Glacial-isostatic Adjustment and the Viscosity Structure Underlying the Vatnajökull Ice Cap,Iceland

We examine the dependence of glacial-isostatic adjustment (GIA) due to changes in the Vatnajökull Ice Cap, Iceland, on the underlying viscosity structure. Iceland offers a unique case study for GIA research, with a thinner elastic lithosphere underlain by a low-viscosity zone or asthenosphere, as opposed to regions such as Fennoscandia or North America described by a thicker lithosphere, while not necessarily featuring an asthenosphere.A laterally homogeneous spherical earth model is used consisting of an elastic lithosphere, a viscoelastic asthenosphere, a viscoelastic upper and lower mantle and a fluid core. We examine the response of the earth model to three ice models with circular plans and cross-section profiles based on the assumption of perfectly plastic material, but with different load histories. These are: (1) A history where the ice cap grows from a AD 900 minimum to a maximum at 1890, followed by a uniform decrease until 1991, continuing to the present day at an average rate based on recent mass-balance measurements, (2) a history that is the same as the first, except for constant ice volumes prior to 1890, and (3) a history that is again the same as the first model, except that the post-1991 changes correspond to the measured mass-balance values. We first compare the response to each ice model using typical earth-model parameters for Iceland presented in the literature. We then undertake a parameter-space search, where we assess the importance of lithosphere thickness, asthenosphere viscosity and basal asthenosphere depth, to predicted vertical-displacement rates, and compare them to rates determined from GPS measurements obtained from campaigns conducted between 1991 and 1999.The earth-viscosity structure that provides the optimum predictions with respect to the GPS-derived vertical-displacement rates consists of an elastic lithosphere with a thickness of between 20 and 30 km, an asthenosphere viscosity between 1 and 2 × 10¹⁸ Pa s, and a basal asthenosphere depth between 250 km and possibly greater than 400 km. We find that the very low asthenosphere viscosity values of ca. 10¹⁷ Pa s sometimes suggested in the literature are not necessary to account for the rapid vertical-displacement rates observed, which are the result of the contemporary decrease in the mass of the ice cap not considered previously.     

Glacial isostatic adjustment at the Laurentide ice sheet margin: Models and observations in the Great Lakes region

Glacial Isostatic Adjustment (GIA) modelling in North America relies on relative sea level information which is primarily obtained from areas far away from the uplift region. The lack of accurate geodetic observations in the Great Lakes region, which is located in the transition zone between uplift and subsidence due to the deglaciation of the Laurentide ice sheet, has prevented more detailed studies of this former margin of the ice sheet. Recently, observations of vertical crustal motion from improved GPS network solutions and combined tide gauge and satellite altimetry solutions have become available. This study compares these vertical motion observations with predictions obtained from 70 different GIA models. The ice sheet margin is distinct from the centre and far field of the uplift because the sensitivity of the GIA process towards Earth parameters such as mantle viscosity is very different. Specifically, the margin area is most sensitive to the uppermost mantle viscosity and allows for better constraints of this parameter. The 70 GIA models compared herein have different ice loading histories (ICE-3/4/5G) and Earth parameters including lateral heterogeneities. The root-mean-square differences between the 6 best models and the two sets of observations (tide gauge/altimetry and GPS) are 0.66 and 1.57 mm/yr, respectively. Both sets of independent observations are highly correlated and show a very similar fit to the models, which indicates their consistent quality. Therefore, both data sets can be considered as a means for constraining and assessing the quality of GIA models in the Great Lakes region and the former margin of the Laurentide ice sheet.     

