Effects Of Glacial Isostatic Adjustment Research Articles

Effects of Glacial Isostatic Adjustment on Fault Reactivation and Its Consequences on Radionuclide Migration in Crystalline Host Rocks

AbstractTo assess the robustness of a safety case for a deep geological repository (DGR), it is necessary to analyze a range of scenarios covering likely, less likely, and hypothetical future developments. Crystalline rock can, under ideal conditions, provide a suitable hydrogeologic barrier due to its extremely low matrix permeability. However, this host rock is often fractured, which can compromise its hydro-mechanical (HM) barrier function. We quantify how faults that are prone to reactivation during glacial events can affect radionuclide migration around a DGR in a crystalline host rock. We extend a previously developed finite element model of coupled fluid flow and radionuclide transport to numerically solve the component transport problem before and after fault reactivation. Assuming that fault reactivation is triggered by changes in mechanical boundary conditions, we derive heterogeneous permeability distributions in the reactivated faults by evaluating the Coulomb failure stress criterion of finite element solutions of a complementary hydro-mechanical problem. Specifically, we evaluate the consequences of glacial isostatic adjustment (GIA) during a glacial cycle. We find that the increased permeability in the reactivated faults accelerates the migration of radionuclides along the fault by channeling the flow, while it is reduced in the direction perpendicular to the fault. The channeling observed is also a result of heterogeneous permeability enhancement, and the flow fields differ from those of the previous model which postulated a homogeneous permeability enhancement. Although the proposed numerical workflow has been applied to the case of GIA, it is adaptable to study hydro-mechanical processes induced by seismic events or by hydrofracking in enhanced geothermal systems.

Relative sea-level sensitivity in the Eurasian region to Earth and ice-sheet model uncertainty during the Last Interglacial

Fingerprinting the source and rate of the melt of polar ice sheets during the Last Interglacial is a key research challenge. This is reliant on high-quality relative sea-level constraints, and the correction of this data for the effects of glacial isostatic adjustment driven by ice sheet cover changes prior to the interglacial. However, both the spatial and temporal evolution of past ice sheets and the Earth’s rheological structure that serve as inputs to glacial isostatic adjustment predictions are significantly uncertain. This study sets out to determine the relative influence of each of these inputs on modelled values of Last Interglacial relative sea levels and how this influence varies spatially. To answer this question, we use a palaeo ice-sheet model and a gravitationally consistent glacial isostatic adjustment model. We develop new numerical tools to generate plausible ice-sheet extent and histories, quantify relative sea-level uncertainty, and perform a Sobol sensitivity analysis facilitated by the use of Gaussian process emulation. We find that Earth model parameters are the dominant contributors to relative sea-level uncertainty in most Eurasian regions, but that relative sea-level values in the Barents-Kara Sea are most influenced by ice-sheet loading, while the timing of the deglaciation has the greatest impact in the Baltic Sea. Our results show that the magnitude and rate of relative sea-level change is relatively insensitive to the specific timing of ice-sheet retreat, as well as the configuration of the far-field North American ice sheet. Overall, our work suggests that the coastlines of the southern North Sea and the English Channel are least influenced by relative sea-level uncertainty and are the most suitable for future data collection studies aiming to limit the influence of glacial isostatic adjustment.

Characterization of Changes in Groundwater Storage in the Lachlan Catchment, Australia, Derived From Observations of Surface Deformation and Groundwater Level Data

AbstractGlobal Positioning System (GPS) deformation measurements were combined with groundwater level data to examine the spatiotemporal variability of groundwater storage in the Lachlan catchment located in central New South Wales (Australia). After correcting for effects of glacial isostatic adjustment, non‐tidal oceanic and atmospheric loading as well as hydrologic loading using existing models, we show that the seasonal and interannual variability of ground deformation and hydraulic head level data, extracted using wavelet time‐frequency analysis, exhibits an in‐phase behavior, indicating that the observed surface deformation is the poroelastic response to groundwater pressure change in aquifer system. Combination of GPS displacement and groundwater level change enables the estimation of elastic skeletal specific storage coefficients, which were then used for estimating groundwater storage changes. The estimated groundwater storage changes clearly reflect the four climate events of the Lachlan catchment since 1996: (a) the Millennium drought over 1996–2009, (b) the 2011–2012 La Nina and two significant floods in 2012 and 2016, (c) the drought conditions from mid‐2017 to late‐2019, and (d) the return of La Nina conditions since early 2020. We also found annual and long‐term groundwater storage variations of respectively and over the period 2012–2021. Moreover, we show that groundwater level fluctuations can be predicted from GPS displacement measurements and storage coefficients with sufficient accuracy (80% correlation and 70% RMS reduction when compared in terms of seasonal cycle). This study provides essential information that can contribute to future groundwater planning, management, and control over the Australian continent.

