satellite gravity and the mass balance of the antarctic ice sheet changes in the earth s gravity field with time have important applications to a broad range of disciplines any process that involves a large enough horizontal redistribution of mass either within the earth or on or above its surface is potentially detectable in particular when ice sheets grow or shrink gravity changes as mass is redistributed in the solid earth and between the oceans and the ice sheets the sources of global sea level rise about 2 mm a 1 over the last century and in particular the contribution of the antarctic ice sheet thereto are not well understood gravity measurements can help to diminish this uncertainty the technology currently exists to measure gravity with high accuracy by a dual satellite mission in which the distance between the satellites is precisely monitored we estimate from recent studies that temporal changes in the gravity field as determined by a satellite gravity mission lasting 5 years at an orbital height of 400 km would be sensitive to changes in the overall mass of the antarctic ice sheet to a precision corresponding to better than 0 01 mm a 1 of sea level change however the effects of three other phenomena that could each produce a temporally varying gravity signal with characteristics comparable to that caused by a change in antarctic ice postglacial rebound inter annual variability in snowfall and atmospheric pressure trends also need to be evaluated postglacial rebound could be partly separated from ice mass changes with the aid of global positioning system campaigns and numerical models of rebound that use improved determinations of mantle viscosity also provided by the gravity mission determination of inter annual ice mass changes will be aided by measurements of moisture flux divergence around the perimeters of the ice sheets and direct observations of inter annual changes by the gravity satellite itself the removal of pressure effects over antarctica will become more effective as the number of automatic weather stations in the interior of the continent increases even after corrections are made for these factors the uncertainties they cause limit the accuracy in the determination of the contribution of the antarctic ice sheet to sea level change to about 0 5 mm a 1 however there is a strong complementarity between gravity measurements and the surface height measurements that will be produced by nasa s laser altimeter mission early next century together they should be able to determine that contribution to an accuracy of about 0 1 mm a 1

a model computation of the temporal changes of surface gravity and geoidal signal induced by the evolving greenland ice sheet this paper deals with present day gravity changes in response to the evolving greenland ice sheet we present a detailed computation from a 3 d thermomechanical ice sheet model that is interactively coupled with a self gravitating spherical viscoelastic bedrock model the coupled model is run over the last two glacial cycles to yield the loading evolution over time based on both the ice sheet s long term history and its modern evolution averaged over the last 200 years results are presented of the absolute gravity trend that would arise from a ground survey and of the corresponding geoid rate of change a satellite would see from space the main results yield ground absolute gravity trends of the order of 1 gal yr 1 over the ice free areas and total geoid changes in the range between 0 1 and 0 3 mm yr 1 these estimates could help to design future measurement campaigns by revealing areas of strong signal and or specific patterns although there are uncertainties associated with the parameters adopted for the earth s rheology and aspects of the ice sheet model given the instrumental accuracy of a particular surveying method these theoretical trends could also be useful to assess the required duration of a measurement campaign according to our results the present day gravitational signal is dominated by the response to past loading changes rather than current mass changes of the greenland ice sheet we finally discuss the potential of inferring the present day evolution of the greenland ice sheet from the geoid rate of change measured by the future geodetic grace mission we find that despite the anticipated high quality data from satellites such a method is compromised by the uncertainties in the earth model the dominance of isostatic recovery on the current bedrock signal and other inaccuracies inherent to the method itself

geochemistry and zircon u pb ages of adakitic rocks from the dulan area of the north qaidam uhp terrane north tibet constraints on the timing and nature of regional tectonothermal events associated with collisional orogeny abstract geochemistry and u pb ages of leucosomes and tonalites in a high pressure granulite unit of the dulan area have been determined to constrain the tectonothermal evolution related to collision and thickening of lower crust in the north qaidam mountains nqd leucosomes and tonalites show a marked chemical resemblance to adakites 1 high la yb and sr y and low y and hree 2 high al 2 o 3 and low mg values with obvious positive eu anomalies and 3 slightly positive e nd t values zircon u pb analysis of leucosomes and tonalites yielded 206 pb 238 u ages of 428 437 ma and 436 437 ma respectively which constrain the emplacement ages of the adakitic rocks petrological geochronological and geochemical characters indicate that the adakitic rocks may have been derived from partial melting of a thickened mafic lower crust 50 km suggesting a dominating source regime of synchronous high pressure mafic granulites contemporary magmatism in other units of the nqd shows evidence of a widespread tectonothermal event during early silurian 420 450 ma that includes metamorphism magmatism and anatexis related to collision and thickening of lower crust