Glacial isostatic adjustment at the Laurentide ice sheet margin: Models and observations in the Great Lakes region

Glacial Isostatic Adjustment (GIA) modelling in North America relies on relative sea level information which is primarily obtained from areas far away from the uplift region. The lack of accurate geodetic observations in the Great Lakes region, which is located in the transition zone between uplift and subsidence due to the deglaciation of the Laurentide ice sheet, has prevented more detailed studies of this former margin of the ice sheet. Recently, observations of vertical crustal motion from improved GPS network solutions and combined tide gauge and satellite altimetry solutions have become available. This study compares these vertical motion observations with predictions obtained from 70 different GIA models. The ice sheet margin is distinct from the centre and far field of the uplift because the sensitivity of the GIA process towards Earth parameters such as mantle viscosity is very different. Specifically, the margin area is most sensitive to the uppermost mantle viscosity and allows for better constraints of this parameter. The 70 GIA models compared herein have different ice loading histories (ICE-3/4/5G) and Earth parameters including lateral heterogeneities. The root-mean-square differences between the 6 best models and the two sets of observations (tide gauge/altimetry and GPS) are 0.66 and 1.57 mm/yr, respectively. Both sets of independent observations are highly correlated and show a very similar fit to the models, which indicates their consistent quality. Therefore, both data sets can be considered as a means for constraining and assessing the quality of GIA models in the Great Lakes region and the former margin of the Laurentide ice sheet.     

Recent advances in understanding ice sheet dynamics

Glaciers and ice sheets play a dynamic role in Earth's climate system, influencing regional- and global-scale climate and responding to climate change on time scales from years to millennia. They are also an integral part of Earth's landscape in alpine and polar regions, where they are an active agent in isostatic, tectonic, and Earth surface processes. This review paper summarizes recent progress in understanding and modelling ice sheet dynamics, from the microphysical processes of ice deformation in glaciers to continental-scale processes that influence ice dynamics. Based on recent insights and research directions, it can be expected that a new generation of ice sheet models will soon replace the current standard. Improvements that can be foreseen in the near future include: (i) the addition of internally-consistent evolutionary equations for ice crystal fabric (anisotropic flow laws), (ii) more generalized flow laws that include different deformation mechanisms under different stress regimes, (iii) explicit incorporation of the effects of chemical impurities and grain size (dynamic recrystallization) on ice deformation, (iv) higher-order stress solutions to the momentum balance (Stokes' equation) that governs ice sheet flow, and (v) the continued merger of ice sheet models with increasingly complex Earth systems models, which include fully-coupled subglacial hydrological and geological processes. Examples from the Greenland Ice Sheet and Vatnajökull Ice Cap, Iceland are used to illustrate several of these new directions and their importance to glacier dynamics.     

Postglacial isostatic adjustment in a self-gravitating spherical earth with power-law rheology

Since microphysics cannot say definitively whether the rheology of the mantle is linear or non-linear, the aim of this paper is to constrain mantle rheology from observations related to the glacial isostatic adjustment (GIA) process—namely relative sea-levels (RSLs), land uplift rate from GPS and gravity-rate-of-change from GRACE. We consider three earth model types that can have power-law rheology (n = 3 or 4) in the upper mantle, the lower mantle or throughout the mantle. For each model type, a range of A parameter in the creep law will be explored and the predicted GIA responses will be compared to the observations to see which value of A has the potential to explain all the data simultaneously. The coupled Laplace finite-element (CLFE) method is used to calculate the response of a 3D spherical self-gravitating viscoelastic Earth to forcing by the ICE-4G ice history model with ocean loads in self-gravitating oceans. Results show that ice thickness in Laurentide needs to increase significantly or delayed by 2 ka, otherwise the predicted uplift rate, gravity rate-of-change and the amplitude of the RSL for sites inside the ice margin of Laurentide are too low to be able to explain the observations. However, the ice thickness elsewhere outside Laurentide needs to be slightly modified in order to explain the global RSL data outside Laurentide. If the ice model is modified in this way, then the results of this paper indicate that models with power-law rheology in the lower mantle (with A  10⁻³⁵ Pa⁻³ s⁻¹ for n = 3) have the highest potential to simultaneously explain all the observed RSL, uplift rate and gravity rate-of-change data than the other model types.     

