Refined discrete and empirical horizontal gradients in VLBI analysis

Abstract

Missing or incorrect consideration of azimuthal asymmetry of troposphere delays is a considerable error source in space geodetic techniques such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). So-called horizontal troposphere gradients are generally utilized for modeling such azimuthal variations and are particularly required for observations at low elevation angles. Apart from estimating the gradients within the data analysis, which has become common practice in space geodetic techniques, there is also the possibility to determine the gradients beforehand from different data sources than the actual observations. Using ray-tracing through Numerical Weather Models (NWMs), we determined discrete gradient values referred to as GRAD for VLBI observations, based on the standard gradient model by Chen and Herring (J Geophys Res 102(B9):20489-20502, 1997. https://doi.org/10.1029/97JB01739) and also for new, higher-order gradient models. These gradients are produced on the same data basis as the Vienna Mapping Functions 3 (VMF3) (Landskron and Böhm in J Geod, 2017. https://doi.org/10.1007/s00190-017-1066-2), so they can also be regarded as the VMF3 gradients as they are fully consistent with each other. From VLBI analyses of the Vienna VLBI and Satellite Software (VieVS), it becomes evident that baseline length repeatabilities (BLRs) are improved on average by 5% when using a priori gradients GRAD instead of estimating the gradients. The reason for this improvement is that the gradient estimation yields poor results for VLBI sessions with a small number of observations, while the GRAD a priori gradients are unaffected from this. We also developed a new empirical gradient model applicable for any time and location on Earth, which is included in the Global Pressure and Temperature 3 (GPT3) model. Although being able to describe only the systematic component of azimuthal asymmetry and no short-term variations at all, even these empirical a priori gradients slightly reduce (improve) the BLRs with respect to the estimation of gradients. In general, this paper addresses that a priori horizontal gradients are actually more important for VLBI analysis than previously assumed, as particularly the discrete model GRAD as well as the empirical model GPT3 are indeed able to refine and improve the results.

Sensitivity of GNSS tropospheric gradients to processing options

“…A good correlation between GPS and NWM gradients was found for inland stations but not for coastal ones. More recently Li et al (2015) and Lu et al (2016) showed that with the upcoming finalization of new systems such as Galileo and BeiDou the improved observation geometry yields more robust tropospheric gradient estimates. Li et al (2015) found an improvement of about 20 %-35 % for the multi-GNSS processing when compared with NWMs and 21 %-28 % when compared to WVR.…”

Authors' responses to Referees' comments

“…√ h −1 , the weighted root-mean-square (RMS) difference compared to the WVR gradients varied between 0.8 and 1.0 mm for both the GPS and the VLBI gradients. Using multi-GNSS observations, Li et al (2015) found a significant increase in the correlation coefficient to about 0.6 when compared to ECMWF gradients, while the one for the GPS alone was typically below 0.5. In addition, they found that the RMS difference of the gradient was reduced to about 25 %-35 % by multi-GNSS processing.…”

Atmospheric bending effects in GNSS tomography

“…where ZHD is the zenith hydrostatic delay, ZWD is the zenith wet delay and mf h and mf w are the corresponding mapping functions, which describe the elevation (ε) dependency of the signal delay. The elevation-dependent and azimuth (α)-dependent first-order horizontally asymmetric term G(ε, α) reflects local variations in the atmospheric conditions; see MacMillan (1995), Chen and Herring (1997) or Landskron and Böhm (2018). In practice, e.g., when using the VMF1 mapping function (Böhm et al, 2006) or similar mapping concepts, the tropospheric delay due to atmospheric bending is absorbed by the hydrostatic mapping function term mf h .…”