the influence of decadal to millennial scale ice mass changes on present day vertical land motion in greenland implications for the interpretation of gps observations 1 we show predictions of present day vertical land motion in greenland using a recently developed glacial isostatic adjustment gia model calibrated using both relative sea level rsl observations and geomorphological constraints on ice extent predictions from our gia model are in agreement with the relatively small number of gps measurements of absolute vertical motion from south and southwest greenland this suggests that our model of ice sheet evolution over the holocene period is reasonably accurate the uplift predictions are highly sensitive to variations of upper mantle viscosity thus depending on the earth model adopted different periods of ice loading change dominate the present day response in particular regions of greenland we also consider the possible influence of more recent changes in the ice sheet by applying a second ice model specifically a surface mass balance smb model which covers the period 1866 to 2005 predictions from this model suggest that decadal scale smb changes over the past 140 years play only a small role in determining the present day viscous response at the sub mm yr level in most locations for a range of earth model parameters high rates of peripheral thinning from 1995 to 2005 predicted using the smb model produce large elastic uplift rates 6 mm yr in west and southwest greenland this suggests that in some areas close to the ice margin modern surface mass balance changes have a dominant control on present day vertical land motion

effects on post glacial rebound from the hard rheology in the transition zone summary we analyse the influences of a viscosity increase in the transition zone between 420 and 670 km on the geophysical signatures induced by post glacial rebound ranging from the perturbations in the earth s rotation to the short wavelength features associated with the migration of the peripheral bulge a self gravitating model is adopted consisting of an elastic lithosphere a three layer viscoelastic mantle and an inviscid core the horizontal displacements and velocities and the stress pattern are extremely sensitive to the viscosity increase and to the chemical stratification of the transition zone the hardening of the upper and the chemical density jumps in mantle below the 420 discontinuity induces a channel effect which contaminates the horizontal deformation both in the near field and in the far field from the ice sheets these findings indicate that intraplate geodetic data can be used to put bounds on the viscosity increase in the transition zone and on the amount of chemical stratification in the mantle the stress field induced in the lithosphere by the pleistocenic ice sheet disintegration is a very sensitive function of mantle viscosity stratification the existence of seismic activity along passive continental margins of previously glaciated areas requires a substantial viscosity increase in the mantle with the viscosity of the transition zone acting as a controlling parameter a viscously stratified mantle is responsible for a delayed upward migration of stress in the lithosphere which can account for the seismicity today

bedrock displacements in greenland manifest ice mass variations climate cycles and climate change the greenland gps network gnet uses the global positioning system gps to measure the displacement of bedrock exposed near the margins of the greenland ice sheet the entire network is uplifting in response to past and present day changes in ice mass crustal displacement is largely accounted for by an annual oscillation superimposed on a sustained trend the oscillation is driven by earth s elastic response to seasonal variations in ice mass and air mass i e atmospheric pressure observed vertical velocities are higher and often much higher than predicted rates of postglacial rebound pgr implying that uplift is usually dominated by the solid earth s instantaneous elastic response to contemporary losses in ice mass rather than pgr superimposed on longer term trends an anomalous pulse of uplift accumulated at many gnet stations during an approximate six month period in 2010 this anomalous uplift is spatially correlated with the 2010 melting day anomaly

