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The isostatic response of the Earth to past mass exchange between ice sheets and oceans, so-called glacial isostatic adjustment (GIA), is an important geodynamic process in North America. Modelling GIA observables provides one of the few direct methods for estimating Earth viscosity structure. We investigate here the requirement for anomalously high mantle viscosities to fit the relative sea level (RSL) data along the Atlantic and Gulf coasts of North America found in recent GIA studies. We demonstrate that this requirement is primarily related to the modelled geometry and evolution of the peripheral bulge of the Laurentide ice sheet. We show that a 3D Earth model with a global average viscosity in the upper mantle of 0.3 × 10 21 Pa s and 3 × 10 22 Pa s in the lower mantle, which is consistent with both the Richmond Gulf (Hudson Bay) relaxation time and several recent global analyses, is able to produce a much improved fit to the Gulf and Atlantic coast RSL data relative to the 1D Earth model results when no lateral structure is applied. Therefore, we conclude that realistic implementations of lateral structure can explain the markedly different viscosity inferences obtained using 1D GIA models and RSL data from different regions of North America. A necessary caveat is that there are significant differences among the computed RSL curves corresponding to the three different realisations of lateral structure considered here, demonstrating significant uncertainty associated with this model input.

We infer the GIA signal and its uncertainty along the central Pacific coast of North America using 680 sea-level index points and over 20,000 model runs sampling >700 (1-D) Earth viscosity models and 29 ice sheet reconstructions. Due to the large spatial extent and different tectonic settings of the study area, we divided it into three sub-regions (northern, central and southern) for which model parameters were inferred separately. Also, given that this region is tectonically active, the influence of this process (as well as sediment isostatic adjustment) was accounted for where possible by removing it from the data using published estimates. Our results indicate that it is not possible to produce an acceptable to for all of the RSL data with a single set of model parameters, suggesting significant lateral variability in viscous structure. Specifically, low viscosities (1019–1020 Pas) are inferred in the upper mantle within the northern region (southwestern British Columbia and northwest Washington) compared to those inferred (2–5 × 1020 Pas) for the central and southern regions (extending from southern Washington to southern California). High quality model fits were obtained for all data except those from the northern region where no single parameter set was able to capture both the rapid and large RSL fall during the late glacial and the monotonic rise during the mid-to-late Holocene at all localities. This suggests the need for an Earth model that incorporates departures from a linear Maxwell rheology (as applied here) and/or lateral variations in viscosity structure. Using our optimal model parameter sets, we show that GIA is a significant contributor to both contemporary vertical land motion and relative sea level change in our study region and so should be considered when interpreting observations of these signals and for making future relative sea level projections. Model output of present-day vertical land motion at 483 GPS stations and sea-level change at 56 tide gauge stations is provided (with estimated uncertainty) so that these data can be used to study non-GIA processes more accurately.

Despite elevated summer insolation forcing during the early Holocene, global ice sheets retained nearly half of their volume from the Last Glacial Maximum, as indicated by deglacial records of global mean sea level (GMSL). Partitioning the GMSL rise among potential sources requires accurate dating of ice-sheet extent to estimate ice-sheet volume. Here, we date the final retreat of the Laurentide Ice Sheet with 10 Be surface exposure ages for the Labrador Dome, the largest of the remnant Laurentide ice domes during the Holocene. We show that the Labrador Dome deposited moraines during North Atlantic cold events at ∼10.3 ka, 9.3 ka and 8.2 ka, suggesting that these regional climate events helped stabilize the retreating Labrador Dome in the early Holocene. After Hudson Bay became seasonally ice free at ∼8.2 ka, the majority of Laurentide ice-sheet melted abruptly within a few centuries. We demonstrate through high-resolution regional climate model simulations that the thermal properties of a seasonally ice-free Hudson Bay would have increased Laurentide ice-sheet ablation and thus contributed to the subsequent rapid Labrador Dome retreat. Finally, our new 10 Be chronology indicates full Laurentide ice-sheet had completely deglaciated by 6.7 ± 0.4 ka, which re quires that Antarctic ice sheets contributed 3.6–6.5 m to GMSL rise since 6.3–7.1 ka.

