revisiting tectonic corrections applied to pleistocene sea level highstands tectonic displacement contaminates estimates of peak eustatic sea level and equivalently minimum continental ice volumes determined from the elevation of quaternary interglacial highstand markers for sites at which a stratigraphic or geomorphic marker of peak marine isotope stage mis 5e sea level exists the standard approach for estimating local tectonic uplift or subsidence rates takes the difference between the elevation of the local highstand marker and a reference mis 5e eustatic value commonly chosen as 6 m and divides by the age of the marker the resulting rate is then applied to correct the elevation of all other local observed sea level markers for tectonic displacement including peak highstands of different ages e g mis 5a mis 5c and mis 11 under the assumption that the tectonic rate remained constant over those periods this approach introduces two potentially significant errors first the peak eustatic value adopted for mis 5e in most previous studies i e 6 m is likely incorrect second local peak sea level during mis 5e is characterized by significant departures from eustasy due to glacial isostatic adjustment in response to both successive glacial interglacial cycles and excess polar ice sheet melt relative to present day values we use numerical models of glacial isostatic adjustment that incorporate both of these effects to quantify the plausible range of the combined error and show that even at sites far from melting ice sheets local peak sea level during mis 5e may depart from eustasy by 2 4 m or more we also demonstrate that the associated error in the estimated tectonic rates can significantly alter previous estimates of peak eustatic sea level during quaternary highstands notably those associated with earlier interglacials e g mis 11

the sea level fingerprint of west antarctic collapse recent projections of sea level rise after a future collapse of thewest antarctic ice sheet for example the fourth intergovernmental panel on climate change assessment report assume that meltwater will spread uniformly that is eustatically across the oceans once marine based sectors of the west antarctic are filled a largely neglected 1977 study predicted that peak values would be 20 higher than the eustatic in the north pacific and 5 to 10 higher along the u s coastline we show with use of a state of the art theory that the sea level rise in excess of the eustatic value will be two to three times higher than previously predicted for u s coastal sites

the impact of groundwater depletion on spatial variations in sea level change during the past century continental groundwater loss during the past century has elevated sea level by up to 25 mm the mass unloading associated with this depletion locally uplifts earth s solid surface and depresses the geoid leading to slower relative sea level rise near areas of significant groundwater loss we computed spatial variations in sea level using a model of the solid earth s response to estimates of groundwater depletion during the past century and find large negative deviations of 0 4 mm yr along the coastlines of western north america and southern asia this approximately corresponds to the difference between rates of sea level rise measured by tide gauges in these regions since 1930 and average rates inferred from global reconstructions groundwater induced regional variations in sea level can be larger than those due to postglacial rebound and interseismic deformation and should become increasingly important in the future as both groundwater depletion and sea level rise accelerate

three dimensional finite element modelling of earth s viscoelastic deformation effects of lateral variations in lithospheric thickness summary we have developed a 3 d spherical finite element model to study the dynamic response to surface loads of a self gravitating and incompressible earth with 3 d viscoelastic structure we have forced our model with the ice 3g deglaciation history of tushingham peltier to study the effects of laterally varying lithospheric thickness on observations of post glacial rebound pgr the laterally varying lithospheric thicknesses are derived from estimates of the thermal structure of the oceanic lithosphere and from elastic thicknesses on continents as estimated from studies of long term geological loads our calculations show that the effects of lithospheric structure on the relative sea level change rslc depend on the locations of the observation sites and on the size of loads the rslc at the centre of the north american ice sheet is significantly less sensitive to lithospheric thickness compared with the rslc at the centre of the fennoscandian ice sheet at the peripheral bulges the rslc tends to be more sensitive to lithospheric thickness the rslc is controlled by local lithospheric thickness the rslc at a given location as predicted using models with laterally varying lithospheric thickness can be reproduced using a 1 d model with a uniform lithospheric thickness equal to the local lithospheric thickness coupled with efficient parallel computing we believe that the finite element model that we present here can be used to address a variety of viscoelastic deformation problems in geodynamics

the rotational stability of an ice age earth summary predictions of glaciation induced changes in the earth s rotation vector exhibit sensitivities to earth structure that are unique within the suite of long wavelength observables associated with glacial isostatic adjustment henceforth gia and despite nearly a quarter of a century of research these sensitivities remain enigmatic previous predictions of present day true polar wander tpw speed driven by gia have indicated for example a strong sensitivity to variations in the thickness of the elastic lithosphere and the treatment phase or chemical of the density discontinuity at 670 km depth nakada recently presented results that suggest that the predictions are also sensitive to the adopted rheology of the lithosphere however his results have introduced an intriguing paradox in particular predictions generated using a model with an extremely high viscosity lithospheric lid do not converge to results for a purely elastic lithosphere of the same thickness mitrovica as cited by nakada has suggested that the paradox originates from an inaccuracy in the traditional rotation theory e g wu peltier associated with the treatment of the background equilibrium rotating form upon which any load and rotation induced perturbations are superimposed we revisit these issues using a new treatment of the linearized euler equations governing load induced rotation perturbations on viscoelastic earth models we demonstrate that our revised theory in which the background form of the planet combines a hydrostatic component and an observationally inferred excess ellipticity resolves the apparent paradox calculations using the revised theory indicate that earlier predictions based on earth models with purely elastic lithospheric lids are subject to large errors indeed previously noted sensitivities of tpw speed predictions to the thickness and rheology elastic versus viscous of the lithosphere largely disappear in the application of the new theory significant errors are also incurred by neglecting the stabilizing influence of the earth s excess ellipticity finally we demonstrate that the contribution from rotational feedback on predictions of present day rates of change of the geoid sea surface and crustal velocities are overestimated by the traditional rotation theory and this has implications for analyses of ongoing satellite e g grace missions and geodetic gps surveys

recent controversies in predicting post glacial sea level change abstract we compare recent developments in the numerical prediction of post glacial sea level changes and comment on the controversies associated with these developments we conclude that 1 the broad shelf effect discussed by peltier and drummond 2002 in the context of water load modelling at migrating shorelines is incorporated into the sea level algorithms of johnston 1993 and milne et al 1999 and 2 the procedure used by yokoyama et al 2000 to infer an ice equivalent post lgm sea level rise of 130 135 m is technically sound

the sea level fingerprints of ice sheet collapse during interglacial periods abstract studies of sea level during previous interglacials provide insight into the stability of polar ice sheets in the face of global climate change commonly these studies correct ancient sea level highstands for the contaminating effect of isostatic adjustment associated with past ice age cycles and interpret the residuals as being equivalent to the peak eustatic sea level associated with excess melting relative to present day of ancient polar ice sheets however the collapse of polar ice sheets produces a distinct geometry or fingerprint of sea level change which must be accounted for to accurately infer peak eustatic sea level from site specific residual highstands to explore this issue we compute fingerprints associated with the collapse of the greenland ice sheet west antarctic ice sheet and marine sectors of the east antarctic ice sheet in order to isolate regions that would have been subject to greater than eustatic sea level change for all three cases these fingerprints are more robust than those associated with modern melting events when applied to infer eustatic sea level because 1 a significant collapse of polar ice sheets reduces the sensitivity of the computed fingerprints to uncertainties in the geometry of the melt regions and 2 the sea level signal associated with the collapse will dominate the signal from steric effects we evaluate these fingerprints at a suite of sites where sea level records from interglacial marine isotopes stages mis 5e and 11 have been obtained using these results we demonstrate that previously discrepant estimates of peak eustatic sea level during mis5e based on sea level markers in australia and the seychelles are brought into closer accord

