Simultaneous multiplicative column-normalized method (SMART) for 3-D ionosphere tomography in comparison to other algebraic methods

Abstract

Abstract. The accuracy and availability of satellite-based applications like GNSS positioning and remote sensing crucially depends on the knowledge of the ionospheric electron density distribution. The tomography of the ionosphere is one of the major tools to provide link specific ionospheric corrections as well as to study and monitor physical processes in the ionosphere.In this paper, we introduce a simultaneous multiplicative column-normalized method (SMART) for electron density reconstruction. Further, SMART+ is developed by combining SMART with a successive correction method. In this way, a balancing between the measurements of intersected and not intersected voxels is realised. The methods are compared with the well-known algebraic reconstruction techniques ART and SART. All the four methods are applied to reconstruct the 3-D electron density distribution by ingestion of ground-based GNSS TEC data into the NeQuick model.The comparative case study is implemented over Europe during two periods of the year 2011 covering quiet to disturbed ionospheric conditions. In particular, the performance of the methods is compared in terms of the convergence behaviour and the capability to reproduce sTEC and electron density profiles. For this purpose, independent sTEC data of four IGS stations and electron density profiles of four ionosonde stations are taken as reference. The results indicate that SMART significantly reduces the number of iterations necessary to achieve a predefined accuracy level. Further, SMART+ decreases the median of the absolute sTEC error up to 15, 22, 46 and 67 % compared to SMART, SART, ART and NeQuick respectively.

Three-dimensional data assimilation for ionospheric reference scenarios

“…The correct characterization of the vertical shape of the profiles becomes a difficult task when assimilating only ground-based sTEC because of limited vertical information included in these data (see e.g. McNamara et al, 2008McNamara et al, , 2011Minkwitz et al, 2015;Gerzen and Minkwitz, 2016). The inclusion of space-based sTEC improves the geometry situation.…”

“…The adjusted version of the NeQuick model serves as the initial guess for SMART+ (see Gerzen and Minkwitz, 2016), which is a fusion of the algebraic iterative tomography method SMART and a three-dimensional successive correction method (SCM). SMART+ assimilates the groundand space-based TEC as well as F2 layer characteristics from ionosondes and IRO profiles available over the observed area.…”

“…The SMART+ method (see Gerzen and Minkwitz, 2016) is applied here to solve the LSE. SMART+ combines SMART and three-dimensional SCM.…”

“…Thereafter, an extrapolation from the intersected voxels to those not intersected by any TEC ray path is done using the three-dimensional SCM method, assuming a Gaussian covariance model for the electron densities (see Gerzen and Minkwitz, 2016). Figure 7 presents as an example the reconstructed electron density on DOY 295, 12:30 UT.…”

“…Several approaches had been tested for the ionospheric imaging combining actual direct and indirect measurements with either an empirical or a physical model background (see e.g. Angling and Cannon, 2004;Angling, 2008;Schunk et al, 2004;Wang et al, 2004;Scherliess et al, 2009;Brunini et al, 2011;Pezzopane et al, 2011;Galkin et al, 2012;Minkwitz et al, 2015Minkwitz et al, , 2016Gerzen and Minkwitz, 2016).…”