Postglacial isostatic adjustment in a self-gravitating spherical earth with power-law rheology

Since microphysics cannot say definitively whether the rheology of the mantle is linear or non-linear, the aim of this paper is to constrain mantle rheology from observations related to the glacial isostatic adjustment (GIA) process—namely relative sea-levels (RSLs), land uplift rate from GPS and gravity-rate-of-change from GRACE. We consider three earth model types that can have power-law rheology (n = 3 or 4) in the upper mantle, the lower mantle or throughout the mantle. For each model type, a range of A parameter in the creep law will be explored and the predicted GIA responses will be compared to the observations to see which value of A has the potential to explain all the data simultaneously. The coupled Laplace finite-element (CLFE) method is used to calculate the response of a 3D spherical self-gravitating viscoelastic Earth to forcing by the ICE-4G ice history model with ocean loads in self-gravitating oceans. Results show that ice thickness in Laurentide needs to increase significantly or delayed by 2 ka, otherwise the predicted uplift rate, gravity rate-of-change and the amplitude of the RSL for sites inside the ice margin of Laurentide are too low to be able to explain the observations. However, the ice thickness elsewhere outside Laurentide needs to be slightly modified in order to explain the global RSL data outside Laurentide. If the ice model is modified in this way, then the results of this paper indicate that models with power-law rheology in the lower mantle (with A ∼ 10⁻³⁵ Pa⁻³ s⁻¹ for n = 3) have the highest potential to simultaneously explain all the observed RSL, uplift rate and gravity rate-of-change data than the other model types.     

Present State and Prospects of Ice Sheet and Glacier Modelling

Since the late 1970s, numerical modelling has become established as an important technique for the understanding of ice sheet and glacier dynamics, and several models have been developed over the years. Ice sheet models are particularly relevant for predicting the possible response of ice sheets to climate change. Recent observations suggest that ice dynamics could play a crucial role for the contribution of ice sheets to future sea level rise under global warming conditions, and the need for further research into the matter was explicitly stated in the Fourth Assessment Report (AR4) of the United Nations Intergovernmental Panel on Climate Change (IPCC). In this paper, we review the state of the art and current problems of ice sheet and glacier modelling. An outline of the underlying theory is given, and crucial processes (basal sliding, calving, interaction with the solid Earth) are discussed. We summarise recent progress in the development of ice sheet and glacier system models and their coupling to climate models, and point out directions for future work.     

基于ICESat块域分析法探测2003～2008年南极冰盖质量变化

利用2003～2008年间的ICESat卫星激光测高数据,通过块域交叉点分析提取南极大陆冰盖表面高程变化信息,同时探讨了卫星激光测高不同任务间的系统偏差,结合冰盖地表粒雪密度模型探测南极大陆冰盖质量变化,并对其原因做了初步分析.结果显示南极大陆冰盖高度变化具有明显的年周期信号,平均周年振幅为2.21 cm.在南极大陆的...     

Glacial Isostatic Adjustment and Contemporary Sea Level Rise: An Overview

Glacial isostatic adjustment (GIA) encompasses a suite of geophysical phenomena accompanying the waxing and waning of continental-scale ice sheets. These involve the solid Earth, the oceans and the cryosphere both on short (decade to century) and on long (millennia) timescales. In the framework of contemporary sea-level change, the role of GIA is particular. In fact, among the processes significantly contributing to contemporary sea-level change, GIA is the only one for which deformational, gravitational and rotational effects are simultaneously operating, and for which the rheology of the solid Earth is essential. Here, I review the basic elements of the GIA theory, emphasizing the connections with current sea-level changes observed by tide gauges and altimetry. This purpose is met discussing the nature of the “sea-level equation” (SLE), which represents the basis for modeling the sea-level variations of glacial isostatic origin, also giving access to a full set of geodetic variations associated with GIA. Here, the SLE is employed to characterize the remarkable geographical variability of the GIA-induced sea-level variations, which are often expressed in terms of “fingerprints”. Using harmonic analysis, the spatial variability of the GIA fingerprints is compared to that of other components of contemporary sea-level change. In closing, some attention is devoted to the importance of the “GIA corrections” in the context of modern sea-level observations, based on tide gauges or satellite altimeters.     

