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Determining recent Antarctic ice volume changes from satellite altimeter measurements of ice height requires a correction for contemporaneous vertical crustal deformation. This correction must consider two main sources of crustal deformation: (1) ongoing glacial isostatic adjustment (GIA), that is, the deformational, gravitational and rotational response to late Pleistocene and Holocene ice and ocean mass changes; and (2) modern ice mass flux. In this study, we seek to quantify the uncertainties associated with each of these corrections. Corrections of ice height changes for (1) have generally involved the adoption of global models of GIA defined by some preferred combination of ice history and mantle viscoelastic structure. We have computed the GIA correction generated from a coupled ice sheet – sea level model and a realistic earth model incorporating three-dimensional viscoelastic structure. Integrating the difference between this correction and those from recent GIA analyses widely adopted in the literature yields an uncertainty in total present-day ice volume change equivalent to approximately 10 % of Antarctic ice mass loss inferred for the previous decade. This reinforces earlier work indicating that ice histories characterized by relatively high excess ice volume at the Last Glacial Maximum may be introducing significant error in estimates of modern melt rates. Regarding correction (2), a spatially invariant scaling has commonly been used to convert GIA-corrected ice height changes obtained from satellite altimetry into ice volume estimates. We adopt modeling results based on a projection of Antarctic ice mass flux over the next 40 years to demonstrate a spatial variability in the scaling of up to 10 % across the ice sheet. Furthermore, using these calculations, we find an error in the projected net ice volume change of up to 4.5 mm GMSL equivalent forty years after present, with most of the difference arising in areas of West Antarctica above mantle zones of low viscosity. [ABSTRACT FROM AUTHOR]

Models of glacial isostatic adjustment (GIA) play a central role in the interpretation of various geologic and geodetic data to understand and simulate past and future changes in ice sheets and sea level, and infer rheological properties of the deep Earth. A relatively recent advance has been the development of models that include 3D Earth structure, as opposed to 1D, spherically symmetric structure. However, a major limitation in employing 3D GIA models is their high computational expense. As such, we have developed a method using artificial neural networks (ANNs) and the Tensorflow library to emulate the influence of 3D Earth models with the goal of more affordably constraining the parameter space of these models: specifically the radial (1D) viscosity profile upon which the lateral variations are added. This study provides an initial "proof of concept" assessment of using ANNs to emulate the influence of lateral Earth structure on GIA model output. Our goal is to test whether the fast surrogate model can accurately predict the difference in these outputs (i.e., RSL and uplift rates) for the 3D case relative to the SS case. If so, the surrogate model can be used with a computationally efficient SS (Earth) GIA model to generate output that reproduces output from a 3D (Earth) GIA model. Evaluation of the surrogate model performance for deglacial RSL indicates that it is able to provide useful estimates of this field throughout the parameter space when trained on only ≈ 15 % (≈ 50) of the parameter vectors considered (330 in total). Our results indicate that the ANN:model misfits, while not negligible, are of a scale such that useful predictions of deglacial RSL changes can be made. We applied the surrogate model in a model:data comparison exercise using RSL data distributed along the North American coasts from the Canadian Arctic to the US Gulf coast. We find that the surrogate model is able to successfully reproduce the data:model misfit values such that the region of minimum misfit either overlaps the 3D GIA model results, or is within two increments in the parameter space. The surrogate model can, therefore, be used to accurately explore this aspect of the 3D Earth model parameter space. While the 3D Earth models can outperform the SS Earth models for some regional subsets of the RSL data set, the SS Earth models still produce better fits overall. In summary, this work demonstrates the utility of machine learning in 3D Earth GIA modelling and so future work to expand on this analysis is warranted. [ABSTRACT FROM AUTHOR]

