Glacial‐isostatic adjustment (GIA) is the key process controlling relative sea‐level (RSL) and paleo‐topography. The viscoelastic response of the solid Earth is controlled by its viscosity structure. ...Therefore, the appropriate choice of Earth structure for GIA models is still an important area of research in geodynamics. We construct 18 3D Earth structures that are derived from seismic tomography models and are geodynamically constrained. We consider uncertainties in 3D viscosity structures that arise from variations in the conversion from seismic velocity to temperature variations (factor r) and radial viscosity profiles (RVP). We apply these Earth models to a 3D GIA model, VILMA, to investigate the influence of such structure on RSL predictions. The variabilities in 3D Earth structures and RSL predictions are investigated for globally distributed sites and applied for comparisons with regional 1D models for ice center (North America, Antarctica) and peripheral regions (Central Oregon Coast, San Jorge Gulf). The results from 1D and 3D models reveal substantial influence of lateral viscosity variations on RSL. Depending on time and location, the influence of factor r and/or RVP can be reverse, for example, the same RVP causes lowest RSL in Churchill and largest RSL in Oregon. Regional 1D models representing the structure beneath the ice and 3D models show similar influence of factor r and RVP on RSL prediction. This is not the case for regional 1D models representing the structure beneath peripheral regions indicating the dependence on the 3D Earth structure. The 3D Earth structures of this study are made available.
Plain Language Summary
Around 21,000 years ago, sea level was 130 m below present‐day and large ice sheets with thicknesses of several kilometers were covering parts of North America and northern Europe. The response of the solid Earth due to ice‐sheet loading is called the glacial‐isostatic adjustment (GIA) and has caused subsidence of several hundreds of meters below ice sheets. The deformation behavior depends on the structure of the Earth's interior from the crust to the mantle. From seismic waves, we gain insight into the 3D Earth structure that varies laterally and with depth. However, there are still many unknowns characterizing feasible Earth structures. Therefore, the consideration of geodynamic and geological constraints is particularly essential, for example, for the validation of GIA models. Here, we use GIA models and implement an ensemble of geodynamically constrained 3D Earth structures, as well as Earth structures which vary with depth alone (1D), to simulate the sea level over the last 120,000 years. We investigate how uncertainties in the 3D Earth structure influence the predicted RSL variability.
Key Points
We create an ensemble of geodynamically constrained 3D Earth structures that vary in conversion from seismic tomography models to viscosity
We predict the relative sea‐level over the last deglaciation period and investigate the effect of 3D Earth structure variations
We observe variability in the response which cannot be reproduced by applying regionally adapted 1D Earth models
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•Local Green's functions to estimate hydrological loading displacements.•Consideration of heterogeneities in Earth's crust.•Scatter plots show dependency between loading response and ...local crustal structure.•Crustal stratification influences near-field displacements.•Impact of crustal structure is relevant for hydrological loading displacements.
The influence of the elastic Earth properties on seasonal or shorter periodic surface deformations due to atmospheric surface pressure and terrestrial water storage variations is usually modeled by applying a local half-space model or an one dimensional spherical Earth model like PREM from which a unique set of elastic load Love numbers, or alternatively, elastic Green's functions are derived. The first model is valid only if load and observer almost coincide, the second model considers only the response of an average Earth structure. However, for surface loads with horizontal scales less than 2500km2, as for instance, for strong localized hydrological signals associated with heavy precipitation events and river floods, the Earth elastic response becomes very sensitive to inhomogeneities in the Earth crustal structure.
We derive a set of local Green's functions defined globally on a 1°×1° grid for the 3-layer crustal structure TEA12. Local Green's functions show standard deviations of ±12% in the vertical and ±21% in the horizontal directions for distances in the range from 0.1° to 0.5°. By means of Green's function scatter plots, we analyze the dependence of the load response to various crustal rocks and layer thicknesses. The application of local Green's functions instead of a mean global Green's function introduces a variability of 0.5–1.0mm into the hydrological loading displacements, both in vertical and in horizontal directions. Maximum changes due to the local crustal structures are from −25% to +26% in the vertical and −91% to +55% in the horizontal displacements. In addition, the horizontal displacement can change its direction significantly. The lateral deviations in surface deformation due to local crustal elastic properties are found to be much larger than the differences between various commonly used one-dimensional Earth models.