Measured and modelled absolute gravity changes in Greenland

In glaciated areas, the Earth is responding to the ongoing changes of the ice sheets, a response known as glacial isostatic adjustment (GIA). GIA can be investigated through observations of gravity change. For the ongoing assessment of the ice sheets mass balance, where satellite data are used, the study of GIA is important since it acts as an error source. GIA consists of three signals as seen by a gravimeter on the surface of the Earth. These signals are investigated in this study. The ICE-5G ice history and recently developed ice models of present day changes are used to model the gravity change in Greenland. The result is compared with the initial measurements of absolute gravity (AG) change at selected Greenland Network (GNET) sites.We find that observations are highly influenced by the direct attraction from the ice and ocean. This is especially evident in the measurements conducted at the GNET station near the Helheim Glacier. The effect of the direct attraction diminishes at sites that are more than one degree from the source. Here, the dominant signal is the effect of the elastic signal from present day ice mass changes. We find agreement between the measured and modelled gravity changes at all but one site. This agreement only holds when the direct attraction is considered. For one site, there is no agreement, indicating that some improvements to the modelling results or the processing of the gravity data are needed. In addition, more AG measurements are needed to strengthen the time series of gravity change.     

Improved Constraints on Models of Glacial Isostatic Adjustment: A Review of the Contribution of Ground-Based Geodetic Observations

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.     

Meltwater discharge through the subglacial bed and its land‐forming consequences from numerical experiments in the Polish lowland during the last glaciation

Numerical experiments suggest that the last glaciation severely affected the upper lithosphere groundwater system in NW Poland: primarily its flow pattern, velocities and fluxes. We have simulated subglacial groundwater flow in two and three spatial dimensions using finite difference codes for steady‐state and transient conditions. The results show how profoundly the ice sheet modifies groundwater pressure heads beneath and some distance beyond the ice margin. All model runs show water discharge at the ice forefield driven by ice‐sheet‐thickness‐modulated, down‐ice‐decreasing hydraulic heads. In relation to non‐glacial times, the transient 3D model shows significant changes in the groundwater flow directions in a regionally extensive aquifer ca. 90 m below the ice–bed interface and up to 40 km in front of the glacier. Comparison with empirical data suggests that, depending on the model run, only between 5 and 24% of the meltwater formed at the ice sole drained through the bed as groundwater. This is consistent with field observations documenting abundant occurrence of tunnel valleys, indicating that the remaining portion of basal meltwater was evacuated through a channelized subglacial drainage system. Groundwater flow simulation suggests that in areas of very low hydraulic conductivity and adverse subglacial slopes water ponding at the ice sole was likely. In these areas the relief shows distinct palaeo‐ice lobes, indicating fast ice flow, possibly triggered by the undrained water at the ice–bed interface. Owing to the abundance of low‐permeability strata in the bed, the simulated groundwater flow depth is less than ca. 200 m. Copyright © 2009 John Wiley & Sons, Ltd.     

Topography and ice sheet growth

This paper uses a numerical ice sheet model to investigate the role of topography in influencing ice sheet growth. The model is applied to the maritime, mid-latitude uplands of Scotland and relies on a series of assumptions about mass balance, topography, and ice flow. It is driven by an imposed pattern of temperature change. The model is able to predict effectively the extent and thickness of the Loch Lomond ice sheet, using a palaeotemperature curve based on Coleoptera assemblages. A series of experiments with a stepped, constant July air temperature depression suggests that in Scotland a change in excess of ?3·0°C is necessary to initiate ice sheet growth; that steady state ice caps build up at changes of ?3 to ? 6·5°C; and that large ice sheets build up at changes of more than ? 6·625°C. The bifurcation revealed by the last two types of behaviour is the result of topography. Both the vertical amplitude and the spatial distribution of bedrock basins and ridges are important in determining the pattern, rate, and extent of ice sheet growth. The implication is that topography plays an important role in determining the dynamics of ice sheet growth.     