separation of the geodetic consequences of past and present ice mass change influence of topography with application to svalbard norway polar regions such as greenland svalbard and antarctica are deforming today because of both the present day ice mass pdim change of glaciers and the glacial isostatic adjustment gia following the pleistocene deglaciation observations handled in these areas contain both the contributions from the pdim change and gia this study aims at separating them by considering two specific gravity variation to vertical displacement ratios we first review the case of the viscoelastic rebound gia subsequent to the pleistocene deglaciation leading to a ratio c v the outcome of previous studies is that c v is approximately equal to 0 15 gal mm and almost independent of the deglaciation history ice geometry and viscosity profile of the mantle similarly we consider the elastic deformation resulting from pdim change which leads to a second ratio c e n several studies have shown that c e n approx 0 26 mu gal mm if one assumes that the changing glaciers are thin layers over the surface of a spherical earth model in this case we show that the separation between the contributions from pdim change and gia is unique if both gravity and height changes observations are available at the same station next we focus on c e n and show that according to the deglaciation glaciation context and from colocated gravity variation and ground vertical velocity measurements one can deduce a range of possible values for c e n studying the influence of the topography on c e n we first show that it tends to positive values if most of surrounding ice mass changes above the altitude of the observation site and to values lower than 0 26 gal mm if changes are below we next apply our general formalism to the case of the past and pdim changes in svalbard norway we compute the ratio c e n at the geodetic observatory at ny alesund and show the influence of the topography of the surrounding glaciers on the measured gravity and uplift rates we show that if the ice mass change is spatially uniform c e n does not depend on the speed of ice mass change and hence the separation of the contributions from pdim changes and gia can still be done univocally however if the ice mass change is not spatially uniform c e n depends on both the speed of ice mass change and the volume of ice change rate

predictions of antarctic crustal motions driven by present day ice sheet evolution and by isostatic memory of the last glacial maximum detectable crustal motion and secular rate of change of solid surface gravity may be produced by the earth s response to present day and past ice mass changes in antarctica scenarios of present day ice mass balance previously utilized to explore the global geodetic signatures of the antarctic ice sheet produce elastic crustal responses that are typically bounded by uplift rates 5 mm yr horizontal motion 1 mm yr and solid surface gravity change rates 1 gal yr in a restricted locality one scenario produces uplift rates slightly in excess of 10 mm yr and correspondingly enhanced horizontal and gravity rates in contrast the viscoelastic response to ice mass changes occurring since last glacial maximum lgm exceeds 5 mm yr uplift over substantial portions of west antarctica for a wide range of plausible choices of timing and magnitude of deglaciation and mantle viscosity similarly viscoelastic gravity rate predictions exceed 1 gal yr decrease over large regions confirming suggestions that a global positioning system gps and absolute gravity based program of crustal monitoring in antarctica could potentially detect postglacial rebound a published revision to the climap model of the antarctic ice sheet at lgm herein called the d91 model features a substantially altered west antarctic ice sheet reconstruction this revision predicts a spatial pattern of present day crustal motion and surface gravity change that diverges strikingly from climap based models peak d91 crustal rates assuming deglaciation begins at 12 kyr and ends at 5 kyr are around 16 mm yr uplift 2 mm yr horizontal and 2 5 gal yr gravity tabulated crustal response predictions for selected antarctic bedrock sites indicate critical localities in the interior of west antarctica where expected responses are large and d91 predictions differ from climap based models by a factor of 2 or more observations of the postglacial rebound signal in antarctica might help constrain antarctic mass balance and contribution to sea level rise over the past 20 000 years

simple models for late holocene and present day patagonian glacier fluctuations and predictions of a geodetically detectable isostatic response summary the late holocene glacial moraine chronology in the southernmost south american andes includes four 14c dated neoglacial advances and retreats these are used as proxy information to characterize mass fluctuation of the patagonian icefields during the last 5000 years modelled ice loads force a phase lagged viscoelastic gravitational deformation of the solid earth the ancient glacier fluctuations may therefore drive present day crustal motion even in the absence of present day ice mass imbalance numerical models show that such rates of present day uplift and subsidence are larger than those driven by the viscous memory of late pleistocene deglaciation both spherical and flat earth models are employed the latter being used to study exhaustively the evects of glacial load history on the predicted vertical crustal velocity recent assessment of net mass balance from 1944 to 1985 indicates that the southern patagonian icefield has significantly deteriorated due to snout retreat and thinning volume loss rates are estimated at about 3 4 9 3 km3 yr 1 the predicted vertical isostatic response to this recession and to the modelled holocene neoglaciations is at a marginally detectable level 1m m yr 1 if the mantle asthenosphere beneath patagonia has a viscosity of about 1021 pa s however for reduced mantle viscosities the younger holocene glacial load histories predict larger signatures in fact if the viscosity is about 2 1020 pa s or lower then geodetically detectable vertical motion may be driven by a regional little ice age lia 1400 1750 ad glacier advance and subsequent 20th century retreat although this value for mantle viscosity is lower than thought typical of continental shield mantle 1021 pa s it is consistent with inversions for post seismic relaxation time constants in island arc environments and in regions with significant neogene continental tectonism in the viscosity regime of 5 1018 2 1019 pa s the predicted rates of vertical crustal motion are similar to those presently occurring in fennoscandia and hudson bay 5 10 mm yr 1 geodetic data may be sensitive to the time integrated growth and subsequent retreat of patagonian glacier ice mass over the last 600 years

