The study of glacial isostatic adjustment (GIA) is gaining an increasingly important role within the geophysical community. Understanding the response of the Earth to loading is crucial in various contexts, ranging from the interpretation of modern satellite geodetic measurements (e.g. GRACE and GOCE) to the projections of future sea level trends in response to climate change. Modern modelling approaches to GIA are based on various techniques that range from purely analytical formulations to fully numerical methods. Despite various teams independently investigating GIA, we do not have a suitably large set of agreed numerical results through which the methods may be validated; a community benchmark data set would clearly be valuable. Following the example of the mantle convection community, here we present, for the first time, the results of a benchmark study of codes designed to model GIA. This has taken place within a collaboration facilitated through European Cooperation in Science and Technology (COST) Action ES0701. The approaches benchmarked are based on significantly different codes and different techniques. The test computations are based on models with spherical symmetry and Maxwell rheology and include inputs from different methods and solution techniques: viscoelastic normal modes, spectral-finite elements and finite elements. The tests involve the loading and tidal Love numbers and their relaxation spectra, the deformation and gravity variations driven by surface loads characterized by simple geometry and time history and the rotational fluctuations in response to glacial unloading. In spite of the significant differences in the numerical methods employed, the test computations show a satisfactory agreement between the results provided by the participants

Abstract. We present regional-scale mass balances for 25 drainage basins of the Antarctic Ice Sheet (AIS) from satellite observations of the Gravity and Climate Experiment (GRACE) for time period January 2003 to September 2012. Satellite gravimetry estimates of the AIS mass balance are strongly influenced by mass movement in the Earth interior caused by ice advance and retreat during the last glacial cycle. Here, we develop an improved glacial-isostatic adjustment (GIA) estimate for Antarctica using newly available GPS uplift rates, allowing us to more accurately separate GIA-induced trends in the GRACE gravity fields from those caused by current imbalances of the AIS. Our revised GIA estimate is considerably lower than previous predictions, yielding an estimate of apparent mass change of 53 ± 18 Gt yr−1. Therefore, our AIS mass balance of −114 ± 23 Gt yr−1 is less negative than previous GRACE estimates. The northern Antarctic Peninsula and the Amundsen Sea sector exhibit the largest mass loss (−26 ± 3 Gt yr−1 and −127 ± 7 Gt yr−1, respectively). In contrast, East Antarctica exhibits a slightly positive mass balance (26 ± 13 Gt yr−1), which is, however, mostly the consequence of compensating mass anomalies in Dronning Maud and Enderby Land (positive) and Wilkes and George V Land (negative) due to interannual accumulation variations. In total, 6% of the area constitutes about half the AIS imbalance, contributing 151 ± 7 Gt yr−1 (ca. 0.4 mm yr−1) to global mean sea-level change. Most of this imbalance is caused by ice-dynamic speed-up expected to prevail in the near future.

We present a new set of global and local sea-level projections at example tide gauge locations under the RCP2.6, RCP4.5, and RCP8.5 emissions scenarios. Compared to the CMIP5-based sea-level projections presented in IPCC AR5, we introduce a number of methodological innovations, including (i) more comprehensive treatment of uncertainties, (ii) direct traceability between global and local projections, and (iii) exploratory extended projections to 2300 based on emulation of individual CMIP5 models. Combining the projections with observed tide gauge records, we explore the contribution to total variance that arises from sea-level variability, different emissions scenarios, and model uncertainty. For the period out to 2300 we further breakdown the model uncertainty by sea-level component and consider the dependence on geographic location, time horizon, and emissions scenario. Our analysis highlights the importance of local variability for sea-level change in the coming decades and the potential value of annual-to-decadal predictions of local sea-level change. Projections to 2300 show a substantial degree of committed sea-level rise under all emissions scenarios considered and highlight the reduced future risk associated with RCP2.6 and RCP4.5 compared to RCP8.5. Tide gauge locations can show large (> 50%) departures from the global average, in some cases even reversing the sign of the change. While uncertainty in projections of the future Antarctic ice dynamic response tends to dominate post-2100, we see substantial differences in the breakdown of model variance as a function of location, time scale, and emissions scenario.

