Glacial Isostatic Adjustment Models Research Articles

Late Holocene relative sea-level records from coral microatolls in Singapore

Late Holocene relative sea-level (RSL) data are important to understand the drivers of RSL change, but there is a lack of precise RSL records from the Sunda Shelf. Here, we produced a Late Holocene RSL reconstruction from coral microatolls in Singapore, demonstrating for the first time the utility of Diploastrea heliopora microatolls as sea-level indicators. We produced 12 sea-level index points and three marine limiting data with a precision of < ± 0.2 m (2σ) and < ± 26 years uncertainties (95% highest density region). The data show a RSL fall of 0.31 ± 0.18 m between 2.8 and 0.6 thousand years before present (kyr BP), at rates between − 0.1 ± 0.3 and − 0.2 ± 0.7 mm/year. Surface profiles of the fossil coral microatolls suggest fluctuations in the rate of RSL fall: (1) stable between 2.8 and 2.5 kyr BP; (2) rising at ~ 1.8 kyr BP; and (3) stable from 0.8 to 0.6 kyr BP. The microatoll record shows general agreement with published, high-quality RSL data within the Sunda Shelf. Comparison to a suite of glacial isostatic adjustment (GIA) models indicate preference for lower viscosities in the mantle. However, more high quality and precise Late Holocene RSL data are needed to further evaluate the drivers of RSL change in the region and better constrain GIA model parameters.

GNET Derived Mass Balance and Glacial Isostatic Adjustment Constraints for Greenland

AbstractMonitoring the Greenland mass balance (GMB) is crucial in the context of global sea level rise. Currently, three main methods are used to measure GMB, with the primary source of uncertainty arising from the glacial isostatic adjustment (GIA) contribution. Here, we propose a novel approach based on a simple methodology that uses the entire Greenland GNSS network (GNET) as an instrument to monitor the present‐day mass changes. Our method is validated against GRACE‐derived GMB, and we find a very good agreement. This leads to an independent methodology for estimating present‐day mass changes from GNSS, bridging the gap between GRACE and GRACE‐FO in GMB estimates. Through a combined analysis of GMB from GRACE and GNET, we identify a consistency relation between the gravity and uplift signature of GIA, providing a new robust constraint for GIA models.

Decoding the Interplay Between Tidal Notch Geometry and Sea‐Level Variability During the Last Interglacial (Marine Isotope Stage 5e) High Stand

AbstractRelic coastal landforms (fossil corals, cemented intertidal deposits, or erosive features carved onto rock coasts) serve as sea‐level index points (SLIPs), that are widely used to reconstruct past sea‐level changes. Traditional SLIP‐based sea‐level reconstructions face challenges in capturing continuous sea‐level variability and dating erosional SLIPs, such as tidal notches. Here, we propose a novel approach to such challenges. We use a numerical model of cliff erosion embedded within a Monte Carlo simulation to investigate the most likely sea‐level scenarios responsible for shaping one of the best‐preserved tidal notches of Last Interglacial age in Sardinia, Italy. Results align with Glacial Isostatic Adjustment model predictions, indicating that synchronized or out‐of‐sync ice‐volume shifts in Antarctic and Greenland ice sheets can reproduce the notch morphology, with sea level confidently peaking at 6 m and only under a higher than present erosion regime. This new approach yields insight into sea‐level trends during the Last Interglacial.

Effects of Andrade and Burgers rheologies on glacial isostatic adjustment modeling in Antarctica

Variations in ice mass deform the Earth and modify its gravity field, a process known as Glacial Isostatic Adjustment (GIA). GIA in Antarctica remains poorly constrained due to the cumulative effect of past and present ice-mass changes, the unknown history of the past ice-mass change, and the uncertainties on the mechanical properties of the Earth. This paper investigates the effect of using Andrade and Burgers viscoelastic rheologies, rather than the commonly used Maxwell rheology, to model GIA-induced deformation in Antarctica. The Love number and Green's function formalism are used to compute the radial surface displacements and the gravity changes induced by the past and present ice-mass changes. We consider an Earth model whose elastic properties and radial structure are averaged from the Preliminary Reference Earth Model and two viscosity profiles to account for the recently published results on the present ice-mass changes. Using the three rheological laws affects the temporal response of the Earth differently, leading to smaller discrepancies than those induced by the two viscosity structures. The differences are the largest between Maxwell and Burgers rheologies during the 100–1000 years following the beginning of the surface-mass change. Results show that using the Andrade and Burgers rheologies allows the Earth to respond on decennial to centennial time scales, up to 10 m more than Maxwell. Considering only the recent ice-mass changes, the deformation rates derived from Burgers and Andrade rheologies are several times larger than those estimated by Maxwell rheology.