利用黏弹性有限元模型研究挪威北海北部地区末次冰期以来的冰后回弹和应力演化

挪威北海北部在末次冰期存在较大范围的冰盖,其冰盖的加载和卸载会对地表变形和内部应力调整产生重要影响.本文基于Maxwell黏弹性本构关系,根据初应力法自主开发了一套Maxwell黏弹性体有限元程序,它可以考虑重力和构造加载、地球介质弹性的纵向和横向不均匀性以及黏性的分层性,可以计算冰川载荷变化引起的地球表面变形及内部应力状态的变化.利用它研究了挪威北海北部1.1 Ma以来的冰川载荷变化、特别是两万多年以来冰盖的消退引起的地表冰后回弹.结果表明,自2万年以来,冰后回弹效应在冰盖载荷变化的不同阶段呈现明显的时空变化,现今地表垂直变化速率为几个毫米/年,与观测结果一致.下地壳和上地幔的黏弹性松弛效应明显,上地壳的应力状态在现今海岸线两侧存在差异性,水平和垂直正应力变化可达几十兆帕,剪应力变化有一个先增加后迅速减小至零的过程,与古地震、现今地震时空分布及应力测量结果也比较符合,研究结果有助于加深对冰后回弹的动力学过程的认识.     

联合GRACE和ICESat数据分离南极冰川均衡调整(GIA)信号

2002年发射的GRACE重力卫星为南极冰盖质量平衡提供了一种新的测量方式,但由于南极GIA模型的不确定较大,进而影响GRACE结果的可靠性.本文联合2003—2009年的GRACE和ICESat等数据实现了南极GIA信号的分离,联合方法所分离的GIA不依赖于不确定性很大的冰负荷等假设模型,而是直接基于卫星观测数据估算而来的,具有更大的可靠性.在分离过程中,本文提出了冰流速度加权改正法和GPS球谐拟合改正法对GIA结果进行精化,同时引入了南极GPS观测站的位移数据对分离的GIA进行详细的评估和验证,GPS验证表明经过冰流速度加权和GPS球谐拟合双改正后的GIA结果精度明显得到提高.最后本文利用所分离的GIA对GRACE和ICESat结果进行了改正,得到2003—2009年南极冰盖质量变化的趋势为-66.7±54.5 Gt/a(GRACE)和-77.2±21.5Gt/a(ICESat),相比采用其他的GIA模型,本文的GIA结果使GRACE和ICESat这两种不同观测技术得到的南极冰盖质量变化结果更加趋于一致.     

Late Weichselian relative sea-level changes and ice sheet history in southeast Greenland

Relative sea-level (RSL) observations from the margins of the Greenland Ice Sheet (GIS) provide information regarding the timing and rate of deglaciation and constraints on geophysical models of ice sheet evolution. In this paper we present the first RSL record for the southeast sector of the GIS based on field observations completed close to Ammassalik. The local marine limit is c. 69 m above sea-level (asl) and is dated to c. 11 k cal. yrs BP (thousand calibrated years before present) and is a minimum date for ice free conditions at the study site. RSL fell to c. 24 m asl by 9.5 k cal. yrs BP and continued to fall at a decreasing rate to reach close to present by 6.5 k cal. yrs BP. Our chronology agrees with radiocarbon dates from offshore cores that indicate ice free conditions on the adjacent mid-shelf by 15 k cal. yrs BP. We compare the new RSL data with predictions generated using two recently published glaciological models of the GIS that differ in the amount and timing of ice loading and unloading over our study area. These two GIS models are coupled to the same Earth viscosity model and background (global) ice model to aid in the data-model comparison. Neither model provides a close fit to the RSL observations. Based on a preliminary sensitivity study using a suite of Earth viscosity models, we conclude that the poor data-model fit is most likely due to an underestimate of the local ice unloading. An improved fit could be achieved by delaying the retreat of a thicker ice sheet across the continental shelf. A thick ice sheet extending well onto the continental shelf is in agreement with other recent observations elsewhere in east and south Greenland.     