relative sea level rise around east antarctica during oligocene glaciation during the middle and late eocene 48 34 myr ago the earth s climate cooled and an ice sheet built up on antarctica the stepwise expansion of ice on antarctica induced crustal deformation and gravitational perturbations around the continent close to the ice sheet sea level rose despite an overall reduction in the mass of the ocean caused by the transfer of water to the ice sheet here we identify the crustal response to ice sheet growth by forcing a glacial hydro isostatic adjustment model with an antarctic ice sheet model we find that the shelf areas around east antarctica first shoaled as upper mantle material upwelled and a peripheral forebulge developed the inner shelf subsequently subsided as lithosphere flexure extended outwards from the ice sheet margins consequently the coasts experienced a progressive relative sea level rise our analysis of sediment cores from the vicinity of the antarctic ice sheet are in agreement with the spatial patterns of relative sea level change indicated by our simulations our results are consistent with the suggestion that near field processes such as local sea level change influence the equilibrium state obtained by an ice sheet grounding line

ice age paleotopography a gravitationally self consistent theory of postglacial relative sea level change is used to infer the variation of surface ice and water cover since the last glacial maximum lgm the results show that lgm ice volume was approximately 35 percent lower than suggested by the climap reconstruction and the maximum heights of the main laurentian and fennoscandian ice complexes are inferred to have been commensurately lower with respect to sea level use of these ice age boundary conditions in atmospheric general circulation models will yield climates that differ significantly from those previously inferred on the basis of the climap data set

slowdown in antarctic mass loss from solid earth and sea level feedbacks introduction geodetic investigations of crustal motions in the amundsen sea sector of west antarctica and models of ice sheet evolution in the past 10 000 years have recently highlighted the stabilizing role of solid earth uplift on polar ice sheets one critical aspect however that has not been assessed is the impact of short wavelength uplift generated by the solid earth response to unloading over short time scales close to ice sheet grounding lines areas where the ice becomes afloat here we present a new global simulation of antarctic evolution at high spatiotemporal resolution that captures solid earth processes stabilizing and destabilizing ice sheets these include interactions with global eustatic sea level rise slr self attraction and loading sal of the oceans earth s rotational feedback to sal and elastic uplift of the solid earth rationale in antarctica dynamic thinning and retreat of ice streams has been the main driver of mass loss over the past decades largely controlled by how grounding lines migrate and interact with bedrock pinning points studies have shown that the physical representation of grounding line dynamics gld can only be captured through simulations with a horizontal resolution higher than 1 km current models of slr that incorporate solid earth processes with viscoelastic response tend to involve gld that is resolved at much coarser resolutions 25 to 100 km and involve time steps on the order of decades such resolution bounds are incompatible with capturing the complex bed topography of the ice streams of west antarctica that are vulnerable to rapid retreat in addition a resolution of 25 to 100 km is inherently too coarse to capture short wavelength elastic uplift generated by fast gld elastic uplift generated by a 2 km grounding line retreat modeled as loss of 100 m thick ice from a disk of 2 km radius can reach 52 mm near the grounding line centroid of the equivalent disk at coarser resolutions say 16 km the same model generates uplift one order of magnitude lower this implies that uplift generated in simulations at coarse resolutions might underestimate how much uplift is generated during ungrounding of active areas of antarctica such as thwaites glacier tg where highly complex grounding line geometries and associated retreat are observed over short time scales on the order of years our goal was therefore to carry out a sensitivity study of sea level and ice flow related processes that incorporate kilometer scale resolutions and global processes involving solid earth dynamics results our sensitivity study spans 500 years and demonstrates how in antarctica tg is particularly prone to negative feedback from sal and elastic uplift at year 2350 including these feedbacks leads to a 20 year delay in dynamic mass loss of tg corresponding to a 26 8 reduction in sea level contribution along with a reduction in grounding line retreat of 38 and elastic uplift rates reaching 0 25 m year at year 2100 though this negative feedback is considerably lower with a 1 34 reduction in sea level contribution only not including a kilometer scale resolution representation of such processes will lead to projections of slr that will significantly overestimate antarctic ice sheet contribution over several centuries conclusion for 21st century projections the effects we have modeled here remain negligible however for the period starting 2250 and after slr projections that would not account for such dynamic geodetic effects run the risk of consistently overestimating by 20 to 40 relative sea level estimates our approach shows that significant stabilization in grounding line migration occurs when uplift rates start approaching 10 cm year this has strong implications for late quaternary reconstructions of slr for example in which the inclusion of these solid earth processes will allow slr modelers to gain a better grasp of the time scales involved in reaching maximum coastal inundation levels during extended warm periods

glacial isostatic adjustment on 3 d earth models a finite volume formulation summary we describe and present results from a finite volume fv parallel computer code for forward modelling the maxwell viscoelastic response of a 3 d self gravitating elastically compressible earth to an arbitrary surface load we implement a conservative control volume discretization of the governing equations using a tetrahedral grid in cartesian geometry and a low order linear interpolation the basic starting grid honours all major radial discontinuities in the preliminary reference earth model prem and the models are permitted arbitrary spatial variations in viscosity and elastic parameters these variations may be either continuous or discontinuous at a set of grid nodes forming a 3 d surface within the regional or global modelling domain in the second part of the paper we adopt the fv methodology and a spherically symmetric earth model to generate a suite of predictions sampling a broad class of glacial isostatic adjustment gia data types 3 d crustal motions long wavelength gravity anomalies these calculations based on either a simple disc load history or a global late pleistocene ice load reconstruction ice 3g are benchmarked against predictions generated using the traditional normal mode approach to gia the detailed comparison provides a guide for future analyses e g what grid resolution is required to obtain a specific accuracy and it indicates that discrepancies in predictions of 3 d crustal velocities less than 0 1 mm yr 1 are generally obtainable for global grids with 3 106 nodes however grids of higher resolution are required to predict large amplitude 1 cm yr 1 radial velocities in zones of peak post glacial uplift e g james bay to the same level of absolute accuracy we conclude the paper with a first application of the new formulation to a 3 d problem specifically we consider the impact of mantle viscosity heterogeneity on predictions of present day 3 d crustal motions in north america in these tests the lateral viscosity variation is constructed with suitable scaling from tomographic images of seismic s wave heterogeneity and it is characterized by approximately 2 orders of magnitude peak to peak lateral variations within the lower mantle and 1 order of magnitude variations in the bulk of the upper mantle below the asthenosphere we find that the introduction of 3 d viscosity structure has a profound impact on horizontal velocities indeed the magnitude of the perturbation of order 1 mm yr 1 is as large as the prediction generated from the underlying 1 d radial reference model and it far exceeds observational uncertainties currently being obtained from space geodetic surveying the relative impact of lateral viscosity variations on predicted radial motions is significantly smaller

