GPS time-variable seasonal signals modeling

Abstract

Seasonal signals (annual plus semi-annual) in GPS time series are of great importance for understanding the evolution of regional mass, i.e. ice and hydrology. Conventionally these signals (annual and semi-annual) are derived by least-squares fitting of harmonic terms with a constant amplitude and phase. In reality, however, such seasonal signals are modulated, i.e. they will have a time-variable amplitude and phase. Recently, Davis et al. (2012) proposed a Kalman filter based approach to capture the stochastic seasonal behavior of geodetic time series.

In this study, a non-parametric approach, singular spectrum analysis (SSA) is introduced. It uses time domain data to extract information from short and noisy time series without prior knowledge of the dynamics affecting the time series. A prominent benefit is that obtained trends are not necessarily linear and extracted oscillations can be amplitude and phase modulated. In this work, the capability of SSA for analyzing time-variable seasonal signals from GPS time series is investigated. We also compare SSA-based results to two model-based results, i.e. least-squares analysis and Kalman filtering. Our results show that singular spectrum analysis could be a viable and complementary tool for exploring modulated oscillations from GPS time series.

Based on the SSA-derived seasonal signals, we look into the effects of the input noise variances in the framework of Kalman filtering. Two Kalman filtering based approaches with different process noise models are compared over 79 GPS sites. We find that the basic Kalman filtering technique with the input noise model suggested by Davis et al. (2012) turns out to be optimal.