Feasibility of a global inversion for spatially resolved glacial isostatic adjustment and ice sheet mass changes proven in simulation experiments

Estimating mass changes of ice sheets or of the global ocean from satellite gravimetry strongly depends on the correction for the glacial isostatic adjustment (GIA) signal. However, geophysical GIA models are different and incompatible with observations, particularly in Antarctica. Regional inversions have resolved GIA over Antarctica without ensuring global consistency, while global inversions have been mostly constrained by a priori GIA patterns. For the first time, we set up a global inversion to simultaneously estimate ice sheet mass changes and GIA, where Antarctic GIA is spatially resolved using a set of global GIA patterns. The patterns are related to deglaciation impulses localized along a grid over Antarctica. GIA associated with four regions outside Antarctica is parametrized by global GIA patterns induced by deglaciation histories. The observations we consider here are satellite gravimetry, satellite altimetry over Antarctica and Greenland, as well as modelled firn thickness changes. Firn thickness changes are also parametrized to account for systematic errors in their modelling. Results from simulation experiments using realistic signals and error covariances support the feasibility of the approach. For example, the spatial RMS error of the estimated Antarctic GIA effect, assuming a 10-year observation period, is 31% and 51%, of the RMS of two alternative global GIA models. The integrated Antarctic GIA error is 8% and 5%, respectively, of the integrated GIA signal of the two models. For these results realistic error covariances incorporated in the parameter estimation process are essential. If error correlations are neglected, the Antarctic GIA RMS error is more than twice as large.Highlightsbullet We present a globally consistent inversion approach to co-estimate glacial isostatic adjustment effects together with changes of the ice mass and firn air content in Greenland and Antarctica. bullet The inversion method utilizes data sets from satellite gravimetry, satellite altimetry, regional climate modelling, and firn modelling together with the full error-covariance information of all input data. bullet The simulation experiments show that the proposed GIA parametrization in Antarctica can resolve GIA effects unpredicted by geophysical modelling, despite realistic input-data limitations.

Stabilizing effect of bedrock uplift on retreat of Thwaites Glacier, Antarctica, at centennial timescales

Viscoelastic rebound of the solid Earth upon the removal of ice loads has the potential to inhibit marine ice sheet instability, thereby forestalling ice-sheet retreat and global mean sea-level rise. The timescale over which the solid Earth - ice sheet system responds to changes in ice thickness and bedrock topography places a strong control on the spatiotemporal influence of this negative feedback mechanism. In this study, we assess the impact of solid-earth rheological structure on model projections of the retreat of Thwaites Glacier, West Antarctica, and the concomitant sea-level rise by coupling the dynamic ice sheet model MALI to a regional glacial isostatic adjustment (GIA) model. We test the sensitivity of model projections of ice-sheet retreat and associated sea-level rise across a range of four different solid-earth rheologies, forced by standard ISMIP6 ocean and atmospheric datasets for the RCP8.5 climate scenario. These model parameters are applied to 500-year, coupled ice-sheet - GIA simulations. For the mantle viscosity best supported by observations, the negative GIA feedback leads to a reduction in mass loss that remains above 20% after about a hundred years. Mass-loss reduction peaks at 50% around 2300, which is when a control simulation without GIA experiences its maximum rate of retreat. For a weaker solid-earth rheology that is unlikely but compatible with observational uncertainty, mass loss reduction remains above 50% after 2150. At 2100, mass loss reduction is 10% for the best-fit rheology and 25% for the weakest rheology. At the same time, we estimate that water expulsion from the rebounding solid Earth beneath the ocean near Thwaites Glacier may increase sea-level rise by up to 20% at five centuries. Additionally, the reduction in ice-sheet retreat caused by GIA is substantially reduced under stronger climate forcings, suggesting that the stabilizing feedback of GIA will also be an indirect function of emissions scenario. We hypothesize that feedbacks between the solid Earth - ice sheet system are controlled by a competition between the spatial extent and timescale of bedrock uplift relative to the rate of grounded ice retreat away from the region of most rapid unloading. Although uncertainty in solid-earth rheology leads to large uncertainty in future sea-level rise contribution from Thwaites Glacier, under all plausible parameters the GIA effects are too large to be ignored for future projections of Thwaites Glacier of more than a century.