a proposed nomenclature for stages and series for the cambrian of laurentia an internally consistent succession of six named regional stages from youngest to oldest sunwaptan steptoean marjuman delamaran dyeran montezuman with their boundaries defined by regional extinction events within the trilobite record is proposed for the trilobite bearing rocks of laurentia sub trilobite stage s are recommended but unnamed the three youngest stages have been named previously but the lower boundary of the marjuman is shifted downward the three older stages within the trilobite record are new if deemed necessary four regional series are also suggested from youngest to oldest millardan lincolnian waucoban and begadean each of the three youngest series accommodates two stages

a new projection of sea level change in response to collapse of marine sectors of the antarctic ice sheet we present gravitationally self consistent predictions of sea level change that would follow the disappearance of either the west antarctic ice sheet wais or marine sectors of the east antarctic ice sheet eais our predictions are based on a state of the art pseudo spectral sea level algorithm that incorporates deformational gravitational and rotational effects on sea level as well as the migration of shorelines due to both local sea level variations and changes in the extent of marine based ice cover if we define the effective eustatic value eev as the geographically uniform rise in sea level once all marine based sectors have been filled with water then we find that some locations can experience a sea level rise that is 40 per cent higher than the eev this enhancement is due to the migration of water away from the zone of melting in response to the loss of gravitational attraction towards the ice sheet load self attraction the expulsion of water from marine areas as these regions rebound due to the unloading and the feedback into sea level of a contemporaneous perturbation in earth rotation in the wais case this peak enhancement is twice the value predicted in a previous projection that did not include expulsion of water from exposed marine sectors of the west antarctic or rotational feedback the peak enhancements occur over the coasts of the united states and in the indian ocean in the wais melt scenario and over the south atlantic and northwest pacific in the eais scenario we conclude that accurate projections of the sea level hazard associated with ongoing global warming should be based on a theory that includes the complete suite of physical processes described above

late caradoc graptolitic faunal gradients across the iapetus ocean late caradoc graptolite assemblages across the iapetus ocean in wales and scotland became progressively more disparate despite the narrowing of the ocean we compare faunal distributions in continuous sections from opposite sides of iapetus at whitland in south wales and hartfell score in the southern uplands of scotland a comprehensive graptolite range chart is given for each the graptolite assemblages from the clingani biozone are subdivided into a lower ensigraptus caudatus subzone and upper dicellograptus morrisi subzone at both localities though the faunas differ in detail higher in the sequence the distinctive scottish linearis biozone fauna is not recognizable at whitland its presumed equivalent being a fauna dominated by variable morphotypes of the genus normalograptus this suggests that environmental gradients depth and or temperature were changing more rapidly than the geography significantly the subsequent inception of limestone deposition at whitland was approximately contemporaneous with widespread replacement of black mudstones by oxic bioturbated sediments elsewhere in the welsh basin and in scotland this was possibly a response to an early phase of cooling prior to the end ordovician glaciation in wales the claimed hiatus at the caradoc ashgill boundary may rather reflect biofacies variation

early proterozoic geomagnetic field in western laurentia implications for paleolatitudes local rotations and stratigraphy abstract the east west trending post orogenic subvertical cleaver dykes from the great bear magmatic arc are dated by the u pb baddeleyite method to be 1740 5 4 ma they have a mean direction of magnetization of d i 136 5 and 57 4 k 64 95 4 5 based on samples from 17 diabase dykes a mean location 65 7 n 118 03 w and a corresponding paleopole at 19 4 n 83 3 w a95 6 1 studies of baked contacts country rocks distant from dykes and later intrusions that cut them show that the dykes became magnetized soon after intrusion the paleopole is not significantly different from that obtained from the 1759 1 ma post orogenic jan lake granite from the hudsonian orogen in southeast saskatchewan these paleopoles fall among a cluster previously determined from post orogenic overprints in a wide variety of rocks and geological settings across laurentia their mean is 20 8 n 94 5 w a95 5 2 collectively they record a widespread remagnetization episode following the hudsonian orogeny during which the polarity of the field remained constant this single polarity interval the cleaver superchron has a mean age of approximately 1747 ma and its duration is at least 13 million years but is probably much longer with further refinement it could become a global statigraphical marker there are 18 paleopoles from red beds and igneous rocks which record the paleofield in western laurentia mainly over an extended interval we estimate to be at least 100 million years between about 1960 and 1830 ma during the hudsonian orogeny over this interval western laurentia remained at a low and essentially constant latitude reversals of the geomagnetic field occurred opposed magnetizations being of approximately equal frequency there are numerous magnetochrons which could in future assist in regional stratigraphic correlations on the basis of six studies we estimate that the reference paleopole for this interval is at 1 1 s 71 7 w a95 12 1 n 6 paleopoles from the other 12 studies are spread over a 100 arc indicating large variable rotations about local vertical axes which probably resulted from transcurrent faulting caused by indentation of the bordering archean slave and superior cratons during the hudsonian orogeny these reference paleopoles show that during the hudsonian orogeny western laurentia was in paleolatitudes of 15 30 during post hudsonian time ca 1750 ma paleolatitudes were about 20 higher paleowind directions inferred by others indicate that laurentia during these intervals was in the northern hemisphere

the sea level fingerprint of the 8 2 ka climate event the 8 2 ka cooling event was an abrupt widespread climate instability there is general consensus that the episode was likely initiated by a catastrophic outflow of proglacial lakes agassiz and ojibway through the hudson strait with subsequent disruption of the atlantic meridional overturning circulation however the total discharge and flux during the 8 2 ka event remain uncertain we compute the sea level signature or fingerprint associated with the drainage of lakes agassiz and ojibway as well as the expected sea level signal over the same time period due to glacial isostatic adjustment gia in response to the late pleistocene deglaciation our analysis demonstrates that sites relatively close to the lakes including the west and gulf coasts of the united states have small signals due to the lake release and potentially large gia signals and thus they may not be optimal field sites for constraining the outflow volume other sites such as the east coast of south america and western africa have significantly larger signals associated with the lake release and are thus better choices in this regard

on post glacial sea level i general theory summary modern analyses of sea level changes due to glacial isostatic adjustment gia are based on the classic sea level equation derived by farrell clark 1976 geophys j r astr soc 46 647 667 the connection between global sea level variations and changes to ocean height that is assumed within this equation breaks down in the presence of a time varying shoreline geometry we present a generalized sea level equation that overcomes this difficulty we also derive analytic expressions for and present schematic illustrations of the error in the ocean height change over finite time intervals introduced in published efforts to incorporate shoreline evolution into the theory of gia induced sea level change this comparison includes studies of shoreline migration due to either local sea level changes or the growth and ablation of marine based ice we conclude that the theories applied by johnston 1993 geophys j int 114 615 634 milne 1998 phd thesis university of toronto toronto and co workers are more accurate than the procedure advocated by peltier 1994 science 265 195 201 1998a geophys res lett 25 3955 3958 1998b rev geophys 114 615 634 although an improvement in the latter has recently been reported peltier drummond 2002 geophys res lett 29 10 1029 2001gl014273 our generalized theory is valid for any earth model in a companion paper we derive the equations necessary to treat the special case of a spherically symmetric linear viscoelastic and rotating earth and we quantify errors associated with previous work

