Glacial Isostatic Adjustment Models Research Articles

Crustal deformation across the Southern Patagonian Icefield observed by GNSS

Geodetic GNSS observations at 43 sites well distributed over the Southern Patagonian Icefield region yield site velocities with a mean accuracy of 1 mm/a and 6 mm/a for the horizontal and vertical components, respectively. These velocities are analyzed to reveal the magnitudes and patterns of vertical and horizontal present-day crustal deformation as well as their primary driving processes. The observed vertical velocities confirm a rapid uplift, with rates peaking at 41 mm/a, causally related to glacial-isostatic adjustment (GIA). They yield now an unambiguous preference between two competing GIA models. Remaining discrepancies between the preferred model and our observations point toward an effective upper mantle viscosity even lower than 1.6⋅1018 Pas and effects of lateral rheological heterogeneities. An analysis of the horizontal strain and strain-rate fields reveals some complex superposition, with compression dominating in the west and extension in the east. This deformation field suggests significant contributions from three processes: GIA, a western interseismic tectonic deformation field related to plate subduction, and an extensional strain-rate field related to active Patagonian slab window tectonics.

Evidence for postglacial signatures in gravity gradients: A clue in lower mantle viscosity

The Earth's surface was depressed under the weight of ice during the last glaciations. Glacial Isostatic Adjustment (GIA) induces the slow recession of the trough that is left after deglaciation and is responsible for a contemporary uplift rate of more than 1 cm/yr around Hudson Bay. The present-day residual depression, an indicator of still-ongoing GIA, is difficult to identify in the observed topography, which is predominantly sensitive to crustal heterogeneities. According to the most widespread GIA models, which feature a viscosity of 2–3×1021 Pa s on top of the lower mantle, the trough is approximately 100 m deep and cannot explain the observed gravity anomalies across North America. These large anomalies are therefore usually attributed to subcontinental density heterogeneities in the tectosphere or to slab downwelling in the deep mantle.Here, we use observed gravity gradients (GG) to show that the uncompensated GIA trough is four times larger than expected and that it is the main source of the North American static gravity signal. We search for the contribution to these GGs from mantle mass anomalies, which are deduced from seismic tomography and are mechanically coupled to the global mantle flow. This contribution is found to be small over Laurentia, and at least 82% of the GGs are caused by GIA. Such a contribution from GIA in these GG observations implies a viscosity that is greater than 1022 Pa s in the lower mantle.Our conclusions are a plea for GIA models with a highly viscous lower mantle, which confirm inferences from mantle dynamic models. Any change in GIA modelling has important paleoclimatological and environmental implications, encouraging scientists to re-evaluate the past ice history at a global scale. These implications, in turn, affect the contribution of bedrock uplift to the contemporaneous mass balance over Antarctica and Greenland and thus the present-day ice-melting rate as deduced from the GRACE space mission. Additionally, studies of the thermo-chemical structure of the lithosphere/crust under North America that exploit gravity or geodetic data should be corrected for a GIA model, which is not the case today.

Assessing the impact of vertical land motion on twentieth century global mean sea level estimates

AbstractNear‐global and continuous measurements from satellite altimetry have provided accurate estimates of global mean sea level in the past two decades. Extending these estimates further into the past is a challenge using the historical tide gauge records. Not only is sampling nonuniform in both space and time, but tide gauges are also affected by vertical land motion (VLM) that creates a relative sea level change not representative of ocean variability. To allow for comparisons to the satellite altimetry estimated global mean sea level (GMSL), typically the tide gauges are corrected using glacial isostatic adjustment (GIA) models. This approach, however, does not correct other sources of VLM that remain in the tide gauge record. Here we compare Global Positioning System (GPS) VLM estimates at the tide gauge locations to VLM estimates from GIA models, and assess the influence of non‐GIA‐related VLM on GMSL estimates. We find that the tide gauges, on average, are experiencing positive VLM (i.e., uplift) after removing the known effect of GIA, resulting in an increase of 0.24 ± 0.08 mm yr−1 in GMSL trend estimates from 1900 to present when using GPS‐based corrections. While this result is likely dependent on the subset of tide gauges used and the actual corrections used, it does suggest that non‐GIA VLM plays a significant role in twentieth century estimates of GMSL. Given the relatively short GPS records used to obtain these VLM estimates, we also estimate the uncertainty in the GMSL trend that results from limited knowledge of non‐GIA‐related VLM.

