Estimation of the vertical land motion from GNSS time series and application in quantifying sea-level rise

Sea-level rise observed at tide gauges must be corrected for vertical land motion, observed with GNSS, to obtain the absolute sea-level rise with respect to the centre of the Earth. Both the sea-level and vertical position time series contain temporal correlated noise that need to be taken into account to obtain the most accurate rate estimates and to ensure realistic uncertainties. Satellite altimetry directly observes absolute sea-level rise but these time series also exhibit colored noise. In this chapter we present noise models for these geodetic time series such as the commonly used first order Auto Regressive (AR), the General Gauss Markov (GGM) and the ARFIMA model. The theory is applied to GNSS and tide gauge data from the Pacific Northwest coast.