Session B1: Atmospheric Effects, GNSS Remote Sensing, and Scientific Applications

A Method of Estimating Residual Bending Error in GNSS-RO Absolute TEC
Jaehee Chang, Andrew K. Sun, Jihyeok Park, Jiyun Lee, Korea Advanced Institute of Science and Technology; Jade Morton, University of Colorado at Boulder
Location: Beacon B

Total electron content (TEC) derived from Global Navigation Satellite System (GNSS) radio occultation (RO) measurements is a fundamental parameter for reconstructing the electron density distribution in the ionosphere. The conventional method for TEC estimation using dual-frequency GNSS RO measurements relies on the assumption of straight-line propagation. However, ionospheric refraction causes signals at different frequencies to deviate from the straight-line path, leading to discrepancies between the estimated dual-frequency TEC and the true TEC along the straight-line. This discrepancy, referred to simply as the residual bending error, can limit the accuracy of TEC estimates.
The residual bending error is dependent on the vertical gradient of refractivity, which is a function of the gradient of electron density in the ionosphere. The magnitude of this error varies with factors such as solar activity, local time, and the geographical location of the occultation event. Simulation studies have demonstrated that daytime solar maximum conditions may lead to residual bending errors on the order of 10 TECU (Høeg et al., 1998; Hoque & Jakowski, 2010). As the current solar cycle approaches its maximum phase, the effect of ionospheric ray path bending must be thoroughly investigated to achieve accurate TEC retrieval using GNSS RO measurements.
Several methods for the estimation and correction of residual bending errors have been proposed over the past decades. Early work by Gu & Brunner (1990) and Brunner & Gu (1991) introduced corrections for refraction and higher-order effects in the dual-frequency linear combination of phase paths, although their focus was primarily on ground-based GNSS positioning. Nevertheless, applying their model in practical cases presents a challenge as it requires a priori knowledge of the refractive index gradients along the ray path. Other studies, such as those by Høeg et al. (1998) and Syndergaard (1999, 2000), presented analytical models for the refraction residual in occultation measurements under the assumption of spherical symmetry. In such case, the residual bending error is mainly dependent on the TEC gradient, which can be estimated directly from the measurements. However, an accurate estimation still requires auxiliary information on the electron density distribution (Syndergaard, 2002). Hoque & Jakowski (2011) proposed an empirical model based on ray tracing simulation results, but this also relies on a good estimate for ionospheric parameters such as maximum ionization NmF2.
Syndergaard (2002) addressed these limitations by proposing a model-independent method of combining L1 and L2 excess phases to eliminate first-order effects of refraction and dispersion. Utilizing the frequency dependence of refraction residuals in L1 and L2 phase observables, as derived by Syndergaard (2000), this approach allows for the correction of residual bending errors based solely on dual-frequency phase measurements and precise orbit determination (POD) data. While validated through ray tracing simulations using simple ionospheric models, this methodology has not undergone validation using real measurements. In order to adequately capture the temporal and spatial variations of the actual ionosphere and its ray path bending effects, extensive monitoring with real measurements is necessary.
In the present work, we assess the residual bending error in dual-frequency TEC using Global Positioning System (GPS) radio occultation measurements from COSMIC-2, based on the methodology proposed by Syndergaard (2002). Building on the work of Chang et al. (2024), which examined the residual bending error in relative TEC obtained from phase observations only, this research incorporates pseudorange measurements needed for absolute TEC retrieval in order to address the constant bias in relative TEC arising from phase ambiguities. This requires consideration of refraction and dispersion effects on both phase and pseudorange measurements, which propagate as additional errors in phase-to-pseudorange leveling.
For this purpose, we implemented an algorithm to retrieve L1 and L2 ionospheric excess phase data necessary for estimating the residual bending error. This requires external data such as LEO and GPS satellite precise orbit and clock information to remove the geometric range and clock biases in the phase measurements. For the precise removal of the clock biases, we utilize single-differencing with simultaneously tracked reference and occulting GPS satellite observations, along with the high-rate (5-second sampling interval) GPS clock estimates from the Center for Orbit Determination in Europe (CODE) which can effectively capture GPS clock fluctuations.
In our analysis, the residual bending error in dual-frequency TEC was quantified across various solar activity conditions during Solar Cycle 25. The results confirmed that residual bending error is more pronounced during high solar activity in regions with high vertical TEC gradients, which is consistent with theoretical derivations. Additionally, larger errors were observed in the late afternoon to post-sunset hours, likely due to the rapid recombination in the ionospheric E region inducing a strong vertical gradient. In some cases, the residual bending error was shown to exceed 30 TECU, with an additional leveling error contribution of several TECU. This research presents a practical approach for assessing residual bending errors in absolute TEC retrievals using real observational data, with a specific emphasis on its sensitivity to solar activity and local time, thereby contributing to the enhancement of TEC accuracy through the correction of the residual bending error.