basal temperature conditions of the greenland ice sheet during the glacial cycles a high resolution three dimensional thermomechanical ice sheet model which includes isostasy the possibility of ice sheet expansion on the continentalshelf and refined climatic parameterisations was used to investigate the basal thermal regime of the greenland ice sheet the thermodynamic calculations takeinto account the usual terms of heat flow within the ice a thermal active bedrock layer in transient situations and all of the effects associated with changes inice thickness and flow pattern basal temperature conditions are documented with respect to glacial interglacial shifts in climatic boundary conditions both insteady state as during simulations over the last two glacial cycles using the grip d180 record it is found that the basal temperature field shows a largesensitivity in steady state experiments but that during a glacial cycle basal temperature variations are strongly damped in particular in central areas acomparison has been made with measured data from deep ice cores and implications are discussed

steady state characteristics of the greenland ice sheet under different climates the greenland ice sheet is modelled to simulate its extent and volume in warmer climates and also to find out whether the ice sheet would re form on theice free bedrock under present climatic conditions the ice sheet model is a three dimensional thermo mechanical model with a fine resolution grid thebedrock surface beneath the ice sheet was mapped using radio echo sounding measurements by the electromagnetic institute copenhagen the modelexperiments show that increased temperature will result in ice margin retreat but the ice sheet is relatively stable it takes a rather high temperature rise of atleast 6ic for the ice sheet to disappear completely which indicates that the ice sheet probably survived the last interglacial also it appears that the greenlandice sheet is not a mere relict ice mass from a previously colder climate but that the ice sheet will still re form on the bare bedrock under the present or evenslightly warmer climatic conditions

glacial geological geomorphological research in west greenland used to test an ice sheet model abstract ice sheet modeling is an essential tool for estimating the effect of climate change on the greenland ice sheet the large spatial and long term temporal scale of ice sheet models limits the amount of data which can be used to test model results a framework for the analysis of glacial geological data to test ice sheet models is illustrated by a case study in west greenland a geological scenario of ice margin positions since the last glacial maximum is based on a review of existing literature and new datings of moraine systems ages of moraine systems and associated accuracy ranges are interpolated to a 1 1 km grid over an area of about 57 500 km 2 resampling to a 20 20 km grid on an ice sheet model coordinates permits a quantitative comparison with modeled ice marginal positions in view of the uncertainties in the geological scenario with moraine system ages having an absolute uncertainty of 700 to 3300 cal yr the greenland ice sheet model of huybrechts provides a reasonable simulation of the deglaciation pattern in central west greenland modeled timing of the position of the ice margin generally precedes the geological record by 900 yr the difference between geology and model is large for areas without proper geological information and small but still about 500 950 yr for well dated moraine systems model deficiencies in west greenland are probably related to the forcing function driving ablation estimates and especially the forcing function for sea level and the description of calving processes should he reviewed critically the simplified topography used by the model could also induce errors although topography used in models neglects possible important features such as ice streams we do not find any significant trend between differences and relief amplitude missing moraines on the southern part of the shelf and absence of geological information from beneath the present ice sheet affect the character and quality of the geological scenario

