## 1 Introduction  
The polar regions namely the Arctic and the Antarctic are the locations of the geographical and geomagnetic poles. The magnetic field lines over the polar caps penetrate to the Earth or extend outward to connect with the interplanetary magnetic field. The large-scale magnetospheric electric field, formed by the interaction between the magnetosphere and solar wind, is mapped to the high-latitude ionosphere along the magnetic field lines with high conductivity; meanwhile, changes in the ionosphere can also modulate the magnetospheric electric field. These interactions result in a highly variable polar ionosphere. The total electron content (TEC) is one of the significant parameters of the ionosphere, which represents the integration of the electron density along the path of the radio signal [1; 2; 3]. The ionospheric delay error of the radio signal is directly proportional to the TEC [3]. Therefore, it is not only of great scientific significance to detect the spatiotemporal distribution and variation of the polar ionospheric TEC, but also of great guiding significance to the global navigation satellite system (GNSS) high-precision positioning, navigation, timing (PNT) service, radio communication, and other human space activities in the polar regions. The study of the polar ionospheric variation requires accurate ionospheric models. The most commonly used ones include broadcast ionospheric models, empirical ionospheric models, and global ionospheric map (GIM) models provided by the International GNSS Service (IGS) [4; 5; 6; 7]. However, they have degraded accuracy in mapping the ionospheric TEC of the polar regions [7]. Thanks to rapid development, GNSS, measurements can now provide adequate accuracy for mapping the polar TEC and have become the widely used method for ionospheric research [8; 9; 2; 10]. According to the dispersive properties of the ionosphere, the TEC along a given path from the receiver to the satellite can be estimated by using dual-frequency or multifrequency GNSS measurements, and the regional TEC can be further mapped with different ionospheric models. The commonly used models for regional TEC mapping mainly include the polynomial (POLY) function model, the generalized trigonometric series function (GTSF) model, the spherical harmonic (SH) function model, and the spherical cap harmonic (SCH) function model [11; 12; 13; 14; 3]. These models have their own advantages and disadvantages, and they have optimal performances only under the appropriate conditions. [PERSON] et al. [12] evaluated the applicability of these ionospheric models in the Arctic region. [PERSON] et al. [16] mapped the Antarctic ionospheric TEC and analyzed the variation characteristics using the SCH model. Due to the special geographical location of the polar regions, here the ionosphere is affected by variable phenomena, such as the polar day and night alternation, the Weddell Sea anomaly (WSA), and ionospheric storms. Polar day indicates the phenomenon in which the Sun stays above the horizon for more than 24 h, while polar night refers to night lasting for more than 24 h. The WSA means that the electronic density at nighttime is larger than that in the daytime over the regions of Antarctic Peninsula and Weddell Sea in summer. The maximum of the daily electronic density occurs from 22:00 to 4:00 local time (LT) and the minimum appears from 12:00 to 18:00 LT. The polar days and nights as well as the WSA have significant impacts on ionospheric models [7]. When an ionospheric storm occurs, ionization patches are often present. They are formed in the F layer, and their electronic density is more than twice than that of the surrounding areas [17; 18]. The ionization patches lead to several difficulties with regard to radio signals, including phase advance, time delay, and Doppler shifts [19]. The movements of the ionization patches and associated density gradients have severe interference on high-frequency radio communication and satellite navigation.