We present a new set of global and local sea‐level projections at example tide gauge locations under the RCP2.6, RCP4.5, and RCP8.5 emissions scenarios. Compared to the CMIP5‐based sea‐level ...projections presented in IPCC AR5, we introduce a number of methodological innovations, including (i) more comprehensive treatment of uncertainties, (ii) direct traceability between global and local projections, and (iii) exploratory extended projections to 2300 based on emulation of individual CMIP5 models. Combining the projections with observed tide gauge records, we explore the contribution to total variance that arises from sea‐level variability, different emissions scenarios, and model uncertainty. For the period out to 2300 we further breakdown the model uncertainty by sea‐level component and consider the dependence on geographic location, time horizon, and emissions scenario. Our analysis highlights the importance of local variability for sea‐level change in the coming decades and the potential value of annual‐to‐decadal predictions of local sea‐level change. Projections to 2300 show a substantial degree of committed sea‐level rise under all emissions scenarios considered and highlight the reduced future risk associated with RCP2.6 and RCP4.5 compared to RCP8.5. Tide gauge locations can show large ( > 50%) departures from the global average, in some cases even reversing the sign of the change. While uncertainty in projections of the future Antarctic ice dynamic response tends to dominate post‐2100, we see substantial differences in the breakdown of model variance as a function of location, time scale, and emissions scenario.
Key Points
We have developed a new set of global and local sea‐level projections for the 21st century and extended to 2300 that are rooted in CMIP5 climate model simulations, including more comprehensive treatment of uncertainty than previously reported in IPCC AR5
Analysis of local sea‐level projections and tide gauge data suggests that local variability will dominate the total variance in sea‐level change for the coming decades at all locations considered
The extended sea‐level projections highlight the substantial multicentury sea‐level rise commitment under all RCP scenarios and the dependence of modeling uncertainty on geographic location, time horizon, and climate scenario
We present regional-scale mass balances for 25 drainage basins of the Antarctic Ice Sheet (AIS) from satellite observations of the Gravity and Climate Experiment (GRACE) for time period January 2003 ...to September 2012. Satellite gravimetry estimates of the AIS mass balance are strongly influenced by mass movement in the Earth interior caused by ice advance and retreat during the last glacial cycle. Here, we develop an improved glacial-isostatic adjustment (GIA) estimate for Antarctica using newly available GPS uplift rates, allowing us to more accurately separate GIA-induced trends in the GRACE gravity fields from those caused by current imbalances of the AIS. Our revised GIA estimate is considerably lower than previous predictions, yielding an estimate of apparent mass change of 53 plus or minus 18 Gt yr super(-1). Therefore, our AIS mass balance of -114 plus or minus 23 Gt yr super(-1) is less negative than previous GRACE estimates. The northern Antarctic Peninsula and the Amundsen Sea sector exhibit the largest mass loss (-26 plus or minus 3 Gt yr super(-1) and -127 plus or minus 7 Gt yr super(-1), respectively). In contrast, East Antarctica exhibits a slightly positive mass balance (26 plus or minus 13 Gt yr super(-1)), which is, however, mostly the consequence of compensating mass anomalies in Dronning Maud and Enderby Land (positive) and Wilkes and George V Land (negative) due to interannual accumulation variations. In total, 6% of the area constitutes about half the AIS imbalance, contributing 151 plus or minus 7 Gt yr super(-1) (ca. 0.4 mm yr super(-1)) to global mean sea-level change. Most of this imbalance is caused by ice-dynamic speed-up expected to prevail in the near future.
Summary
The study of glacial isostatic adjustment (GIA) is gaining an increasingly important role within the geophysical community. Understanding the response of the Earth to loading is crucial in ...various contexts, ranging from the interpretation of modern satellite geodetic measurements (e.g. GRACE and GOCE) to the projections of future sea level trends in response to climate change. Modern modelling approaches to GIA are based on various techniques that range from purely analytical formulations to fully numerical methods. Despite various teams independently investigating GIA, we do not have a suitably large set of agreed numerical results through which the methods may be validated; a community benchmark data set would clearly be valuable. Following the example of the mantle convection community, here we present, for the first time, the results of a benchmark study of codes designed to model GIA. This has taken place within a collaboration facilitated through European Cooperation in Science and Technology (COST) Action ES0701. The approaches benchmarked are based on significantly different codes and different techniques. The test computations are based on models with spherical symmetry and Maxwell rheology and include inputs from different methods and solution techniques: viscoelastic normal modes, spectral-finite elements and finite elements. The tests involve the loading and tidal Love numbers and their relaxation spectra, the deformation and gravity variations driven by surface loads characterized by simple geometry and time history and the rotational fluctuations in response to glacial unloading. In spite of the significant differences in the numerical methods employed, the test computations show a satisfactory agreement between the results provided by the participants.
