Assessment of tropospheric slant factor models: Comparison with three dimensional ray-tracing and impact of geodetic positioning

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The tropospheric delay still remains a limiting factor to the accuracy of space based positioning techniques. If this effect is not properly modeled it can adversely effect the accuracy and precision of station coordinates derived from these techniques. Particulary susceptible to errors in the delay, is the station height parameter which is important for geophysical studies such as studying sea level rise and isostatic adjustment and for the realization of a stable reference frame. Ray-tracing through numerical weather models has been shown to be very beneficial for the development of mapping functions which model the elevation angle dependence of the tropospheric delay. Typically, due to computational constraints, only the vertical profile above the site is utilized, and the atmosphere is assumed to be spherically symmetric, therefore ignoring the azimuth-dependence of the delay. Instead of only using the vertical profile, it is possible to make no assumptions about the nature of the atmosphere and use the full information provided by the numerical weather model. Ray-tracing through the 3D state of the numerical weather model, generally referred to as 3D ray-tracing, makes it possible to model both the elevation angle- and azimuth-dependence of the tropospheric delay. This contribution is divided into two parts, first an assessment of current mapping functions and functional formulations for describing both the elevation angle- and azimuthdependence of the tropospheric delay is performed using the three dimensional ray-tracing as truth data. The results of this experiment indicate that currently, the Vienna Mapping Function 1 (VMF1) should be used for all geodetic applications, and if necessary, the Global Mapping Function (GMF) can serve as an acceptable replacement without introducing a significant bias into the station position. Secondly, the Marini expression, truncated at three coefficients, is capable of modeling 3D ray-traced delays down to the 3° elevation angle with sub-millimeter accuracy and therefore it’s use as the basis of current mapping functions is supported. In terms of modeling the asymmetry of the tropospheric delay with respect to azimuth, the Chen & Herring linear horizontal gradient formulation was found to be the best candidate when estimating the gradient parameters from space geodetic observations, although some tuning of the elevation dependent term may still be possible. The benefit of the higher order functional formulations was somewhat dependent on the nature of the asymmetric delay, although in general, the second degree spherical harmonics were better able to model the asymmetry of the delay at low elevation angles. In terms of estimating the unknown coefficients using the space geodetic observations, these higher order functions may not be practical as they introduce more unknown parameters into the design matrix. However, these formulations may be useful for providing asymmetric delay corrections in a convenient closed-form which can be distributed to end users. The second experiment investigated the use of three dimensional ray-tracing at the observation level for the reduction of space geodetic observations. This consisted of a global precise point positioning (PPP) campaign comparing four strategies to modeling the delay. It was found that the use of three dimensional ray-tracing gave identical performance in the horizontal station repeatability as the current recommended approach of estimating two gradient parameters from the space geodetic observations, while in the vertical domain the estimation of the gradient parameters resulted in a small improvement. Both of these methods performed better than ignoring the asymmetric nature of the tropospheric delay all together. Although the ray-traced zenith delays and the estimated zenith delays using the PPP approach agreed to the 3 mm level, the ray-traced zenith delays could not capture the short term fluctuations which occur, mainly due to the presentee of water vapor in the atmosphere. For this reason, it was still necessary to estimate a residual zenith delay parameter in order to achieve sub-cm repeatability in the vertical component.