sea level change glacial rebound and mantle viscosity fornorthern europe northwestern europe remains a key region for testing models of glacial isostasy because of the good geological record of crustal response to the glacial unloading since the time of the last glacial maximum models for this rebound and associated sea level change require a detailed knowledge of the ice sheet geometry including the ice thickness through time existing ice sheet reconstructions are strongly model dependent and inversions of sea level data for the mantle response may be a function of the model assumptions thus inverse solutions for the sea level data are sought that include both ice and earth model parameters as unknowns sea level data from fennoscandia the north sea the british isles and the atlantic and english channel coasts have been evaluated and incorporated into the solutions the starting ice sheet for fennoscandia is based on a reconstruction of a model by denton hughes 1981 that is characterized by quasi parabolic cross sections and symmetry about the load centre both global northwestern europe as a whole and regional subsets of the data solutions have been made for earth model parameters and ice height scaling parameters the key results are as follows 1 the response of the upper mantle to the changing ice and water loads is spatially relatively homogenous across scandinavia the north sea and the british isles 2 this response can be adequately modelled by an effective elastic lithosphere of thickness 65 85 km and by an effective upper mantle viscosity from the base of the lithosphere to the 670 km depth seismic discontinuity of about 3 4 1020 pa s the effective lower mantle viscosity is at least an order of magnitude greater 3 the ice thickness over scandinavia at the time of maximum glaciation was only about 2000 m much less than the 3400 m assumed in the denton hughes model 4 the ice profiles are asymmetric about the centre of the ice sheet with those over the western part being consistent with quasi parabolic functions whereas the ice heights over the eastern and southern regions increase much more slowly with distance inwards from the ice margin

terminal antarctic melting inferred from a far field coastal site abstract the contribution of the antarctic ice sheet ais to deglacial sea level rise is poorly constrained this shortfall gives rise to concerns because incorrect ais estimates impact significantly on our ability to predict sea level change in the course of global warming given the scarcity of geological data and the complexity of the antarctic response to glacio isostatic adjustment processes there is a need for accurate data to constrain the timing of the ice sheet retreat here we provide such data on the holocene antarctic melting through an isolated geographic site on the northern hemisphere which we show is sensitive to the antarctic signal using both our site and other mid latitudinal relative sea level sites our model provides a consensus estimate that the ais released water corresponding to 5 m equivalent sea level at 8 ka and ceased melting at 6 ka this is different to most ais models which release an equal amount of water at 11 ka or after 6 ka our findings change model assumptions about the terminal ais melting and show that future holocene sea level research should focus on broad shelves and large coast embayments in the mid latitudes

mid holocene grounding line retreat and readvance at whillans ice stream west antarctica author s venturelli ra siegfried mr roush ka li w burnett j zook r fricker ha priscu jc leventer a rosenheim be

a new inference of mantle viscosity based upon joint inversion of convection and glacial isostatic adjustment data we present new profiles of mantle viscosity derived on the basis of non linear occam style joint inversions of an extensive set of data associated with mantle convection and glacial isostatic adjustment gia the convection related observables include satellite derived free air gravity harmonics the geodetically inferred excess ellipticity of the cmb and tectonic plate motions the gia constraints involve two classes of observables previously shown to be relatively insensitive to errors in the late pleistocene ice history the so called fennoscandian relaxation spectrum frs and a set of site specific decay times determined from the postglacial sea level history in hudson bay and sweden the inverted viscosity profiles show a significant three orders of magnitude increase from the upper mantle mean value of f4 10 20 pa s to a high viscosity 10 23 pa s peak at

evolution of a coupled marine ice sheet sea level model we investigate the stability of marine ice sheets by coupling a gravitationally self consistent sea level model valid for a self gravitating viscoelastically deforming earth to a 1 d marine ice sheet shelf model the evolution of the coupled model is explored for a suite of simulations in which we vary the bed slope and the forcing that initiates retreat we find that the sea level fall at the grounding line associated with a retreating ice sheet acts to slow the retreat in simulations with shallow reversed bed slopes and or small external forcing the drop in sea level can be sufficient to halt the retreat the rate of sea level change at the grounding line has an elastic component due to ongoing changes in ice sheet geometry and a viscous component due to past ice and ocean load changes when the ice sheet model is forced from steady state on short timescales 500 years viscous effects may be ignored and grounding line migration at a given time will depend on the local bedrock topography and on contemporaneous sea level changes driven by ongoing ice sheet mass flux on longer timescales an accurate assessment of the present stability of a marine ice sheet requires knowledge of its past evolution

on postglacial geoid subsidence over the equatorial oceans we develop two new spectral formalisms for the gravitationally self consistent solution of the sea level equation which governs the redistribution of glacial meltwater on a visco elastic earth the first is a purely spectral technique based on an extension of theory outlined by dahlen 1976 for determining the equilibrium oceanic tide on an elastic planet using this technique with a feasible spherical harmonic truncation level l 30 we can obtain convergence in the computed sea level variations within the degree range l 10 we also develop a second pseudospectral technique however which permits the construction of gravitationally self consistent solutions to much higher degree and order l 100 the pseudospectral formalism is employed here to develop a comprehensive physical explanation for the global pattern of present day sea level variations due to ongoing glacial isostatic adjustment in particular we focus upon a mechanism which we term equatorial ocean syphoning that acts to draw water toward the oceanic portion of the collapsing peripheral bulge that encircles previously glaciated regions the collapse of the forebulge induces a flow of water which is required to maintain hydrostatic equilibrium the syphoning mechanism dominates the relative sea level rsl variation in oceans in the far field of the ice sheets that is beyond the peripheral bulge during periods such as the interglacial of the past 4000 years during which the volume of the ice sheets has not apparently changed appreciably while at the same time isostatic adjustment persists the rsl change in the near field is in contrast dominated by the local vertical displacement of the solid surface finally comparison of gravitationally self consistent predictions of rsl change in the far field with the observational data at small pacific island sites has provided an upper bound of 1 to 2 m for the eustatic sea level rise produced by any recent last 3000 years melting of the antarctic ice sheet

correlation for the lower palaeozoic the global correlation standards now agreed for the ordovician and silurian systems and partly so for the cambrian system are summarized correlation of the international series and stages with the traditional and revised british series and stages is reviewed as well as with those in north america laurentia

sea level as a stabilizing factor for marine ice sheet grounding lines climate change could potentially destabilize marine ice sheets which would affect projections of future sea level rise1 2 3 4 specifically an instability mechanism5 6 7 8 has been predicted for marine ice sheets such as the west antarctic ice sheet that rest on reversed bed slopes whereby ice sheet thinning or rising sea level leads to irreversible retreat of the grounding line however existing analyses of this instability mechanism have not accounted for deformational and gravitational effects that lead to a sea level fall at the margin of a rapidly shrinking ice sheet9 10 11 here we present a suite of predictions of gravitationally self consistent sea level change following grounding line migration our predictions vary the initial ice sheet size and also consider the contribution to sea level change from various subregions of the simulated ice sheet using these results we revisit a canonical analysis of marine ice sheet stability5 and demonstrate that gravity and deformation induced sea level changes local to the grounding line contribute a stabilizing influence on ice sheets grounded on reversed bed slopes we conclude that accurate treatments of sea level change should be incorporated into analyses of past and future marine ice sheet dynamics