A large ensemble of ice sheet projections to the end of the 21st century have been compiled within community-based initiatives. These ensembles allow for assessment of uncertainties in projections associated with climate forcing and a wide range of parameters governing ice sheet and shelf dynamics, including ice-ocean interactions. Herein, we compute geographically variable sea level 'fingerprints' associated with ∼320 simulations of polar ice sheet projections included in the Ice Sheet Model Intercomparison Project for CMIP6 and ∼180 projections of glacier mass changes from the Glacier Model Intercomparison Project. We find a strong correlation (coefficient > 0.97) between all fingerprints of Greenland Ice Sheet projections when considering a global region outside the near field of the ice sheet. Consistency in the fingerprints for the Antarctic Ice Sheet (AIS) projections is much weaker, though correlation coefficients > 0.80 were found for all projections with global mean sea level (GMSL) greater than 10 cm. The far-field variability in the fingerprints associated with the AIS is due in large part to the sea level change driven by Earth rotation changes. The size and position of the AIS on the south pole makes the rotational component of the sea level fingerprint highly sensitive to the geometry of the ice mass flux, a geometry that becomes more consistent as the GMSL associated with the ice sheet projection increases. Finally, the fingerprints of glacier mass flux show an intermediate level of consistency, with contributions from Antarctic glaciers being the primary driver of decorrelation. [ABSTRACT FROM AUTHOR]

We present the first results that focus on the influence of lateral Earth structure on Greenland glacial isostatic adjustment (GIA) using a model that can explicitly incorporate 3-D Earth structure. In total, eight realizations of lateral viscosity structure were developed using four global seismic velocity models and two global lithosphere (elastic) thickness models. Our results show that lateral viscosity structure has a significant influence on model output of both deglacial relative sea level (RSL) changes and present-day rates of vertical land motion. For example, lateral structure changes the RSL predictions in the Holocene by several tens of metres in many locations relative to the 1-D case. Modelled rates of vertical land motion are also significantly affected, with differences from the 1-D case commonly at the mm yr−1 level and exceeding 2 mm yr−1 in some locations. The addition of lateral structure considered here is unable to account for previously identified data model RSL misfits in northern and southern Greenland, suggesting limitations in the adopted ice model and/or the existence of processes not included in our model. Our results show large data model discrepancies in uplift rates when applying a 1-D viscosity model tuned to fit the RSL data; these discrepancies cannot be reconciled by adding the realizations of lateral structure considered here. In many locations, the spread in model output for the eight different 3-D earth models is of similar amplitude or larger than the influence of lateral structure (as defined by the average of all eight model runs). This reflects the differences between the four seismic and two lithosphere models used and implies a large uncertainty in defining the GIA signal given that other aspects that contribute to this uncertainty (e.g. scaling from seismic velocity to viscosity) were not considered in this study. In order to reduce this large model uncertainty, an important next step is to develop more accurate constraints on Earth structure beneath Greenland based on regional geophysical data sets. [ABSTRACT FROM AUTHOR]

A gravitationally self-consistent, global sea level model with 3D viscoelastic Earth structure is interactively coupled to a 3D dynamic ice sheet model, and the coupled model is applied to simulate the evolution of ice cover, sea level changes, and solid Earth deformation over the last deglaciation, from 40 ka to the modern. The results show that incorporating lateral variations in Earth's structure across Antarctica yields local differences in the modeled ice history and introduces significant uncertainty in estimates of both relative sea level change and modern crustal motions through the last deglaciation. An analysis indicates that the contribution of glacial isostatic adjustment to modern records of sea level change and solid Earth deformation in regions of Antarctica underlain by low mantle viscosity may be more sensitive to ice loading during the late Holocene than across the last deglaciation. [ABSTRACT FROM AUTHOR]

It 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 latter, for example, reveals an underappreciated sensitivity of ongoing and future sea level change along the U.S. West Coast to the geometry of ice mass flux in the region. Finally, the practical utility of these kernels is illustrated by computing sea level predictions at a suite of sites associated with annual variability in Greenland ice mass since 2003 constrained by satellite gravity measurements. [ABSTRACT FROM AUTHOR]

