Simulation studies for the tropospheric delays

Members of the VLBI2010 Committee have carried out a series of Monte Carlo simulations 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. 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 the 25 realizations. However, with more experience in simulations, one should rather create 50 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.]

abcd

Figure 1 (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.

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

Figure 3 (from Tierno Ros et al. 2013)

Ongoing and future tasks:

• Source based scheduling with four sources observed at a time allows increasing the cutoff elevation angle. It should be assessed what is the benefit when using a higher cutoff elevation angle.

• 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.

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.

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.

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.

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

Tierno Ros