Groundwater storage changes in the Tibetan Plateau and adjacent areas revealed from GRACE satellite gravity data

Understanding groundwater storage (GWS) changes is vital to the utilization and control of water resources in the Tibetan Plateau. However, well level observations are rare in this big area, and reliable hydrology models including GWS are not available. We use hydro-geodesy to quantitate GWS changes in the Tibetan Plateau and surroundings from 2003 to 2009 using a combined analysis of satellite gravity and satellite altimetry data, hydrology models as well as a model of glacial isostatic adjustment (GIA). Release-5 GRACE gravity data are jointly used in a mascon fitting method to estimate the terrestrial water storage (TWS) changes during the period, from which the hydrology contributions and the GIA effects are effectively deducted to give the estimates of GWS changes for 12 selected regions of interest. The hydrology contributions are carefully calculated from glaciers and lakes by ICESat-1 satellite altimetry data, permafrost degradation by an Active-Layer Depth (ALD) model, soil moisture and snow water equivalent by multiple hydrology models, and the GIA effects are calculated with the new ICE-6G_C (VM5a) model. Taking into account the measurement errors and the variability of the models, the uncertainties are rigorously estimated for the TWS changes, the hydrology contributions (including GWS changes) and the GIA effect. For the first time, we show explicitly separated GWS changes in the Tibetan Plateau and adjacent areas except for those to the south of the Himalayas. We find increasing trend rates for eight basins: +2.46±2.24 Gt/yr for the Jinsha River basin, +1.77±2.09 Gt/yr for the Nujiang-Lancangjiang Rivers Source Region, +1.86±1.69 Gt/yr for the Yangtze River Source Region, +1.14±1.39 Gt/yr for the Yellow River Source Region, +1.52±0.95 Gt/yr for the Qaidam basin, +1.66±1.52 Gt/yr for the central Qiangtang Nature Reserve, +5.37±2.17 Gt/yr for the Upper Indus basin and +2.77±0.99 Gt/yr for the Aksu River basin. All these increasing trends are most likely caused by increased runoff recharges from melt water and/or precipitation in the surroundings. We also find that the administrative actions such as the Chinese Ecological Protection and Construction Project help to store more groundwater in the Three Rivers Source Region, and suggest that seepages from the Endorheic basin to the west of it are a possible source for GWS increase in this region. In addition, our estimates for GWS changes basically confirm previous results along Afghanistan, Pakistan, north India and Bangladesh, and clearly reflect the excessive use of groundwater. Our results will benefit the water resource management in the study area, and are of particular significance for the ecological restoration in the Tibetan Plateau.

Eastern Mediterranean sea levels through the last interglacial from a coastal-marine sequence in northern Israel

A last interglacial (Marine Isotope Stage, MIS5e) marine-coastal sequence has been identified along the Galilee coast of Israel, with the type section located at Rosh Hanikra (RH). The microtidal regime and tectonic stability, along with the detailed stratigraphy of the RH shore, make the study region ideally suited for determining relative sea level (RSL) through the MIS5e interval in the eastern Mediterranean. The sequence contains fossilized microtidal subunits at a few meters above the current sea level. Unfortunately, all fossils were found to be altered, so that U-Th datings cannot be considered to represent initial deposition. We contend that U-Th dating of Strombus bubonius shells (recrystallized to calcite) suffices to indicate a lower limit of ?110 ± 8 ka for the time sea level dropped below the RH sedimentary sequence. The RH-section comprises three main subunits of a previously determined member (the Yasaf Member): (a) a gravelly unit containing the diagnostic gastropod Strombus bubonius Lamarck (Persististrombus latus), which was deposited in the intertidal to super-tidal stormy zone; (b) Vermetidae reef domes indicating a shallow-water depositional environment; and (c) coarse to medium-sized, bioclastic sandstone, probably deposited in the shallow sub-tidal zone. The sequence overlies three abrasion platforms that are cut by tidal channels at elevations of +0.8 m, +2.6 m and +3.4 m, and which are filled with MIS5e sediments. We present a detailed study of the sequence, with emphasis on stratigraphic, sedimentological, and palaeontological characteristics that indicate sea-level changes. Although without precise absolute dating, the stratigraphic sequence of RH through MIS5e allows us to identify a time-series of RSL positions, using the elevations of three stratigraphic subunits. Reconstructed RSL values range from +1.0 m to +7 m (with uncertainly < 1 m), and most fall within a narrow range of +1.0 to +3.3 m. Toward the end of MIS5e, RSL exceeded about +7 m. Glacial isostatic adjustment (GIA) modelling using multiple ice histories suggests that GIA corrections range between about ?1.8 m and +5.4 m. This implies that global mean sea level resided between ?0.8 m and +8.7 m during most of MIS5e. The absolute GIA correction would not be constant through the interglacial, and reduces to a range of ?1.2 m to+ 2.4 m towards the end of the interglacial.

