# GPS Time Series Analysis from Aboa the Finnish Antarctic Research Station
## 3 Results
### Time Series Analysis
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Component** & **Noise Model** & **Velocity (mm/y)** & **Annual (mm)** & **Semian. (mm)** & **AIC** & **BIC** \\ \hline \multirow{3}{*}{North} & FlickerGGM & \(11.20\pm 0.03\) & \(0.23\pm 0.12\) & \(0.26\pm 0.12\) & \(17\),\(712.2\) & \(17\),\(757.7\) \\  & GGM & \(11.20\pm 0.03\) & \(0.19\pm 0.10\) & \(0.24\pm 0.11\) & \(17\),\(694.5\) & \(17\),\(752.9\) \\  & Powerlaw & \(11.23\pm 0.09\) & \(0.22\pm 0.12\) & \(0.24\pm 0.11\) & \(17\),\(704.5\) & \(17\),\(756.4\) \\ \hline \multirow{3}{*}{East} & FlickerGGM & \(1.46\pm 0.05\) & \(0.38\pm 0.15\) & \(0.22\pm 0.10\) & \(15\),\(048.7\) & \(15\),\(094.2\) \\  & GGM & \(1.46\pm 0.03\) & \(0.36\pm 0.10\) & \(0.18\pm 0.08\) & \(14\),\(970.1\) & \(15\),\(028.6\) \\  & Powerlaw & \(1.46\pm 0.05\) & \(0.36\pm 0.10\) & \(0.18\pm 0.07\) & \(14972.6\) & \(15024.5\) \\ \hline \multirow{3}{*}{Up} & FlickerGGM & \(0.71\pm 0.04\) & \(2.31\pm 0.23\) & \(2.07\pm 0.23\) & \(28\),\(733.6\) & \(28\),\(779.0\) \\  & GGM & \(0.71\pm 0.05\) & \(2.31\pm 0.28\) & \(2.07\pm 0.28\) & \(28\),\(674.9\) & \(28\),\(733.3\) \\ \cline{1-1}  & Powerlaw & \(0.79\pm 0.35\) & \(2.43\pm 0.57\) & \(2.14\pm 0.42\) & \(28\),\(736.1\) & \(28\),\(788.0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Estimated trend and seasonality parameters for different noise models for the GIPSY solution. Aboa coordinate time series contain temporally correlated coloured noise which spectral index is closer to flicker noise. The noise of the horizontal components is characterised by an average spectral index \(\kappa=-0.8\) and average amplitude of \(5\,\mathrm{mm}/\mathrm{y}^{0.20}\), whereas the noise of the vertical component has similar nature \(\kappa=-0.9\) but three times larger amplitude, i.e. \(16\,\mathrm{mm}/\mathrm{y}^{0.22}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Component** & **Noise Model** & **Velocity (mm/y)** & **Annual (mm)** & **Semiann. (mm)** & **AIC** & **BIC** \\ \hline \multirow{3}{*}{North} & FlickerGGM & \(11.10\pm 0.05\) & \(1.44\pm 0.23\) & \(0.37\pm 0.16\) & 18,598.6 & 18650.4 \\  & GGM & \(11.09\pm 0.04\) & \(1.43\pm 0.16\) & \(0.35\pm 0.12\) & 18,553.9 & 18,618.7 \\  & Powerlaw & \(11.14\pm 0.09\) & \(1.44\pm 0.17\) & \(0.33\pm 0.12\) & 18,558.4 & 18,616.7 \\ \hline \multirow{3}{*}{East} & FlickerGGM & \(1.49\pm 0.06\) & \(0.85\pm 0.26\) & \(0.29\pm 0.15\) & 19,952.4 & 20,004.2 \\  & GGM & \(1.48\pm 0.04\) & \(0.83\pm 0.17\) & \(0.22\pm 0.11\) & 19,850.1 & 19,914.9 \\  & Powerlaw & \(1.50\pm 0.09\) & \(0.82\pm 0.17\) & \(0.22\pm 0.11\) & 19,855.0 & 19,913.3 \\ \hline \multirow{3}{*}{Up} & FlickerGGM & \(0.38\pm 0.11\) & \(3.11\pm 0.49\) & \(1.12\pm 0.37\) & 26,283.4 & 26,335.2 \\  & GGM & \(0.39\pm 0.11\) & \(3.10\pm 0.48\) & \(1.11\pm 0.36\) & 26,287.0 & 26,351.9 \\ \cline{1-1}  & Powerlaw & \(0.45\pm 0.34\) & \(3.11\pm 0.50\) & \(1.13\pm 0.35\) & 26,297.3 & 26,355.6 \\ \hline \end{tabular}
\end{table} 
Table 6: Estimated trend and seasonality parameters for different noise models for the RTKLIB solution. Figure 11: Power spectral density plots for both solutions and all components. Figure 12 depicts the coordinate residuals after removing the outliers, trend, annual and semiannual periodic signals. The rms error is reduced to less than 2 mm for the horizontal components and below 6 mm for the vertical component. Figure 13 displays the horizontal movement. Since the beginning of operation on 1 February 2003, Aboa station has moved about 175.5 mm in the North direction at a rate of 11.23 \(\pm\) 0.09 mm/y and about 29.5 mm in the East direction at a rate of 1.46 \(\pm\) 0.05 mm/y (see Tables 5 and 6). Figure 14 illustrates the movement in the vertical direction and its signal decomposition. The vertical movement consists of a linear trend and seasonal signals. The trend was found to be upwards at a rate of 0.79 \(\pm\) 0.35 mm/year. The seasonal signals include annual and semiannual components.