Laurentia crustal motion observed using TOPEX/POSEIDON radar altimetry over land

A new method to estimate the vertical crustal motion from satellite altimetry over land was developed. The method was tested around Hudson Bay, where the observed vertical motion is largely caused by the incomplete glacial isostatic adjustment (GIA) as a result of the Laurentide ice sheet deglaciation since the last glacial maximum (LGM). Decadal (1992–2003) TOPEX/POSEIDON radar altimetry data over land surfaces were used. The results presented here are improved compared to a previous study (Lee, H., Shum, C.K., Kuo, C.Y., Yi, Y., Braun, A., 2008. Application of TOPEX altimetry for solid Earth deformation studies. Terr. Atmos. Ocean. Sci. 19, 37–46. doi:10.3319/TAO.2008.19.1-2.37(SA).) which estimated vertical motion only over relatively flat land surfaces (standard deviation of the height variation <40 cm). In this study, we extended the concept of traditional 1-Hz (one-per-frame) radar altimeter ocean stackfiles to build 10-Hz (10-per-frame) land stackfiles over Hudson Bay land regions, and succeeded in obtaining vertical motion estimates over much rougher surfaces (standard deviation of the height variation <2 m). 90-m C-band Shuttle Radar Topography Mission (SRTM) Digital Elevation Model (DEM) is used as a reference surface to select an optimal waveform retracker, to correct surface gradient errors, and to calculate land surface anomalies. Here, we developed an alternative retracker, called the modified threshold retracker, resulting in decadal vertical motion time series over a 1500 km by 1000 km region covering northern Ontario, northeastern Manitoba, and the Great Lakes region which is at the margin of the former Laurentide ice sheet. The average of the estimated uncertainties for the vertical motion is 2.9 mm/year which is comparable to 2.1 mm/year of recent GPS solutions. The estimated vertical motion is compared with other geodetic observations from GPS, tide gauge/altimetry, GRACE, and several GIA models. The data agree best with the laterally varying 3D GIA model, RF3S20 (β = 0.4) whereas the combination of land altimetry solution with other measurements match best with the models RF3S20 (β = 0.0) or RF3S20 (β = 0.2) in terms of mean and standard deviation of the differences. It is anticipated that this innovative technique could potentially be used to provide additional constraints for GIA model improvement, and be applied to other geodynamics studies.     

Evaluation of the glacial isostatic adjustment (GIA) models for Antarctica based on GPS vertical velocities

Due to the scarcity of data, modeling the glacial isostatic adjustment(GIA) for Antarctica is more difficult than it is for the ancient ice sheet area in North America and Northern Europe. Large uncertainties are observed in existing GIA models for Antarctica. Modern space-based geodetic measurements provide checks and constraints for GIA models. The present-day uplift velocities of global positioning system(GPS) stations at 73 stations in Antarctica and adjacent regions from 1996 to 2014 have been estimated using GAMIT/GLOBK version 10.5 with a colored noise model. To easily analyze the effect of difference sources on the vertical velocities, and for easy comparison with both GIA model predictions and GPS results from Argus et al.(2014) and Thomas et al.(2011), seven sub-regions are divided. They are the northern Antarctic Peninsula, the Filchner-Ronne Ice Shelf, the Amundsen Sea coast, the Ross Ice Shelf, Mount Erebus, inland Southwest Antarctica and the East Antarctic coast,respectively. The results show that the fast uplift in the north Antarctic Peninsula and Pine Island Bay regions may be caused by the elastic response to snow and ice mass loss. The fast subsidence near Mount Erebus may be related to the activity of a magma body. The uplift or subsidence near the East Antarctic coast is very slow while the uplift for the rest regions is mainly caused by GIA. By analyzing the correlation and the associated weighted root mean square(WRMS) between the GIA predictions and the GPS velocities, we found that the ICE-6G_C(VM5a) model and the Geruo 13 model show the most consistency with our GPS results, while the W12a and IJ05_R2 series models show poor consistency with our GPS results. Although improved greatly in recent years, the GIA modeling in Antarctica still lags behind the modeling of the North American. Some GPS stations, for example the Bennett Nunatak station(BENN), have observed large discrepancies between GIA predictions and GPS velocities.Because of the large uncertainties in calculating elastic responses due to the significant variations of ice and snow loads, the GPS velocities still cannot be used as a precise constraint on GIA models.     

