Landon Urquhart

Comparison of Ray-Tracing Packages for Troposphere Delays

A comparison campaign to evaluate and compare troposphere delays from different ray-tracing software was carried out under the umbrella of the International Association of Geodesy Working Group 4.3.3 in the first half of 2010 with five institutions participating: the GFZ German Research Centre for Geosciences (GFZ), the Groupe de Recherche de Geodesie Spatiale, the National Institute of Information and Communications Technology (NICT), the University of New Brunswick, and the Institute of Geodesy and Geophysics of the Vienna University of Technology. High-resolution data from the operational analysis of the European Centre for Medium-Range Weather Forecasts (ECMWF) for stations Tsukuba (Japan) and Wettzell (Germany) were provided to the participants of the comparison campaign. The data consisted of geopotential differences with respect to mean sea level, temperature, and specific humidity, all at isobaric levels. Additionally, information about the geoid undulations was provided, and the participants computed the ray-traced total delays for 5° elevation angle and every degree in azimuth. In general, we find good agreement between the ray-traced slant factors from the different solutions at 5° elevation if determined from the same pressure level data of the ECMWF. Standard deviations and biases are at the 1-cm level (or significantly better for some combinations). Some of these discrepancies are due to differences in the algorithms and the interpolation approaches. If compared with slant factors determined from ECMWF native model level data, the biases can be significantly larger.

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

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.

A Priori Gradients in the Analysis of Space Geodetic Observations

We introduce a static a priori gradient model (APG) based on a spherical harmonic expansion up to degree and order nine to describe the azimuthal asymmetry of tropospheric delays. APG is determined from climatology data of the European Centre for Medium-Range Weather Forecasts (ECMWF), and the refined model can be used in the analysis of observations from Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI). Comparisons reveal that gradients estimated in GNSS analysis are mostly smaller than those provided by APG. This difference is also confirmed by station and source coordinate changes if APG is used in GNSS and VLBI analysis.

Generation and Assessment of VMF1-Type Grids Using North-American Numerical Weather Models

Numerical weather models (NWM) have become an important source of atmospheric data for modeling error sources in geodetic positioning. One example of this is the development of the Vienna Mapping Functions (VMF1) and ray-traced zenith delays which are derived from the European Centre for Medium-range Weather Forecasts (ECMWF) datasets. These products are provided on an operational basis through the GGOS Atmosphere project. In general, relatively little consideration has been given to the choice of NWM on the derived mapping functions and zenith delay products. In this investigation we compare the gridded-VMF1 mapping functions and ray-traced zenith delays derived from the ECMWF to equivalent products derived by ray-tracing through the National Center for Environmental Prediction (NCEP) Reanalysis model. We have chosen to compare the gridded version of these products as they are available for any location on Earth, rather than only specific stations and have been shown to be essentially equivalent in terms of accuracy. This paper also includes a discussion about a systematic production of gridded-VMF1 and ray-traced zenith delays derived from the NCEP datasets (and from the Canadian Meteorological Center GEM model) on an operational basis. The benefits of the service would include: (1) a backup in the event of the ECMWF VMF1 or zenith delays being unavailable; (2) greater compatibility with other NWM derived corrections, such as atmospheric pressure loading and; (3) the availability of tropospheric delay products derived from an independent source and ray-tracing algorithms should provide more robustness for combination products which use these models.

Global Assessment of UNB’s Online Precise Point Positioning Software

The GPS Analysis and Positioning Software (GAPS) is a GPS precise point positioning (PPP) application developed at the University of New Brunswick (UNB). GAPS exists in two forms: a web-based positioning service, to which users can upload GPS observations to be processed, and a command-line executable version, which can be used to process large amounts of GPS data in a fast and convenient manner. The objective of this paper is to summarize the main approach used in the online version of GAPS; to present the modeling options available to the user through the online interface, and to assess the accuracy of GAPS by processing a global network of IGS stations for a period 1 year; and to assess the achievable accuracy of GAPS by comparing the results with external sources and similar evaluations encountered in the literature. Results obtained indicate that GAPS can achieve at least 1 cm level accuracy for any component at any location in the world.

Fitting of NWM Ray-Traced Slant Factors to Closed-Form Tropospheric Mapping Functions

In this paper we investigate the fitting of ray-tracing results to closed-form expressions. We focus on the variation of the delay with elevation angle and azimuth. For the elevation angle-dependence we compare the continued fraction form of Yan and Ping (Astron J 110(2):934–993, 1995) with that of Marini (Radio 11 Sci 7(2):223–231, 1972) (normalized to yield unity at zenith and found negligible differences between the two functional formulations for the hydrostatic case, while for the non-hydrostatic case, the Yan and Ping model performed marginally better. Since the ray-tracing results do not necessarily assume azimuthal symmetry, we have to account for the azimuth-dependence. For that we compare the linear gradient model of Davis et al. (Radio Sci 28(6):1003–1018, 1993) with the inclusion of second order terms (Seko et al., J Meteorol Soc Jpn 82(1B):339–350, 2004) and arbitrary spherical harmonics. These functional forms performed very well for the hydrostatic case, although for the non-hydrostatic case there were some large biases, particularly in the spherical harmonics of order 1, degree 1 and the 2nd order polynomial case.