Patterns of glacio‐isostatic adjustment in mainland Scotland: new data from western central Scotland, proximal to the zone of maximum rebound

The results of geomorphological mapping and survey of Lateglacial and Holocene displaced shorelines in the Clyde estuary and around Loch Lomond, western central Scotland are described. On the basis of morphology, sedimentology, altitude and radiocarbon dating, four discrete shorelines are identified and are correlated with previously identified Scottish displaced shorelines. The shoreline formerly referred to as the Main Postglacial Shoreline is renamed the Menteith Shoreline. This body of data, combined with data on displaced shorelines for Scotland as a whole has been analysed using Gaussian quadratic trend surface analysis in order to determine the centre of glacio‐isostatic displacement for each shoreline. These Gaussian models of palaeo‐relative sea‐level suggest that the zone of greatest displacement lay NNW of Loch Lomond in the Lateglacial then moved SSE to the region of Loch Lomond during the Holocene and the Clyde in the Late Holocene. The factors responsible for the movement of the zone of greatest uplift are discussed, including temporal variations in the ice‐sheet thickness, variations in water load in the adjacent sea‐lochs and neotectonic processes. Comparison is made with glacial isostatic adjustment (GIA) models. A sensitivity analysis has been carried out on the use of Gaussian trend surface analysis glacio‐isostatic modelling and this is included in the research evaluation, and reported in full in the Supporting Information files, along with the raw data used throughout this study.

Globally consistent estimates of high-resolution Antarctic ice mass balance and spatially resolved glacial isostatic adjustment

Abstract. A detailed understanding of how the Antarctic ice sheet (AIS) responds to a warming climate is needed because it will most likely increase the rate of global mean sea level rise. Time-variable satellite gravimetry, realized by the Gravity Recovery and Climate Experiment (GRACE) and Gravity Recovery and Climate Experiment Follow-On (GRACE-FO) missions, is directly sensitive to AIS mass changes. However, gravimetric mass balances are subject to two major limitations. First, the usual correction of the glacial isostatic adjustment (GIA) effect by modelling results is a dominant source of uncertainty. Second, satellite gravimetry allows for a resolution of a few hundred kilometres only, which is insufficient to thoroughly explore causes of AIS imbalance. We have overcome both limitations by the first global inversion of data from GRACE and GRACE-FO, satellite altimetry (CryoSat-2), regional climate modelling (RACMO2), and firn densification modelling (IMAU-FDM). The inversion spatially resolves GIA in Antarctica independently from GIA modelling jointly with changes of ice mass and firn air content at 50 km resolution. We find an AIS mass balance of −144 ± 27 Gt a−1 from January 2011 to December 2020. This estimate is the same, within uncertainties, as the statistical analysis of 23 different mass balances evaluated in the Ice sheet Mass Balance Inter-comparison Exercise (IMBIE; Otosaka et al., 2023b). The co-estimated GIA corresponds to an integrated mass effect of 86 ± 21 Gt a−1 over Antarctica, and it fits better with global navigation satellite system (GNSS) results than other GIA predictions. From propagating covariances to integrals, we find a correlation coefficient of −0.97 between the AIS mass balance and the GIA estimate. Sensitivity tests with alternative input data sets lead to results within assessed uncertainties.

Impact of the combination and replacement of SLR-based low-degree gravity field coefficients in GRACE solutions

