The neutral atmosphere (mostly the troposphere in the lowest ten kilometers of the atmosphere) delays radio signals emitted by satellites, e.g. of GNSS (Global Navigation Satellite Systems), or by distant radio sources observed by VLBI (Very Long Baseline Interferometry). In recent years, data from numerical weather models (e.g. from the European Centre for Medium-Range Weather Forecasts, ECMWF) have been used to improve the accuracy of the analysis of space geodetic observations.
If done rigorously, direct ray-tracing through numerical weather models has to be carried out for every single observation — a task which might be feasible for VLBI or normal points of Satellite Laser Ranging (SLR), but not for GNSS with the huge number of stations, satellites, and observations. Alternatively, data from numerical weather models can be used to develop troposphere delay models which are based on a limited number of coefficients that hold for a certain area, time, and/or azimuth/elevation range. The latter approach reduces the number of calculations considerably, allowing to provide the coefficients globally and for the complete history of space geodetic observations.
Within project GGOS Atmosphere, we determine hydrostatic and wet zenith delays together with the coefficients of the Vienna Mapping Functions (VMF1) which map the zenith delays to lower elevation angles. These parameters are provided on a global grid (2.0° x 2.5° latitude-longitude) every six hours, which is the usual time resolution of ECMWF data, and we also determine these parameters for selected VLBI and GNSS sites.
An alternative provider of the Vienna Mapping Function 1 coefficients is the University of New Brunswick. Their coefficients based on data of the National Centers of Environmental Prediction (NCEP) and the Canadian Model (CMC) and more information on their products can be found here.
Additionally, we developed analytical backup functions, which can be used if the VMF1 or the corresponding zenith delays are not available. The Global Mapping Functions (GMF) are 'mean' Vienna Mapping Functions 1, and the Global Pressure and Temperature model (GPT) provides pressure and temperature in the vicinity of the Earth surface. Both analytical models, GMF and GPT, are spherical harmonic expansions up to degree and order nine, and both need the station coordinates and the day of the year as input parameter. The pressure from GPT can be used to determine the hydrostatic zenith delay which is then in agreement with a long term average of the hydrostatic zenith delays that are provided with the VMF1. The figure shows the excellent agreement between terrestrial reference frames determined with ECMWF/VMF1 and GPT/GMF. In 2013, an udpate to both GPT and GMF has been developed which is called GPT2 and is based on 5° as well as 1° grids and contains annual and semi-annual harmonic functions.
|Residuals of the 14-parameter similarity transformation between VMF1/ECMWF and GMF/GPT terrestrial reference frames. The arrows refer to the horizontal, the color scale to the vertical residuals (from Steigenberger et al., 2009).|
Additionally, we provide other parameters like the heights of the 200 hPa pressure levels, or the mean temperatures to convert wet zenith delay to precipitable water. Within a recently approved new FWF-project called 'Radiate VLBI' we do direct ray-tracing for all VLBI observations and to use those delays with our in-house Vienna VLBI Software (VieVS).
T. Nilsson, J. Böhm, D. D. Wijaya, A. Tresch, V. Nafisi, H. Schuh. Path Delays in the Neutral Atmosphere, in J. Böhm and H. Schuh (eds): Atmospheric Effects in Space Geodesy, Springer Verlag, ISBN 978-3-642-36931-5, pp. 73-136, 2013.
K. Lagler, M. Schindelegger, J. Böhm, H. Krásná, T. Nilsson. GPT2: Empirical slant delay model for radio space geodetic techniques, Geophys. Res. Lett., Vol. 40, 1069–1073, doi:10.1002/grl.50288, 2013.
V. Nafisi, M. Madzak, J. Böhm, A. A. Ardalan, H. Schuh. Ray-traced tropospheric delays in VLBI analysis, Radio Science, Vol. 47, RS2020, doi:10.1029/2011RS004918, 2012.
J. Böhm, B. Werl, H. Schuh. Troposphere mapping functions for GPS and very long baseline interferometry from European Centre for Medium-Range Weather Forecasts operational analysis data, J. Geophys. Res., Vol. 111, B02406, doi:10.1029/2005JB003629, 2006.