Ray-traced Delays in the Atmosphere for Geodetic VLBI

Tropospheric delay modeling is the major error source in the analysis of geodetic Very Long Baseline Interferometry (VLBI) observations, and in order to comply with the ambitious accuracy goals of 1 mm in position and 0.1 mm/year in velocity for the terrestrial reference frame set for the Global Geodetic Observing System (GGOS), it is imperative to improve the tropospheric correction models. The determination of slant delays by ray- tracing through high-resolution data from numerical weather models is the most rigorous approach possible today, and their application in VLBI data analysis is on principle suited for replacing the common strategy of using mapping functions and horizontal tropospheric gradients. In project RADIATE VLBI we will determine ray-traced delays for the whole history of about five million geodetic VLBI observations since 1979 from operational analysis and re-analysis data of the European Centre for Medium-range Weather Forecasts (ECMWF) as well as for all upcoming VLBI observations from forecasting data to have the delays available in real-time. In order to avoid the download of huge datasets with meteorological information, the ray-traced delays will be computed on the supercomputers of the ECMWF with ray-tracing algorithms that have been developed at the Vienna University of Technology in the last years. The ray-traced delays are then used in global VLBI solutions to assess the impact on terrestrial and celestial reference frames as well as on Earth orientation parameters, and the ray-traced delays will be made freely available to the scientific community. Furthermore, ray-traced delays from forecasting data of the ECMWF will be used in near real-time applications, in particular for the analysis of Intensive sessions. For a limited time span of three years, we will calculate ray-traced delays which are uniformly distributed over the sky above all geodetic VLBI sites with a six-hourly time resolution. These delays will then be used to improve tropospheric delay models, e.g. by adding an azimuth-dependence to the mapping function coefficients or higher order spherical harmonics to the horizontal tropospheric gradients. All these new models will again be applied in global VLBI solutions, and the results will be compared to those from standard approaches and from the solutions with ray-traced delays for every observation. With its rigorous approach of applying ray-traced delays through numerical weather models for every observation and with improved tropospheric delay models, project RADIATE VLBI will deliver innovative and unique VLBI results of highest accuracy for the terrestrial and celestial reference frame as well as for the Earth orientation parameters.

While atmospheric effects on the propagation of radio waves take place in the whole atmosphere, the troposphere as the lowest part plays a key role with its weather phenomena and the highly variable distribution of humidity. Modelling the delays in the troposphere of the signals from extragalactic radio sources in the analysis of geodetic Very Long Baseline Interferometry (VLBI) observations and of the signals from Global Navigation Satellite Systems (GNSS), such as the U.S. Global Positioning System (GPS) or the European Galileo, is a major error source influencing the accuracy of these space geodetic techniques. In particular, insufficient models may affect station coordinates and the terrestrial reference frame. The goal of the project RADIATE VLBI was to challenge the existing tropospheric delay models, thereby developing improved and new methods for the tropospheric calibration.We used the concept of "ray-tracing" to determine values of those delays through applying electromagnetic wave equations onto data of numerical weather models provided by the European Centre for Medium-range Weather Forecasts (ECMWF). In the first part of project RADIATE VLBI we developed a sophisticated and fast ray-tracing program called RADIATE. This program was then used to determine slant tropospheric delays for all (more than 10 million) geodetic VLBI observations and to derive improved tropospheric delay models, such as the Vienna Mapping Function 3 (VMF3).We found that the application of ray-traced delays in VLBI analysis in particular improves the solution of VLBI sessions with a small number of observations or if no tropospheric gradients are estimated. The newly developed VMF3 slightly improves the accuracy of the terrestrial reference frame with an impact on station heights up to two millimetres. Ray-traced delays and tropospheric gradients, the latter derived together with VMF3, do have a significant impact on the celestial reference frame with source declination changes up to more than 50 microarcseconds. In parallel to 6-hourly coefficients of the VMF3, we also derived so-called empirical delay models such as GPT3, which is fully consistent with VMF3 but only contains annual and semi-annual terms.Although we could confirm that existing tropospheric delay models are already at a very high level of accuracy, we do provide new models (VMF3, GPT3, gradients) which improve the accuracy of geodetic parameters. However, it should be stressed that further research in tropospheric delay modelling is required to reach the goal of one millimetre accuracy in daily station coordinates. On the other hand, all models developed in project RADIATE VLBI may be implemented in positioning and navigation devices with GNSS receivers such as smartphones.