Bayesian modelling of piecewise trends and discontinuities to improve the estimation of coastal vertical land motion

One of the major sources of uncertainty affecting vertical land motion (VLM) estimations are discontinuities and trend changes. Trend changes are most commonly caused by seismic deformation, but can also stem from long-term (decadal to multidecadal) surface loading changes or from local origins. Although these issues have been extensively addressed for Global Navigation Satellite System (GNSS) data, there is limited knowledge of how such events can be directly detected and mitigated in VLM, derived from altimetry and tide-gauge differences (SATTG). In this study, we present a novel Bayesian approach to automatically and simultaneously detect such events, together with the statistics commonly estimated to characterize motion signatures. Next to GNSS time series, for the first time, we directly estimate discontinuities and trend changes in VLM data inferred from SATTG. We show that, compared to estimating a single linear trend, accounting for such variable velocities significantly increases the agreement of SATTG with GNSS values (on average by 0.36 mm/year) at 339 globally distributed station pairs. The Bayesian change point detection is applied to 606 SATTG and 381 GNSS time series. Observed VLM, which is identified as linear (i.e. where no significant trend changes are detected), has a substantially higher consistency with large-scale VLM effects of glacial isostatic adjustment (GIA) and contemporary mass redistribution (CMR). The standard deviation of SATTG (and GNSS) trend differences with respect to GIA+CMR trends is by 38% (and 48%) lower for time series with constant velocity compared to variable velocities. Given that in more than a third of the SATTG time series variable velocities are detected, the results underpin the importance to account for such features, in particular to avoid extrapolation biases of coastal VLM and its influence on relative sea-level-change determination. The Bayesian approach uncovers the potential for a better characterization of SATTG VLM changes on much longer periods and is widely applicable to other geophysical time series.

Seismic Contributions to Secular Changes in Global Geodynamic Parameters

AbstractSecular changes in global geodynamic parameters (polar motion excitation, length of day, and J2, etc.) are significant to understand internal mass transport in the solid Earth system and surface geophysical fluids related to global climate. However, the glacial isostatic adjustment (GIA) and climate‐driven surface mass redistribution are insufficient to explain the origin. We are motivated to report the significance of seismic effect in the pursuit of understanding the budget of secular changes in geodynamic parameters. The seismic effect is comparable to the GIA effect and amounts to 20% or larger (up to 30%) of the observed secular changes in global geodynamic parameters. Therefore, the seismic effect must be treated as one key mechanism of driving secular changes in geodynamic parameters, which is critical to invert rheological structure, clarify internal dynamic processes, and reveal the physical evolution of the Earth.

Glacial isostatic adjustment in the Red Sea: Impact of 3-D Earth structure

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.

A GNSS velocity field for crustal deformation studies: The influence of glacial isostatic adjustment on plate motion models