A glacial isostatic adjustment model for the central and northern Laurentide Ice Sheet based on relative sea level and GPS measurements

The thickness and equivalent global sea level contribution of an improved model of the central and northern Laurentide Ice Sheet is constrained by 24 relative sea level histories and 18 present-day GPS-measured vertical land motion rates. The final model, termed Laur16, is derived from the ICE-5G model by holding the timing history constant and iteratively adjusting the thickness history, in four regions of northern Canada. In the final model, the last glacial maximum (LGM) thickness of the Laurentide Ice Sheet west of Hudson Bay was ~3.4-3.6 km. Conversely, east of Hudson Bay, peak ice thicknesses reached ~4 km. The ice model thicknesses inferred for these two regions represent, respectively, a ~30 per cent decrease and an average ~20-25 per cent increase to the load thickness relative to the ICE-5G reconstruction, which is generally consistent with other recent studies that have focussed on Laurentide Ice Sheet history. The final model also features peak ice thicknesses of 1.2-1.3 km in the Baffin Island region, a modest reduction relative to ICE-5G and unchanged thicknesses for a region in the central Canadian Arctic Archipelago west of Baffin Island. Vertical land motion predictions of the final model fit observed crustal uplift rates well, after an adjustment is made for the elastic crustal response to present-day ice mass changes of regional ice cover. The new Laur16 model provides more than a factor of two improvement of the fit to the RSL data (?2 measure of misfit) and a factor of nine improvement to the fit of the GPS data (mean squared error measure of fit), compared to the ICE-5G starting model. Laur16 also fits the regional RSL data better by a factor of two and gives a slightly better fit to GPS uplift rates than the recent ICE-6G model. The volume history of the Laur16 reconstruction corresponds to an up to 8 m reduction in global sea level equivalent compared to ICE-5G at LGM.

Relative sea-level changes during the Holocene in the Río de la Plata, Argentina and Uruguay: A review

This study critically reviews the relative sea-level (RSL) data from the Río de la Plata (RDP) (Argentina and Uruguay) in order to analyze the Holocene RSL changes in this region and thus capture the general trend illustrated by both the data and the high-degree polynomial regression analyses which show good agreement with the ICE-6G_C (VM6) model. The previously inferred Holocene sea-level histories reconstructed from palynological and diatom records from the northern and the southern RDP are also compared to the RSL curves proposed in this work. Analysis of the RSL database revealed that the RSL rose to reach the present level at or before c. 7000 cal yr BP, with the peak of the sea-level highstand c. +4 m between c. 6000 and 5500 cal yr BP (depending on the statistical method used) or at c. 7000 cal yr BP according to the ICE-6G model prediction, gradually falling after this time to the present position. The subaerial data tell a consistent story for the last 6000 years for the RDP but the subsurface data are not in agreement with these data or with the glacial isostatic adjustment (GIA) predictions. Since much of the subaerial data come from shells on beaches, beach ridges and storm beaches, they cannot be strictly interpreted as RSL index points. It seems likely that the predicted curves are somewhat high and could be overestimated. The “smooth” model of the late Holocene sea-level decline is in close agreement with both the GIA model predictions and the reconstruction of RSL from palynological and diatom records. The models provide no evidence to suggest that there has been a significant trend of change in the speed of sea-level fall or oscillations during the falling stage system tract. The non-parametric regression model, the GIA predictions and the trend inferred by palynological and diatom data trace out a slow sea-level fall for the last c. 6000 cal yr BP. We critically assessed published Holocene sea-level data from the RDP to produce a Holocene RSL curve of sufficient quality to provide a location in this area for testing theoretical models for the Atlantic coast of South America.

Modelling sea level data from China and Malay-Thailand to estimate Holocene ice-volume equivalent sea level change

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 × 1020 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.

