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Abstract Ionospheric delay modeling is not only important for Global Navigation Satellite System (GNSS) based space weather study and monitoring, but also an efficient tool to speed up the convergence time of Precise Point Positioning (PPP). In this study, a novel model, denoted as Quasi-4-Dimension Ionospheric Modeling (Q4DIM) is proposed for wide-area high precision ionospheric delay correction. In Q4DIM, the Line Of Sight (LOS) ionospheric delays from a GNSS station network are divided into different clusters according to not only the location of latitude and longitude, but also satellite elevation and azimuth. Both Global Ionosphere Map (GIM) and Slant Ionospheric Delay (SID) models that are traditionally used for wide-area and regional ionospheric delay modeling, respectively, can be regarded as the special cases of Q4DIM by defining proper grids in latitude, longitude, elevation, and azimuth. Thus, Q4DIM presents a resilient model that is capable for both wide-area coverage and high precision. Four different sets of clusters are defined to illustrate the properties of Q4DIM based on 200 EUREF Permanent Network (EPN) stations. The results indicate that Q4DIM is compatible with the GIM products. Moreover, it is proved that by inducting the elevation and azimuth angle dependent residuals, the precision of the 2-dimensional GIM-like model, i.e., Q4DIM 2-Dimensional (Q4DIM-2D), is improved from around 1.5 Total Electron Content Units (TECU) to better than 0.5 TECU. In addition, treating Q4DIM as a 4-dimensional matrix in latitude, longitude, elevation, and azimuth, whose sparsity is less than 5%, can result in its feasibility in a bandwidth-sensitive applications, e.g., satellite-based Precising Point Positioning Real-Time Kinematic (PPP-RTK) service. Finally, the advantages of Q4DIM in PPP over the 2-dimensional models are demonstrated with the one month's data from 30 EPN stations in both high solar activity year 2014 and low solar activity year 2020.

Abstract As a new Ionosphere Associate Analysis Center (IAAC) of the International GNSS Service (IGS), Chinese Academy of Sciences (CAS) started the routine computation of the real-time, rapid, and final Global Ionospheric Maps (GIMs) in 2015. The method for the generation of CAS rapid and final GIMs and recent updates are presented in the paper. The quality of CAS post-processed GIMs is assessed during 2015–2018 after the maximum of solar cycle 24. To perform an independent and fair assessment, Jason-2/3 Vertical Total Electron Contents (VTEC) are first used as the references over the ocean. GPS differential Slant TECs (dSTEC) generated from 55 Multi-GNSS Experimental (MGEX) stations of the IGS are also employed, which provides a complementing way to evaluate the ability of electron content models to reproduce the spatial and temporal gradients in the ionosphere. During the test period, Jet Propulsion Laboratory (JPL) GIMs present significantly positive deviations compared to the Jason VTEC and GPS dSTEC. Technical University of Catalonia (UPC) rapid GIM UQRG exhibits the best performance in both Jason VTEC and GPS dSTEC analysis. The CAS GIMs show comparable performance with the results of the first four IAACs of the IGS. As expected, the poor performance of all GIMs is in equatorial regions and the high latitudes of the southern hemisphere. The consideration of generating multi-layer or three-dimensional ionospheric maps is emphasized to mitigate the inadequacy of ionospheric single-layer assumption in the presence of pronounced latitudinal gradients. The use of ionospheric observations from the new GNSS constellations and other space- or ground-based observation techniques is also suggested in the generation of future GIMs, given the sparse GPS/GLONASS stations in the southern hemisphere.