the lageos constraint on deep mantle viscosity results from a new normal mode method for the inversion of viscoelastic relaxation spectra the recently observed acceleration in the node of the orbit of the lageos satellite has previously been shown to provide a good constraint on the viscosity of the earth s mantle beneath the 670 km seismic discontinuity this paper explores the extent to which the previously inferred lower mantle viscosity may be traded off against variations of other properties of the radial viscoelastic structure we show explicitly that the nontidal acceleration of rotation inferred from the lageos data and predicted as a consequence of the earth s response to the last deglaciation event of the current ice age is relatively insensitive both to variations of lithospheric thickness and to the presence or absence of plausible chemical heterogeneity across the 670 km interface it therefore provides a high quality constraint on the viscosity of the deep mantle with the upper mantle viscosity fixed at the nominal value of 1021 pa s the bounds on lower mantle viscosity lm are such that 2 1021 pa s lm 6 1021 pa s even when allowance is made for the presence of a viscous boundary layer at the base of the upper mantle such as would exist if the mantle convective circulation were layered

the dynamic response of the greenland and antarctic ice sheets to multiple century climatic warming new calculations were performed to investigate the combined response of the greenland and antarctic ice sheets to a range of climatic warming scenarios over the next millennium use was made of fully dynamic 3d thermomechanic ice sheet models which were coupled to a two dimensional climate model the experiments were initialized with simulations over the last two glacial cycles to estimate the present evolution and were subsequently forced with temperature scenarios resulting from greenhouse emission scenarios which assume equivalent co2 increases of two four and eight times the present 1990 a d value by the year 2130 a d and a stabilization after that the calculations brought to light that during the next century short term effect the background evolution trend would dominate the response of the antarctic ice sheet but would be negligible for the greenland ice sheet on that timescale the greenland and antarctic ice sheets would roughly balance one another for the middle scenario similar to the ipcc96 is92a scenario with respective contributions to the worldwide sea level stand on the order of about 610 cm on the longer term however both ice sheets would contribute positively to the worldwide sea level stand and the most important effect would come from melting on the greenland ice sheet sensitivity experiments highlighted the role of ice dynamics and the height massbalance feedback on the results it was found that ice dynamics cannot be neglected for the greenland ice sheet not even on a century timescale but becomes only important for antarctica on the longer term the latter is related to an increased outflow of ice into the ice shelves and to the grounding line retreat of the west antarctic ice sheet which are both found to be sensitive to basal melting below ice shelves and the effective viscosity of the ice shelves stretching parameters to their limits yielded a combined maximum rate of sea level rise of 85 cm century21 of which 60 cm would originate from the greenland ice sheet alone

atmospheric co2 variations over the last climatic cycle 160 000 years deduced from the vostok ice core antarctica abstract

predictions of vertical uplift caused by changing polar ice volumes on a viscoelastic earth measurements of crustal uplift from bedrock around the edges of antarctica or greenland could help constrain the mass balance of those ice caps present day changes in ice could cause vertical displacement rates of several mm yr around antarctica and up to 10 15 mm yr around greenland horizontal displacement rates are likely to be about 1 3 the vertical rates the viscoelastic response of the earth to past changes in ice could cause uplift rates that are several times larger by measuring both gravity and vertical displacements it is possible to remove the viscoelastic effects so that the observations can be used to constrain present day thickness changes

present day uplift patterns over greenland from a coupled ice sheet visco elastic bedrock model we present results from a fully coupled ice bedrock model calculation of the greenland ice sheet and the underlying earth during the last two glacial cycles the method treats the mutual interaction between the ice and the bedrock and yields the main glacial isostatic characteristics of the ice sheet evolution and the bedrock adjustment since the last glacial maximum by taking advantage of the splitting of the present day rate of bed uplift into a viscous and an elastic component these results allow one to distinguish between the bedrock response to the past and present ice sheet evolution respectively

viscous gravitational relaxation summary this paper is concerned with a detailed examination of the response of maxwell models of the planet to surface mass loads particular attention is devoted to an examination of the factors which determine the isostatic response since the understanding of this response is crucial in a number of different geodynamic problems one particular example which we discuss in detail is concerned with the prediction of free air gravity anomalies produced by large scale deglaciation events using the methods developed here we are able to provide the first direct assessment of the importance of initial isostatic disequilibrium on the observed relative sea level variations and free air gravity anomalies forced by the melting of the laurentide ice sheet we are therefore able to estimate the extent to which such initial disequilibrium might influence the inference of mantle viscosity from isostatic adjustment data our calculations establish that free air gravity data although they are sensitive to the degree of initial disequilibrium provide an extremely high quality constraint upon the viscosity of the lower mantle