GRACE and GRACE Follow-On (FO) missions provide time-variable gravity field models of unprecedented quality that allow for the hydrological, oceanic, and ice mass change studies on a global scale. However, the very low-degree coefficients derived from GRACE and GRACE-FO are of inferior quality due to thermal effects acting on satellites and malfunctioning of the onboard accelerometers. Therefore, C20 and C30 coefficients describing the Earth’s oblateness and the pear shape of the Earth, respectively, are being replaced by values derived from satellite laser ranging (SLR) in the standard GRACE solutions. This study assesses the impact of the replacement of low-degree gravity field coefficients in GRACE/GRACE-FO solutions by SLR data on the trend and seasonal signals of ice mass changes in Greenland and Antarctica. We found that the replacement of the low-degree gravity field coefficients changes the estimates of trends by 4, 8, and 22 Gt/year in Greenland, West, and East Antarctica, respectively, depending on the source of SLR coefficients and period for which the coefficients are replaced. In SLR and GRACE solutions, all coefficients of the same order and the same parity of degrees are strongly correlated. Therefore, replacing only two selected coefficients may lead to a biased solution. Thus, we propose to combine GRACE with SLR solutions up to a degree and order 10 × 10 to properly consider the sensitivity of each of the techniques to gravity field coefficients, instead of replacing two coefficients from SLR in GRACE solutions. The combined solution reduces the residual trend of post-glacial rebound from 1.2 to 0.9 Gt/year and from − 57.8 to − 57.0 Gt/year in Scandinavia and South Canada, respectively, when compared to GRACE/GRACE-FO solutions with the replacement of coefficients. The SLR-GRACE combination reduces the noise in the GRACE/GRACE-FO solutions by 8%, from 38 to 35 Gt, in the Fennoscandia region. In the periods when GRACE is at the end of its mission and observations are disrupted, the weights adjust the contribution from SLR and GRACE based on relative ratio of variances from each techniques. Thus, the combined solutions are more consistent with independent geophysical models of glacial isostatic adjustment, and the combinations are affected by smaller noise than the standard GRACE solutions and properly account for different sensitivities of SLR and GRACE techniques to low-degree time-variable gravity field coefficients.

Coastal Lagoonal Evolution within the Early Holocene Humber Estuary, eastern England

ABSTRACTRapid sea‐level rise during the Early Holocene around the North Sea coastal lowlands provided conditions under which estuarine and coastal features, with no modern equivalents, could be created. Investigation of nearshore sediments within the Outer Humber Estuary, UK, has identified a tidal lagoonal system, created between c. 9000 and 7800 cal a bp. These sequences show the initial flooding of a carr woodland, prior to the establishment of more saline conditions as the tidal lagoonal system developed. Inter‐core comparisons, based on diatom and pollen analyses, suggest variations in the structure of a tidal lagoon setting, which probably lasted for only a brief period before being submerged by rising sea levels. The absence of an erosive contact in several of the sequences studied has permitted the creation of the oldest sea‐level index points for the Outer Humber Estuary, providing validation for the current glacial isostatic adjustment models for the region.

Imprint of relative sea level histories on Last Interglacial coral preservation

SUMMARY Fossil corals are commonly used to reconstruct Last Interglacial (∼125 ka, LIG) sea level. Sea level reconstructions assume the water depth at which the coral lived, called the ‘relative water depth’. However, relative water depth varies in time and space due to coral reef growth in response to relative sea level (RSL) changes. RSL changes can also erode coral reefs, exposing older reef surfaces with different relative water depths. We use a simplified numerical model of coral evolution to investigate how sea level history systematically influences the preservation of corals in the Bahamas and western Australia, regions which house &amp;gt;100 LIG coral fossils. We construct global ice histories spanning the uncertainty of LIG global mean sea level (GMSL) and predict RSL with a glacial isostatic adjustment model. We then simulate coral evolution since 132 ka. We show that preserved elevations and relative water depths of modelled LIG corals are sensitive to the magnitude, timing and number of GMSL highstand(s). In our simulations, the influence of coral growth and erosion (i.e. the ‘growth effect’) can have an impact on RSL reconstructions that is comparable to glacial isostatic adjustment. Thus, without explicitly accounting for the growth effect, additional uncertainty is introduced into sea level reconstructions. Our results suggest the growth effect is most pronounced in western Australia due to Holocene erosion, but also plays a role in the Bahamas, where LIG RSL rose rapidly due to the collapsing peripheral bulge associated with Laurentide Ice Sheet retreat. Despite the coral model's simplicity, our study highlights the utility of process-based RSL reconstructions.

