6.3 System Stability
6.3.1 Behavior of Atomic Clocks
The estimation of zenith wet delay parameters and the interpretation of the residuals in the VLBI data analysis are closely linked to the stability of the hydrogen maser clocks feeding the local oscillators and other necessary electronics. In the case of the parameter estimation, the general assumption is that there are non-negligible correlations between the estimates of the atmosphere and the clock parameters. However, when studying the correlation matrix of the estimated parameters the correlations are only around 0.3 (Nothnagel et al. 2002) which is still in the range of weak correlations.
The relative clock behavior is generally estimated in the form of a clock polynomial plus continuous piece-wise linear (CPWL) offsets while for the zenith path delays it is only the CPWL offsets. Both have a time resolution of 60 minutes, normally. Clocks and atmosphere are not resolved any further to keep the significance of the residuals. It should be emphasized that no soft constraints in the form of pseudo observations are used for the clocks, which usually are necessary to stabilize the equation system due to missing observations in some piece-wise linear segments. However, due to the clearly increased number of observations in case of the WHISP sessions, these constraints are omitted here. Consequently, we do not expect any adverse effects from that side on the estimates of the zenith wet delays because any clock variations on a time scale beyond 1 hour are covered by the CPWL estimates. Individual observations and the respective residuals within the one hour periods are considered to be more affected by variations in the clock behavior at shorter time scales.
Usually, the telescopes are separated too far from each other so that a direct clock comparison is impossible. However, at Wettzell we are in the favorable situation that the two telescopes are close enough together that a two-way time transfer with a fiber-optics link (TWOTT) can be realized (Kodet et al. 2016b). In the last years, a very precise two-way time transfer (TWTT) using a coaxial cable as the transmission link (Pánek et al. 2013) was developed and implemented with high effort in order to identify unaccounted system delays at the Geodetic Observatory Wettzell.
The general principle of the TWTT approach is depicted in Fig. 6.2. The system is divided into two units, A and B, which are connected by a transmission link. Both units consist of a timing signal generator (TSG) and an event timer (ET) measuring the arrival times of timing signals. The output
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Figure 6.2: The general setup of the Two-Way Time Transfer system, which is divided into two units A und B connected by a transmission link, each consisting of a timing signal generator (TSG) and an event timer (ET) measuring the arrival times of timing signals. The output of the TSG and the input of the ET are connected to the transmission link by a network of five branches and three splitters and couplers, providing feedback of the transmitted signals back to the ET and the bidirectional use of the transmission line. The delays of the branches and the transmission link are denoted by τAi=1...5,τBi=1...5 andτL(Kodet et al. 2016a).
of the TSG and the input of the ET in both units are connected to the transmission link. Therefore, a network of five branches connected with three splitters and couplers, is used, which provides feedback of the transmitted signals back to the ET and the bidirectional use of the transmission line. All branches and the transmission link have delays, which are referred to as τAi=1...5, τBi=1...5
and τL, respectively (see Fig. 6.2). Analyzing the TWTT process provides the opportunity to investigate the influence of the partial delays within the TWTT units on the resulting uncertainty of the time transfer (Kodet et al. 2016a). The main disadvantage of this method results from the substantial increase of the uncertainty of the time transfer with the length of the transmission link due to the propagation loss at high frequencies(Kodet et al.2016a). To overcome this issue, the TWTT system was redesigned by using optical telecommunications technology. This results in the two-way optical time transfer (TWOTT) system implementing standard small form-factor pluggable optical transceivers, which leads to an increased area where the time transfer can be guaranteed with picosecond accuracy(Kodet et al. 2016b).
Due to the rather involved evaluation process, this link had only been active during the WHISP7 experiment, but not for the other WHISP sessions. For this reason, the following arguments have to be discussed on the basis of WHISP7 and two further routine IVS sessions (on 26 October and 21 December 2015,Nothnagel et al.2015) where the 20 m (Wz) and the 13.2 m (Wn) telescopes observed simultaneously.
The TWOTT provides clock offsets with sampling rates of 1 s between the two hydrogen masers involved in the experiments, which supply the radio telescopes with a reference frequency. In Fig. 6.3, the stability of the two involved H-Masers is compared, which is expressed as Allan deviation (ADEV) during the two IVS sessions mentioned above. Concluding, the H-Masers have the same stability of 8.3−13/τ for averaging times up to 300 s with dominant white phase modulation, and for averaging times longer than 300 s the white frequency modulation is the dominant noise floor.