Rapid early Holocene sea-level rise in Prydz Bay, East Antarctica

Prydz Bay is one of the largest embayments on the East Antarctic coast and it is the discharge point for approximately 16% of the East Antarctic Ice Sheet. Geological constraints on the regional ice sheet history include evidence of past relative sea-level change at three sites; the Vestfold Hills, Rauer Islands and Larsemann Hills. In this paper we compile updated regional relative sea-level data from these sites. We compare these with a suite of relative sea-level predictions derived from glacial isostatic adjustment models and discuss the significance of departures between the models and the field evidence. The compiled geological data extend the relative sea-level curve for this region to 11,258calyr BP and include new constraints based on abandoned penguin colonies, new isolation basin data in the Vestfold Hills, validation of a submarine relative sea-level constraint in the Rauer Islands and recalibrated radiocarbon ages at all sites dating from 12,728calyr BP. The field data show rapid increases in rates of relative sea level rise of 12–48mm/yr between 10,473 (or 9678) and 9411calyr BP in the Vestfold Hills and of 8.8mm/yr between 8882 and 8563calyr BP in the Larsemann Hills. The relative sea-level high stands of ≥8.8m from 9411 to after 7564calyr BP (Vestfold Hills) and ≥8m at 8563 and 7066calyr BP (Larsemann Hills) are over-predicted by some of the glacial isostatic adjustment models considered here, suggesting that assumptions relating to the magnitude and timing of regional ice loss since the Last Glacial Maximum may need revising. In the Vestfold Hills and Rauer Islands the final deglacial sea-level rise was almost exactly cancelled out by local rebound between 9411 and 5967calyr BP and this was followed by a near exponential decay in relative sea-level. In the Larsemann Hills the sea-level data suggest that the rate of ice retreat in this region was not uniform throughout the Holocene. Swath bathymetric surveys of the benthic seafloor topography show the presence of multiple offshore basins. These are a priority for further study as those that remained free of grounded ice should provide precise constraints on relative sea-level rise and ice sheet history during the most rapid phases of the last major deglaciation.

Incomplete separability of Antarctic plate rotation from glacial isostatic adjustment deformation within geodetic observations

Geodetic measurements of Antarctic solid Earth deformation include signals from plate rotation and glacial isostatic adjustment (GIA). Through simulation, we investigate the degree to which these signals are separable within horizontal GPS site velocities that commonly define plate rotation estimates and that promise new constraints on models of GIA. Using a suite of GIA model predictions that incorporate both 1-D and 3-D Earth rheologies, we show that, given the present location of GPS sites within East Antarctica, unmodelled or mismodelled GIA signal within GPS velocities produces biased estimates of plate rotation. When biased plate rotation is removed from the GPS velocities, errors as large as 0.8 mm yr−1 are introduced; a value commonly larger than the predicted GIA signal magnitude. In the absence of reliable forward models of plate rotation or GIA then Antarctic geodetic velocities cannot totally and unambiguously constrain either process, especially GIA.

An examination of spatial variability in the timing and magnitude of Holocene relative sea-level changes in the New Zealand archipelago

Holocene relative sea-level (RSL) changes have been reconstructed for four regions within the New Zealand archipelago: the northern North Island (including Northland, Auckland, and the Coromandel Peninsula); the southwest coast of the North Island; the Canterbury coast (South Island); and the Otago coast (South Island). In the North Island the RSL highstand commenced c. 8100–7240 cal yr BP when present mean sea-level (PMSL) was first attained. This is c. 600–1400 years earlier than has been previously indicated for the New Zealand region as a whole, and is consistent with recent Holocene RSL reconstructions from Australia. In North Island locations the early-Holocene sea-level highstand was quite pronounced, with RSL up to 2.75 m higher than present. In the South Island the onset of highstand conditions was later, with the first attainment of PMSL being between 7000–6400 cal yr BP. In the mid-Holocene the northern North Island experienced the largest sea-level highstand, with RSL up to 3.00 m higher than present. This is demonstrably higher than the highstand recorded for the southwest North Island and Otago regions. A number of different drivers operating at a range of scales may be responsible for the spatial and temporal variation in the timing and magnitude of RSL changes within the New Zealand archipelago. One possible mechanism is the north-south gradient in RSL that would arise in the intermediate field around Antarctica in response to the reduced gravitational attraction of the Antarctic Ice Sheet (AIS) as it lost mass during the Holocene. This gradient would be enhanced by the predicted deformation of the lithosphere in the intermediate field of the Southern Ocean around Antarctica due to hydro-isostatic loading and mass loss of the AIS. However, no such long-wavelength signals in sea-surface height or solid Earth deformation are evident in glacial isostatic adjustment (GIA) model predictions for the New Zealand region, while research from Australia has suggested that north-south variations in Holocene RSL changes due to hydro-isostatic influences are limited or non-existent. At the regional-to local-scale, post-glacial meltwater loading on the continental shelf around New Zealand is predicted by GIA modelling to have a significant effect on the timing and magnitude of RSL changes through the phenomenon of continental levering. The spatial variation in continental levering is controlled by the configuration of the coast and the width of the adjacent continental shelf, with continental levering providing a robust explanation for the observed spatial and temporal variations in RSL changes. Further research is required to characterise the regional and local effects of different tectonic regimes, wave climates, and sediment regimes. These are potentially very significant drivers of RSL variability at the regional-to local-scale. However, the magnitude of their potential effects remains equivocal.

