The 95% Confidence Interval for GNSS-Derived Site Velocities

Abstract

Linear trends, or site velocities, derived from global navigation satellite system (GNSS) positional time series have been commonly applied to site stability assessments, structural health monitoring, sea-level rise, and coastal submergence studies. The uncertainty of the velocity has become a big concern for stringent users targeting structural or ground deformation at a few millimeters per year. GNSS-derived positional time series are autocorrelated. Consequently, conventional methods for calculating the standard errors of the linear trends result in unrealistically small uncertainties. This article presents an approach to accounting for the autocorrelation with an effective sample size (Neff). A robust methodology has been developed to determine the 95% confidence interval (95%CI) for the site velocities. It is found that the 95%CI fits an inverse power-law relationship over the time span of the time series (vertical direction: 95%CI=5.2T−1.25; east–west or north–south directions: 95%CI=1.8T−1.0). For static GNSS monitoring projects, continuous observations longer than 2.5 and 4 years are recommended to achieve a 95%CI below 1 mm/year for the horizontal and vertical site velocities, respectively; continuous observations longer than 7 years are recommended to achieve a 95%CI below 0.5 mm/year for the vertical land movement rate (subsidence or uplift). The 95%CI from 7-year GNSS time series is equivalent to the 95%CI of the sea-level trend derived from 60-year tide gauge observations. The method and the empirical formulas developed through this study have the potential for broad applications in geosciences, sea-level and coastal studies, and civil and surveying engineering.