Usage of virtual TEC observations from empirical models for global ionospheric TEC modeling with spherical harmonic function

Global Navigation Satellite System (GNSS) is one of the valuable techniques used in researching ionospheric total electron content (TEC). GNSS observations above ground-based stations can be used to obtain high-precision ionospheric TEC with the so-called inverse technique. Subsequently, regional and/or global ionospheric TEC models could be established with some modeling techniques. Ionospheric TEC modeling with GNSS has become a great significance for improving the accuracy of GNSS navigation and positioning, as well as analyzing the ionospheric spatial structure, which is a great motivation to the development of ionospheric TEC modeling. There is no doubt that it is easier to get a satisfactory ionospheric TEC modeling result if the used stations are evenly distributed. However, stations are usually unevenly distributed because of some practical factors. For instance, there are few stations in ocean and Antarctic region. Due to lack of GNSS observations in ocean and Antarctic regions, ionosphere pierce points (IPPs) in these regions are also unevenly distributed or even blank. Consequently, the accuracy of ionospheric modeling is less satisfactory and some negative TEC values without physical meaning even occurred. In order to improve the accuracy of global ionospheric modeling, this work tries to solve this problem by using virtual TEC observations from empirical ionospheric models as constraints in global ionospheric TEC modeling. The spherical harmonic function was employed as the modeling technique, three empirical ionospheric models, Klobuchar, International Reference Ionosphere (IRI) and NeQuick, are used to calculate virtual TEC observations in four regions with no IPP, and GNSS observations above 279 global stations are used to calculate the ionospheric TEC values. Through experimental analysis, this work compares the accuracy improvement in global ionospheric modeling by using additional empirical constraints, and studies performance of the three used empirical ionospheric models in different IPP-blank regions. The results show that additional virtual TEC observations could effectively improve the accuracy of global ionospheric TEC modeling, especially for regions with very few IPPs. The contribution of TEC constraints from empirical models to global ionospheric modeling in different epochs is different. Taking the results in UT11 as an example, three empirical ionospheric models can improve the accuracy of global ionospheric modeling from 11.43 TECU to 3.28, 3.42 and 4.15 TECU, respectively. Generally, improvement performances of the three used empirical ionospheric models in mid-high latitude region and Antarctic are comparably, while Klobuchar model is relatively advantaged in mid-latitude region and IRI model outperforms the others in equator region.