Tomography Reconstruction of Ionospheric Electron Density with Empirical Orthonormal Functions Using Korea GNSS Network

Abstract

In South Korea, there are about 80 Global Positioning System (GPS) monitoring stations providing total electron content (TEC) every 10 min, which can be accessed through Korea Astronomy and Space Science Institute (KASI) for scientific use. We applied the computerized ionospheric tomography (CIT) algorithm to the TEC dataset from this GPS network for monitoring the regional ionosphere over South Korea. The algorithm utilizes multiplicative algebraic reconstruction technique (MART) with an initial condition of the latest International Reference Ionosphere-2016 model (IRI-2016). In order to reduce the number of unknown variables, the vertical profiles of electron density are expressed with a linear combination of empirical orthonormal functions (EOFs) that were derived from the IRI empirical profiles. Although the number of receiver sites is much smaller than that of Japan, the CIT algorithm yielded reasonable structure of the ionosphere over South Korea. We verified the CIT results with NmF2 from ionosondes in Icheon and Jeju and also with GPS TEC at the center of South Korea. In addition, the total time required for CIT calculation was only about 5 min, enabling the exploration of the vertical ionospheric structure in near real time.

Assimilation of Multiple Data Types to a Regional Ionosphere Model With a 3D‐Var Algorithm (IDA4D)

“…To improve on estimations of climatologic models and still obtain a full 3-D picture of the ionosphere, tomography techniques have extensively been applied (e.g., Hong et al, 2017;Raymund et al, 1990;Saito et al, 2016;Seemala et al, 2014;Ssessanga et al, 2015Ssessanga et al, , 2017Tsai et al, 2002). However, ionosphere tomography techniques have a deficiency of not being able to adequately spread observation information within the grid, specifically over remote areas where measurements are lacking.…”

Fast determination of geometric matrix in ionosphere tomographic inversion with unevenly spaced curvilinear voxels

“…To obtain a segment, the voxels that intersect a ray should first be identified. Although detailed procedures are not presented, finding such voxels using the AP approach (Hong et al 2017) can be implemented by an intersection test on the voxels inside the minimal bounding box (MBB) of the auxiliary plane. Nevertheless, the number of voxels to be tested remains large if the MBB is large.…”

“…Wen et al (2007) and Zheng et al (2018) showed that iteration procedures in which the relaxation parameter is chosen dynamically improve convergence. Hong et al (2017) argued that tomographic inversion could be accelerated if many electron density unknowns are replaced by a few empirical orthonormal functions (EOFs). Regardless, a more generic way to accelerate inversion is to use parallel computing technology.…”

“…Due to the large number of rays and voxels, geometric matrix determination is often inefficient and may take more time than the tomographic model solving process. For example, in a test with 684,400 voxels, 60,794 rays (among which 41,611 are valid rays) and 500 iterations (far enough to converge in this case) run on a desktop environment and are presented in the performance tests section, geometric matrix determination using an auxiliary plane (AP) approach (Hong et al 2017) costs 262 seconds, while the tomographic model solving process using a simultaneous multiplicative column normalized method (Gerzen and Minkwitz 2016) or an improved algebraic reconstruction technique (Wen et al 2007) takes 45 seconds or 31 seconds. Basically, computing the geometric matrix is not very complicated and can be performed with a basic knowledge of receiver-satellite geometry.…”

“…In the curvilinear voxel model, the edges of the voxels are curved. For the curvilinear voxel model, Hong et al (2017) proposed an AP approach for geometric matrix computation by introducing an auxiliary plane defined by a ray and the center of the earth. Possibly due to the simplicity of the problem, detailed procedures for computing the geometric matrix are not provided by the traditional approach and the AP approach.…”