SUMMARYThe two main causes of global-scale secular deformation of the Earth are tectonic plate motion and glacial isostatic adjustment (GIA). We create a bespoke global 3D GNSS surface velocity field ‘NCL20’ to investigate tectonic plate motion and the effect of GIA on plate motion models (PMMs), drawing on a set of 1D and 3D GIA model predictions. The main motivation for creating NCL20 is to include a larger number of GNSS sites in the most GIA-affected areas of investigation, namely North America, Europe, and Antarctica. We do this using the IGS repro2 data and other similarly processed GNSS data sets. Our final GNSS velocity field has horizontal uncertainties mostly within ±0.5 mm yr–1 and vertical uncertainties mostly within ±1 mm yr–1 (at 95 per cent confidence), which make it suitable for testing GIA models. We generate a suite of 117 global GIA model predictions by combining three different ice history models (ICE-5G, ICE-6G and W12) with a range of 1D and 3D Earth models. By subtracting this ensemble from the GNSS velocity field, we identify and compare a range of PMMs which are expected to be unaffected by GIA. Our method allows us to include GNSS sites that are typically excluded from PMM estimations due to their location in GIA-affected regions. We demonstrate that significant GIA-related horizontal motion outside of the rapidly uplifting regions may bias PMMs if left uncorrected. Based on their ability to explain the observed surface velocity field, a group of best-performing GIA models is selected for three regions of interest: North America, Europe and Antarctica. The range of GIA predictions in each best-performing group is assumed to represent the uncertainty in regional GIA modelling insofar as it can be constrained by present-day geodetic velocities. In the horizontal component, we note that 3D GIA models show more variation in the direction of predicted velocities than 1D GIA models, confirming that horizontal velocities are strongly sensitive to lateral variations in Earth structure. Furthermore, for Antarctica the variation in predicted GIA vertical velocities suggests that the total GIA contribution to annual gravimetric mass change ranges from –3 to 22 Gt yr–1 depending on which of the best-performing GIA models is used.

Extraction of GRACE/GRACE-FO observed mass change patterns across Antarctica via independent component analysis (ICA).

Here we qualitatively analyse the mass change patterns across Antarctica via independent component analysis (ICA), a statistics-based blind source separation method to extract signals from complex data sets, in an attempt to reduce uncertainties in the glacial isostatic adjustment (GIA) effects and improve understanding of Antarctic Ice Sheet (AIS) mass-balance. We extract the six leading independent components from gravimetric data acquired during the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) missions. The results reveal that the observed continental-scale mass changes can be effectively separated into several spatial patterns that may be dominated by different physical processes. Although the hidden independent physical processes cannot be completely isolated, some significant signals, such as glacier melt, snow accumulation, periodic climatic signals, and GIA effects, can be determined without introducing any external information. We also observe that the time period of the analysed data set has a direct impact on the ICA results, as the impacts of extreme events, such as the anomalously large snowfall events in the late 2000s, may cause dramatic spatial and temporal changes in the ICA results. ICA provides a unique and informative approach to obtain a better understanding of both AIS-scale mass changes and specific regional-scale spatiotemporal signal variations.

GRACE-based estimates of groundwater variations over North America from 2002 to 2017

GRACE-based estimates for groundwater storage (GWS) changes in North America substantially depend upon correction of glacial isostatic adjustment (GIA) effects, which are usually removed with GIA models. In this study, GIA effects are eliminated by employing an independent separation approach with the aid of Global Navigation Satellite System (GNSS) vertical velocity data. Our goal is to provide an independent estimate for monthly GWS changes within North America in 1-degree-grids and their trends over the whole GRACE mission lifetime from April 2002 to June 2017. This estimate is derived from the release-6 version of GRACE monthly level-2 data, GNSS data, land surface models for soil moisture and snow water equivalent, and satellite altimetric lake level data. We find a GWS anomaly in form of an increasing trend in Saskatchewan, which affects the Saskatchewan Province and the states of Montana, North Dakota and Minnesota, and 4 GWS anomalies with declining trends in Nevada, California, Arizona and Texas, respectively. The monthly changes of these GWS anomalies, except for the one in Nevada, are validated by well level data. We provide results for average monthly GWS changes and the trends for the 5 anomalies but also in separate form for the 13 affected states or provinces. The increasing trends of the Saskatchewan GWS anomaly and the affected 3 states are related to increasing precipitation and can be elucidated by the decreasing drought intensity level. On the contrary, the declining trends in GWS can be explained by weakening precipitation and are mostly supported by the increasing drought intensity level in the other 4 anomalies and the affected states, which are Nevada, California, Arizona, New Mexico, Texas, Oklahoma, Kansas, and Colorado. Our estimates of monthly GWS changes and their trends can serve as alternative and beneficial input for the sustainable management of groundwater resources in North America.