Estimating Sea-Level Allowances for Atlantic Canada using the Fifth Assessment Report of the IPCC

Sea-level allowances at 22 tide-gauge sites along the east coast of Canada are determined based on projections of regional sea-level rise for the Representative Concentration Pathway 8.5 (RCP8.5) from the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR5) and on the statistics of historical tides and storm surges (storm tides). The allowances, which may be used for coastal infrastructure planning, increase with time during the twenty-first century through a combination of mean sea-level rise and the increased uncertainty of future projections with time. The allowances show significant spatial variation, mainly a consequence of strong regionally varying relative sea-level change as a result of glacial isostatic adjustment (GIA). A methodology is described for replacement of the GIA component of the AR5 projection with global positioning system (GPS) measurements of vertical crustal motion; this significantly decreases allowances in regions where the uncertainty of the GIA models is large. For RCP8.5 with GPS data incorporated and for the 1995–2100 period, the sea-level allowances range from about 0.5 m along the north shore of the Gulf of St. Lawrence to more than 1 m along the coast of Nova Scotia and southern Newfoundland.

Observed changes in the Earth's dynamic oblateness from GRACE data and geophysical models.

A new methodology is proposed to estimate changes in the Earth’s dynamic oblateness (Delta {J_{2}} or equivalently, -sqrt{5}Delta {C_{20}}) on a monthly basis. The algorithm uses monthly Gravity Recovery and Climate Experiment (GRACE) gravity solutions, an ocean bottom pressure model and a glacial isostatic adjustment (GIA) model. The resulting time series agree remarkably well with a solution based on satellite laser ranging (SLR) data. Seasonal variations of the obtained time series show little sensitivity to the choice of GRACE solutions. Reducing signal leakage in coastal areas when dealing with GRACE data and accounting for self-attraction and loading effects when dealing with water redistribution in the ocean is crucial in achieving close agreement with the SLR-based solution in terms of de-trended solutions. The obtained trend estimates, on the other hand, may be less accurate due to their dependence on the GIA models, which still carry large uncertainties.

Late Quaternary evolution and sea-level history of a glaciated marine embayment, Bantry Bay, SW Ireland

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 (40km long, 5–10km 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. 80m 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-14.6kacal 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 13.5kacal BP than predicted by existing glacial isostatic adjustment models.

Uplift rates from a new high-density GPS network in Palmer Land indicate significant late Holocene ice loss in the southwestern Weddell Sea

The measurement of ongoing ice-mass loss and associated melt water contribution to sea-level change from regions such as West Antarctica is dependent on a combination of remote sensing methods. A key method, the measurement of changes in Earth's gravity via the GRACE satellite mission, requires a potentially large correction to account for the isostatic response of the solid Earth to ice-load changes since the Last Glacial Maximum. In this study, we combine glacial isostatic adjustment modelling with a new GPS dataset of solid Earth deformation for the southern Antarctic Peninsula to test the current understanding of ice history in this region. A sufficiently complete history of past ice-load change is required for glacial isostatic adjustment models to accurately predict the spatial variation of ongoing solid Earth deformation, once the independently-constrained effects of present-day ice mass loss have been accounted for. Comparisons between the GPS data and glacial isostatic adjustment model predictions reveal a substantial misfit. The misfit is localized on the southwestern Weddell Sea, where current ice models under-predict uplift rates by approximately 2 mm yr−1. This under-prediction suggests that either the retreat of the ice sheet grounding line in this region occurred significantly later in the Holocene than currently assumed, or that the region previously hosted more ice than currently assumed. This finding demonstrates the need for further fieldwork to obtain direct constraints on the timing of Holocene grounding line retreat in the southwestern Weddell Sea and that GRACE estimates of ice sheet mass balance will be unreliable in this region until this is resolved.