Postseismic Deformation in the Northern Antarctic Peninsula Following the 2003 and 2013 Scotia Sea Earthquakes

AbstractLarge earthquakes in the vicinity of Antarctica have the potential to cause postseismic viscoelastic deformation affecting measurements of displacement that are used to constrain models of glacial isostatic adjustment (GIA). In November 2013, a Mw 7.7 strike‐slip earthquake occurred in the Scotia Sea, 650 km from the Antarctic Peninsula. GPS time series from the northern Peninsula show a change in rate after this event, indicating a far‐field postseismic deformation signal is present. In this study, we use a finite element model with a suite of 1D and 3D Earth structures to investigate the extent of postseismic deformation in the Antarctic Peninsula. Model output is compared with GPS time series to place constraints on the Earth structure in this region. The preferred Earth structure has a thin lithosphere combined with a Burgers rheology with steady‐state viscosity of 4 × 1018 Pa s and transient viscosity one order of magnitude lower. Our study shows that including 3D Earth structure does not improve the fit. Using the best fitting Earth structure, we run a forward model of the nearby 2003 Mw 7.6 strike‐slip earthquake and combine the predictions for both earthquakes. We show that postseismic deformation is widespread across the northern Peninsula with rates of horizontal deformation up to 1.65 mm/yr for the period 2015–2020, a signal that persists for decades. These results suggest that much of Antarctica may be deforming due to recent postseismic deformation and this signal needs to be accounted for when using GPS observations to constrain geophysical models.

ENSO may have contributed to sea level changes in the Gulf of Thailand during the Late-Holocene

The Gulf of Thailand is ideal for studying eustatic sea level fluctuations in Southeast Asia due to its shallow basin and tectonic stability. However, our understanding of how this region’s relative sea level (RSL) has fluctuated over the Holocene epoch is far from complete. In this study, we used lithostratigraphy, loss on ignition, grain size, and pollen analyses to reconstruct the environmental changes in the Sam Roi Yot wetland, which was significantly influenced by seawater intrusion, driven by fluctuations in RSL in the Gulf of Thailand. Therefore, the analyzed pollen records of the sediment core from the wetland reflected variabilities in the RSL in the Gulf of Thailand. Subsequently, we found that after a sea level highstand prior to 4000 cal y BP, the RSL gradually fell with two significant regressions at c. 2950 and 1850–1450 cal y BP before rising at 1450–1050 cal y BP and declining after that. The inconsistency between RSL reconstruction based on our results and the global sea level changes simulated by the Glacial Isostatic Adjustment (GIA) model further suggests that long–term El Niño Southern Oscillations (ENSO) variabilities may have played a significant role in sea level changes in the Gulf of Thailand over the Late-Holocene period. Thus, during extended El Niño or La Niña conditions, the sea level would have been consistently lower or higher than expected from eustatic and isostatic processes alone. Overall, this study emphasizes the importance of considering regional factors such as ENSO to understand sea level changes in Southeast Asia.

Glacial Isostatic Adjustment modelling of the mid-Holocene sea-level highstand of Singapore and Southeast Asia

The mid-Holocene sea-level highstand refers to higher-than-present relative sea levels (RSLs) in far-field regions between 7000 and 4000 years ago because of equatorial ocean syphoning and continental levering. But the timing, magnitude, and spatial variability of the highstand are uncertain and the highstand parameterization in Glacial Isostatic Adjustment (GIA) modelling is understudied. Here, we use the RSL records of Southeast Asia to investigate the sensitivity of the mid-Holocene highstand properties to Earth and ice model parameters, including lithospheric thickness, mantle viscosity (both 1D and 3D), and deglaciation history of Antarctica and global ice sheets. We found that the Earth model variation only affects the magnitude of the mid-Holocene highstand unless extraordinary low upper mantle viscosity is used. The timing of the highstand moves towards present and there is an absence of the highstand if upper mantle viscosity is < 4.0 × 1019 Pa s or ≤ 1.0 × 1019 Pa s, respectively. Ice model variation changes both the timing and magnitude of the mid-Holocene highstand. Delaying the ice-equivalent sea level will shift the timing of the highstand later and result in a lower highstand magnitude. We produced a mid-Holocene highstand “treasure map” that considers topography change and accommodation space to guide future RSL data collection efforts in Southeast Asia. The highstand “treasure map” indicates that the northeast and central west coast of Malay-Thai Peninsula, east coast of Sumatra, north coast of Java, and southwest coast of Borneo are very likely (90% probability) to preserve mid-Holocene highstand evidence.