Observations of enhanced volcanic frequency during the last deglaciation have led to the hypothesis that ice unloading in glaciated volcanic terrains can promote volcanism through decompression melting in the shallow mantle or a reduction in crustal magma storage time. However, a direct link between regional climate change, isostatic adjustment, and the initiation of volcanism remains to be demonstrated due to the difficulty of obtaining high-resolution well-dated records that capture short-term climate and volcanic variability traced to a particular source region. Here we present an exceptionally resolved record of 19 tephra layers paired with foraminiferal oxygen isotopes and alkenone paleotemperatures from marine sediment cores along the Southeast Alaska margin spanning the last deglacial transition. Major element compositions of the tephras indicate a predominant source from the nearby Mt. Edgecumbe Volcanic Field (MEVF). We constrain the timing of this regional eruptive sequence to 14.6–13.1 ka. The sudden increase in volcanic activity from the MEVF coincides with the onset of Bolling–Allerod interstadial warmth, the disappearance of ice-rafted detritus, and rapid vertical land motion associated with modeled regional isostatic rebound in response to glacier retreat. These data support the hypothesis that regional deglaciation can rapidly trigger volcanic activity. Rapid sea surface temperature fluctuations and an increase in local salinity (i.e., δ18Osw) variability are associated with the interval of intense volcanic activity, consistent with a two-way interaction between climate and volcanism in which rapid volcanic response to ice unloading may in turn enhance short-term melting of the glaciers, plausibly via albedo effects on glacier ablation zones.

The last deglaciation is the most recent interval of large-scale climate change that drove the Greenland ice sheet from continental shelf to within its present extent. Here, we use a database of 645 published 10Be ages from Greenland to document the spatial and temporal patterns of retreat of the Greenland ice sheet during the last deglaciation. Following initial retreat of its marine margins, most land-based deglaciation occurred in Greenland following the end of the Younger Dryas cold period (12.9–11.7 ka). However, deglaciation in east Greenland peaked significantly earlier (13.0–11.5 ka) than that in south Greenland (11.0–10 ka) or west Greenland (10.5–7.0 ka). The terrestrial deglaciation of east and south Greenland coincide with adjacent ocean warming. 14C ages and a recent ice-sheet model reconstruction do not capture this progression of terrestrial deglacial ages from east to west Greenland, showing deglaciation occurring later than observed in 10Be ages. This model-data misfit likely reflects the absence of realistic ice-ocean interactions. We suggest that oceanic changes may have played an important role in driving the spatial-temporal ice-retreat pattern evident in the 10Be data.

This study presents a new model of Holocene ice-volume equivalent sea level (ESL), extending a previously published global ice sheet model (Bassett et al., 2005), which was unconstrained from 10 kyr BP to present. This new model was developed by comparing relative sea level (RSL) predictions from a glacial isostatic adjustment (GIA) model to a suite of Holocene sea level index points from China and Malay-Thailand. Three consistent data-model misfits were found using the Bassett et al. (2005) model: an over-prediction in the height of maximum sea level, the timing of this maximum, and the temporal variation of sea level from the time of the highstand to present. The data-model misfits were examined for a large suite of ESL scenarios and a range of earth model parameters to determine an optimum model of Holocene ESL. This model is characterised by a slowdown in melting at ∼7 kyr BP, associated with the final deglaciation of the Laurentide Ice Sheet, followed by a continued rise in ESL until ∼1 kyr BP of ∼5.8 m associated with melting from the Antarctic Ice Sheet. It was not possible to identify an earth viscosity model that provided good fits for both regions; with the China data preferring viscosity values in the upper mantle of less than 1.5 × 10 20 Pa s and the Malay-Thailand data preferring greater values. We suggest that this inference of a very weak upper mantle for the China data originates from the nearby subduction zone and Hainan Plume. The low viscosity values may also account for the lack of a well-defined highstand at the China sites.

Ireland experienced a spatially complex pattern of relative sea-level (RSL) changes and shoreline development caused by the interplay of isostatic and eustatic (ice equivalent sea level) processes since the Last Glacial Maximum (LGM). Using a combination of high-resolution marine geophysical data, vibrocores, foraminiferal analysis and 10 AMS radiocarbon dates, we reconstruct the Late Quaternary evolution and RSL history of Bantry Bay, a large (40 km long, 5–10 km wide) embayment in SW Ireland. The data indicate two infill phases: one before and one after the LGM, separated by glacial and lowstand sediments. The pre-LGM history is not dated and the depositional history is inferred. A large sediment lobe formed at the outer edge of Bantry Bay as a lowstand ice-proximal glacimarine outwash system as the ice retreated after the LGM, at a sea level ca. 80 m lower than present. Iceberg scour immediately west of this location likely relate to the break-up of the local Kerry–Cork Ice Cap. Long curvilinear ridges, seen both offshore and on top of the sediment lobe, probably formed as shoreface ridges under stronger-than-present tidal currents during a period of RSL stability (pre-14.6 ka cal BP). A subsequent infill phase is characterised by a basin-wide erosional (ravinement) surface and the deposition of inter- and sub-tidal estuarine sediments. Although our data support the general trends, our stratigraphic and radiocarbon data suggest a higher sea level between 11 and 13.5 ka cal BP than predicted by existing glacial isostatic adjustment models.

