Evaluation of the Klobuchar model in TaiWan

Abstract

Ionospheric delay is the mainly error source in Global Navigation Satellite System (GNSS). Ionospheric model is one of the ways to correct the ionospheric delay. The single-frequency GNSS users modify the ionospheric delay by receiving the correction parameters broadcasted by satellites. Klobuchar model is widely used in Global Positioning System (GPS) and COMPASS because it is simple and convenient for real-time calculation. This model is established on the observations mainly from Europe and USA. It does not describe the equatorial anomaly region. South of China is located near the north crest of the equatorial anomaly, where the ionosphere has complex spatial and temporal variation. The assessment on the validation of Klobuchar model in this area is important to improve this model.Eleven years (2003–2014) data from one GPS receiver located at Taoyuan Taiwan (121°E, 25°N) are used to assess the validation of Klobuchar model in Taiwan. Total electron content (TEC) from the dual-frequency GPS observations is calculated and used as the reference, and TEC based on the Klobuchar model is compared with the reference. The residual is defined as the difference between the TEC from Klobuchar model and the reference. It is a parameter to reflect the absolute correction of the model. RMS correction percentage presents the validation of the model relative to the observations. The residuals’ long-term variation, the RMS correction percentage, and their changes with the latitudes are analyzed respectively to access the model.In some months the RMS correction did not reach the goal of 50% purposed by Klobuchar, especially in the winter of the low solar activity years and at nighttime. RMS correction did not depend on the 11-years solar activity, neither the latitudes. Different from RMS correction, the residuals changed with the solar activity, similar to the variation of TEC. The residuals were large in the daytime, during the equinox seasons and in the high solar activity years; they are small at night, during the solstice seasons, and in the low activity years.During 1300–1500 BJT in the high solar activity years, the mean bias was negative, implying the model underestimated TEC on average. The maximum mean bias was 33TECU in April 2014, and the maximum underestimation reached 97TECU in October 2011. During 0000–0200 BJT, the residuals had small mean bias, small variation range and small standard deviation. It suggested that the model could describe the TEC of the ionosphere better than that in the daytime.Besides the variation with the solar activity, the residuals also vary with the latitudes. The means bias reached the maximum at 20–22°N, corresponding to the north crest of the equatorial anomaly. At this latitude, the maximum mean bias was 47TECU lower than the observation in the high activity years, and 12TECU lower in the low activity years. The minimum variation range appeared at 30–32°N in high and low activity years. But the minimum mean bias was at different latitudes in the high and low activity years. In the high activity years, it appeared at 30–32°N, and in the low years it was at 24–26°N. For an ideal model, the residuals should have small mean bias and small variation range. Further study is needed to learn the distribution of the residuals and to improve the model.