high resolution early paleozoic ordovician silurian time scales for much of the geologic time scale resolving power appears to be limited by the duration of biostratigraphic zones and subzones yet these zones exploit the appearance and disappearance events of only a small fraction of the species they span computer algorithms can sequence an order of magnitude more events and make explicit the uncertainties that arise when calibrating the resulting time line an illustrative case history builds an ordovician and silurian time scale from the geologic record of the entire graptolite clade over 1900 species from more than 400 localities and sections worldwide the same approach can be applied to any stratigraphic interval with detailed biostratigraphic observations it provides the foundation for time scales and paleobiologic time lines using logic similar to graphic correlation optimizing algorithms search for a composite sequence of species first and last appearance events that minimizes the implied shortcomings of all the field observations the algorithms minimize the number of species coexistences that are implied but never observed and the net adjustments needed to bring local range charts into agreement with a single composite sequence of events after total section thicknesses have been rescaled to help normalize for variation in depositional rate mean stratigraphic thicknesses are used to scale the intervals between adjacent events in the composite sequence the resulting scaled composite sequence is converted to a relative geologic time scale by identifying stage and zone boundaries within the sequence of graptolite events this relative scale is in turn calibrated by dated volcanic ash beds that were incorporated in the search for the optimal sequence these dated events are also used to test for linearity of the scaled composite the final time scale has a potential resolving power of 0 02 0 1 m y more than ten times better than can be achieved by traditional zones graptolite zones vary widely in duration from as short as 0 1 m y to nearly 5 0 m y the mean duration of zones or zonal groupings calibrated here is 1 44 m y in the ordovician and 0 91 m y in the silurian the average uncertainty in locating zone boundaries in a single composite sequence is about one fourth of the mean zone duration the variance resulting from differences in time scales developed from differing numbers of field observations and in response to changes in the optimization criteria gives a very conservative measure of the overall robustness of the method these differences indicate an average uncertainty in the age of graptolite zone boundaries that is more nearly equal to the mean zone duration for zone duration the mean uncertainty amounts to about one half of the length of an average zone

subglacial basins their origin and importance in glacial systems and landscapes closed topographic basins are found beneath contemporary ice masses and within the footprint of former ice masses in all glaciated regions we present the first integrated review of subglacial basin occurrence and formation and the implications of such basins for glaciological processes and the evolution of landscape our purpose is to motivate research in areas where understanding of basin origin and process significance is weak basins on the order of 10 102 m deep and 102 103 m long are produced by glacial erosion of subglacial rock and or sediment and are known as overdeepenings outlet and valley glaciers can overdeepen their beds far below sea level or local fluviatile base level larger basins typically in ice sheet contexts may have a pre glacial usually tectonic origin subglacial basins are important glaciologically because they require ice water and sediment to ascend an adverse subglacial slope in order to exit the glacial system the efficiency of which is dependent upon the gradient of the adverse slope and that of the ice surface basins thus influence subglacial drainage system morphology and transmissivity the thickness and distribution of basal ice and sediment layers and the mechanisms and dynamics of ice flow adverse gradients that exceed 11 times that of the ice surface may even permit the formation of subglacial lakes we speculate that in comparison to ice masses with few or no subglacial basins those with numerous or very large basins may respond to climatic changes with unexpected vigour in addition erosion rates and transport pathways of water and sediment through the glacial system and the expression of these processes in the sediment and landform record may be unexpectedly complex further our review shows that in a warming climate ice masses resting on adverse slopes will be vulnerable to rapid and potentially catastrophic retreat new lakes in subglacial basins exposed by mountain glacier retreat will present an increasing hazard and subglacial lakes may drain catastrophically on even longer time scales we speculate that the glacial excavation and post glacial filling of basins in mountainous regions should contribute importantly to climate related changes in isostasy and relief although the controls on overdeepening and their influence on other glacial and landscape processes remain uncertain we hypothesise that overdeepened glacial systems reflect an equilibrium ice bed geometry that maximises the efficiency of ice discharge improved understanding of overdeepening processes especially overdeepened bed hydrology is therefore necessary to understand fully the dynamic behaviour of valley and outlet glaciers and thus the fate of earth s largest ice masses

estimates of twenty first century sea level changes for norway in this work we establish a framework for estimating future regional sea level changes for norway following recently published works we consider how different physical processes drive non uniform sea level changes by accounting for spatial variations in 1 ocean density and circulation 2 ice and ocean mass changes and associated gravitational effects on sea level and 3 vertical land motion arising from past surface loading change and associated gravitational effects on sea level an important component of past and present sea level change in norway is glacial isostatic adjustment central to our study therefore is a reassessment of vertical land motion using a far larger set of new observations from a permanent gnss network our twenty first century sea level estimates are split into two parts firstly we show regional projections largely based on findings from the fourth assessment report of the intergovernmental panel on climate change ipcc ar4 and dependent on the emission scenarios a2 a1b and b1 these indicate that twenty first century relative sea level changes in norway will vary between 0 2 to 0 3 m 1 sigma 0 13 m secondly we explore a high end scenario in which a global atmospheric temperature rise of up to 6 c and emerging collapse for some areas of the antarctic ice sheets are assumed using this approach twenty first century relative sea level changes in norway are found to vary between 0 25 and 0 85 m min max 0 45 m we attach no likelihood to any of our projections owing to the lack of understanding of some of the processes that cause sea level change

on the robustness of predictions of sea level fingerprints summary the rapid melting of the earth s ice reservoirs will produce geographically distinct patterns of sea level change that have come to be known as sea level fingerprints a basic gravitationally self consistent theory for computing these patterns appeared in the 1970s however recent highly discrepant fingerprint calculations have led to suggestions that the algorithms and or theoretical implementation adopted in many previous predictions is not robust we present a suite of numerical predictions including benchmark comparisons with analytic results that counter this argument and demonstrate the accuracy of most published predictions moreover we show that small differences apparent in calculations published by some groups can be accounted for by subtle differences in the underlying physics the paper concludes with two sensitivity analyses 1 we present the first ever calculation of sea level fingerprints on earth models with 3 d variations in elastic structure and density and conclude that this added complexity has a negligible effect on the predictions 2 we compare fingerprints of polar ice sheet mass flux computed under the very common assumption of a uniform melt distribution to fingerprints calculated using melt geometries constrained by analysing recent trends in grace gravity data predictions in the near field of the ice sheets are sensitive to the assumed melt geometry however this sensitivity also extends to the far field particularly in the case of antarctic mass changes because of the strong dependence of the rotational feedback signal on the melt geometry we conclude that inferences of ice sheet mass flux based on modern sea level constraints should consider these more realistic melt geometries