The thickness of the lithosphere inferred in most glacial isostatic adjustment (GIA) modelling studies tends to be significantly thinner than when found through seismic or thermal modelling studies. In those GIA studies, the lithosphere tends to be modelled as a plate of uniform and very high viscosity. We develop and test Earth models that include depth-dependent viscosity in the lithosphere to consider the implications for inferring lithospheric thickness from observed relative sea-level (RSL) changes. We find that when comparing predictions of RSL between the traditional plate lithosphere models and those with viscous structure, the latter produce RSL predictions that most closely resemble those from traditional models that are 10 s of km thinner. The greatest sensitivity to this change in the Earth model is most evident in regions loaded by relatively small ice sheets such as the British Isles. We also find that the effective elastic thickness of the lithosphere models with viscous structure is time-dependent, with thinning by tens of kilometres over a timescale of ∼10 kyr.

The rate of change of surface gravity, dg/dt, and vertical deformation rate of the solid surface, du/dt, are two observables of glacial isostatic adjustment (GIA). They contribute with different information on the same phenomenon. Their relation contains information of the underlying physics and a trustworthy relation allows to combine these observations to strengthen the overall observational accuracy of the phenomenon. In this paper we investigate the predicted relation between dg/dt and du/dt in previously glaciated areas. We use the normal mode approach for one dimensional earth models and solutions of the sea level equation with time-dependent coastline geometry. Numerical predictions of dg/dt and du/dt are computed for Laurentia, Fennoscandia and the British Isles respectively, using six different earth models. Within each region a linear trend is then fitted using the relation dg/dt = C du/dt + dg_0/dt. The estimated C and dg_0/dt differ more between the regions than between different earth models within each region. For Fennoscandia C ≈ −0.163 μGal/mm and for Laurentia C ≈ −0.152 μGal/mm. Maximum residuals between the linear trend and spatially varying model predictions of dg/dt are 0.04 μGal/yr in Fennoscandia and 0.17 μGal/yr in Laurentia. For the British Isles the results are harder to interpret, mainly since this region is located on the zero uplift isoline of Fennoscandia. In addition, we show temporal variation of the relation since the last glacial maximum till present-day. The temporal and spatial variation of the relation between dg/dt and du/dt can be explained by (i) the elastic respectively viscous proportion of the total signal and (ii) the spectral composition of the regional signal. Additional local effects, such as the Newtonian attraction and elastic deformation from local sea level changes, are examined in a case study for six stations in the Nordic absolute gravity network. The influence of these local effects on the relation between View the dg/dt and du/dt is negligible except for extreme locations close to the sea.

Lake Superior represents an important component of the aquatic ecosystem in North America. Along its south shore, ongoing lake-level rise, accelerated erosion, and wetland loss are major environmental concerns to coastal communities. A better prediction of the future of this shore requires placing the instrumental lake-level records in a geological context. However, our knowledge of the late-Holocene history of the world's largest freshwater body remains fragmentary. Here we present a sedimentary record of late-Holocene relative lake-level changes by dating transgressive basal peats resting directly on a sandy substrate along a bathymetric gradient in Bark Bay Slough, Wisconsin. Our record shows a moderate lake-level rise at 1.4±0.2 mm/yr from about 2200 to 1250 cal yr BP as a result of relatively slow differential uplift of Bark Bay relative to the controlling outlet at Port Huron. The rise accelerated to 2.3±0.2 mm/yr at about 1250 cal yr BP when Sault Ste. Marie emerged as the controlling outlet, thereby separating Superior from Lakes Michigan–Huron and giving rise to the modern hydrographic regime of the upper Great Lakes. The timing of this event in our record is about 1000 yr later than that estimated in most previous studies, but our data complement and confirm the younger age of lake separation inferred using a different methodology. Our results not only provide pertinent information for hydrological regulation, navigation operation, and infrastructural design in the upper Great Lakes, but also provide insight into freshwater wetland succession on flooded coasts.

Relative sea-level (RSL) reconstructions from the circum-Caribbean region were interpreted using a glacial isostatic adjustment (GIA) model with the aims to quantify the contribution of this process to both the temporal and spatial forms of the RSL observations and remove the GIA signal to estimate land ice volume change (eustasy) during the mid-to-late Holocene. To infer an optimal GIA parameter set, the RSL data were used to determine best-fitting Earth viscosity model parameters for two different global ice histories. The RSL data indicate a clear preference (95% confidence) for relatively high viscosity values: > 0.8 × 1021 Pas in the upper mantle and > 3 × 1022 Pas in the lower mantle. The data were not able to discriminate (at 95% confidence) between lithospheric thickness values ranging between 71 and 120 km, although the thickest value considered produced the best fits. RSL predictions based on the best-fitting model parameters indicate a spatial variability across the region of up to ~ 7 m during the early to mid-Holocene which is large enough to introduce significant error when using the entire dataset to produce a single regional RSL curve without correcting for GIA. When corrected for GIA, the most precise data from the region indicate about 3–4 m of land ice melt (eustasy) from ~ 7 cal kyr B.P. to ~ 3–2 cal kyr B.P., although we note that there is considerable scatter in these corrected data. This likely reflects GIA model limitations, such as the assumption of lateral homogeneity in a region that contains several plate boundaries, the influence of tectonic processes (which were not modelled), as well as errors and an underestimate of the uncertainty in the RSL reconstructions.