State-of-the-art in studies of glacial isostatic adjustment for the British Isles: a literature review

ABSTRACTUnderstanding the effects of glacial isostatic adjustment (GIA) of the British Isles is essential for the assessment of past and future sea-level trends. GIA has been extensively examined in the literature, employing different research methods and observational data types. Geological evidence from palaeo-shorelines and undisturbed sedimentary deposits has been used to reconstruct long-term relative sea-level change since the Last Glacial Maximum. This information derived from sea-level index points has been employed to inform empirical isobase models of the uplift in Scotland using trend surface and Gaussian trend surface analysis, as well as to calibrate more theory-driven GIA models that rely on Earth mantle rheology and ice sheet history. Furthermore, current short-term rates of GIA-induced crustal motion during the past few decades have been measured using different geodetic techniques, mainly continuous GPS (CGPS) and absolute gravimetry (AG). AG-measurements are generally employed to increase the accuracy of the CGPS estimates. Synthetic aperture radar interferometry (InSAR) looks promising as a relatively new technique to measure crustal uplift in the northern parts of Great Britain, where the GIA-induced vertical land deformation has its highest rate. This literature review provides an in-depth comparison and discussion of the development of these different research approaches.

Late Glacial to Holocene relative sea-level change in Assynt, northwest Scotland, UK

Relative sea-level change (RSL), from the Late Glacial through to the late Holocene, is reconstructed for the Assynt region, northwest Scotland, based on bio- and lithostratigraphical analysis. Four new radiocarbon-dated sea-level index points help constrain RSL change for the Late Glacial to the late Holocene. These new data, in addition to published material, capture the RSL fall during the Late Glacial and the rise and fall associated with the mid-Holocene highstand. Two of these index points constrain the Late Glacial RSL history in Assynt for the first time, reconstructing RSL falling from 2.47±0.59mOD to 0.15±0.59mOD at c. 14,000–15,000calyrBP. These new data test model predictions of glacial isostatic adjustment (GIA), particularly during the early deglacial period which is currently poorly constrained throughout the British Isles. Whilst the empirical data from the mid- to late-Holocene to present matches quite well with the recent GIA model output, there is a relatively poor fit between the timing of the Late Glacial RSL fall and early Holocene RSL rise. This mismatch, also evident elsewhere in northwest Scotland, may result from uncertainties associated with both the global and local ice components of GIA models.

Numerical and computational aspects of some block-preconditioners for saddle point systems

Element-wise approximation of the Schur complement (EWS) for saddle point matrices.Spectral bounds are shown when the Schur complement is symmetric negative definite.EWS leads to a numerically and computationally optimal iterative solver.Numerical simulations on various computer architectures. Linear systems with two-by-two block matrices are usually preconditioned by block lower- or upper-triangular systems that require an approximation of the related Schur complement. In this work, in the finite element framework, we consider one special such approximation, namely, the element-wise Schur complement. It is sparse and its construction is perfectly parallelizable, making it an appropriate ingredient when building preconditioners for iterative solvers executed on both distributed and shared memory computer architectures. For saddle point matrices with symmetric positive (semi-)definite blocks we show that the Schur complement is spectrally equivalent to the so-constructed approximation and derive spectral equivalence bounds. We also illustrate the quality of the approximation for nonsymmetric problems, where we observe the same good numerical efficiency.Furthermore, we demonstrate the computational and numerical performance of the corresponding preconditioned iterative solution method on a large scale model benchmark problem originating from the elastic glacial isostatic adjustment model discretized using the finite element method.