Refining patterns of melt with forward stratigraphic models of stable Pleistocene coastlines

Abstract. The warmest peak of the Last Interglacial (ca. 128–116 ka) is considered a process analogue and is often studied to better understand the effects of a future warmer climate on the Earth's system. In particular, significant efforts have been made to better constrain ice sheet contributions to the peak Last Interglacial sea level through field observation of paleo relative sea level indicators. Along tropical coastal margins, these observations are predominantly based on fossil shallow coral reef sequences, which also provide the possibility of gathering reliable U-series chronological constraints. However, the preservation of many Pleistocene reef sequences is often limited to a series of discrete relative sea level positions within the interglacial, where corals suitable for dating were preserved. This, in turn, limits our ability to understand the continuous evolution of paleo relative sea level through an entire interglacial, also affecting the possibility of unraveling the existence and pattern of sub-stadial sea level oscillations. While the interpretation of lithostratigraphic and geomorphologic properties is often used to overcome this hurdle, geological interpretation may present issues related to subjectivity when dealing with missing facies or incomplete sequences. In this study, we try to step back from a conventional approach, generating a spectrum of synthetic Quaternary subtropical fringing reefs for a site in southwestern Madagascar (Indian Ocean). We use the Dionisos forward stratigraphic model (from Beicip-Franlab) to build a fossil reef at this location. In each model run, we use distinct Greenland and Antarctica ice sheet melt scenarios produced by a coupled ANICE–SELEN glacial isostatic adjustment model. The resulting synthetic reef sequences are then used test these melt scenarios against the stratigraphic record. We propose that this sort of stratigraphic modeling may provide further quantitative control when interpreting Last Interglacial reef sequences.

Simulation of a fully coupled 3D glacial isostatic adjustment – ice sheet model for the Antarctic ice sheet over a glacial cycle

Abstract. Glacial isostatic adjustment (GIA) has a stabilizing effect on the evolution of the Antarctic ice sheet by reducing the grounding line migration following ice melt. The timescale and strength of this feedback depends on the spatially varying viscosity of the Earth's mantle. Most studies assume a relatively long and laterally homogenous response time of the bedrock. However, the mantle viscosity is spatially variable, with a high mantle viscosity beneath East Antarctica and a low mantle viscosity beneath West Antarctica. For this study, we have developed a new method to couple a 3D GIA model and an ice sheet model to study the interaction between the solid Earth and the Antarctic ice sheet during the last glacial cycle. With this method, the ice sheet model and GIA model exchange ice thickness and bedrock elevation during a fully coupled transient experiment. The feedback effect is taken into account with a high temporal resolution, where the coupling time steps between the ice sheet and GIA model are 5000 years over the glaciation phase and vary between 500 and 1000 years over the deglaciation phase of the last glacial cycle. During each coupling time step, the bedrock elevation is adjusted at every ice sheet model time step, and the deformation is computed for a linearly changing ice load. We applied the method using the ice sheet model ANICE and a 3D GIA finite element model. We used results from a regional seismic model for Antarctica embedded in the global seismic model SMEAN2 to determine the patterns in the mantle viscosity. The results of simulations over the last glacial cycle show that differences in mantle viscosity of an order of magnitude can lead to differences in the grounding line position up to 700 km and to differences in ice thickness of the order of 2 km for the present day near the Ross Embayment. These results underline and quantify the importance of including local GIA feedback effects in ice sheet models when simulating the Antarctic ice sheet evolution over the last glacial cycle.

The Lambousa (Cyprus) Fishtank in a Quasi-Stable Coastal Area of the Eastern Mediterranean, a Notable Marker for Testing GIA Models

The Lambousa fishtank, an archaeological structure entirely carved in bedrock, can be easily recognized and measured in the plan on Google Earth (GE). We surveyed in situ this excellent archaeological marker in 2016 through direct measurements using traditional field instruments, such as metric tapes and invar rods, and terrestrial photogrammetry using Structure from Motion (SfM) methods. The bedrock on which the fishtank is founded is an Upper Pleistocene calcarenite also containing Persistrombus latus. The age of the studied fishtank has not been previously published, but on the basis of the construction technique and the interpretation provided by Archaelogist and references therein, we believe that it was built in the period between 2.1 and 1.8 ka BP, like similar fishtanks in the Mediterranean area. Architectural structures consist of evident foot walks (Crepido), a stone base, and a tunnel that allows for seawater exchange during high tides. The tunnel is at the same altitude as the Crepido, which lies around the fishtank. These architectural components allow us to evaluate the palaeo-sea level with significant precision during the time when the fishtank was active. MIS 5.5 coastal deposits that outcrop in the study area are located at a maximum altitude of a few meters, while the inner margin of the MIS 5.5 terrace allows us to hypothesize “quasi-tectonic stability”. We have also obtained several predictions of the contribution from Glacial Isostatic Adjustment (GIA) to relative sea level at Lambousa for the past 3.5 kyr, according to models ICE-6G (VM5a), ICE-7G (VM7), and one of the GIA models by the Australian National University ANU) Research group.