tropical tales of polar ice evidence of last interglacial polar ice sheet retreat recorded by fossil reefs of the granitic seychelles islands abstract in the search for a record of eustatic sea level change on glacial interglacial timescales the seychelles ranks as one of the best places on the planet to study owing to its location with respect to the former margins of northern hemisphere ice sheets that wax and wane on orbital cycles the local or relative sea level history is predicted to lie within a few meters of the globally averaged eustatic signal during the last interglacial period we have surveyed and dated last interglacial fossil corals to ascertain peak sea level and hence infer maximum retreat of polar ice sheets during this time interval we observe a pattern of gradually rising sea level in the seychelles between 129 and 125 thousand years ago ka with peak eustatic sea level attained after 125 ka at 7 6 1 7 m higher than present after accounting for thermal expansion and loss of mountain glaciers this sea level budget would require 5 8 m of polar ice sheet contribution relative to today s volume of which only 2 m came from the greenland ice sheet this result clearly identifies the antarctic ice sheet as a significant source of melt water most likely derived from one of the unstable marine based sectors in the west and or east antarctic ice sheet furthermore the establishment of a 5 9 1 7 m eustatic sea level position by 128 6 0 8 ka would require that partial ais collapse was coincident with the onset of the sea level highstand

global geoid and sea level changes due to present day ice mass fluctuations we predict gravitationally self consistent global geoid and relative sea level rsl perturbations due to present day melting of ice complexes including the antarctic and greenland ice sheets and a suite of mountain glaciers and ice sheets classic analyses of sea level change indicate that these perturbations will depart significantly from eustatic i e geographically uniform trends e g woodward 1888 farrell and clark 1976 although this result has not always been appreciated in modern analyses mass flux of individual ice reservoirs will produce unique geometries of sea level change and this distinctiveness admits the possibility of using global geoid sea surface and rsl signatures of recent climate change to infer the ongoing mass balance of each reservoir rather than simply the net mass flux as an example we show that perturbations to the geoid arising from noneustatic water loads associated with each ice reservoir are sufficiently large at low degrees to be theoretically measurable within 5 years by the grace satellite mission we complete the study by reanalyzing tide gauge data at 23 sites selected by douglas 1997 in a recent analysis of global rsl rise traditionally estimates of global sea level rise are generated by taking the mean of a set of secular tide gauge trends that have been corrected for the influence of ongoing glacial isostatic adjustment gia related to the late pleistocene glacial cycles the common assumption in such studies is that the geographic scatter in the residual gia corrected trends is due to errors in the gia model or unmodeled processes e g tectonics we consider a large suite of gia model predictions and apply a least squares approach to the gia corrected tide gauge trends to estimate the weighting of various present day sea level signatures we find that the fit to the residual rsl trends is significantly improved and that the procedure is able to resolve a long standing observation of anomalously low sea level rates in europe this preliminary analysis which is relatively insensitive to changes in the assumed geometry of the present day mass balance assumes that ocean thermal expansion is globally uniform however the procedure can be easily extended to incorporate a realistic steric contribution once the geometry of the process is sufficiently well constrained

the effect of spatially non uniform water loads on prediction of sea level change summary numerical modelling of postglacial rebound predics a spatially variable pattern of sea level change yet many previous models predicting late pleistocene sea level change either neglect the load of water added to the oceans or assume a spatially uniform time dependent load over the whole ocean this is a poor approximation of the load near the former ice sheet since sea level change varies geographically in addition the coastline goemetry changes through time a spectral technique has been used to solve the sea level equation on an earth model with axisymmetric distribution of ice and oceans and also for a realistic ice ocean configuration the axisymmetric model is useful for demonstrating the fundamental physics involved in sea level changes caused by changes in surface loads in particular it can be seen that the elastic and gravitational response to the load is spread over a great distance whereas the viscous response is more localized a realistic ice ocean configuration has been used to demonstrate that neglect of the melt water load underestimates the amount of uplift in fennoscandia and other regions where rebound occurs in the ocean as previously noted by wu peltier 1983 in hudson bay and that movement of the coastlines and spatially varying water loads must both be included in calculations for the north sea and other near field regions with shallow seas sea level calculations including these effects and careful analysis of the sea level and ice melting record are required to determine modifications to the viscosity profile and ice model inferred by previous inaccurate models of the ocean load in the near field

postglacial sea level change on a rotating earth summary we present a complete derivation of the equation governing long term sea level variations on a spherically symmetric self gravitating maxwell viscoelastic planet this new sea level equation extends earlier work by incorporating in a gravitationally self consistent manner both a time dependent ocean continent geometry and the in uence of contemporaneous perturbations to the rotation vector of the planet we also outline an e cient pseudo spectral numerical methodology for the solution of this equation and present a variety of predictions based on a suite of earth models of relative sea level rsl variations due to glacial isostatic adjustment gia these results show that the contribution to the predicted rsl signal from gia induced perturbations to the rotation vector can reach 7 8 m over the postglacial period in geographic regions where the rotationally induced signal is a maximum this result is sensitive to variations in the adopted lower mantle viscosity and is relatively insensitive to variations in the adopted lithospheric thickness we also show that the rotationally induced component of rsl change is su cient to in uence previous estimates of late holocene melting events and ongoing sea level change due to giawhich were based on a rsl theory for a non rotating earth in particular estimates of antarctic melting over the last 5 kyr based on the amplitude of sea level highstands from the australian region may require an adjustment downwards of the order of 0 5 m of equivalent sea level rise furthermore present day rates of sea level change are perturbed by as much as 0 2 mm yr 1 by the rotational component of sea level change and this has implications for gia corrections of the global tide gauge record over the period from the last glacial maximum to the present we predict a distinctly non monotonic variation in the rotation induced component of rsl this is in agreement with our previous preliminary study milne mitrovica 1996 but contrasts signi cantly with predictions presented by han wahr 1989 and bills james 1996 we demonstrate that the disagreement arises as a consequence of approximations adopted in the latter studies we furthermore refute an assertion by bills james 1996 that previously published constraints on mantle viscosity and ice sheet histories which did not incorporate a rotation induced rsl component are largely invalidated by this omission

the proterozoic cambrian transition within the charnian supergroup of central england and the antiquity of the ediacara fauna a revised interpretation for the charnian supergroup is suggested from ichnological and lithological comparisons with the cambrian of nuneaton and other parts of the avalonian superterrane late neoproterozoic volcaniclastic sediments contain an ediacara fauna in the maplewell group these are succeeded by one or more inferred erosional breaks and overlain by passive margin sediments quartzarenites glauconitic greywackes pelites of the brand group which yield cambrian trace fossils including abundant large teichichnus this transformation is compared with that between the neoproterozoic caldecote volcanic formation and the cambrian hartshill formation at nuneaton the hanging rocks formation of the brand group lies above a major erosional break but shares a volcanogenic island arc petrology with the underlying maplewell group conglomeratic sandstones at the base of the brand hills formation contain purple pelite clasts comparable with underlying lithologies plus clasts of weathered diorite showing granophyric textures identical to those seen in the enigmatic south charnwood diorites nd sm isotope studies confirm the geochemical similarity between these diorites and those that intruded the caldecote volcanics at nuneaton previously u pb zircon dated at 603 2 ma these strong similarities with the nuneaton succession suggest that deposition of the brand hills formation in the cambrian was preceded by the local unroofing of diorite and erosion of underlying mudrocks much as seen in other parts of avalonia a date of 603 2 ma for the south charnwood diorites provides a minimum age for the local ediacara fauna but this is in need of substantiation

