Melting glaciers, ice caps and ice sheets have made an important contribution to sea-level rise through the last century. Self-attraction and loading effects driven by shrinking ice masses cause a spatially varying redistribution of ocean waters that affects reconstructions of past sea level from sparse observations. We model the solid-earth response to ice mass changes and find significant vertical deformation signals over large continental areas. We show how deformation rates have been strongly varying through the last century, which implies that they should be properly modelled before interpreting and extrapolating recent observations of vertical land motion and sea-level change.@en

Present-day mass redistribution increases the total ocean mass and, on average, causes the ocean bottom to subside elastically. Therefore, barystatic sea level rise is larger than the resulting global mean geocentric sea level rise, observed by satellite altimetry and GPS-corrected tide gauges. We use realistic estimates of mass redistribution from ice mass loss and land water storage to quantify the resulting ocean bottom deformation and its effect on global and regional ocean volume change estimates. Over 1993-2014, the resulting globally averaged geocentric sea level change is 8% smaller than the barystatic contribution. Over the altimetry domain, the difference is about 5%, and due to this effect, barystatic sea level rise will be underestimated by more than 0.1 mm/yr over 1993-2014. Regional differences are often larger: up to 1 mm/yr over the Arctic Ocean and 0.4 mm/yr in the South Pacific. Ocean bottom deformation should be considered when regional sea level changes are observed in a geocentric reference frame.@en

Uncertainty in the geocenter position and its subsequent motion affects positioning estimates on the surface of the Earth and downstream products such as site velocities, particularly the vertical component. The current version of the International Terrestrial Reference Frame, ITRF2014, derives its origin as the long-term averaged center of mass as sensed by satellite laser ranging (SLR), and by definition, it adopts only linear motion of the origin with uncertainty determined using a white noise process. We compare weekly SLR translations relative to the ITRF2014 origin, with network translations estimated from station displacements from surface mass transport models. We find that the proportion of variance explained in SLR translations by the model-derived translations is on average less than 10%. Time-correlated noise and nonlinear rates, particularly evident in the Y and Z components of the SLR translations with respect to the ITRF2014 origin, are not fully replicated by the model-derived translations. This suggests that translation-related uncertainties are underestimated when a white noise model is adopted and that substantial systematic errors remain in the data defining the ITRF origin. When using a white noise model, we find uncertainties in the rate of SLR X, Y, and Z translations of ±0.03, ±0.03, and ±0.06, respectively, increasing to ±0.13, ±0.17, and ±0.33 (mm/yr, 1 sigma) when a power law and white noise model is adopted.@en

We present a finite-element model of post-seismic solid Earth deformation built in the software package Abaqus (version 2018). The model is global and spherical, includes self-gravitation and is built for the purpose of calculating post-seismic deformation in the far field (1/4300gkm) of major earthquakes. An earthquake is simulated by prescribing slip on a fault plane in the mesh and the model relaxes under the resulting change in stress. Both linear Maxwell and biviscous (Burgers) rheological models have been implemented and the model can be easily adapted to include different rheological models and lateral variations in Earth structure, a particular advantage over existing models. We benchmark the model against an analytical coseismic solution and an existing open-source post-seismic model code, demonstrating good agreement for all fault geometries tested. Due to the inclusion of self-gravity, the model has the potential for predicting deformation in response to multiple sources of stress change, for example, changing ice thickness in tectonically active regions.@en

In Antarctica, Global Positioning System (GPS) vertical time series exhibit non-linear signals over a wide range of temporal scales. To explain these non-linearities, a number of hypotheses have been proposed, among them the short-term rapid solid Earth response to contemporaneous ice mass change. Here we use GPS vertical time series to reveal the solid Earth response to variations in surface mass balance (SMB) in the Southern Antarctic Peninsula (SAP). At four locations in the SAP we show that interannual variations of SMB anomalies cause measurable elastic deformation. We use regional climate model SMB products to calculate the induced displacement assuming a perfectly elastic Earth. Our results show a reduction of the misfit when fitting a linear trend to GPS time series corrected for the elastic response to SMB variations. Our results imply that, for a better understanding of the glacial isostatic adjustment signal in Antarctica, SMB variability must be considered.@en