS observations. MARS can handle very large data sets of observations and is an adaptive and flexible method, which can be applied to both linear and non-linear problems. The basis functions are directly obtained from the observations and have space partitioning prop- erty resulting in an adaptive model. This property helps to avoid numerical problems and computational inefficiency caused by the num- ber of coefficients, which has to be increased to detect the local variations of the ionosphere. Since the fitting procedure is additive it does not require gridding and is able to process large amounts of data with large gaps. Additionally the model complexity can be controlled by the user via limiting the maximal number of coefficients and the order of products of the basis functions. In this study the MARS algo- rithm is applied to real data sets over Europe for regional ionosphere modeling. The results are compared with the results of Bernese GPS Software over the same region. Ó 2010 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Ionosphere; GPS; MARS; Regional modeling 1. Introduction GNSS and particularly the Global Positioning System (GPS) are widely used to monitor and model the iono- sphere in terms of the Total Electron Content (TEC) which is described by the total number of electrons in a column of 1m 2 cross section along the signal path through the ionosphere. Its unit is the Total Electron Con- tent Unit (TECU) and 1 TECU = 10 16 electrons/m 2 (Liu and Gao, 2003). The integral of the electron density along the signal path between the GPS satellite and the receiver is defined as Slant Total Electron Content (STEC). When using only ground-based GPS observations, the iono- sphere is often represented by a single spherical layer of infinitesimal thickness at a certain height, since ground- based observations are not sensitive enough to the radial geometry of the ionosphere (Dettmering, 2003; Jin et al., 2006, 2008). In this approach it is assumed that all elec- trons are concentrated in a spherical layer. STEC is con- verted to the Vertical Total Electron Content (VTEC) in a single layer model which is spatially a two dimensional function with respect to latitude and longitude. Many works have been done in the literature for the generation of ionospheric maps of the VTEC using GPS observations (Mannucci et al., 1998; Hernandez-Pajares et al., 1999; Schaer, 1999; Yuan and Ou, 2002; Brunini et al., 2004; 0273-1177/$36.00 Ó 2010 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2010.02.030 * Corresponding author. Address: Middle East Technical University (METU), Civil Engineering Department, Geomatics Engineering Division, 06531 Ankara, Turkey. Tel.: +90 312 210 24 40; fax: +90 312 210 54 01. E-mail addresses: muratd@bilgigis.com (M. Durmaz), karsliog@ metu.edu.tr (M.O. Karslioglu), nmetinn@gmail.com (M. Nohutcu). www.elsevier.com/locate/asr Available online at www.sciencedirect.com Advances in Space Research 46 (2010) 180–189