Ice core records were recently used to infer elevation changes of the Greenland ice sheet throughout the Holocene. The inferred elevation changes show a significantly greater elevation reduction than those output from numerical models, bringing into question the accuracy of the model-based reconstructions and, to some extent, the estimated elevation histories. A key component of the ice core analysis involved removing the influence of vertical surface motion on the δ 18 O signal measured from the Agassiz and Renland ice caps. We re-visit the original analysis with the intent to determine if the use of more accurate land uplift curves can account for some of the above noted discrepancy. To improve on the original analysis, we apply a geophysical model of glacial isostatic adjustment calibrated to sea-level records from the Queen Elizabeth Islands and Greenland to calculate the influence of land height changes on the δ 18 O signal from the two ice cores. This procedure is complicated by the fact that δ 18 O contained in Agassiz ice is influenced by land height changes distant from the ice cap and so selecting a single location at which to compute the land height signal is not possible. Uncertainty in this selection is further complicated by the possible influence of Innuitian ice during the early Holocene (12–8 ka BP). Our results indicate that a more accurate treatment of the uplift correction leads to elevation histories that are, in general, shifted down relative to the original curves at GRIP, NGRIP, DYE-3 and Camp Century. In addition, compared to the original analysis, the 1-σ uncertainty is considerably larger at GRIP and NGRIP. These changes reduce the data-model discrepancy reported by Vinther et al. (2009) at GRIP, NGRIP, DYE-3 and Camp Century. A more accurate treatment of isostasy and surface loading also acts to improve the data-model fits such that the residuals at all four sites for the period 8 ka BP to present are significantly reduced compared to the original analysis. Prior to 8 ka BP, the possible influence of Innuitian ice on the inferred elevation histories prevents a meaningful comparison.

The absence of basal peat in the stratigraphic sequences of the southern Bay of Biscay has long precluded the development of Holocene sea-level curves. We have approached this problem by combining the indicative depositional meaning (derived from the micropalaeontological composition and sand content) with radiocarbon ages of 55 borehole samples obtained from three estuarine areas of the southern Bay of Biscay. These new sea-level index points have produced the first complete Holocene sea-level curve from this area. We further reviewed all available sea-level data from SW Europe to provide the regional trend and use these data to calibrate a recently developed isostatic model. Field data and model reconstructions present a good agreement for the region considered. A north-south trend is apparent in the data and this is shown to be dominated by the influence of the deglaciation of Eurasian ice sheets, as suggested by previous studies for this region. However, some data-model discrepancy in the south of the Iberian Peninsula suggests that local factors tend to dominate during the late Holocene. On comparing our results to estimates of recent sea-level rise obtained from tide gauges and high-resolution proxy records, it is clear that this region has experienced a significant acceleration in sea level during the past century or so.

This paper presents new evidence regarding relative sea-level (RSL) changes and vertical land motions at three sites in Greenland since 1300 A.D., a time interval that spans the later part of the Medieval Climate Anomaly (MCA) and the Little Ice Age (LIA). We observe RSL rise at two sites in central west Greenland from c. − 0.80 ± 0.20 m at c. 1300 A.D. to c. − 0.20 m ± 0.25 m at c. 1600 A.D., after which RSL slowed and then stabilised. At a third site in south Greenland, we observe RSL rise from c. − 1.40 ± 0.20 m at c. 1400 A.D. until c. 1750 A.D., after which RSL slowed and was stable during at least the latter part of the 20th century. The c. 1600 A.D. RSL slow-down seen at the two former sites is surprising because it occurs during the LIA when one might expect the ice sheet to be gaining mass and causing RSL to rise. We interpret this RSL slowdown to indicate a period of enhanced regional mass loss from central west Greenland since c. 1600 A.D. and propose two hypotheses for this loss: first, a reduction in precipitation during cold and dry conditions and second, higher air temperatures and increased peripheral surface melt of the ice sheet from this date onwards. The latter hypothesis is compatible with a well-established temperature seesaw between western Greenland and northern Europe and, potentially, a previously identified shift from a positive to generally more negative NAO conditions around 1400 to 1600 A.D. Our study shows how RSL data from Greenland can provide constraints on the timing of ice sheet fluctuations in the last millennium and challenges the notion that during cold periods in northern Europe the ice sheet in west Greenland gained mass.

