Atmosphere Delays
The neutral atmosphere (mostly the troposphere in the lowest ten kilometers
of the atmosphere) delays radio signals emitted by satellites, e.g., of the 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 and thus allows
that the coefficients can be provided globally and for the complete history of
space geodetic observations.
Within the project GGOS Atmosphere, we provide hydrostatic and wet zenith delays
together with the coefficients of the so-called Vienna Mapping Functions (VMF1)
which map the zenith delays to lower elevation angles. These parameters are provided
on a global grid (2.5 time 2.0 degrees in longitude and latitude, respectively) every
six hours, which is the usual time resolution of ECMWF data, and we also determine
these parameters for selected VLBI, and GNSS sites.
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.
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| 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. Our future plan is to do direct ray-tracing for all VLBI observations, and to use those delays with our in-house Vienna VLBI Software (VieVS).