Abstract
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.
Highlights
The spatial–temporal state of the ionospheric electron density distribution, including, for example, the peak characteristics of the different ionospheric layers and the slant total electron content (STEC) along a ray path, is useful information for almost all radio systems
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
Considering the scatter plot of the NeQuick model, it is visible that there is a discrepancy between the measured STEC and estimated STEC for both periods with μ up to −19.4 TECU
Summary
The spatial–temporal state of the ionospheric electron density distribution, including, for example, the peak characteristics of the different ionospheric layers and the slant total electron content (STEC) along a ray path, is useful information for almost all radio systems (see Bust and Mitchell, 2008). One common idea is the stabilization of the ill-posed inverse problem of ionospheric tomography by means of a physical or empirical background model providing a first guess of the electron density distribution. The given electron densities are modified according to the measurements without touching the model coefficients itself Minkwitz et al.: Gradient-enhanced kriging of the electron density
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