1German Aerospace Center (DLR), Institute of Communications and Navigation, Kalkhorstweg 53, 17235 Neustrelitz, Germany
2Helmholtz Institute Freiberg for Resource Technology, Division of Modelling and Evaluation, Halsbruecker Str. 34, 09599 Freiberg, Germany
3TU Bergakademie Freiberg, Faculty of Mathematics and Computer Science, Prueferstr. 9, 09599 Freiberg, Germany
4Universitat Politècnica de Catalunya, Departement of Applied Mathematics IV, Jordi Girona 1–3, 08034, Barcelona, Spain
Received: 17 Aug 2016 – Revised: 26 Oct 2016 – Accepted: 28 Oct 2016 – Published: 14 Nov 2016
Abstract. The estimation of the ionospheric electron density by kriging is based on the optimization of a parametric measurement covariance model. First, the extension of kriging with slant total electron content (STEC) measurements based on a spatial covariance to kriging with a spatial–temporal covariance model, assimilating STEC data of a sliding window, is presented. Secondly, a novel tomography approach by gradient-enhanced kriging (GEK) is developed. Beyond the ingestion of STEC measurements, GEK assimilates ionosonde characteristics, providing peak electron density measurements as well as gradient information. Both approaches deploy the 3-D electron density model NeQuick as a priori information and estimate the covariance parameter vector within a maximum likelihood estimation for the dedicated tomography time stamp. The methods are validated in the European region for two periods covering quiet and active ionospheric conditions. The kriging with spatial and spatial–temporal covariance model is analysed regarding its capability to reproduce STEC, differential STEC and foF2. Therefore, the estimates are compared to the NeQuick model results, the 2-D TEC maps of the International GNSS Service and the DLR's Ionospheric Monitoring and Prediction Center, and in the case of foF2 to two independent ionosonde stations. Moreover, simulated STEC and ionosonde measurements are used to investigate the electron density profiles estimated by the GEK in comparison to a kriging with STEC only. The results indicate a crucial improvement in the initial guess by the developed methods and point out the potential compensation for a bias in the peak height hmF2 by means of GEK.
Minkwitz, D., van den Boogaart, K. G., Gerzen, T., Hoque, M., and Hernández-Pajares, M.: Ionospheric tomography by gradient-enhanced kriging with STEC measurements and ionosonde characteristics, Ann. Geophys., 34, 999-1010, doi:10.5194/angeo-34-999-2016, 2016.