The aim of this investigation is to develop a method for the analysis of crustal strain determined by station networks that continuously measurements of Global Navigation Satellite Systems (GNSS). The major new ingredient is that we require a simultaneous minimum of the observation error and the elastic and potential energy implied by the deformation. The observations that we analyse come from eight years worth of daily solutions from continuous BIFROST GPS measurements in the permanent networks of the Nordic countries and their neighbours. Reducing the observations with best fitting predictions for the effects of glacial isostatic adjustment (GIA) we find strain rates of maximum 5 nano/yr in the interior of the rebound area predominantly as areal strain. The largest strain rates are found in the Finnmarken area, where however the GNSS network density is much lower than in the central and southern parts. The thick-plate adjustment furnishes a simultaneous treatment of 3-D displacements and the ensuing elastic and potential energy due to the deformation. We find that the strain generated by flexure due to GIA is important. The extensional regime seen at the surface turns over into a compressive style already at moderated depth, some 50 km.

We present the latest 3D velocity field of the Fennoscandian glacial isostatic adjustment (GIA) process from BIFROST. It is derived from more than 4800 days (13 years) of data at more than 80 permanent GPS sites. We use the GAMIT/GLOBK and the GIPSY/OASIS II software packages for GPS analysis and compare the results. The solution has an internal accuracy at the level of 0.2 mm/year (1 sigma) for horizontal velocities at the best sites. We also present a revised GIA prediction model. At the best sites, the optimal model agrees with the observations to within 0.4 mm/year. However, the model systematically overpredicts the magnitude of horizontal rates in the north. We discuss limitations in computed and presented GNSS station velocities, where especially possible instability over time causing non-linear pattern in vertical time series are considered. In extension, preliminary results from an investigation applying revised analysis strategies on a sparse subset of the database are presented, indicating possible improvements for the future.

Relative sea level (RSL) data provide important long-term (century to millennial-scale) constraints on ice load history in Greenland. In this paper we present the results of a litho-, bio- and chronostratigraphic study designed to reconstruct RSL during the last millennium from salt marsh deposits recovered from a field site near to the town of Sisimiut, west Greenland. The stratigraphy at three marshes typically records an upwards transition from freshwater to salt marsh deposits. We use a quantitative (transfer function) and subjective model to reconstruct palaeomarsh elevation and changes in mean tide level (MTL) from 16 sediment profiles from these marshes. These palaeomarsh elevations are placed in a chronological framework established by 18 radiocarbon dated index points. Both models yield similar results and show MTL rose from −0.60 ± 0.20 m at c. 600 cal a BP to reach −0.10 ± 0.20 m at c. 400 cal a BP. After this time, MTL remained close to present (±0.20 m) until the present day although low sedimentation rates limit the resolution of our reconstructions during this interval. The initial rise in RSL can be explained by the dominance of non-Greenland processes, notably the collapse of the Laurentide forebulge, over local (Greenland) solid Earth uplift caused by postglacial ice unloading. This is despite some reloading of the crust that occurred during the neoglacial expansion of the Greenland Ice Sheet in this part of west Greenland. The slow-down in RSL at 400 cal a BP does not record either a change in the rate of Laurentide forebulge collapse or a change in eustatic sea level. We argue instead that this slow-down records the effects of a sustained reduction in local (Greenland) ice mass that persists over most of the past 400 years. The latter interval is widely acknowledged as a period of generally cooler than present conditions associated with the later stages of the Little Ice Age. During this period, field evidence suggests that in many areas the ice sheet had reached its maximum late Holocene extent. It is not obvious at this stage how to reconcile an expanding ice sheet with a reduction in ice load during this interval although we hypothesise it could reflect one or more of; i) a change in ice sheet dynamics; ii) reduced mass accumulation caused by cold and dry conditions, and; iii) a lagged response to earlier periods of climate warming.