Since the frequency offset between the two H-Masers is ∆ff
0 = 2.1−13 (Jan Kodet, pers. comm.), the linear trend was subtracted to allow for a better recognition of the small-scale variations (e.g.,
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Figure 6.3: The stability of the two H-Masers used in Wz and Wn expressed by Allan deviation (ADEV) for 26 October 2015 (red) and 21 December 2015 (black); by courtesy of Jan Kodet (Technical University of Munich, Geodetic Observatory Wettzell, Germany).
Fig. 6.4, red). Two phenomena can be identified, the one is a short-scale fluctuation of about 8 ps within a few tenths of seconds and the other one are smooth variations of an hourly time-scale. While the first group is essential for the characterization of the observation by observation variability, the latter one is rather well behaved and should easily be compensated for by the hourly CPWL offsets.
At least, this is the expectation.
However, when plotting the estimates for the same periods (see also Fig. 6.4, black), these only coincide very roughly with the TWOTT values (red). The differences at the level of 20-30 ps in the better case (e.g., for the VLBI session on 21 December 2015; see Fig. 6.4(a)) or up to 60 ps in the other extreme case (e.g., for the experiment on 26 October 2015; see Fig. 6.4(b)) cannot be explained by additional effects caused by the cable links between the hydrogen maser clocks and the VLBI electronics because these variations are expected to be rather smooth, mostly following the daily temperature cycle.
Fortunately, the TWOTT system could be activated simultaneously to the last WHISP experiment.
The corresponding measurement (red) and the clock correction parameters derived from the VLBI estimation process (brown) for the same period are depicted in Fig. 6.5. At first glance, the differ-ences perform similar to the better case of the routine IVS sessions. Concerning the modeling of the clock behavior, different parametrization settings have been used to allow for a better understand-ing of the level of difference to the TWOTT measurements. First, the clocks are parametrized as a quadratic polynomial and additional piece-wise linear functions with interval lengths of 60 min-utes. As already mentioned, the clock parameters are supplemented by soft constraints in the form of pseudo observations. In the standard data analysis, these pseudo observations are less heavily weighted, e.g., byσclo= 2·10−14ss. The clock parameters referring to the standard case are repre-sented by dark brown dots in Fig. 6.5. A second adjustment is performed turning off the additional soft constraints, which leads to the clock parameters in light brown. Similarly, this procedure is repeated for piece-wise linear segments of 30 and 20 minutes, respectively. The solution using a
82 6. Case Study: The WHISP Project
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Figure 6.4: Two-way time transfer measurements (red) and VLBI estimates (CPWLF and quadratic polynomial, black) for two VLBI sessions on 21 December 2015 (a) and 26 October 2015 (b).
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Figure 6.5: Two-way time transfer measurements (red) and VLBI estimates (CPWLF and quadratic polynomial) for different parametrization settings for the clocks and WHISP7: CPWLF 60 min. with (dark brown) and without (light brown) constraints; CPWLF 30 min. with (dark green) and without (light green) constraints; CPWLF 20 min. with (dark blue) and without (light blue) constraints.
30 minute interval with and without constraints are depicted in dark and light green, while the results of the adjustment with even shorter piece-wise linear intervals of 20 minutes are represented in dark and light blue for the two settings applying and turning off the constraints.
First, it is noteworthy, that for solution intervals of 30 or 60 minutes, the effect of the pseudo observations seems to be negligible, except for the first CPWL segment, and, therefore, the pseudo observations could in principle be neglected. However, the situation looks worse when reducing the piece-wise linear interval to 20 minutes. As soon as the soft constraints are turned off, the scatter of the clock estimates is clearly increasing, while the performance of the solution applying constraints is similar to the adjustment with CPWLF of 30 minutes. Most likely, the number of observations in the respective intervals is sufficient in a segment of 30 to 60 minutes, but not for shorter interval lengths below 30 minutes. However, also for the solutions showing a better clock behavior, the VLBI estimates coincide only very roughly with the TWOTT values, and the differences for the WHISP7 experiment are assessed to be in the order of magnitude of 20-30 ps.
The unexpected differences between the clock parameter estimates and the TWOTT measurements are in fact confirmed by the findings of Kodet et al. (2016a). They can only be explained by the assumption that the clock estimates compensate for more than the clock effect but rather anything else with an unmodeled clock-like behavior. With the CPWL estimates of one-hour long intervals we should have caught all the clock-like variations within the one-hour periods. Taking this into account, the 8 ps variations measured with the TWOTT is considered as the value to be taken for characterizing the noise component induced by the relative clock behavior in the post-fit residuals in Sec. 6.4.
84 6. Case Study: The WHISP Project