The provision of accurate models of Glacial Isostatic Adjustment (GIA) is presently a priority need in climate studies, largely due to the potential of the Gravity Recovery and Climate Experiment (GRACE) data to be used to determine accurate and continent-wide assessments of ice mass change and hydrology. However, modelled GIA is uncertain due to insufficient constraints on our knowledge of past glacial changes and to large simplifications in the underlying Earth models. Consequently, we show differences between models that exceed several mm/year in terms of surface displacement for the two major ice sheets: Greenland and Antarctica. Geodetic measurements of surface displacement offer the potential for new constraints to be made on GIA models, especially when they are used to improve structural features of the Earth’s interior as to allow for a more realistic reconstruction of the glaciation history. We present the distribution of presently available campaign and continuous geodetic measurements in Greenland and Antarctica and summarise surface velocities published to date, showing substantial disagreement between techniques and GIA models alike. We review the current state-of-the-art in ground-based geodesy (GPS, VLBI, DORIS, SLR) in determining accurate and precise surface velocities. In particular, we focus on known areas of need in GPS observation level models and the terrestrial reference frame in order to advance geodetic observation precision/accuracy toward 0.1 mm/year and therefore further constrain models of GIA and subsequent present-day ice mass change estimates.

It is well known that sea level variations exhibit temporal correlation. This is sometimes ignored in the estimation process of the sea level rise or taken into account using a first-order autoregressive model. We have verified that this stochastic model is accurate for yearly tide gauge and sea level reconstruction time-series but it underestimates the real rate uncertainty in satellite altimetry and monthly tide gauge data by a factor of 1.3–1.5 and sometimes even 2. Similar results were found for sea level acceleration. An original finding is that in 13–17 per cent of the tide gauge data, we found random walk which increases the rate uncertainty on average by an additional factor of 3. The estimation errors presented in this research should be added to the other sources of uncertainty, such as the vertical land movement, spatial correlation and altimeter drift, to obtain the total sea level rate and acceleration error.