Field data constraining the rate and spatial pattern of deglaciation and relative sea-level (RSL) change on the Antarctic Peninsula (AP) are relatively sparse, but are needed to improve regional ice sheet and RSL change models, and contribute to better model predictions of future sea-level rise. We investigated the geomorphology, sedimentology and quartz-fraction single aliquot regeneration optically-stimulated luminescence (SAR-OSL) geochronology of elevated deltas around two epishelf lakes, Ablation Lake (AL) and Moutonnee Lake (ML), Alexander Island, Antarctic Peninsula. AL and ML are dammed by George VI Ice Shelf, and maintain a direct hydraulic connection to the sea; hence, their water levels are controlled by changes in RSL. Our aim was to provide new terrestrial constraints on RSL and deglaciation for the southern AP by comparing the formation processes, age and altitude of the AL and ML deltas with: (1) existing RSL curves for the AP; (2) isostatically-coupled AP ice sheet models, and (3) existing AP deglaciation history and SAR-OSL ages from elevated deltas around the nearby inland Hodgson Lake (HL). Although there was insufficient quartz in the ML samples for SAR-OSL dating, the 4.6 ± 0.4 ka SAR-OSL age of the elevated delta at AL represents the last time active deltas were forming higher than present day lake level, and implies: (1) a fall in RSL of up to 14.4 m since the mid-Holocene in this part of Alexander Island, which is consistent with existing field-based RSL chronologies for the AP; (2) relatively smaller ice masses than suggested by some (but not all) isostatically-coupled ice sheet models since the mid-Holocene, and (3) significant mid-Holocene thinning of the AP ice sheets, which is consistent with regional sediment core data and cosmogenic exposure ages, and the 4.4 ± 0.7 ka SAR-OSL age of the lowermost HL delta.

We constrain a three-dimensional thermomechanical model of Greenland ice sheet (GrIS) evolution from the Last Glacial Maximum (LGM, 21 ka BP) to the present-day using, primarily, observations of relative sea level (RSL) as well as field data on past ice extent. Our new model (Huy2) fits a majority of the observations and is characterised by a number of key features: (i) the ice sheet had an excess volume (relative to present) of 4.1 m ice-equivalent sea level at the LGM, which increased to reach a maximum value of 4.6 m at 16.5 ka BP; (ii) retreat from the continental shelf was not continuous around the entire margin, as there was a Younger Dryas readvance in some areas. The final episode of marine retreat was rapid and relatively late (c. 12 ka BP), leaving the ice sheet land based by 10 ka BP; (iii) in response to the Holocene Thermal Maximum (HTM) the ice margin retreated behind its present-day position by up to 80 km in the southwest, 20 km in the south and 80 km in a small area of the northeast. As a result of this retreat the modelled ice sheet reaches a minimum extent between 5 and 4 ka BP, which corresponds to a deficit volume (relative to present) of 0.17 m ice-equivalent sea level. Our results suggest that remaining discrepancies between the model and the observations are likely associated with non-Greenland ice load, differences between modelled and observed present-day ice elevation around the margin, lateral variations in Earth structure and/or the pattern of ice margin retreat.

Perturbations to the Earth's gravity field and solid surface associated with glacial isostatic adjustment (GIA) cause the total (observable) sea-level change to depart from the eustatic curve, which is defined as a spatially uniform height shift of the ocean surface to accommodate any mass gained/lost from grounded ice. In this study we apply a state-of-the-art model of GIA-induced sea-level change to quantify the magnitude and spatial form of this departure at the global scale for a range of model parameters with an aim to identify regions that are well suited to obtain accurate and precise estimates of eustatic sea level (and therefore past grounded ice volume). In general, our results indicate that eustatic sea level is not a directly measurable quantity and so must be estimated by subtracting a model-derived estimate of non-eustatic contributions from observations. In this regard, we use our results to isolate regions where this procedure can be applied with optimal accuracy and precision. That is, where (1) the GIA predictions are relatively insensitive to plausible ranges in input parameters and (2) where the non-eustatic contribution is small (i.e., the predicted sea level closely approximates the eustatic value). We present maps that can be employed by the field community to identify areas where sea-level reconstructions would be well suited to arrive at robust estimates of eustatic sea level. Note that sea-level changes associated with tectonic motion and changes in ocean water temperature/salinity, which also lead to departures from eustasy, are not considered in this analysis.

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

We compare numerical predictions of glaciation-induced sea-level change to data from 8 locations around the Antarctic coast in order to test if the available data preclude the possibility of a dominant Antarctic contribution to meltwater pulse IA (mwp-IA). Results based on a subset of 7 spherically symmetric earth viscosity models and 6 different Antarctic deglaciation histories indicate that the sea-level data do not rule out a large Antarctic source for this event. Our preliminary analysis indicates that the Weddell Sea is the most likely source region for a large (∼9 m) Antarctic contribution to mwp-IA. The Ross Sea is also plausible as a significant contributor (∼5 m) from a sea-level perspective, but glacio-geological field observations are not compatible with such a large and rapid melt from this region. Our results suggest that the Lambert Glacier component of the East Antarctic ice sheet experienced significant retreat at the time of mwp-IA, but only contributed ∼0.15 m (eustatic sea-level change). All of the ice models considered under-predicted the isostatic component of the sea-level response in the Antarctic Peninsula and the Soya Coast region of the East Antarctic ice sheet, indicating that the maximum ice thickness in these regions is underestimated. It is therefore plausible that ice melt from these areas, the Antarctic Peninsula in particular, could have made a significant contribution to mwp-IA.