true polar wander as a mechanism for second order sea level variations long term wander of the rotation pole can be a significant contributor to second order time scales of 100 million years sea level variations numerical predictions based on realistic viscoelastic earth models and paleomagnetically constrained polar motion yield global scale differential sea level trends that can be as large as 200 meters from the results presented here it is argued that the well documented second order cretaceous tertiary sea level cycle should be reinterpreted as some combination of a eustatic and a regionally varying rotational signal

global tidal impacts of large scale ice sheet collapses recent studies show that the glaciers draining both the west antarctic and the greenland ice sheets are experiencing an accelerated ice loss highlighting the possibility of large scale ice sheet retreat and sea level rise in the coming centuries and millennia these sea level changes would vary spatially and could significantly alter global tides as the latter are highly dependent on bathymetry or water column thickness under ice shelves and basin shape this paper investigates how the principal semi diurnal m2 tidal amplitudes and energy dissipation respond to the non uniform sea level changes induced by complete ice sheet collapses the sea level changes are calculated using gravitationally self consistent sea level theory and the tides are simulated using an established tidal model results from the simulations show global and spatially heterogeneous changes in tidal amplitudes in addition pronounced changes in tidal energy dissipation occur in both the open ocean and in shelf seas also altering the location of tidal mixing fronts these changes have the potential to impact ocean mixing and hence large scale currents and climate patterns and the contribution of shelf sea to the global carbon cycle the new results highlight the importance of considering changes in the tides in predictions of future climate and reconstructions of past climate phases such as the last interglacial

sea level fingerprinting as a direct test for the source of global meltwater pulse ia the ice reservoir that served as the source for the meltwater pulse ia remains enigmatic and controversial we show that each of the melting scenarios that have been proposed for the event produces a distinct variation or fingerprint in the global distribution of meltwater we compare sea level fingerprints associated with various melting scenarios to existing sea level records from barbados and the sunda shelf and conclude that the southern laurentide ice sheet could not have been the sole source of the meltwater pulse whereas a substantial contribution from the antarctic ice sheet is consistent with these records

postglacial sealevels on a spherical self gravitating viscoelastic earth effects of lateral viscosity variations in the upper mantle on the inference of viscosity contrasts in the lower mantle abstract previous studies of lateral viscosity variations on postglacial rebound often neglect the spherical shape of the earth and the self gravity of the solid earth and oceans in this paper the consistent sealevel equation is solved by the coupled laplace finite element method for a spherical self gravitating incompressible maxwell earth it confirms the importance of self gravity in the oceans on sealevel computation near the ice margin where the data are most sensitive to the existence of lateral variations in lithospheric thickness and asthenospheric viscosity the effects of lateral variations in lower mantle viscosity asthenospheric viscosity and lithospheric thickness are investigated this paper confirms the finding of earlier investigations the combined effect of lateral viscosity variations in the lower mantle with reverse viscosity contrasts in the upper mantle is also investigated for sealevel data near the center of rebound the effect of lateral viscosity contrast in the lower mantle can be masked by the existence of a reverse lateral viscosity contrasts in the upper mantle however this is not the case for sealevel data just outside the ice margin

relative sea level trends in new york city during the past 1500 years new york city nyc is threatened by 21st century relative sea level rsl rise because it will experience a trend that exceeds the global mean and has high concentrations of low lying infrastructure and socioeconomic activity to provide a long term context for anticipated trends we reconstructed rsl change during the past 1500 years using a core of salt marsh sediment from pelham bay in the bronx foraminifera and bulk sediment 13c values were used as sea level indicators the history of sediment accumulation was established by radiocarbon dating and recognition of pollution and land use trends of known age in down core elemental isotopic and pollen profiles the reconstruction was generated within a bayesian hierarchical model to accommodate multiple proxies and to provide a unified statistical framework for quantifying uncertainty we show that rsl in nyc rose by 1 70 m since 575 ce including 0 38 m since 1850 ce the rate of rsl rise increased markedly at 1812 1913 ce from 1 0 to 2 5 mm y

eurasian ice sheet collapse was a major source of meltwater pulse 1a 14 600 years ago rapid sea level rise caused by the collapse of large ice sheets is a threat to human societies in the last deglacial period the rate of global sea level rise peaked at more than 4 cm yr 1 during meltwater pulse 1a which coincided with the bolling warming event some 14 650 years ago however the sources of the meltwater have proven elusive and the contribution from eurasian ice sheets has been considered negligible here we present a regional carbon 14 calibration curve for the norwegian sea and recalibrate marine 14c dates linked to the eurasian ice sheet retreat we find that marine based sectors of the eurasian ice sheet collapsed at the bolling transition and lost an ice volume of 4 5 7 9 m sea level equivalents sle over 500 years during peak melting 3 3 6 7 m sle of ice was lost potentially explaining up to half of meltwater pulse 1a a mean meltwater flux of 0 2 sv over 300 years was injected into the norwegian sea and the arctic ocean at a time when proxy evidence suggests vigorous atlantic meridional overturning circulation our reconstruction shows that massive marine based ice sheets can collapse in as little as 300 500 years marine based sections of the eurasian ice sheet collapsed rapidly during a warming event 14 600 years ago and contributed to the meltwater pulse 1a event according to a recalibrated age model for sediments from the norwegian sea

ice retreat in wilkes basin of east antarctica during a warm interglacial efforts to improve sea level forecasting on a warming planet have focused on determining the temperature sea level and extent of polar ice sheets during earth s past interglacial warm periods1 3 about 400 000 years ago during the interglacial period known as marine isotopic stage 11 mis11 the global temperature was 1 to 2 degrees celsius greater2 and sea level was 6 to 13 metres higher1 3 sea level estimates in excess of about 10 metres however have been discounted because these require a contribution from the east antarctic ice sheet3 which has been argued to have remained stable for millions of years before and includes mis114 5 here we show how the evolution of 234u enrichment within the subglacial waters of east antarctica recorded the ice sheet s response to mis11 warming within the wilkes basin subglacial chemical precipitates of opal and calcite record accumulation of 234u the product of rock water contact within an isolated subglacial reservoir up to 20 times higher than that found in marine waters the timescales of 234u enrichment place the inception of this reservoir at mis11 informed by the 234u cycling observed in the laurentide ice sheet where 234u accumulated during periods of ice stability6 and was flushed to global oceans in response to deglaciation7 we interpret our east antarctic dataset to represent ice loss within the wilkes basin at mis11 the 234u accumulation within the wilkes basin is also observed in the mcmurdo dry valleys brines8 10 indicating11 that the brine originated beneath the adjacent east antarctic ice sheet the marine origin of brine salts10 and bacteria12 implies that mis11 ice loss was coupled with marine flooding collectively these data indicate that during one of the warmest pleistocene interglacials the ice sheet margin at the wilkes basin retreated to near the precipitate location about 700 kilometres inland from the current position of the ice margin which assuming current ice volumes would have contributed about 3 to 4 metres13 to global sea levels