Not a bathtub: A consideration of sea-level physics for archaeological models of human migration

Accurately reconstructing past sea level is key to simulating potential migration pathways of ancient hominins, including early Homo sapiens. Models of ancient human migration events commonly construct estimates of paleoenvironments using the “bathtub” model, in which sea level is assumed to rise and fall according to a “eustatic” (global average) value over time. However, large uncertainties exist on past ice sheet sizes and shapes, particularly prior to the Last Glacial Maximum (LGM), ∼26,000 years ago. Moreover, regional sea level varies significantly due to the effects of glacial isostatic adjustment (GIA). That process includes Earth's gravitational, deformational, and rotational response to changing surface (ice plus ocean) loads across the ice age. Here, we offer an updated account of the physics of GIA-induced sea-level change and consider the impacts of these effects, together with a newly published ice sheet history, on sea-level changes across the last glacial cycle. As illustrations, we highlight the significance of these issues for studies of ancient human migration from Sunda to Sahul and for the timing of the final, post-LGM flooding of the Strait of Dover. These examples demonstrate the importance of incorporating updated ice sheet histories and accurate sea-level physics into archaeological research.

The impact of 3-D Earth structure on far-field sea level following interglacial West Antarctic Ice Sheet collapse

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.

Strain Accumulation and Release Rate in Canada: Implications for Long‐Term Crustal Deformation and Earthquake Hazards

AbstractTo advance the understanding of crustal deformation and earthquake hazards in Canada, we analyze seismic and geodetic data sets and robustly estimate the crust strain accumulation and release rate by earthquakes. We find that less than 20% of the accumulated strain is released by earthquakes across the study area providing evidence for large‐scale aseismic deformation. We attribute this to glacial isostatic adjustment (GIA) in eastern Canada, where predictions from the GIA model account for most of the observed discrepancy between the seismic and the geodetic moment rates. In western Canada, only a small percentage (<20%) of the discrepancy can be attributed to GIA‐related deformation. We suspect that this may reflect the inaccuracy of the GIA model to account for heterogeneity in Earth structure or indicate that the present‐day effect of GIA in western Canada is limited due to the fast response of the upper mantle to the deglaciation of the Cordillera Ice Sheet. At locations of previously identified seismic source zones, we speculate that the unreleased strain is been stored cumulatively in the crust and will be released as earthquakes in the future. The Gutenberg‐Richter model predicts, however, that the recurrence interval can vary significantly in Canada, ranging from decades near plate boundary zones in the west to thousands of years in the stable continental interior. Our attempt to quantify the GIA‐induced deformation provides the necessary first step for the integration of geodetic strain rates in seismic hazard analysis in Canada.

Mapping terrestrial water storage changes in Canada using GRACE and GRACE-FO.

This study focused upon the estimation and analysis of terrestrial water storage (TWS changes) across the Canadian landscape. The estimation was performed using Gravity Recovery and Climate Experiment (GRACE) data from April 2002 to June 2017, and GRACE Follow-On (GRACE-FO) observations from June 2018 to December 2019. Removing the gravity effects of Glacial Isostatic Adjustment (GIA) signals and leakage is required to have realistic estimations of TWS changes in the Canadian landmass. In this study, GIA correction was based on a regional-scale modeling of uplift rate. To evaluate the performance compared to the latest GIA models, a comparison was made to uplift rate derived from 149 GPS stations over the study area. Refined TWS changes showed strong seasonal patterns (between -160mm and 80mm). The slope of the trend was positive (6.6mm/year) for the period combining both GRACE and GRACE-FO. The trend increases to 45mm/year over the 17-year period across central Canada, especially in regions surrounding Hudson Bay. For GRACE, maximum TWS variations occurred between February and April; for GRACE-FO, it occurred with a 2-month lag earlier during the short period being considered. Uncertainties in TWS variations that were derived by GRACE increased towards the end of the mission. Uncertainty for GRACE-FO is lower than that at the beginning of GRACE. The TWS changes extracted from the used approach were compared to Mascon solutions TWS changes products (GRCTellus JPL MSCNv02 and CSR MSCNv02), by using two steps: 1) the Water Global Assessment Prognosis hydrological model (WGHM), and 2) TWS changes derived from in-situ precipitation and potential evapotranspiration data. In all the cases our approach provided the best correlations and lower root mean square errors, compared to the Mascon products.

