Monte Carlo SSA to detect time-variable seasonal oscillations from GPS-derived site position time series

- Monte Carlo SSA is introduced to extract time-variable seasonal oscillations from continual GPS observations.
- AR(1) null hypothesis noise model may be misleading in surrogate data tests for GPS seasonal oscillations.
- MLE technique is an effective solution to confirm whether Monte Carlo SSA really works.
- SSA may absorb colored noise.
- Seasonal signals are resulting from a combination of geophysical loading and systematic error.

We explore the capability of singular spectrum analysis (SSA) to extract time-variable seasonal oscillations from continual GPS observations and demonstrate the statistical assessment on the colored noise (in particular the first-order autoregressive AR(1) noise) using Monte Carlo SSA (MCSSA) methodology. We provide example applications to ~ 15-year vertical coordinate time series for 36 globally distributed International GNSS Service (IGS) sites. We find the SSA-filtered seasonal signals can easily pass the confidence interval and hypothesis tests of MCSSA. However, maximum likelihood estimate (MLE) results show that 72% of sites have their flicker noise amplitudes reduced after removing SSA-filtered annual signal, implying that the SSA-filtered seasonal signals may contain an artificial signal driven by colored noise. Therefore, the AR(1) null hypothesis noise model may be misleading in surrogate data tests for GPS seasonal signals. Moreover, comparison between SSA-filtered GPS annual signals and joint geophysical model predictions (non-tidal atmospheric loading + non-tidal ocean loading + hydrological loading) confirms that seasonal signals are resulting from a combination of mass loading and systematic error.