GPS Solutions

, Volume 18, Issue 3, pp 345–354 | Cite as

Assessment of troposphere mapping functions using three-dimensional ray-tracing

  • Landon Urquhart
  • Felipe G. Nievinski
  • Marcelo C. Santos
Original Article


The troposphere delay is an important source of error for precise GNSS positioning due to its high correlation with the station height parameter. It has been demonstrated that errors in mapping functions can cause sub-annual biases as well as affect the repeatability of GNSS solutions, which is a particular concern for geophysical studies. Three-dimensional ray-tracing through numerical weather models (NWM) is an excellent approach for capturing the directional and daily variation of the tropospheric delay. Due to computational complexity, its use for positioning purposes is limited, but it is an excellent tool for evaluating current state-of-the-art mapping functions used for geodetic positioning. Many mapping functions have been recommended in the past such as the Niell Mapping Function (NMF), Vienna Mapping Function 1 (VMF1), and the Global Mapping Function (GMF), which have been adopted by most IGS analysis centers. A new Global Pressure Temperature model (GPT2) has also been developed, which has been shown to improve upon the original atmospheric model used for the GMF. Although the mapping functions mentioned above use the same functional formulation, they vary in terms of their atmospheric source and calibration approach. A homogeneous data set of three-dimensional ray-traced delays is used to evaluate all components of the mapping functions, including their underlying functional formulation, calibration, and compression method. Additionally, an alternative representation of the VMF1 is generated using the same atmospheric source as the truth data set to evaluate the differences in ray-tracing methods and their effect on the end mapping function. The results of this investigation continue to support the use of the VMF1 as the mapping function of choice when geodetic parameters are of interest. Further support for the GPT2 and GMF as reliable back-ups when the VMF1 is not available was found due to their high consistency with the NWM-derived mapping function. Additionally, a small latitude-dependent bias in station height was found in the current mapping functions. This bias was identified to be due to the assumption of a constant radius of the earth and was largest at the poles and at the equator. Finally, an alternative version of the VMF1 is introduced, namely the UNB-VMF1 which provides users with an independent NWM-derived mapping function to support geodetic positioning.


Troposphere Numerical weather models Mapping functions 



The authors would like to acknowledge the Canadian Meteorological Center and Environment Canada for providing access to the CMC-GEM, Johannes Boehm for the Vienna Mapping Functions made available under the GGOS Atmosphere project at the Institute of Geodesy and Geophysics at the Vienna University of Technology. The first and third author would like to thank the Natural Sciences and Engineering Research Council (NSERC) for providing funding for this research. The second author acknowledges funding by Capes/Fulbright.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Landon Urquhart
    • 1
    • 2
  • Felipe G. Nievinski
    • 3
  • Marcelo C. Santos
    • 1
  1. 1.Department of Geodesy and Geomatics EngineeringUniversity of New BrunswickFrederictonCanada
  2. 2.Nexteq NavigationCalgaryCanada
  3. 3.Department of Aerospace Engineering SciencesUniversity of ColoradoBoulderUSA

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