Interannual glacier and lake mass changes over Scandinavia from GRACE

SUMMARY The Gravity Recovery and Climate Experiment (GRACE) satellite gravimetry observations have been widely used in the study of glaciers. However, there is still no detailed GRACE-based study of the glaciers over the Scandinavian Mountains (SCAMs), where the glaciers are debris-covered and the effects of glacial isostatic adjustment (GIA) are significant. In this paper, GRACE observations are combined with climate data to analyse interannual mass changes in glacier and lake areas over Scandinavia during the period from 2003 to 2016. An inversion algorithm, the constrained forward modelling method, is used to recover the signals of glaciers and lakes from GRACE observations. Our results show that the total glacier mass loss rate over Scandinavia is –1.0 ± 1.1 Gt yr–1 during our study period. We find that the glacier accumulation regime in different subregions of the SCAMs may be different. The glacier mass change in the central SCAMs tends to be mainly driven by precipitation. Two rapid transitions from dry/wet years to wet/dry years in the lake area in south Scandinavia are identified by multiple data. The transitions are likely caused by changes in atmospheric circulation, that is surface wind. The mass changes of Scandinavia can be primarily explained by the influence of winds. We find that the glacier area is controlled by both the northerly and southerly winds, while the lake area is mainly driven by the southerly winds. This discrepancy leads to the different mechanisms of mass change in glacier and lake areas. We also discuss the influence of GIA, and suggest that the GRACE-derived long-term hydrology trends over Scandinavia may be unreliable and need to be verified. Our study indicates that GRACE data have potential in detecting small-scale glacier changes.

A global semi-empirical glacial isostatic adjustment (GIA) model based on Gravity Recovery and Climate Experiment (GRACE) data

Abstract. The effect of glacial isostatic adjustment (GIA) on the shape and gravity of the Earth is usually described by numerical models that solve for both glacial evolution and Earth's rheology, being mainly constrained by the geological evidence of local ice extent and globally distributed sea level data, as well as by geodetic observations of Earth's rotation. In recent years, GPS and GRACE observations have often been used to improve those models, especially in the context of regional studies. However, consistency issues between different regional models limit their ability to answer questions from global-scale geodesy. Examples are the closure of the sea level budget, the explanation of observed changes in Earth's rotation, and the determination of the origin of the Earth's reference frame. Here, we present a global empirical model of present-day GIA, solely based on GRACE data and on geoid fingerprints of mass redistribution. We will show how the use of observations from a single space-borne platform, together with GIA fingerprints based on different viscosity profiles, allows us to tackle the questions from global-scale geodesy mentioned above. We find that, in the GRACE era (2003–2016), freshwater exchange between land and oceans has caused global mean sea level to rise by 1.2±0.2 mm yr−1, the geocentre to move by 0.4±0.1 mm yr−1, and the Earth's dynamic oblateness (J2) to increase by 6.0±0.4×10-11 yr−1.