on postglacial sea level summary an exact method is presented for calculating the changes in sea level that occur when ice and water masses are rearranged on the surface of elastic and viscoelastic non rotating earth models the method is used to calculate the instantaneous elastic and delayed vi scoelastic sea level changes following the partial melting of late quaternary ice sheets we find that there can be large errors in the usual assumption that changes in sea level are uniform over the ocean basins if a quantity of ice equivalent to a uniform 100 m rise in sea level melts from the laurentide and fennoscandian ice sheets then in the south pacific the instantaneous rise in sea level can be as large as 120m in the north atlantic the instantaneous rise is always less than 100 m there is a zone in the north atlantic with almost no sea level change and near greenland and norway the sea level falls rather than rises by over 100 m one thousand years after the melting a forebulge migrating towards the ice loads causes water to flow from the south pacific into the north pacific suggesting that raised beaches should occur in the south pacific the gravitational attraction of an ice mass upon a nearby ocean tends to hold sea level high in the vicinity of the ice this extra load near the ice may have a significant influence on postglacial isostatic adjustment

laurentide cordilleran ice sheet saddle collapse as a contribution to meltwater pulse 1a the source or sources of meltwater pulse 1a mwp 1a at 14 5 ka recorded at widely distributed sites as a sea level rise of 10 20 m in less than 500 years is uncertain a recent ice modeling study of north america and greenland gregoire et al 2012 has suggested that the collapse of an ice saddle between the laurentide and cordilleran ice sheets with a eustatic sea level equivalent esle of 10 m may have been the dominant contributor to mwp 1a to test this suggestion we predict gravitationally self consistent sea level changes from the last glacial maximum to the present day associated with the gregoire et al 2012 ice model we find that a combination of the saddle collapse scenario and melting outside north america and greenland with an esle of 3 m yields sea level changes across mwp 1a that are consistent with far field sea level records at barbados tahiti and sunda shelf

near field hydro isostasy the implementation of a revised sea level equation summary we describe how the existing sea level equation incorrectly predicts the change in sea level and thus the ocean load in ice covered subgeoidal geographic regions during periods of deglaciation we go on to present a new sea level equation that overcomes this problem and we describe how this equation can be solved in a gravitationally self consistent manner by employing a well known spectral technique application of the new theory to predict relative sea level rsl histories and present day 3 d solid surface deformation rates in northeastern canada based on a single earth model characterized by a lithospheric thickness of 100 km and upper and lower mantle viscosities of 5 1020 and 5 1021 pa s respectively demonstrates that a significant error is introduced when the original theory is employed to predict the oceanic component of the surface load predictions of rsl curves show a discrepancy of 40 per cent at sites where data have been obtained and employed to constrain models of earth viscosity structure and ice sheet histories this error will significantly bias estimates of mantle viscosity structure and ice thicknesses that are based on the original theory in addition predictions of 3 d deformation rates differ by up to 25 per cent in some regions and so future applications that employ these data to constrain models of the glacial isostatic adjustment process should adopt the improved sea level theory in contrast estimates of inverse decay times from the predicted rsl curves are insensitive to within the observational error to the improvement in the surface load introduced by the new theory thus viscosity structure inferences based on this parametrization and the original sea level equation are unaffected by the error in the ocean load finally the new theory predicts a eustatic i e globally uniform rise in sea level over the postglacial period that is 11 m lower than that determined via the original theory therefore estimates of the global ice budget at the last glacial maximum based on far field rsl data and the original sea level theory will be too small by 10 per cent

quantifying the sensitivity of sea level change in coastal localities to the geometry of polar ice mass flux abstractit has been known for over a century that the melting of individual ice sheets and glaciers drives distinct geographic patterns or fingerprints of sea level change and recent studies have highlighted the implications of this variability for hazard assessment and inferences of meltwater sources these studies have computed fingerprints using simplified melt geometries however a more generalized treatment would be advantageous when assessing or projecting sea level hazards in the face of quickly evolving patterns of ice mass flux in this paper the usual fingerprint approach is inverted to compute site specific sensitivity kernels for a global database of coastal localities these kernels provide a mapping between geographically variable mass flux across each ice sheet and glacier and the associated static sea level change at a given site kernels are highlighted for a subset of sites associated with melting from greenland antarctica and the alaska yukon british columbia glacier system the l

antarctic ice dynamics amplified by northern hemisphere sea level forcing sea level rise due to ice loss in the northern hemisphere in response to insolation and greenhouse gas forcing is thought to have caused grounding line retreat of marine based sectors of the antarctic ice sheet ais 1 3 such interhemispheric sea level forcing may explain the synchronous evolution of global ice sheets over ice age cycles recent studies that indicate that the ais experienced substantial millennial scale variability during and after the last deglaciation4 7 roughly 20 000 to 9 000 years ago provide further evidence of this sea level forcing however global sea level change as a result of mass loss from ice sheets is strongly nonuniform owing to gravitational deformational and earth rotational effects8 suggesting that the response of ais grounding lines to northern hemisphere sea level forcing is more complicated than previously modelled1 2 6 here using an ice sheet model coupled to a global sea level model we show that ais dynamics are amplified by northern hemisphere sea level forcing as a result of this interhemispheric interaction a large or rapid northern hemisphere sea level forcing enhances grounding line advance and associated mass gain of the ais during glaciation and grounding line retreat and mass loss during deglaciation relative to models without these interactions the inclusion of northern hemisphere sea level forcing in our model increases the volume of the ais during the last glacial maximum about 26 000 to 20 000 years ago triggers an earlier retreat of the grounding line and leads to millennial scale variability throughout the last deglaciation these findings are consistent with geologic reconstructions of the extent of the ais during the last glacial maximum and subsequent ice sheet retreat and with relative sea level change in antarctica3 7 9 10

postglacial sea level change on a rotating earth first results from a gravitationally self consistent sea level equation we present and solve a gravitationally self consistent sea level equation which governs postglacial sea level variations on a spherically symmetric self gravitating viscoelastic and rotating earth we find that the inclusion of a glacio isostatically induced rotational excitation can significantly affect previous predictions of both present day sea level rates and postglacial sea level histories which were based on a theory that assumed a non rotating earth model to illustrate we consider present day sea level rates and tide gauge corrections along the us east coast and relative sea level curves in the far field of the late pleistocene ice sheets

spatial variations in the rate of sea level rise caused by the present day melting of glaciers and ice sheets the redistribution of surface water mass associated with the melting of glacial ice causes uplift near areas of mass depletion depression of the seafloors and changes in the earth s gravitational field which perturb the ocean surface as a result local spatial variations exist in the rate of sea level rise tide gauges on continental coastlines measure a sea level rise 5 smaller than the global average tide gauges in the hemisphere opposite a source of continental mass depletion measure sea level rise 10 to 20 greater than the global average produced by that source while satellites make measurements 10 too low because most long duration tide gauges are in the northern hemisphere if the sources of sea level rise are unbalanced between the two hemispheres estimates of global sea level rise could be in error by 10 to 20 individual tide gauges could be more seriously unrepresentative if they are near regions of significant present day mass depletion

reassessment of the potential sea level rise from a collapse of the west antarctic ice sheet theory has suggested that the west antarctic ice sheet may be inherently unstable recent observations lend weight to this hypothesis we reassess the potential contribution to eustatic and regional sea level from a rapid collapse of the ice sheet and find that previous assessments have substantially overestimated its likely primary contribution we obtain a value for the global eustatic sea level rise contribution of about 3 3 meters with important regional variations the maximum increase is concentrated along the pacific and atlantic seaboard of the united states where the value is about 25 greater than the global mean even for the case of a partial collapse