We determine the contribution of glacial isostatic adjustment ( GIA) to future relative sea-level change for the North American coastline between Newfoundland and Texas. We infer GIA model parameters using recently compiled and quality-assessed databases of past sea-level changes, including new databases for the United States Gulf Coast and Atlantic Canada. At 13 cities along this coastline, we estimate the GIA contribution to range from a few centimeters (e.g., 3 [−1 to 9] cm Miami) to a few decimeters (e.g., 18 [12-22] cm, Halifax) for the period 2085-2100 relative to 2006-2015 (1− σ ranges given). We provide estimates of uncertainty in the GIA component using two different methods; the more conservative approach produces total ranges (1− σ confidence) that vary from 3 to 16 cm for the cities considered. Contributions from ocean steric and dynamic changes as well as those from changes in land ice are also estimated to provide context for the GIA projections. When summing the contributions from all three processes at the 13 cities considered along this coastline, using median or best-estimate values, the GIA signal comprises 5-38% of the total depending on the adopted climate forcing and location. The contributions from ocean dynamic/steric changes and ice mass loss are similar in amplitude but with spatial variation that approximately cancels, resulting in GIA dominating the net spatial variability north of 35°N. [ABSTRACT FROM AUTHOR]

Sea-level history in the Red Sea region has commonly been interpreted as an accurate proxy for global mean sea level (GMSL), which can be used to constrain global ice volumes and inform a diverse range of regional paleoclimate studies. Previous modeling work has demonstrated, however, that glacial isostatic adjustment (GIA) processes may introduce significant departures from GMSL in this region. The GIA signal is a complex combination of deformational, gravitational, and rotational effects arising from shifting ice and water surface loads and consists of long-wavelength effects superimposed by a short-wavelength signal associated with "continental levering" – a response to local meltwater loading. In this study, we revisit the effects of GIA in the Red Sea region using Earth models characterized by 3-D variations in mantle viscoelastic structure and lithospheric thickness, focusing on the period from Last Glacial Maximum (LGM) to present day. We find that the presence of the Red Sea Rift and low-viscosity upper mantle acts to amplify sea-level rise associated with continental levering, yielding a more pronounced rise for sites toward the center of the Red Sea during deglaciation in comparison to GMSL. In contrast, coastal sites experience a net GIA-induced sea-level fall that acts in opposition to the GMSL rise. Furthermore, while the maximum departure from GMSL occurs close to LGM for northern sites, the GIA signal can peak as late as 14 ka for southern sites. Simulations based on 3-D Earth models tend to show a smaller departure from GMSL than 1-D predictions for most coastal sites, including at the Strait of Bab el-Mandeb at the mouth of the Red Sea, and typically peak at ∼10 m. The opposite is true for sites close to the rift: at these locations the difference between the 1-D and 3-D simulations can reach ∼20 m. We therefore conclude that any mapping from local sea level to GMSL is both location and time dependent and cannot be captured by a simple linear scaling. • Red Sea sea level history does not relate to global mean sea level via linear scaling. • Discrepancy from global mean is model dependent but significant for all models tested. • 3-D models predict greater effects of glacial isostatic adjustment than 1-D models. • Implications for coastal human settlement and migration in the region. [ABSTRACT FROM AUTHOR]

Highlights • Atlantic and Gulf coast relative sea level data require peripheral bulge suppression. • Bulge suppression requires high mantle viscosity in 1-D Earth models. • Bulge suppression also obtained by adding plausible lateral viscosity variations. • Lateral viscosity structure can thus reconcile discrepant 1-D viscosity inferences. Abstract 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. [ABSTRACT FROM AUTHOR]