A commercial finite element approach to modelling Glacial Isostatic Adjustment on spherical self-gravitating compressible earth models

SUMMARYThis paper presents a method that modifies commercial engineering-oriented finite element packages for the modelling of Glacial Isostatic Adjustment (GIA) on a self-gravitating, compressible and spherical Earth with 3-D structures. The approach, called the iterative finite element body and surface force (FEMIBSF) approach, solves the equilibrium equation for deformation using the ABAQUS finite element package and calculates potential perturbation consistently with finite element theory, avoiding the use of spherical harmonics. The key to this approach lies in computing the mean external body forces for each finite element within the Earth and pressure on Earth's surface and core–mantle boundary (CMB). These quantities, which drive the deformation and stress perturbation of GIA but are not included in the equation of motion of commercial finite element packages, are implemented therein. The method also demonstrates how to calculate degree-1 deformation directly in the spatial domain and Earth-load system for GIA models. To validate the FEMIBSF method, loading Love numbers (LLNs) for homogeneous and layered earth models are calculated and compared with three independent GIA methodologies: the normal-mode method, the iterative body force method and the spectral-finite element method. Results show that the FEMIBSF method can accurately reproduce the unstable modes for the homogeneous compressible model and agree reasonably well with the Love number results from other methods. It is found that the accuracy of the FEMIBSF method increases with higher resolution, but a non-conformal mesh should be avoided due to creating the so-called hanging nodes. The role of a potential force at the CMB is also studied and found to only affect the long-wavelength surface potential perturbation and deformation in the viscous time regime. In conclusion, the FEMIBSF method is ready for use in realistic GIA studies, with modelled vertical and horizontal displacement rates in a disc load case showing agreement with other two GIA methods within the uncertainty level of GNSS measurements.

Three-dimensional glacial isostatic adjustment modeling reconciles conflicting geographic trends in North American marine isotope stage 5a relative sea level observations

Abstract Glacial isostatic adjustment (GIA) simulations using earth models that vary viscoelastic structure with depth alone cannot simultaneously fit geographic trends in the elevation of marine isotope stage (MIS) 5a relative sea level (RSL) indicators across continental North America and the Caribbean and yield conflicting estimates of global mean sea level (GMSL). We present simulations with a GIA model that incorporates three-dimensional (3-D) variation in North American viscoelastic earth structure constructed by combining high-resolution seismic tomographic imaging with a new method for mapping this imaging into lateral variations in lithospheric thickness and mantle viscosity. We pair this earth model with a global ice history based on updated constraints on ice volume and geometry. The GIA prediction provides the first simultaneous reconciliation of MIS 5a North American and Caribbean RSL highstands and strengthens arguments that MIS 5a peak GMSL reached values close to that of the Last Interglacial. This result highlights the necessity of incorporating realistic 3-D earth structure into GIA predictions with continent-scale RSL data sets.

Simulating horizontal crustal motions of glacial isostatic adjustment using compressible Cartesian models

SUMMARY Significant land uplift and horizontal motions have been recorded with Global Navigation Satellite Systems (GNSS) in areas such as Alaska, Iceland and the Northern Antarctic Peninsula (NAP) as a result of Glacial Isostatic Adjustment (GIA) due to ice melt after the Little Ice Age. Here, analysis of horizontal displacement rates can be of extra importance, as they are more sensitive to Earth properties in shallower layers than vertical displacement rates. Proper modelling of horizontal displacement rates with dedicated GIA models requires a spherical Earth with compressible rheology. However, in these small areas, the used GIA models are often incompressible using a Cartesian geometry to ease computation and in some cases allow for lateral viscosity changes or more complex rheology. We investigate the validity of modelled horizontal displacement rates using different approximations, that is using spherical or Cartesian Earth structures, and incompressible, material compressible or compressible rheology. Although the lack of self-gravity and sphericity compensate each other in the vertical, this is less the case for the horizontal. For a disc ice sheet with a radius just over 200 km and a thickness of 1000 m, differences due to sphericity are minimal and the modelled horizontal displacement rates of compressible Cartesian models differ from those simulated by a compressible spherical model by 0.63 mm a−1. Thus, compressible Cartesian GIA models can be applied for modelling horizontal displacement rates of small ice sheets like those in Alaska, Iceland and NAP. Unfortunately, the implementation of compressibility in Abaqus that we use here cannot be extended to spherical models as gravity can not be specified for a spherical body. Other modelling approaches are recommended in such cases.

