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.

[1] This study analyzes the uncertainties in the models of the Greenland Ice Sheet (GIS) that arise from ill-constrained geothermal heat flux (GHF) distribution. Within the context of dynamic GIS modeling, we consider the following questions: (i) What is the significance of the differences between the existing GHF models for the GIS modeling studies? (ii) How well does the modeled GIS controlled by the GHF models agree with the observational data? (iii) What are the relative contributions of uncertainties in GHF and climate forcing to the misfit between the observed and modeled present-day GIS? The results of paleoclimatic simulations suggest that differences in the GHF models have a major effect on the history and resulting present-day state of the GIS. The ice sheet model controlled by any of these GHF forcings reproduces the observed GIS state to only a limited degree and fails to reproduce either the topography or the low basal temperatures measured in southern Greenland. By contrast, the simulation controlled by a simple spatially uniform GHF forcing results in a considerably better fit with the observations, raising questions about the use of the three GHF models within the framework of GIS modeling. Sensitivity tests reveal that the misfit between the modeled and measured temperatures in central Greenland is mostly due to inaccurate GHF and Wisconsin precipitation forcings. The failure of the ice sheet model in southern Greenland, however, is mainly caused by inaccuracies in the surface temperature forcing and the generally overestimated GHF values suggested by all GHF models.

[1] In this study, the memory of the Greenland Ice Sheet (GIS) with respect to its past states is analyzed. According to ice core reconstructions, the present-day GIS reflects former climatic conditions dating back to at least 250 thousand years before the present (kyr BP). This fact must be considered when initializing an ice sheet model. The common initialization techniques are paleoclimatic simulations driven by atmospheric forcing inferred from ice core records and steady state simulations driven by the present-day or past climatic conditions. When paleoclimatic simulations are used, the information about the past climatic conditions is partly reflected in the resulting present-day state of the GIS. However, there are several important questions that need to be clarified. First, for how long does the model remember its initial state? Second, it is generally acknowledged that, prior to 100 kyr BP, the longest Greenland ice core record (GRIP) is distorted by ice-flow irregularities. The question arises as to what extent do the uncertainties inherent in the GRIP-based forcing influence the resulting GIS? Finally, how is the modeled thermodynamic state affected by the choice of initialization technique (paleo or steady state)? To answer these questions, a series of paleoclimatic and steady state simulations is carried out. We conclude that (1) the choice of an ice-covered initial configuration shortens the initialization simulation time to 100 kyr, (2) the uncertainties in the GRIP-based forcing affect present-day modeled ice-surface topographies and temperatures only slightly, and (3) the GIS forced by present-day climatic conditions is overall warmer than that resulting from a paleoclimatic simulation.

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S U M M A R YThe influence of changes in surface ice-mass redistribution and associated viscoelastic response of the Earth, known as glacial isostatic adjustment (GIA), on the Earth's rotational dynamics has long been known. Equally important is the effect of the changes in the rotational dynamics on the viscoelastic deformation of the Earth. This signal, known as the rotational feedback, or more precisely, the rotational feedback on the sea level equation, has been mathematically described by the sea level equation extended for the term that is proportional to perturbation in the centrifugal potential and the second-degree tidal Love number.The perturbation in the centrifugal force due to changes in the Earth's rotational dynamics enters not only into the sea level equation, but also into the conservation law of linear momentum such that the internal viscoelastic force, the perturbation in the gravitational force and the perturbation in the centrifugal force are in balance. Adding the centrifugal-force perturbation to the linear-momentum balance creates an additional rotational feedback on the viscoelastic deformations of the Earth. We term this feedback mechanism, which is studied in this paper, as the rotational feedback on the linear-momentum balance.We extend both the time-domain method for modelling the GIA response of laterally heterogeneous earth models developed by Martinec and the traditional Laplace-domain method for modelling the GIA-induced rotational response to surface loading by considering the rotational feedback on linear-momentum balance. The correctness of the mathematical extensions of the methods is validated numerically by comparing the polar-motion response to the GIA process and the rotationally induced degree 2 and order 1 spherical harmonic component of the surface vertical displacement and gravity field. We present the difference between the case where the rotational feedback on linear-momentum balance is considered against that where it is not. Numerical simulations show that the resulting difference in radial displacement and sea level change between these situations since the Last Glacial Maximum reaches values of ±25 and ±1.8 m, respectively. Furthermore, the surface deformation pattern is modified by up to 10 per cent in areas of former or ongoing glaciation, but by up to 50 per cent at the bottom of the southern Indian ocean. This also results in the movement of coastlines during the last deglaciation to differ between the two cases due to the difference in the ocean loading, which is seen for instance in the area around Hudson Bay, Canada and along the Chinese, Australian or Argentinian coastlines.Key words: Sea level change; Geopotential theory; Earth rotation variations. I N T RO D U C T I O NThe redistribution of ice and water over the Earth's surface during glaciation and deglaciation cycles due to changes in climate induces 3-D crustal motion, gravity-field variations and changes in sea level, which is known collectively as glacial isostatic adjustment (GIA). The surface-m...

This study is concerned with the influence of the glacial-isostatic adjustment caused by the last Pleistocene deglaciation on the present-day sea level. The viscoelastic deformation caused by the time-variable ice and ocean loads is simulated by computing the resulting perturbations for a spherical, self-gravitating, incompressible, Maxwell-viscoelastic earth model. The associated variation of the earth rotation is described in terms of the Liouville equation, which is solved by means of the MacCullagh formulae. This allows the determination of the vertical displacement and geoid height and, thus, the solution of the sea-level equation. We test several viscosity and ice models and evaluate them by comparison of the computed response with the Holocene relative sea-level record. Using the optimum combination of viscosity and ice models, we then estimate the influence of the last Pleistocene deglaciation on the tide-gauge measurements. A comparison between the observational and residual linear trends for the tide-gauge measurements shows a significant reduction of the variance and geographical variability for the latter, in particular for the formerly ice-covered regions of North America and Scandinavia. The favoured value determined for the global mean sea-level rise is (1.46±0.2) mm a )1 .

SUMMARY For a spherically symmetric viscoelastic earth model, the movement of the rotation vector due to surface and internal mass redistribution during the Pleistocene glaciation cycle has conventionally been computed in the Laplace‐transform domain. The method involves multiplication of the Laplace transforms of the second‐degree surface‐load and tidal‐load Love numbers with the time evolution of the surface load followed by inverse Laplace transformation into the time domain. The recently developed spectral finite‐element method solves the field equations governing glacial‐isostatic adjustment (GIA) directly in the time domain and, thus, eliminates the need of applying the Laplace‐domain method. The new method offers the possibility to model the GIA‐induced rotational response of the Earth by time integration of the linearized Liouville equation. The theory presented here derives the temporal perturbation of the inertia tensor, required to be specified in the Liouville equation, from time variations of the second‐degree gravitational‐potential coefficients by the MacCullagh's formulae. This extends the conventional approach based on the second‐degree load Love numbers to general 3‐D viscoelastic earth models. The verification of the theory of the GIA‐induced rotational response of the Earth is performed by using two alternative approaches of computing the perturbation of the inertia tensor: a direct numerical integration and the Laplace‐domain method. The time‐domain solution of both the GIA and the induced rotational response of the Earth is readily combined with a time‐domain solution of the sea level equation with a time‐varying shoreline geometry. In a follow‐up paper, we derive the theory for the case when GIA‐induced perturbations in the centrifugal force affect not only the distribution of sea water, but also deformations and gravitational‐potential perturbations of the Earth.