Effect of annual signals on geodetic velocity

[1] Our analysis of Global Positioning System (GPS) site coordinates in a global reference frame shows annual variation with typical amplitudes of 2 mm for horizontal and 4 mm for vertical, with some sites at twice these amplitudes. Power spectrum analysis confirms that GPS time series also contain significant power at annual harmonic frequencies (with spectral indices 1 < a < 2), which indicates the presence of repeating signals. Van Dam et al. [2001] showed that a major annual component is induced by hydrological and atmospheric loading. Unless accounted for, we show that annual signals can significantly bias estimation of site velocities intended for high accuracy purposes such as plate tectonics and reference frames. For such applications, annual and semiannual sinusoidal signals should be estimated simultaneously with site velocity and initial position. We have developed a model to calculate the level of bias in published velocities that do not account for annual signals. Simultaneous estimation might not be necessary beyond 4.5 years, as the velocity bias rapidly becomes negligible. Minimum velocity bias is theoretically predicted at integer-plus-half years, as confirmed by tests with real data. Below 2.5 years, the velocity bias can become unacceptably large, and simultaneous estimation does not necessarily improve velocity estimates, which rapidly become unstable due to correlated parameters. We recommend that 2.5 years be adopted as a standard minimum data span for velocity solutions intended for tectonic interpretation or reference frame production and that we be skeptical of geophysical interpretations of velocities derived using shorter data spans.