a 3 d coupled ice sheet sea level model applied to antarctica through the last 40 ky abstract we present results from a three dimensional ice sheet shelf model of antarctica coupled to a gravitationally self consistent global sea level model that incorporates maxwell viscoelastic deformation of the solid earth the coupled model captures complex post glacial changes in sea level associated with the gravitational deformational and rotational effects of the evolving surface mass ice plus ocean load over the global ocean including at the grounding lines of marine based ice the simulations are initiated at 40 ka and we focus on ice distributions and sea levels from the last glacial maximum to present our results extend and confirm the key conclusions of earlier work using a simplified 1 d ice sheet model by demonstrating that the sea level coupling has a significant stabilizing influence on marine ice sheet grounding lines the feedback of sea level changes into the ice sheet model acts to slow down the retreat and advance of the grounding line relative to simulations in which the full coupling is not incorporated differences in ice thickness between these simulations can reach 1 km close to the grounding line finally we perform preliminary comparisons of our results to relative sea level rsl histories and gps derived present day uplift rates at sites near the margins of antarctica we find that the coupling improves fits to uplift rates in several regions and that the rsl predictions of the coupled model yield a fit to the observations that is comparable to recent uncoupled simulations in which the underlying earth model was varied to obtain a best fit to the rsl histories

evidence for general instability of past climate from a 250 kyr ice core record recent results1 2 from two ice cores drilled in central greenland have revealed large abrupt climate changes of at least regional extent during the late stages of the last glaciation suggesting that climate in the north atlantic region is able to reorganize itself rapidly perhaps even within a few decades here we present a detailed stable isotope record for the full length of the greenland ice core project summit ice core extending over the past 250 kyr according to a calculated timescale we find that climate instability was not confined to the last glaciation but appears also to have been marked during the last interglacial as explored more fully in a companion paper3 and during the previous saale holstein glacial cycle this is in contrast with the extreme stability of the holocene suggesting that recent climate stability may be the exception rather than the rule the last interglacial seems to have lasted longer than is implied by the deep sea specmap record4 in agreement with other land based observations5 6 we suggest that climate instability in the early part of the last interglacial may have delayed the melting of the saalean ice sheets in america and eurasia perhaps accounting for this discrepancy

a comparison of different ways of dealing with isostasy examples from modelling the antarctic ice sheet during the last glacial cycle the bedrock isostatic response exerts a strong control on ice sheet dynamics and is therefore always taken into account in ice sheet models this paperreviews the various methods normally used in the ice sheet modeling community to deal with the bedrock response and compares these with a moresophisticated full earth model each of these bedrock treatments five in total are coupled with a three dimensional thermomechanical ice sheet model underthe same forcing conditions to simulate the antarctic ice sheet during the last glacial cycle the outputs of the simulations are compared on the basis of thetime dependent behavior for the total ice volume and the mean bedrock elevation during the cycle and of the present rate of uplift over antarctica thiscomparison confirms the necessity of accounting for the elastic bending of the lithosphere in order to yield realistic bedrock patterns it furthermoredemonstrates the deficiencies inherent to the diffusion equation in modeling the complex deformation within the mantle nevertheless when characteristicparameters are varied within their range of uncertainty differences within one single method are often of the same order as those between the variousmethods this overview finally tries to point out the main advantages and drawbacks of each of these methods and to determine which one is mostappropriate depending on the specific modeling requirements

predictions of secular geoid changes from late pleistocene and holocene antarctic ice ocean mass imbalance summary estimates on ice volume changes in antarctica from both contemporary mass imbalance during the last hundred to thousand years and ice volume changes during the last glacial cycles are difficult to obtain future satellite gravity missions monitoring secular changes in gravity as a proxy of mass changes of the antarctic ice sheet will therefore provide an additional important constraint on the antarctic ice sheet history we assess the contributions from both past ice volume changes during the last glacial cycles and present ice imbalances over antarctica using a variety of published ice models model predictions of secular changes of the geoid anomaly based on plausible mantle viscosity profiles enable us to discuss the importance of past and present ice volume changes and their characteristic signatures while uncertainties arising from the viscosity profile are of secondary importance for model predictions of the secular change of the geoid anomaly we expect significant bias of the observed signal from uncertainties in the timing of the end of deglaciation which is in agreement with previous studies hence the benefit of inferring present day antarctic ice imbalance from satellite gravity missions will depend on improvements to ice models for the last glacial cycle

