Analysis Impacts of the Varying Heights on Ionospheric Modeling and DCB Estimation

Yan Xiang and Yang Gao

Abstract:	The ionosphere is the active, complex, and ionized part of the atmosphere, and it ranges from about 50 km to more than 1000 km from the earth’s surface. Because the ionosphere is dispersive, ionosphere remote sensing using dual-frequency observations from the Global Navigation Satellite System (GNSS) signals is recognized as a cost-effective approach to monitor the ionosphere. However, the GNSS-derived ionospheric observables are biased due to Differential Code Biases (DCBs) (Xiang et al. 2017). The way to separate ionosphere from the satellite- and receiver-related DCBs is through ionospheric modeling. Precise ionospheric modeling and DCB determination are required for mitigating ionospheric corrections for single-frequency users , for reconstructing ionospheric tomography with precise slant Total Electron Content (TEC), and for shortening the convergence time for PPP when adding ionospheric constraints (Shi et al. 2012). In the ionospheric modeling, in order to separate the ionosphere from the DCBs, mapping function (MF) plays a critical role in that it projects the line-of-sight slant TEC (STEC) to vertical TEC (VTEC). The MF is defined as the ratio between STEC and VTEC based on the assumption of a single-layer model (SLM). The SLM assumes that the ionosphere is condensed into an infinitesimal thickness layer. From the definition, we can see that the MF is larger than 1 and usually smaller than 3. Based on the SLM assumption, the MF depends on the observing elevation and height of the SLM. The MF decreases with the increase of elevation and height. The height is designed to be established at the average altitude of electron density profile peaks (Lanyi and Roth 1988). If this chosen height is lower than the optimal height, the MF tends to be overestimated. Besides, the height also affects the pierce point position that is the interaction between the line of sights and the fixed-height layer. The height typically ranges from 300 km to 500 km (Hernández-Pajares et al. 2005), but for the convenience of the global ionospheric modeling, the height is usually fixed, regardless of daytime or nighttime, at 450 km (Hernández-Pajares et al. 2011; Hernandez-Pajares et al. 2009). However, because the ionosphere is inhomogeneous, the effective heights for SLM vary in location and time, depending on the condition of space weather. Many researchers showed that the MF at a given fixed height has significant errors at the low elevation and the large ionosphere gradient with a fixed height (Birch et al. 2002; Conker and El-Arini 2002; Nava et al. 2007; Palamartchouk 2010; Wang et al. 2016; Zus et al. 2016). When horizontal ionospheric gradients exist, azimuth effects along the line-of-sight are consequential (Conker and El-Arini 2002). Besides, the contributions of topside plasma to the mapping function are also substantial, especially at night when the electron density decreases compared to the topside plasma (Birch et al. 2002). Accordingly, there is a need to investigate the impacts of existing mapping functions on ionospheric modeling and derive improved MF for more accurate ionospheric modeling. There are six general kinds of MFs: (1) the single-layer MF. The simplest and most commonly used, it includes the broadcast model (Klobuchar 1987) and the modified SLM MF (Schaer 1999); (2) the MF that assumes the ionosphere is a spherical shell or flat-plane with thickness. The spherical shell model without thickness is almost the same as the flat-plane model, whereas regardless of the thickness, the MF can be overestimated up to 15% at the pierce point zenith angle of 700 and the height of 200 km (Smith et al. 2008); (3) the two-layer or multi-layer MF. It takes into account the vertical structure of the ionosphere electron density instead of assuming the ionosphere being fixed at an layer with infinitesimal thickness (Hernández-Pajares et al. 1999; Smith et al. 2008). This model is advantageous when there are implicit horizontal gradients and low-elevation observations; (4) the GNSS-data derived MF. Jin et al. (2010) and Birch et al. (2002) proposed to reproduce the height using GNSS data. They also pointed out the topside plasma has a significant effect on the MF, and the MF varies with location and seasons; (5) the MF based on empirical models like IRI and Chapman profile. These models are applied to calculate the average height of electron density or the integral height along the trace (Conker and El-Arini 2002; Zhong et al. 2016); (6) the Potsdam MF. It is proposed to consider the location, elevation, azimuth, and even bending effects (Zus et al. 2016). Some of these mapping functions are compared with each other in Schaer (1999), and the author showed that there is a relative error of 10% with reference to the height of 350 km. Based on these six current methods, the mapping errors to the ionospheric modeling will be investigated. Furthermore, because a unique height for the daytime and nighttime to cancel the mapping errors does not exist, a mapping function with variable heights from the latest IRI 2016 will be developed, aiming to reduce the mapping errors for the ionospheric modeling so that we can achieve more precise DCBs and STEC. The carrier-phase derived ionospheric observables using PPP are used to reduce the leveling errors from the smoothed code measurements. We anticipate smaller ionospheric modeling errors and more stable DCBs occur with the developed mapping function.
Published in:	Proceedings of the 30th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2017) September 25 - 29, 2017 Oregon Convention Center Portland, Oregon
Pages:	4161 - 4175
Cite this article:	Xiang, Yan, Gao, Yang, "Analysis Impacts of the Varying Heights on Ionospheric Modeling and DCB Estimation," Proceedings of the 30th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2017), Portland, Oregon, September 2017, pp. 4161-4175. https://doi.org/10.33012/2017.15359
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