Records of post-glacial sea-level change in the Cascadia subduction zone (North American Pacific coast) analyzed using one-dimensional Earth models suggest upper mantle viscosities <~1020 Pa·s, significantly weaker than those based on observations from cratonic regions in North America. We explore this variability by comparing predictions based on a three-dimensional (3-D) model of the glacial isostatic adjustment process with relative sea-level histories from sites along the Oregon and Washington (USA) and Hudson Bay (northeastern Canada) coasts. We demonstrate that a 3-D mantle viscosity field, with a geometry constrained by seismic tomography and that reflects the tectonic setting of the Cascadia subduction zone, can simultaneously reconcile the rapid rate of late Holocene adjustment observed in central Cascadia and the longer decay times of post-glacial uplift curves in Hudson Bay. Specifically, below the Cascadia subduction zone, this field is characterized by a shallow subduction wedge of low viscosity (<1020 Pa·s) and higher viscosity material associated with subduction of the Juan de Fuca plate. [ABSTRACT FROM AUTHOR]

Predictive modeling of submerged archaeological sites requires accurate sea-level predictions in order to reconstruct coastal paleogeography and associated geographic features that may have influenced the locations of occupation sites such as rivers and embayments. Earlier reconstructions of the paleogeography of parts of the western U.S. coast used an assumption of eustatic sea level, but this neglects the large spatial variations in relative sea level (RSL) associated with glacial isostatic adjustment (GIA) and tectonics. Subsequent work using a one-dimensional (1-D) solid Earth model showed that reconstructions that accounted for GIA result in significant differences from those based on eustatic sea level. However, these analyses neglected the complex three-dimensional (3-D) solid Earth structure associated with the Cascadia subduction zone that has also strongly influenced RSL along the Oregon-Washington (OR-WA) coast, requiring that the paleogeographic reconstructions must also account for this effect. Here we use RSL predictions from a 3-D solid Earth model that have been validated by RSL data to update previous paleogeographic reconstructions of the OR-WA coast for the last 12 kyr based on a 1-D solid Earth model. The large differences in the spatial variations in RSL on the OR-WA continental shelves predicted by the 3-D model relative to eustatic and 1-D models demonstrate that accurate reconstructions of coastal paleogeography for predictive modeling of submerged archaeological sites need to account for 3-D viscoelastic Earth structure in areas of complex tectonics. [ABSTRACT FROM AUTHOR]

The mapping between far-field relative sea level (RSL) records and changes in ice volume or global mean sea level (GMSL) involves a correction for glacial isostatic adjustment (GIA). This mapping is thus sensitive to uncertainties inherent to GIA modeling, including the spatio-temporal history of ice mass changes and viscoelastic Earth structure. Here, we investigate the effect of incorporating lateral variations in Earth structure on predicting far-field sea level in order to determine if this source of model uncertainty significantly impacts estimates of global ice volume at the Last Glacial Maximum (LGM). We consider a set of forty 3-D simulations that sample different Earth model parameters: the adopted lithospheric thickness, the seismic velocity model used to infer lateral temperature variations, the scaling factor used in the conversion from temperature to viscosity, and the spherically averaged "background" viscosity profile. In addition, we consider results based on two ice histories. We present global maps of the differences between these simulations and a set of 1-D simulations at the LGM, as well as RSL histories at 5 locations that have been previously considered in estimates of ice volume at LGM: Barbados, two sites at the Great Barrier Reef, Bonaparte Gulf and Sunda Shelf. We find that the difference between inferences of global mean sea level (GMSL) at LGM based on 3-D and 1-D Earth models peaks in Barbados with differences ranging from ∼2.5 to 11 m, with a mean of ∼6–7 m. At the other sites, the difference ranges from ∼2 to −8 m, with mean differences between ∼0 and −3 m. After comparing different pairs of simulations, we conclude that, in general, the impact of varying the seismic model, lithospheric thickness model, background 1-D model, and scaling factor from temperature to viscosity is significant at far-field sites. Finally, while we do not find a consistent signal at the above far-field sites that would help to reconcile the LGM ice volumes estimated from GIA studies and those estimated from summing regional ice sheet reconstructions, the impact is nonetheless large enough that GIA analyses of RSL records in the far field of ice sheets should include 3-D viscoelastic Earth models. • Far-field RSL estimates of LGM ice volume do not match those from ice sheet reconstructions. • LGM ice volume estimates from RSL records are subject to GIA model uncertainty. • We study uncertainties related to lateral variations in Earth viscosity structure. • Incorporating these lateral variations does not reconcile LGM ice volume estimates. • GIA analyses should account for lateral variations in Earth structure nonetheless. [ABSTRACT FROM AUTHOR]