We employ a coupled model for ice-sheet dynamics and Maxwell viscoelastic solid-Earth dynamics, including a gravitationally consistent description of sea level. With this model, we study the influence of the solid Earth on the future evolution of the West Antarctic Ice Sheet (WAIS). Starting from steady-state conditions close to the present-day configuration of the Antarctic Ice Sheet, we apply different atmospheric and oceanic forcings and solid-Earth rheologies in order to analyse the retreat of the WAIS. Climate forcing is the primary control on the occurrence of WAIS collapse. For moderate climate forcing and weak solid-Earth rheologies, however, we find that the relative sea level (RSL) fall associated with the viscoelastic solid-Earth response due to unloading by WAIS retreat limits the retreat to the Amundsen Sea embayment on time scales of several millennia, whereas stiffer Earth structures yield a collapse under these conditions. Under stronger climate forcing, weak Earth structures associated with the West Antarctic rift system produce a delay of up to 5000 years in comparison to stiffer, Antarctic-average solid-Earth rheologies. Furthermore, we find that sea-level rise from an assumed fast deglaciation of the Greenland Ice Sheet induces WAIS 1

A new synthetic model of the time-variable global gravity field is now available based on realistic mass variability in atmosphere, oceans, terrestrial water storage, continental ice-sheets, and the solid Earth. The updated ESA Earth System Model is provided in Stokes coefficients up to degree and order 180 with a temporal resolution of 6 h covering the time period 1995-2006, and can be readily applied as a source model in future gravity mission simulation studies. The model contains plausible variability and trends in both low-degree coefficients and the global mean eustatic sea level. It depicts reasonable mass variability all over the globe at a wide range of frequencies including multi-year trends, year-to-year variability, and seasonal variability even at very fine spatial scales, which is important for a realistic represen-H. Dobslaw (B) · I. Bergmann-Wolf · R. Dill · V. Klemann · I. Sasgen Department 1: Geodesy and Remote Sensing, Deutsches GeoForschungsZentrum GFZ, Telegrafenberg, tation of spatial aliasing and leakage. In particular on these small spatial scales between 50 and 250 km, the model contains a range of signals that have not been reliably observed yet by satellite gravimetry. In addition, the updated Earth System Model provides substantial high-frequency variability at periods down to a few hours only, thereby allowing to critically test strategies for the minimization of temporal aliasing.

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10The influence of glacial-isostatic adjustment (GIA) on the motion

The influence of the elastic Earth properties on seasonal or shorter periodic surface mass loads due to atmospheric surface pressure and terrestrial water storage variations is usually modeled by applying a local isostatic model like a homogeneous half-space model, or by a one dimensional spherical Earth model like PREM from which a unique set of elastic load Love numbers, or alternatively, elastic Green's functions are derived. The drawbacks of these strategies are that, in the first case, the response according to the local Earth structure is valid only if load and observer almost coincide, or that, in the second case, only the response of an average Earth structure is considered. However, for surface loads with horizontal scales less than 2500 km 2 , as for instance, for strong localized hydrological signals associated with heavy precipitation events and river floods, the Earth elastic response becomes very sensitive to inhomogeneities in the Earth crustal structure.We derive a set of local Green's functions defined for every global 1• × 1• gridcell for the 3-layer crustal structure TEA12. Local Green's functions show standard deviations of ±12% in the vertical and ±21% in the horizontal directions for distances in the range from 0.1• to 0.5• . The application of local Green's functions introduces a variability of 0.5−1.0 mm into the hydrological loading displacements, both in vertical and in horizontal directions. Maximum changes due to the local crustal structures are from −25% to +26% in the vertical and −91% to +55% in the horizontal displacements. In addition, the horizontal displacement changes its direction significantly, even to the opposite. The modeling of a site-dependent crustal response to surface loads provides an alternative way to probe the density and elastic structure of the Earth's crust and mantle by means of observed surface deformations caused by mass re-distributions. In addition, realistic loading models allow the monitoring of mass variations of the hydrosphere and cryosphere in the spatial range between satellite resolution and in-situ observations by the analysis of geodetically measured surface displacements.