Holocene relative sea-level histories of far-field islands in the mid-Pacific

Holocene relative sea-level (RSL) data from far-field islands in the mid-Pacific have been used to validate the ice-melting histories of glacial isostatic adjustment (GIA) models. However, a lack of quality control in the reconstruction of RSL hinders the understanding of regional variability that can constrain ice-equivalent sea-level changes. Here, we present a standardised database of Holocene RSL data from five regions in the mid-Pacific (Cook Islands, Tuamotu Islands, Christmas (Kiritimati) Island, Gilbert Islands and Fiji). We categorised the data as high or low quality based on the susceptibility of samples to age and/or elevation errors. Of the 614 data points that were reviewed, 25% were rejected and 100 sea-level index points (SLIPs) were reinterpreted as limiting data. The new database consists of 141 SLIPs and 262 marine and 56 terrestrial limiting data points reconstructed from a variety of sea-level indicators (e.g., coral microatolls, mangrove peat, beachrock, and beach ridges), of which 71% provide high-quality constraints on RSL. The early to mid Holocene RSL evolution in the Cook Islands, Gilbert Islands and Fiji are poorly constrained due to a lack of high-quality SLIPs and limiting data during this period. The Tuamotu Islands provided the only record of early to mid Holocene evolution of RSL, indicating rapid RSL rise from between −22.9 m and −15.2 m at ∼9.0 ka to between −0.2 m and 0.5 m by ∼6.5 ka, at rates as high as 9.8 ± 5.1 mm/a, with a slowdown in the rate of RSL rise sometime between ∼8.2 ka and ∼6 ka. The Christmas (Kiritimati) Island record indicates stable RSL within ∼1.5 m of present-day levels over the past ∼6.6 ka. In the late Holocene, the Cook Islands record suggests a gradual fall in RSL over the past ∼2.9 ka at rates below 0.1 ± 4.3 mm/a. SLIPs at Fiji also indicate a slight fall in RSL at rates of less than 0.5 ± ∼4.4 mm/a at ∼4 ka, following which RSL fell from above 0.9 m at ∼3 ka to between −0.3 m and 0.6 m by ∼2.5– ∼2.1 ka. We highlight the importance of standardisation and quality control to critically evaluate the processes controlling RSL and validate GIA models. Indeed, the new standardised database has implications for the timing of the mid- Holocene highstand, which has been used to support the ICE-4G and ICE-7G_NA models. Due to the poor constraints of data in the mid-Pacific islands, particularly in the early Holocene, there remains no unique solution for a global ice-melting history.

Fossil Java Sea corals record Laurentide ice sheet disappearance

Abstract The Laurentide ice sheet was the largest late Pleistocene ice mass and the largest contributor to Holocene pre-industrial sea-level rise. While glaciological dates suggest final ice sheet melting between 8 and 6 ka, inversion of sea-level data indicates deglaciation at ca. 7 ka. Here, we present new chronostratigraphic constraints on Laurentide ice sheet disappearance based on Holocene relative sea-level observations from the tectonically stable north coast of Java, Indonesia. Age-elevation data from the flat upper surfaces of 13 fossil intertidal corals (i.e., microatolls) indicate that the Java Sea experienced a relative sea level of 1.3 ± 0.7 m above present between 6.9 and 5.3 ka. To determine uncaptured relative sea-level trends within the observational uncertainties of this apparently constant highstand, we analyzed the internal structure of three sliced microatolls from the same site to produce a high-resolution data set. These data were used to statistically model relative sea-level rates and trends. Employing the data with the model provided evidence for a short-lived rise of relative sea level from 1.0 ± 0.3 m above present at 6.7 ± 0.1 ka to 1.9 ± 0.3 m above present at 6.4 ± 0.1 ka. The end of this rise likely represents the last input of meltwater from the vast Laurentide ice sheet, which, consequently, collapsed at least 400 yr later than assumed by some widely used models of glacial isostatic adjustment. Incorporating these new results into such predictive models will help to better understand the geographical variability of future sea-level rise as a result of global warming.