We present a suite of gravitationally self-consistent predictions of sea-level change since Last Glacial Maximum (LGM) in the vicinity of the Bosphorus and Dardanelles straits that combine signals associated with glacial isostatic adjustment (GIA) and the flooding of the Black Sea. Our predictions are tuned to fit a relative sea level (RSL) record at the island of Samothrace in the north Aegean Sea and they include realistic 3-D variations in viscoelastic structure, including lateral variations in mantle viscosity and the elastic thickness of the lithosphere, as well as weak plate boundary zones. We demonstrate that 3-D Earth structure and the magnitude of the flood event (which depends on the pre-flood level of the lake) both have significant impact on the predicted RSL change at the location of the Bosphorus sill, and therefore on the inferred timing of the marine incursion. We summarize our results in a plot showing the predicted RSL change at the Bosphorus sill as a function of the timing of the flood event for different flood magnitudes up to 100 m. These results suggest, for example, that a flood event at 9 ka implies that the elevation of the sill was lowered through erosion by ∼14–21 m during, and after, the flood. In contrast, a flood event at 7 ka suggests erosion of ∼24–31 m at the sill since the flood. More generally, our results will be useful for future research aimed at constraining the details of this controversial, and widely debated geological event. [ABSTRACT FROM AUTHOR]

Prior to inferring ice sheet stability from past interglacial sea-level records, these records must first be corrected for the contaminating effects of glacial isostatic adjustment (GIA). Typical GIA corrections, however, neglect variability in the signal that may be introduced by Earth's 3-D rheological structure. We predict sea-level changes due to a collapse of the West Antarctic Ice Sheet (WAIS) over an idealized 6 kyr-duration interglacial using four viscoelastic Earth models. Two of these are 3-D viscosity models inferred from seismic tomography. The third is a 1-D (i.e., depth varying) viscosity model that is equivalent to the spherically averaged "background" viscosity profile adopted in both 3-D Earth models. The fourth is a 1-D model that has a higher upper mantle viscosity but still falls within the class of models inferred from independent global GIA studies. We find that the discrepancy between 3-D and 1-D Earth model calculations of sea level in the far field of the melt zone is of order 0.3 m or less, with the 1-D Earth models producing higher sea level than the 3-D simulations. This value is 10% of the global mean sea-level (GMSL) rise associated with modeled ice sheet collapse by the end of the model interglacial (∼3 m) and a similar fraction of far-field sea-level changes. However, the value is a significantly larger fraction (∼60%) of the geographically variable (i.e., non-GMSL) component of the far-field sea-level signal due to GIA associated with modeled WAIS collapse (±0.5 m). Neglecting lateral variations in Earth structure in modeling the response to excess melting of WAIS during the interglacial compounds any error introduced by neglecting such structure in predictions of interglacial sea-level change driven by the preceding glacial cycle. • Interglacial ice sheet reconstructions constrained by GMSL require GIA corrections. • We predict sea-level change due to WAIS collapse using four Earth models. • 1-D Earth models underestimate water flux out of West Antarctica. • 3-D models yield greater subsidence of the peripheral bulge. • 1-D models overestimate sea level by up to ∼0.3 m in the far field. [ABSTRACT FROM AUTHOR]