Nighttime TEC Variation Analysis of Klobuchar Model Based on IGS Data in China

In order to further study the variation characteristics of the nighttime ionospheric accuracy of the Klobuchar model and the correlation between the nighttime ionospheric accuracy of the Klobuchar model and solar activity intensity. In this paper, a method for comparative analysis on solar activity intensity in the high, medium and low solar activity years has been proposed. The GIM provided by the IGS Center from 2008 to 2018 are treated as reference values to analyze the nighttime accuracy of the Klobuchar model for annual, seasonal, and monthly changes in high solar activity, medium solar activity and low solar activity. The results are: (1) The nighttime accuracy of the Klobuchar model is best in the medium solar activity, followed in the low solar activity and the worst in the high solar activity. (2) The Bias and RMS of the Klobuchar model at nighttime had obviously semi-annual and seasonal variations in high and medium solar activity. (3) The nighttime accuracy of the Klobuchar model did not vary with Bias and RMS changes at nighttime.


INTRODUCTION
Ionospheric delay is one of the mainly error sources in Global Navigation Satellite System (GNSS). The delay can be up to 50 meters in the zenith direction, and can be up to 150 meters in the direction of the ground [1,2]. Therefore, it is important to eliminate the ionospheric delay error reasonably and effectively.
The ionospheric delay in satellite navigation and positioning systems can be significantly eliminated by using dual-frequency or multi-frequency methods. But for single-frequency GNSS users, the Klobuchar model is the most effective way to correct for the ionospheric delay.  The Klobuchar model can calculate ionospheric delay data easily for a broadcast ephemeris, satellite elevation, and satellite azimuth only. Because Klobuchar model can compute the ionospheric delay easily and conveniently, they are widely  * Corresponding author. used in single-frequency receivers. However, the Nighttime Vertical Total Electron Content (NVTEC), as a significant parameter in Klobuchar model, has been commonly set to a constant value of 9.23TECU, which will result in 20-30% positioning error. Therefore, in order to meet the requirements of single-frequency users for the accuracy of navigation and position, many researchers are committed to the correction of the nighttime ionospheric VTEC. ZHU et al. [3] uses the solar flux density to revise the nighttime ionospheric VTEC. ZHAO et al. [4] considers that the ionospheric VTEC is closely related to solar activity, then, the nighttime VTEC is corrected by the number of sunspots that characterize the degree of solar activity. WANG et al. [5] considering the nighttime ionospheric delay with the variation of the latitude quadratic parabola, a 10-parameter model is established. Cai et al. [6] the nighttime ionospheric delay is regarded as the cosine function of time, and an 11-parameter regional model is established. ZHANG et al. and XU et al. [7,8] considering the linear variation of the nighttime ionospheric delay with latitude, the improved Klobuc Where, T is the correction of ionospheric time delay, 1 A is the nighttime delay term, which usually set to 5ns.

3
A is the initial phase, which is 50400s.

A and 4
A are the amplitude of the day cosine function and the period of the day cosine function, respectively. t indicates the position corresponding to the initial phase.

The Global Ionospheric Map
The
The GIM data, provided by IGS has higher accuracy than 2~4TECU in different solar activity cycles around the world, meeting the research needs [14]. In this paper, the TEC value provided by the high-precision GIM ionospheric model is used as a reference value. and three statistical indices, including the Precision (Pre), Bias and Root Mean Square (RMS) are introduced for validation. The statistical indices are defined in Eqs.
(2)-(4).    Those further shows that the nighttime accuracy of the Klobuchar model in medium solar activity is better than that in the low and high solar activity.      October, and the maximum in April was larger than in October.
But the minimum monthly mean RMS is only has an annual variation. In addition, the maximum monthly mean RMS, minimum monthly mean RMS and monthly mean RMS have a common change, and they reached the minimum in June. These further illustrate the influence of the nighttime RMS and Bias on solar activity.

SUMMARIES
The Klobuchar model has been widely used by single-frequency GPS users to mitigate the effect of ionospheric delay. The constant value 9.23 TECU, meanwhile, has been generally admissive to describe the nighttime VTEC, which could introduce 20-30 % errors. Therefore, it is of great