Impact of Tropospheric Mismodelling in GNSS Precise Point Positioning: A Simulation Study Utilizing Ray-Traced Tropospheric Delays from a High-Resolution NWM

Abstract

In GNSS analysis, the tropospheric delay is parameterized by applying mapping functions (MFs), zenith delays, and tropospheric gradients. Thereby, the wet and hydrostatic MF are derived under the assumption of a spherically layered atmosphere. The coefficients of the closed-form expression are computed utilizing a climatology or numerical weather model (NWM) data. In this study, we analyze the impact of tropospheric mismodelling on estimated parameters in precise point positioning (PPP). To do so, we mimic PPP in an artificial environment, i.e., we make use of a linearized observation equation, where the observed minus modelled term equals ray-traced tropospheric delays from a high-resolution NWM. The estimated parameters (station coordinates, clocks, zenith delays, and tropospheric gradients) are then compared with the known values. The simulation study utilized a cut-off elevation angle of 3° and the standard downweighting of low elevation angle observations. The results are representative of a station located in central Europe and the warm season. In essence, when climatology is utilized in GNSS analysis, the root mean square error (RMSE) of the estimated zenith delay and station up-component equal about 2.9 mm and 5.7 mm, respectively. The error of the GNSS estimates can be reduced significantly if the correct zenith hydrostatic delay and the correct hydrostatic MF are utilized in the GNSS analysis. In this case, the RMSE of the estimated zenith delay and station up-component is reduced to about 2.0 mm and 2.9 mm, respectively. The simulation study revealed that the choice of wet MF, when calculated under the assumption of a spherically layered troposphere, does not matter too much. In essence, when the ‘correct’ wet MF is utilized in the GNSS analysis, the RMSE of the estimated zenith delay and station up-component remain at about 1.8 mm and 2.4 mm, respectively. Finally, as a by-product of the simulation study, we developed a modified wet MF, which is no longer based on the assumption of a spherically layered atmosphere. We show that with this modified wet MF in the GNSS analysis, the RMSE of the estimated zenith delay and station up-component can be reduced to about 0.5 mm and 1.0 mm, respectively. In practice, its success depends on the ability of current (future) NWM to predict the fourth coefficient of the developed closed-form expression. We provide some evidence that current NWMs are able to do so.

Improving the wet mapping function by numerical weather models

“…In other words, the wet MF which still depends on the elevation angle only, takes into account the deviation from a spherically layered atmosphere. Based on the PPP simulation results presented in Zus et al (2021), it can be concluded that the modification of the wet MF can significantly reduce the errors of the estimated zenith delays and heights. However, they used 𝐶 as 0.0031 in gradient MF at the modification step.…”

“…MF coefficients, 𝑎, 𝑏 and 𝑐, are estimated using non-linear least square estimation. In this study, we followed the same strategy as in Zus et al (2021) with only small modification in the quality check step.…”

“…Those 10 tropospheric delays, i.e., tropospheric delays calculated under the assumption of a spherically layered atmosphere, are the ones we utilize in the determination of the hydrostatic and wet MF coefficients. For details the reader is referred to Zus et al (2021).…”

“…In this study we follow an approach which is very close to the approach proposed by Landskron and Böhm (2018b). We will follow the approach by Zus et al (2021). For some elevation angles the differences between tropospheric delays and tropospheric delays calculated under the assumption of a spherically layered atmosphere are expanded in a Fourier series.…”

“…The ZTD estimates are the main observable in GNSS based atmospheric remote sensing because the Precipitable Water Vapor (PWV), a key quantity in meteorology, can be derived with very little additional uncertainty (Bevis et al, 1992). Recently, Zus et al, (2021) proposed an approach to modify the wet MF and to reduce the errors of estimated heights and ZTDs. They showed that a simple modification of the wet MF reduced the errors from the standard approach from 2.4 mm to 1 mm and 1.8 mm to 0.5 mm for heights and ZTDs, respectively.…”