Response of the Greenland and Antarctic Ice Sheets to Multi-Millennial Greenhouse Warming in the Earth System Model of Intermediate Complexity LOVECLIM

Calculations were performed with the Earth system model of intermediate complexity LOVECLIM to study the response of the Greenland and Antarctic ice sheets to sustained multi-millennial greenhouse warming. Use was made of fully dynamic 3D thermomechanical ice-sheet models bidirectionally coupled to an atmosphere and an ocean model. Two 3,000-year experiments were evaluated following forcing scenarios with atmospheric CO₂ concentration increased to two and four times the pre-industrial value, and held constant thereafter. In the high concentration scenario the model shows a sustained mean annual warming of up to 10°C in both polar regions. This leads to an almost complete disintegration of the Greenland ice sheet after 3,000 years, almost entirely caused by increased surface melting. Significant volume loss of the Antarctic ice sheet takes many centuries to initiate due to the thermal inertia of the Southern Ocean but is equivalent to more than 4 m of global sea-level rise by the end of simulation period. By that time, surface conditions along the East Antarctic ice sheet margin take on characteristics of the present-day Greenland ice sheet. West Antarctic ice shelves have thinned considerably from subshelf melting and grounding lines have retreated over distances of several 100 km, especially for the Ross ice shelf. In the low concentration scenario, corresponding to a local warming of 3?C4°C, polar ice-sheet melting proceeds at a much lower rate. For the first 1,200 years, the Antarctic ice sheet is even slightly larger than today on account of increased accumulation rates but contributes positively to sea-level rise after that. The Greenland ice sheet loses mass at a rate equivalent to 35 cm of global sea level rise during the first 1,000 years increasing to 150 cm during the last 1,000 years. For both scenarios, ice loss from the Antarctic ice sheet is still accelerating after 3,000 years despite a constant greenhouse gas forcing after the first 70?C140 years of the simulation.     

GIA-induced secular variations in the Earth's long wavelength gravity field: Influence of 3-D viscosity variations

Predictions of present day secular variations in the Earth's long wavelength geopotential driven by glacial isostatic adjustment (GIA) have previously been analyzed to infer the radial profile of mantle viscosity and to constrain ongoing cryospheric mass balance. These predictions have been based on spherically symmetric Earth models. We explore the impact of lateral variations in mantle viscosity using a new finite-volume formulation for computing the response of 3-D Maxwell viscoelastic Earth models. The geometry of the viscosity field is constrained from seismic-to-mographic images of mantle structure, while the amplitude of the lateral viscosity variations is tuned by a free parameter in the modeling. We focus on the zonal J˙_? harmonics for degrees ? = 2,…,8 and demonstrate that large-scale lateral viscosity variations of two to three orders of magnitude have a modest, 5-10%, impact on predictions of J˙₂. In contrast, predictions of higher degree harmonics show a much greater sensitivity to lateral variation in viscosity structure. We conclude that future analyses of secular trends (for degree ? > 2) estimated from ongoing (GRACE, CHAMP) satellite missions must incorporate GIA predictions based on 3-D viscoelastic Earth models.