The estimation of robust formal error estimates for geodetic site position is problematic and even more difficult for site velocity. In the context of this study, the primary requirement is to correctly estimate the uncertainty of the vertical position of the BUR1, TBCP and RKCP sites. The difficulty in estimating a realistic uncertainty is three fold:
1) Firstly and most importantly, the uncertainty estimate from GLOBK is biased due to the small sample size of episodic based GPS deployments. Without a significantly larger time series it is difficult to assess the variability of the time series.
2) The short-term estimate of site position may also be contaminated by residual seasonal signals, measurement noise and model uncertainty (amongst others). These effects potentially offset the observed site position from the long-term mean position. The magnitude of this effect is dependent on the exact time of observation and the periodicity and magnitude of the residual geophysical signals (and other components) involved. Studies such as Mao et al. (1999), Dong et al. (2002) investigate these issues, underscoring the frequent underestimation of uncertainty by factors of typically between 2 and 5 for example.
3) The uncertainty in site position (and velocity) is also dependent on the noise model assumed in the time series. Assuming a white noise process in the presence of time-correlated noise processes will result in an underestimation of the uncertainty (see Zhang et al., 1997 and Williams, 2002 for example).
To gain an improved estimate of the uncertainty expected at the BUR1, TBCP and RKCP sites, a significantly long time series is required. For this analysis, the full time series in the vertical component at BUR1 and HOB2 (using 4 years of common data) have been utilised. HOB2 is located near Hobart on the southern Tasmanian coast, with a baseline separation from BUR1 of 232 km. Analysis of the common mode displacement between these two sites provides an indication of the common mode behaviour to be expected between the much closer TBCP and RKCP sites, for which no long term time series solutions are available. The long- term time series for BUR1 and HOB2 were computed as part of an analysis for the TIGA tide gauge monitoring project (Schone, 2005). The analysis represents the
“CTA” analysis centre solution by Assoc. Professor Peter Morgan (see Schone, 2005 for details). The solution was computed using the GAMIT/GLOBK software suite, also adopting a regional analysis approach.
Analysis of the full BUR1 and HOB2 time series (Figure 3-14a) shows significant correlation between their vertical components (correlation coefficient of 0.82 using unsmoothed data and 0.85 using smoothed data, smoothed with a monthly moving average). The weighted RMS variability (assuming a white noise process) of the unsmoothed BUR1 and HOB2 vertical time series is 9.9 mm and 10.9 mm respectively. This variability reduces significantly to 7.2 mm for the residual (the smoothed residual has a standard deviation of just 4.1 mm, Figure 3-14b). Common mode seasonal effects which may be contributing to this signal structure include contributions from un-modelled loading signals (groundwater and atmospheric loading for example) and aliased mis-modelled geophysical signals (solid Earth tide and ocean tide loading for example), as discussed in Penna and Stewart (2003). 1999.5 2000 2000.5 2001 2001.5 2002 2002.5 2003 2003.5 2004 -50 -40 -30 -20 -10 0 10 20 30 40 50 Height (mm) Year
Long-term GPS Time Series, BUR1 and HOB2
BUR1 1999.5 2000 2000.5 2001 2001.5 2002 2002.5 2003 2003.5 2004 -50 -40 -30 -20 -10 0 10 20 30 40 50 Difference (mm) Year
Difference: BUR1 - HOB2
HOB2 BUR1 WRMS: 9.9 mm HOB2 WRMS: 10.9 mm GPS BuoyWindow
Difference WRMS: 7.2 mm (Smoothed Difference Std Dev: 4.1 mm)
(a)
(b)
Figure 3-14 Burnie (BUR1) and Hobart (HOB2) GPS time series. (a) BUR1 and
HOB2 vertical GPS time series, (without error bars and arbitrary offset applied). Note the shaded section which encompasses the GPS buoy deployment window. The bold smoothed
line on both time series shows a 31-day mean. (b) Difference: BUR1-HOB2.
Given the high correlation of BUR1 and HOB2 over ~200 km, we assume the underlying signal at BUR1 (Figure 3-14a) would be largely reflected at the TBCP and RKCP sites. The BUR1 site therefore forms a proxy for our analysis of the
TBCP and RKCP sites. Estimating the components of the noise structure present with the BUR1 and HOB2 time series provides interesting results. Using the methodology described in Williams (2003), white noise estimates are 15.3 mm and 9.4 mm for BUR1 and HOB2 respectively. Power law noise estimates are significantly higher at 19.3 mm/yr1/4 and 22.9 mm/yr1/4 respectively. A further
discussion surrounding the interpretation of this power law noise structure is provided in §3.5. In the context of this study, these results serve to highlight the need to scale uncertainties determined from the GLOBK analysis.
In addition to considering the seasonal (and possibly systematic) structure of the time series, and the influence of the frequency dependent noise structure, the short, episodic deployment of the TBCP and RKCP receivers must be considered. To assess this effect, the episodic determinations of the BUR1 site position are compared against the long term mean estimate, as computed from the long term series (Figure 3-14). The episodic determinations are derived from the GLRED/GLORG repeatability analysis (§3.4.3.2).
2001.6 2001.7 2001.8 2001.9 2002.0 2002.1 2002.2 2002.3 2002.4 2002.5 2002.6 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 Absolute Height (m)
BUR1 Long-Term vs Episodic Time Series
Time
Long-term Episodic
Figure 3-15 Long-term and episodic BUR1 absolute height time series. Values are shown with 1-sigma error bars.
Figure 3-15 shows six determinations of BUR1 position between 2001.7 and 2002.4 (seven determinations were available at both TBCP and RKCP due to equipment failure at the BUR1 site during the second experiment). Output from the GLRED analysis for the BUR1, TBCP, RKCP and HOB2 sites is provided for further inspection in Appendix B. The important observation to be made from Figure 3-15 is that the episodic data does not lie at seasonal or daily extremes, and are well distributed around the trend computed from the long-term time series. The long-term trend passes well within the 1-sigma error estimates for each episodic position determination. Quantitatively, the short-term BUR1 position from our GLOBK analysis falls within 2 mm of the long-term estimate indicating the episodic deployments have satisfactorily sampled the underlying signal. Combining
these analyses with recommendations presented in Mao et al. (1999), Williams (2002) and Williams et al. (2004), we choose a subjective (yet conservative) scaling constant of 5 for our GLOBK positional uncertainties. This results in an uncertainty at the 10 mm level. An additional ‘fixed’ or ‘systematic’ error term of 10 mm is added to the error budget to be carried forward into the following Chapter which focuses on the altimeter calibration. The systematic term is included to recognise many of the systematic components of the GPS analysis strategy discussed throughout this Chapter (for example, variability associated with observation weighting and model selection, methods used to stabilise the reference frame, frequency dependent noise structure and uncertainties associated with handling the scale of the reference frame and the influence of geocentre motion).