Sensitivity of inverse glacial isostatic adjustment estimates over Antarctica

Abstract. Glacial isostatic adjustment (GIA) is a major source of uncertainty for ice and ocean mass balance estimates derived from satellite gravimetry. In Antarctica the gravimetric effect of cryospheric mass change and GIA are of the same order of magnitude. Inverse estimates from geodetic observations hold some promise for mass signal separation. Here, we investigate the combination of satellite gravimetry and altimetry and demonstrate that the choice of input data sets and processing methods will influence the resultant GIA inverse estimate. This includes the combination that spans the full GRACE record (April 2002–August 2016). Additionally, we show the variations that arise from combining the actual time series of the differing data sets. Using the inferred trends, we assess the spread of GIA solutions owing to (1) the choice of different degree-1 and C20 products, (2) viable candidate surface-elevation-change products derived from different altimetry missions corresponding to different time intervals, and (3) the uncertainties associated with firn process models. Decomposing the total-mass signal into the ice mass and the GIA components is strongly dependent on properly correcting for an apparent bias in regions of small signal. Here our ab initio solutions force the mean GIA and GRACE trend over the low precipitation zone of East Antarctica to be zero. Without applying this bias correction, the overall spread of total-mass change and GIA-related mass change using differing degree-1 and C20 products is 68 and 72 Gt a−1, respectively, for the same time period (March 2003–October 2009). The bias correction method collapses this spread to 6 and 5 Gt a−1, respectively. We characterize the firn process model uncertainty empirically by analysing differences between two alternative surface mass balance products. The differences propagate to a 10 Gt a−1 spread in debiased GIA-related mass change estimates. The choice of the altimetry product poses the largest uncertainty on debiased mass change estimates. The spread of debiased GIA-related mass change amounts to 15 Gt a−1 for the period from March 2003 to October 2009. We found a spread of 49 Gt a−1 comparing results for the periods April 2002–August 2016 and July 2010–August 2016. Our findings point out limitations associated with data quality, data processing, and correction for apparent biases.

SELEN<sup>4</sup> (SELEN version 4.0): a Fortran program for solving the gravitationally and topographically self-consistent sea-level equation in glacial isostatic adjustment modeling

Abstract. We present SELEN4 (SealEveL EquatioN solver), an open-source program written in Fortran 90 that simulates the glacial isostatic adjustment (GIA) process in response to the melting of the Late Pleistocene ice sheets. Using a pseudo-spectral approach complemented by a spatial discretization on an icosahedron-based spherical geodesic grid, SELEN4 solves a generalized sea-level equation (SLE) for a spherically symmetric Earth with linear viscoelastic rheology, taking the migration of the shorelines and the rotational feedback on sea level into account. The approach is gravitationally and topographically self-consistent, since it considers the gravitational interactions between the solid Earth, the cryosphere, and the oceans, and it accounts for the evolution of the Earth's topography in response to changes in sea level. The SELEN4 program can be employed to study a broad range of geophysical effects of GIA, including past relative sea-level variations induced by the melting of the Late Pleistocene ice sheets, the time evolution of paleogeography and of the ocean function since the Last Glacial Maximum, the history of the Earth's rotational variations, present-day geodetic signals observed by Global Navigation Satellite Systems, and gravity field variations detected by satellite gravity missions like GRACE (the Gravity Recovery and Climate Experiment). The “GIA fingerprints” constitute a standard output of SELEN4. Along with the source code, we provide a supplementary document with a full account of the theory, some numerical results obtained from a standard run, and a user guide. Originally, the SELEN program was conceived by Giorgio Spada (GS) in 2005 as a tool for students eager to learn about GIA, and it has been the first SLE solver made available to the community.

On Some Properties of the Glacial Isostatic Adjustment Fingerprints

Along with density and mass variations of the oceans driven by global warming, Glacial Isostatic Adjustment (GIA) in response to the last deglaciation still contributes significantly to present-day sea-level change. Indeed, in order to reveal the impacts of climate change, long term observations at tide gauges and recent absolute altimetry data need to be decontaminated from the effects of GIA. This is now accomplished by means of global models constrained by the observed evolution of the paleo-shorelines since the Last Glacial Maximum, which account for the complex interactions between the solid Earth, the cryosphere and the oceans. In the recent literature, past and present-day effects of GIA have been often expressed in terms of fingerprints describing the spatial variations of several geodetic quantities like crustal deformation, the harmonic components of the Earth’s gravity field, relative and absolute sea level. However, since it is driven by the delayed readjustment occurring within the viscous mantle, GIA shall taint the pattern of sea-level variability also during the forthcoming centuries. The shapes of the GIA fingerprints reflect inextricable deformational, gravitational, and rotational interactions occurring within the Earth system. Using up-to-date numerical modeling tools, our purpose is to revisit and to explore some of the physical and geometrical features of the fingerprints, their symmetries and intercorrelations, also illustrating how they stem from the fundamental equation that governs GIA, i.e., the Sea Level Equation.