Modelling the GNSS Time Series: Different Approaches to Extract Seasonal Signals

Seasonal signatures observed within the Global Navigation Satellite System (GNSS) position time series are routinely modelled as annual and semi-annual periods with constant amplitudes over time. However, in this chapter, we demonstrate that these amplitudes can vary significantly over time, by as much as 3 mm at some stations. Different methods have been developed to estimate the time-varying curves. The advantages and disadvantages of those methods are presented for synthetic data, which mimic the real position time series, including their time-changeability and noise properties. For these series, we conclude that the Kalman filter and an adaptation of the Wiener Filtergive the best results. As the Earth’s lithosphere is seasonally loaded and unloaded, we also account for the non-tidal atmospheric, oceanic and continental hydrology loading effects, which contribute the most to the seasonal signatures. We demonstrate that a direct removal of loading effects leads to the significant change in the power of the GPS position time series, especially for frequencies between 8 and 80 cpy; if the noise model is not adapted to this new situation, this causes an underestimation of velocity uncertainty. Therefore, we recommend to use the Kalman filter or adaptive Wiener filtermethods instead to remove the seasonal signal to ensure accurate estimates of the trend error.