We have considered the influence of ocean temperature and salinity changes, mass changes of the Greenland ice sheet (GIS) and the isostatic response of the solid earth to the most recent glacial cycle on 20th century sea-level change along the US east coast with the intention of better understanding the observed signal as well as determining the potential of the tide gauge data for constraining the recent (past 50–100 yr) mass balance of the GIS and earth viscosity structure. Our results show that the signal due to steric changes is large and displays a complex spatial variation which can account for a significant portion of the observed signal. In contrast, that due to changes in the GIS is relatively small and insensitive to the specific geometry of the mass balance model adopted. As a consequence, the tide gauge data alone are not capable of providing useful constraints on either the magnitude or form of recent GIS mass balance. Our inference of mantle viscosity structure based on the tide gauge data was affected dramatically when the steric effect was accounted for: An earth model with an upper mantle viscosity of 8 × 1019 Pa s and a lower mantle viscosity of 5 × 1022 Pa s produced the best fit to the steric-corrected data; the optimal fit to the uncorrected data was obtained for upper and lower mantle viscosities of 5 × 1020 Pa s and 1022 Pa s, respectively.

Holocene data from the Caribbean and the Atlantic coast of South America have been critically assessed and a subset of the best quality data are presented. These data cover a large north–south geographic extent and display a distinct spatial variation. We make the first comparisons of this data set to predictions based on a realistic model of glaciation-induced sea-level change with the main aims of understanding the cause of the observed spatial trend and estimating a eustatic signal for the Holocene. The spatial variation is dominated by the influence of the ice and ocean mass redistribution on sea-level change, with the ice-induced effect dominating the observed north–south trend. A best-fitting model is applied to estimate a Holocene eustatic signal from the observations. We find that the model-corrected data are consistent with a relatively rapid rise of 7–8 mm/yr in the early Holocene with a marked reduction in this rate around 7 cal. kyr BP. From this time until present, the model-corrected data suggest that the volume of mass transfer between ice sheets and oceans was no more than ∼ ± 1 m (eustatic sea-level equivalent).

The permanently recording BIFROST (Baseline Inferences for Fennoscandian Rebound Observations, Sea Level and Tectonics) GPS network was set into operation during the early to mid-1990s to monitor the three-dimensional crustal deformation field in Fennoscandia. We have employed 2500 days of BIFROST GPS data to estimate rates of baseline component change (length, transverse and up). Baselines are less sensitive than single-site position estimates to perturbations in satellite orbits and reference frame realizations. Hence, the baseline time series represent a particularly robust data set for model parameter estimation. We use this data set to outline an evaluation scheme for GPS observations of intraplate horizontal movements. Our results show that the data can be used to infer parameters in a model that simulates the glacial isostatic adjustment (GIA) of the region. This process is widely believed to dominate the present-day deformation field, and analysis of the length and transverse components support this view. The data prefer an elastic lithosphere of thickness 120 km and an upper mantle viscosity in the range ( 3 – 10 ) × 1 0 20 Pa s (to 95% confidence). These results are consistent with those obtained in a previous analysis that considered single-site position estimates. This suggests that the problems associated with perturbations in satellite orbits and reference frame realizations have not significantly impacted the analysis of single-site positions from the BIFROST time series. Subtracting the best-fitting GIA model predictions from the observed baseline rates leaves a horizontal residual field of magnitude less than 1 mm year−1.

It has long been recognised that sea levels along the shores of Atlantic Canada have been rising rapidly during the Holocene in response to isostatic crustal movements. New sea-level data for the Bay of Fundy coast of southern New Brunswick (Little Dipper Harbour) and the Atlantic coast of Nova Scotia (Chezzetcook Inlet) show that late Holocene average rates of sea-level rise in these areas have been 1.0 and 2.5 m per 1000 yr, respectively. Numerical model calculations suggest that the high rates of sea-level rise are due to crustal subsidence produced by the combined effects of Laurentide ice loading (forebulge collapse) and ocean loading of the Scotian shelf. Although ice loading is the dominant contributor to the regional sea-level pattern, ocean loading is also important, contributing up to ∼40% of the total crustal subsidence in some areas. Tide gauges record rates of sea-level rise during the 20th century that are 0.7–1.9 mm/yr higher than late Holocene trends, with the highest residuals occurring in the Bay of Fundy.

