Determination of tidal displacements using the Global Positioning System

Abstract

Recent developments in precise Global Positioning System (GPS) geodesy allow to measure surface deformation at broad timescales with unprecedented global coverage and accuracy. This research mainly focuses on determination of tidal displacements in eight principal semidiurnal and diurnal frequencies using continuous GPS observations from both regional and global networks. The effects of GPS tidal displacement coefficients on long-period signals in position time-series are also investigated. Results from this research may provide independent constraints on dynamics of the Earth's interior. Three-dimensional tidal displacement residuals of eight principal semidiurnal and diurnal constituents after removal of a priori modelled solid Earth tides were estimated from daily GPS observations using a modified precise point positioning (PPP) technique. The daily estimates of tidal displacement parameters and their variance-covariance matrices were then combined using an iterative Kalman filter to yield the final estimates. The tidal displacement estimates for all the constituents, except for K1 and K2, can be resolved fairly well using more than 1,000 days of GPS observations. The K1 and K2 estimates with inferior accuracy are found to be strongly affected by the site's equipment (receiver and antenna) updates and the time-variable GPS constellation geometry, respectively. Tidal displacement estimates at 12 sites in Hong Kong were determined using three to seven years of continuous GPS observations. The results were compared with predictions from seven latest global ocean tide models. Tidal gravity measurements in Hong Kong were also used to validate the GPS results. The study shows that results from both the GPS and gravity measurements agree best with the GOT4.7 and NAO99b models, when the K1 and K2 constituents are excluded. The GPS/model agreements are generally at sub-millimetre level, except for S2, K2 and K1 with relatively larger errors. After removing the systematic biases between the GPS estimates and model predictions, the misfits of M2, S2, N2, O1, P1 and Q1 at all the sites are within 0.5 and 1.0 mm in the horizontal and vertical components, respectively, while K1 and K2 show relatively larger misfits of up to 2.5 mm. Compared with the modelled values, both the GPS and gravity estimates of S2 exhibit large biases with unknown reasons. Tidal displacement estimates at 125 IGS05 reference sites were also obtained from analysis of GPS observations from 1996 to 2006. The GPS estimates were compared with Very Long Baseline Interferometry (VLBI) estimates and seven ocean tide model predictions. The results show that GPS can determine tidal displacements with accuracy superior to VLBI for all the constituents except K2. The Weighted Root Mean Square (WRMS) misfits indicate that GPS is capable of estimating tidal displacements with sub-millimetre accuracy in all the three components for all the constituents except K1 and K2. The AG06a model gives anomalous results compared with both the GPS and VLBI estimates, while the most recent four models (FES2004, TPXO7.1, GOT4.7 and EOT08a) fit the GPS estimates equally well at the global scale. The GPS/model residuals show large-scale spatial coherence for all the constituents except K2. The estimates of the M2 and O1 constituents show the highest signal-to-noise ratios, indicating that both of the constituents are most appropriate to be used to test solid Earth tide models. The GPS tidal displacement coefficients with the sub-millimetre accuracy for all the constituents except K1 and K2 have proved to effectively reduce spurious long-period signals in position time-series. This indicates that GPS tidal displacement coefficients can be used to substitute for model predictions in future global GPS data analysis. The K1 and K2 coefficients with poorer accuracy should be treated with caution. Including K2 corrections, secular variations of more than 1 mm/yr are evident at some sites.