Simulation studies for the tropospheric delays

Members of the VLBI2010 Committee have carried out a series of Monte Carlo simulations (see Figure 1) to assess the error contribution of tropospheric delays, clock errors, and observation noise to parameters estimated with geodetic VLBI, like baseline lengths, station coordinates, or Earth Orientation Parameters (EOP). VLBI2010 simulations have been performed by the Goddard group (with Calc/Solve and Geodyn) and by the Vienna group (in the beginning with the Occam Kalman filter and a dedicated Precise-Point-Positioning tool for VLBI simulations, and later on with the Vienna VLBI Software VieVS).

Figure 1 (from Pany et al. 2011): Workflow of the Monte Carlo simulations. Typically, 25 24h sessions have been simulated and consequently analyzed to determine bias and standard deviation of parameters estimated with the 25 realizations. However, with more experience in simulations, one should rather create 50 or even more realizations.

These studies have shown (e.g., Petrachenko et al. 2009, Pany et al. 2011; various IVS Memoranda) that deficiences in tropospheric delay modeling are the major error source for VLBI2010 among the three sources mentioned above. [It is important to note here, that we did not consider source structure effects for the simulations, nor did we simulate systematic effects. Shabala et al. have submitted a manuscript on source structure simulations to Journal of Geodesy (2014).] Figure 2 illustrates that a mitigation of the tropospheric turbulence clearly helps to improve station positions whereas there is no significant improvement with further improved station clocks and white noise reduction.

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Figure 2 (from Pany et al. 2011): a) median (over all stations) 3D position rms in mm versus structure constant Cn and b) versus effective height H. These two parameters, Cn and H, are the key quantities for the simulation of tropospheric delays according to Nilsson et al. (2007). c) median 3D position rms in mm versus Allan Standard Deviation (ASD) of the clocks and d) versus white noise added per observation. The simulations have been carried out for a 16-station network with the following default values: Cn = 1.0 x 10^-7 m^-1/3 , H = 2 km, wind 10 m/s towards East, ASD = 1 x 10^-14 at 50 minutes, white noise = 4/sqrt(2) ps per baseline observation.

The simulation of tropospheric delays is based on the turbulence model and the strategy described by Nilsson et al. (2007). In Vienna, the source code by Böhm et al. (2007) is applied. The key parameters for this model are the Cn parameter (structure constant), the effective scale height H, and - to a lesser extent - the wind velocity. A recent list of station-wise parameters as determined by Tobias Nilsson from GPS measurements is provided below. In this table, the scale height H is 2000 meters for all sites.

The Monte Carlo simulations have revealed that we need as many observations as possible at the stations with a good sky distribution, together with short intervals for the estimation of wet zenith delays and gradients. For example, if there are observations every 30 seconds, then estimation intervals of about 5 to 10 minutes for zenith delays and gradients (‘rapid gradients’) have proven to yield the best results in terms of baseline lengths and station coordinates.

Figure 3 (from Petrachenko et al. 2009): Median of the rms 3D position rms for uniform sky schedules with regular source-switching intervals ranging from 15 to 360 s. The delay measurement noise was 4 ps per baseline observation, the clock Allan Standard Deviation was 1 x 10^-14 at 50 minutes, and the turbulence parameters were those tabulated in Appendix A in Petrachenko et al. (2009). It is believed that the poorer performance of Occam at longer intervals is due to the fact that its Kalman filter solutions were specifically tuned for shorter source-switching intervals.

In VieVS, source based scheduling (as originally suggested by Bill Petrachenko and Tony Searle at NRCan) has been implemented with the possibility of two or four sources open for observation at a particular time. The Vienna group has been testing how the results with this approach differ from using the classical station based scheduling as also used by SKED. Details are provided in the open-access Journal of Geodesy paper by Sun et al. 2014.

A preliminary evaluation has also been carried out on the impact of the cutoff angle in VLBI observations. Tierno Ros et al. (2013) have taken a 16-station network and they have created schedules (source based with four sources) with cutoff elevation angles 5, 10, 15, and 30 degrees elevation. They find the best results in terms of baseline length repeatabilities for cutoff angles 10 and 15 degrees.

Figure 4 (from Tierno Ros et al. 2013): Difference in baseline length repeatabilities (cutoff 5 degrees minus cutoff 10 degrees).

Ongoing and future tasks:

• Tobias Nilsson is going to implement a Kalman filter to VieVS. It will be highly interesting to test the Kalman filter for VLBI2010 simulations.

References:

J. Sun, J. Böhm, T. Nilsson, H. Krásná, S. Böhm, H. Schuh, New VLBI2010 scheduling strategies and implications on the terrestrial reference frames, Journal of Geodesy, 88, pp. 449-461, 2014. Download

B. Petrachenko, A. Niell, D. Behrend, B. Corey, J. Böhm, P. Charlot, A. Collioud, J. Gipson, R. Haas, T. Hobiger, Y. Koyama, D. MacMillan, Z. Malkin, T. Nilsson, A. Pany, G. Tuccari, Alan Whitney, J. Wresnik, Design Aspects of the VLBI2010 System - Progress Report of the IVS VLBI2010 Committee, NASA/TM-2009-214180, 2009. Download

A. Pany, J. Böhm, D. MacMillan, H. Schuh, T. Nilsson, J. Wresnik, Monte Carlo simulations of the impact of troposphere, clock and measurement errors on the repeatability of VLBI positions, Journal of Geodesy, 85(1), pp. 39-50, doi: 10.1007/s00190-010-0415-1, 2011. Download (or contact Johannes Böhm for a copy)

T. Nilsson, R. Haas, and G. Elgered, Simulations of atmospheric path delays using turbulence models, Proceedings of the 18th European VLBI for Geodesy and Astrometry Working Meeting, 12-13 April 2007, edited by J. Boehm, A. Pany, and H. Schuh, Geowissenschaftliche Mitteilungen, Heft Nr. 79, Schriftenreihe der Studienrichtung Vermessung und Geoinformation, Technische Universitaet Wien, ISSN 1811-8380, 2007. Download of the proceedings

J. Böhm, J. Wresnik, and A. Pany, Simulations of wet zenith delays and clocks, IVS Memorandum 2006-013v03, 2007. Download

J. Böhm, C. Tierno Ros, J. Sun, S. Böhm, H. Krásná, New VLBI2010 scheduling options and implications on terrestrial and celestial reference frames, in: Proceedings of the 21st Meeting of the European VLBI Group for Geodesy and Astrometry, edited by N. Zubko and M. Poutanen, ISBN: 978-951-711-296-3, pp. 39-43, 2013. Download of the proceedings