holocene glacial rebound and sea level change in nw europe summary observations of late pleistocene and holocene sea level change relative to the crust exhibit very considerable variations across nw europe in consequence of the response of the earth s crust to the deglaciation of fennoscandia and of the water added to the oceans from the melting of all late pleistocene ice sheets inversion of sea level observations from a site near the centre of the fennoscandian ice sheet and from three sites located beyond the margin of the ice sheet at the time of maximum glaciation yield a range of plausible models for the earth s response and for the ice models further constraints on this range of models is placed by a comparison of observed sea levels with predicted values at other sites near the former ice sheet margins the resulting mantle parameters are upper mantle viscosity 3 5 x 10 pa s lower mantle viscosity 2 7 x loz1 pa s lithospheric thickness 100150 km these values represent effective parameters that describe the response of the earth to surface loading of short to intermediate wavelengths on a time scale of 104yr the lower mantle viscosity is poorly constrained but the marked increase from upper to lower mantle is a characteristic of all plausible solutions the inversion places a constraint on the total volume of ice in the fennoscandian ice sheet such that the equivalent sea level rise from this contribution is about 13 14 m a less well determined constraint of about 10 m equivalent sea level rise is suggested for the barents kara ice sheet the inversion also indicates that a small amount of melt water from ice sheets far away from europe continued to be added into the oceans during late holocene time so as to raise the equivalent sea level by about 3 m during the past 6000 yr consistent with similar inversions of data from sites in the australian and pacific regions

the eismint benchmarks for testing ice sheet models we present a series of benchmark experiments designed for testing and comparing numerical ice sheet models following the outcome of two eismintworkshops organized to intercompare large scale ice sheet models currently in operation model benchmark experiments are described for ice sheets underfixed and moving margin conditions these address both steady state and time dependent behavior under schematic boundary conditions and with prescribedphysics a comparison was made of each model s prediction of basic geophysical variables such as ice thickness velocity and temperature consensusachieved in the model intercomparison provides reference solutions against which the accuracy and consistency of ice sheet modeling codes can be assessed

a high resolution model of the 100 ka ice age cycle significant improvements to the representation of climate forcing and mass balance response in a coupled two dimensional global energy balance climate model ebm and vertically integrated ice sheet model ism have led to the prediction of an ice volume chronology for the most recent ice age cycle of the northern hemisphere that is close to that inferred from the geological record most significant is that full glacial termination is delivered by the model without the need for new physical ingredients in addition a relatively close match is achieved between the last glacial maximum lgm model ice topography and that of the recently described ice 4g reconstruction these results suggest that large scale climate system reorganization is not required to explain the main variations of the north american na ice sheets over the last glacial cycle lack of sea ice and marine ice dynamics in the model leaves the situation over the eurasian ea sector much more uncertain the incorporation of a gravitationally self consistent description of the glacial isostatic adjustment process demonstrates that the na and ea bedrock responses can be adequately represented by simpler damped relaxation models with characteristic time scales of 3 5ka and 5 ka respectively these relaxation times agree with those independently inferred on the basis of postglacial relative sea level histories

geoid displacement about greenland resulting from past and present day mass changes in the greenland ice sheet 1 predictions are presented of secular changes in the geoid arising from glacial isostatic adjustment gia following the last glacial maximum and from presentday mass changes in the greenland ice sheet gis geoid displacement from ongoing gia is dominated by ice load changes outside of greenland at lower spherical harmonic degrees 2000 m spatial variability is noted when the presentday gis response is expanded to degree and order 32 this is detectable by grace when assuming an optimistic accuracy but is too small by a factor of ca 3 for an alternate accuracy estimate present day gis geoid displacement rates are generally less than the equivalent response from ice mass changes in antarctica patagonia and alaska index terms 1299 geodesy and gravity general or miscellaneous 1645 global change solid earth 1827 hydrology glaciology 1863 citation fleming k z martinec and j hagedoorn 2004 geoid displacement about greenland resulting from past and present day mass changes in the greenland ice sheet geophys res lett 31 l06617