Late Holocene sea-level highstands of amplitude ∼3 m are endemic to equatorial ocean basins. These highstands imply an ongoing and moderate, sub-mm/yr, sea-level fall in the far field of the Late Pleistocene ice cover that has long been linked to the process of glacial isostatic adjustment (GIA; Clark et al., 1978). Mitrovica and Peltier (1991) coined the term ‘equatorial ocean syphoning’ to describe the GIA-induced sea-level fall and they provided the first physical explanation for the process. They argued that water migrated away from far-field equatorial ocean basins in order to fill space vacated by collapsing forebulges at the periphery of previously glaciated regions. We provide a complete physical explanation for the origin of equatorial ocean syphoning, and the associated development of sea-level highstands, using numerical solutions of the equation that governs meltwater redistribution on spherical, viscoelastic Earth models. In particular, we separate the total predicted sea-level change into contributions associated with ice and meltwater loading effects, and, by doing so, isolate a second mechanism that contributes significantly to the ocean syphoning process. Ocean loading at continental margins induces a ‘levering’ of continents and a subsidence of offshore regions that has also long been recognized within the GIA literature (Walcott, 1972). We show that the influx of water into the volume created by this subsidence produces a sea-level fall at locations distant from these margins—indeed over the major ocean basins—that is comparable in amplitude to the syphoning mechanism isolated by Mitrovica and Peltier (1991).

We predict sea-level change since the Last Glacial Maximum (LGM) at four far-field sites (Barbados, Bonaparte Gulf, Huon Peninsula and Tahiti) using a revised theoretical formalism. This formalism includes a time-varying shoreline geometry, an accurate treatment of sea-level variations near regions of ice retreat and the influence of glacial cycle perturbations in Earth rotation. We elucidate the physics of far-field sea-level change by de-constructing the predicted signal into spatially uniform versus spatially varying components, as well as isolating contributions due to the ice load, the ocean load and the rotational potential. We demonstrate that the sum of these three contributions plus the spatially uniform sea-level fall associated the with retreat of grounded marine ice sheets can produce a significant difference between predictions of sea-level change at far-field sites and the eustatic (or meltwater) curve associated with the adopted ice model. This difference is site and time dependent. For example, the total sea-level rise since the LGM predicted using our ice–earth model can be either smaller (e.g., Barbados) or larger (e.g., Tahiti) than the eustatic sea-level change. Finally, we review procedures that have been applied to estimate continental ice volume from far-field sea-level observations and apply these procedures to data from Barbados and Bonaparte Gulf. Applying an ice-earth model that is tuned to fit the Barbados data, we estimate a change in grounded ice volume from the LGM to the present of 43.5–51×106 km3 based on Barbados data and an LGM ice volume estimate of 51×106 km3 based on Bonaparte Gulf data. Our results for the Bonaparte Gulf data are consistent with the recent study by Yokoyama et al. (Nature 406 (2000) 713). These LGM ice volume estimates map into a eustatic (or meltwater) sea-level rise of 115–135 m. Taking into account plausible variations in the adopted radial earth model introduces uncertainties in the range of ±1.5×106 km3 for ice volume estimates based on the Barbados data.

Recent inferences of mantle viscosity based on convection-related observables (long-wavelength nonhydrostatic geoid and free-air gravity harmonics) indicate the presence of a relatively thin low-viscosity region at the base of the upper mantle. We explore the sensitivity of observables associated with glacial isostatic adjustment (GIA) to the viscosity and thickness of this region. These observables include post-glacial relative sea-level (RSL) variations within previously glaciated areas and in the “far field” of the Late Pleistocene ice sheets, as well as anomalies associated with the rotational state of the planet. The latter include present-day secular variations in the geopotential harmonic J 2 (or, equivalently, variations in the rotation rate) and polar wander speed. We find, in contrast to previous suggestions, that the GIA observables (with the exception of polar wander speed) are sensitive to fine-scale low-viscosity structure at the base of the upper mantle. For example, J 2 predictions can be altered by as much as 2×10 −11 yr −1 by the inclusion of a low-viscosity zone. This signal is sufficient to significantly affect both inferences of mantle viscosity and constraints on the present-day melting of large polar ice sheets (Antarctic, Greenland) that are derived using this observable. Indeed, if a low-viscosity region exists, then models that do not include it can overestimate recent polar melting events by as much as 0.5 mm/yr of equivalent eustatic sea-level rise.

In recent years there have been significant advances in the observational and modeling techniques used to reconstruct and interpret paleo records that relate to changes in sea-level and/or ice extent. This special issue, which presents contributions from the PALeo constraints on Sea-level (PALSEA) PAGES/IMAGES/WUN 1 working group, reflects a number of these developments. Here, we provide an overview of the papers presented in this special issue. By bringing insights from very different paleo-archives and methodologies together, we hope that this special issue will encourage new ideas and collaborations in this area of climate science.