Ice sheet mass balance in Antarctica measured by GRACE and its uncertainty

As a critical component of the cryosphere,the Antarctic Ice Sheet(AIS)has strongconnection with the sea level change and global climate change.Accurate quantification of the current spatial and temporal mass changes of AIS is very important to improve our understanding and prediction of its response and contribution to global change.The Gravity Recovery and Climate Experiment(GRACE)mission has provided new and useful observations to detect AIS mass balance since its launch in March 2002.There are significant differences among the GRACE estimates of the total mass change.The big difference is due in part to considerable uncertainty in the accuracy of glacial isostatic adjustment(GIA)signals,and also due to use of different time spans,different versions of GRACE products and different GRACE post-processing methods.Using 124 monthly GRACE gravity field solutions of Release 5(RL05)produced at the Center for Space Research(CSR)of the University of Texas,Austin,spanning the interval from January of 2003 through December of 2013,the mass balance of AIS is estimated by two postprocessing ways:the optimizing averaging kernel method(also named VW)and the combined filter method(the first step is called P5M11 decorrelation filter to remove correlated noise by fitting and subtracting a fifth-order polynomial to even and odd coefficient pairs at spherical harmonic orders eleven and above,the second involves smoothing with a 250 km Gaussian filter).A detailed error analysis is provided including consideration of leakage-in,leakage-out,and errors in modeling mass variations of the atmosphere,ocean and GIA.In addition,a statistical model selection criterion is employed in computation of trends from mass variation time series,and the impact of K1 tidal alias is analyzed.The results reveal that during 2003—2013,the total mass of the ice sheet decreased significantly at change rates of-163±50,-129±41and-81±27Gt/a for three GIA models:GW13,IJ05,W12 a.There was a distinct region with mass loss in the Amundsen Sea Embayment of West Antarctic ice sheet and the Northern Antarctic Peninsula,while an increasing mass gain was concentrated in the Dronning Maud Land and the Enderby Land of East Antarctic ice sheet.Furthermore,we use hypotheses testing and information criteria evaluation to select the best trend model fitting together with sinusoidal functions of annual(365.0-d)and semi-annual(181.0-d)signals and the S2(161.0-d),K1(2725.4-d)and K2(1362.7-d)tidal aliases.We found that K1 tidal alias has a potential to falsify the acceleration estimates.Although it is not good enough to confirm the K1 tidal alias based on an eleven-year time-series,the impact of K1 tidal alias deserves further notice.By comparing the quantities of total mass balance computed by the two different processing methods and three different GIA models in the Antarctica,we find that the differences are less than 15Gt/a between two processing methods,but the largest difference is about 80 Gt/a between different GIA models.The analysis of the uncertainty of GRACE′s estimation of AIS mass balance indicates that the largest source of error is the GIA correction.Our results indicate that during January 2003 to December 2013 the contribution of AIS to sea level rise was about+0.34±0.11mm/a.Significant mass loss increases were limited to the basin that contains Pine Island Glacier along the Amundsen Sea coast of West Antarctica.During the analyzed time period,the total mass acceleration was-8±10Gt/a2,equivalent to+0.02±0.03mm/a2 sea level rise.Results of analysis point to the conclusion that when using agiven GRACE data set with same error correction,the differences of total mass changes are not highly dependent on which post-processing strategies to be used but on the different GIA models.Therefore,a more accurate GIA model is the key for determining Antarctic ice mass change from GRACE in the present and future.

A new glacial isostatic adjustment model of the Innuitian Ice Sheet, Arctic Canada

A reconstruction of the Innuitian Ice Sheet (IIS) is developed that incorporates first-order constraints on its spatial extent and history as suggested by regional glacial geology studies. Glacial isostatic adjustment modelling of this ice sheet provides relative sea-level predictions that are in good agreement with measurements of post-glacial sea-level change at 18 locations. The results indicate peak thicknesses of the Innuitian Ice Sheet of approximately 1600 m, up to 400 m thicker than the minimum peak thicknesses estimated from glacial geology studies, but between approximately 1000 to 1500 m thinner than the peak thicknesses present in previous GIA models. The thickness history of the best-fit Innuitian Ice Sheet model developed here, termed SJD15, differs from the ICE-5G reconstruction and provides an improved fit to sea-level measurements from the lowland sector of the ice sheet. Both models provide a similar fit to relative sea-level measurements from the alpine sector. The vertical crustal motion predictions of the best-fit IIS model are in general agreement with limited GPS observations, after correction for a significant elastic crustal response to present-day ice mass change. The new model provides approximately 2.7 m equivalent contribution to global sea-level rise, an increase of +0.6 m compared to the Innuitian portion of ICE-5G. SJD15 is qualitatively more similar to the recent ICE-6G ice sheet reconstruction, which appears to also include more spatially extensive ice cover in the Innuitian region than ICE-5G.