The problem of compressibility in modelling of viscoelastic deformations of planetary bodies is still a topic under discussion. Studies facing this topic discuss the error when considering a ...stratification of layers with constant material parameters. But homogeneous compressible layers imply that the initial state is not stable. So, any perturbation method applied to this type of state results in an ill-posed problem, evident in a denumerable infinite set of modes in the spectral representation of the solution. Based on the analytic solution of Cambiotti and Sabadini, we discuss any violation from the stable Adams-Williamson condition to result in unphysical behaviour where we concentrate here on the consequences for the horizontal displacement and deformation within the mantle due to surface loading. This focus motivates to revisit the Longman paradox, which discusses the boundary conditions for a compressible fluid core.
Global navigation satellite systems (GNSSs) have revealed that a mega-thrust earthquake that occurs in an island-arc trench system causes post-seismic crustal deformation. Such crustal deformation ...data have been interpreted by combining three mechanisms: afterslip, poroelastic rebound and viscoelastic relaxation. It is seismologically important to determine the contribution of each mechanism because it provides frictional properties between the plate boundaries and viscosity estimates in the asthenosphere which are necessary to evaluate the stress behaviour during earthquake cycles. However, the observation sites of GNSS are mostly deployed over land and can detect only a small part of the large-scale deformation, which precludes a clear separation of the mechanisms. To extend the spatial coverage of the deformation area, recent studies started to use satellite gravity data that can detect long-wavelength deformations over the ocean. To date, compared with theoretical models for calculating the post-seismic crustal deformation, a few models have been proposed to interpret the corresponding gravity variations. Previous approaches have adopted approximations for the effects of compressibility, sphericity and self-gravitation when computing gravity changes. In this study, a new spectral-finite element approach is presented to consider the effects of material compressibility for Burgers viscoelastic earth model with a laterally heterogeneous viscosity distribution. After the basic principles are explained, it is applied to the 2004 Sumatra–Andaman earthquake. For this event, post-seismic deformation mechanisms are still a controversial topic. Using the developed approach, it is shown that the spatial patterns of gravity change generated by the above three mechanisms clearly differ from one another. A comparison of the theoretical simulation results with the satellite gravity data obtained from the Gravity Recovery and Climate Experiment reveals that both afterslip and viscoelastic relaxation are occurring. Considering the spatial patterns in satellite gravity fields is an effective method for investigating post-seismic deformation mechanisms.
Geoscientific modeling and simulation helps to improve our understanding of the complex Earth system. During the modeling process, validation of the geoscientific model is an essential step. In ...validation, it is determined whether the model output shows sufficient agreement with observation data. Measures for this agreement are called goodness of fit. In the geosciences, analyzing the goodness of fit is challenging due to its manifold dependencies: 1) The goodness of fit depends on the model parameterization, whose precise values are not known. 2) The goodness of fit varies in space and time due to the spatio-temporal dimension of geoscientific models. 3) The significance of the goodness of fit is affected by resolution and preciseness of available observational data. 4) The correlation between goodness of fit and underlying modeled and observed values is ambiguous. In this paper, we introduce a visual analysis concept that targets these challenges in the validation of geoscientific models - specifically focusing on applications where observation data is sparse, unevenly distributed in space and time, and imprecise, which hinders a rigorous analytical approach. Our concept, developed in close cooperation with Earth system modelers, addresses the four challenges by four tailored visualization components. The tight linking of these components supports a twofold interactive drill-down in model parameter space and in the set of data samples, which facilitates the exploration of the numerous dependencies of the goodness of fit. We exemplify our visualization concept for geoscientific modeling of glacial isostatic adjustments in the last 100,000 years, validated against sea levels indicators - a prominent example for sparse and imprecise observation data. An initial use case and feedback from Earth system modelers indicate that our visualization concept is a valuable complement to the range of validation methods.
Variations in terrestrial surface water storage cause elastic crustal displacements of several millimeters in the vertical direction on daily to seasonal time scales. Locally, strong signals with ...exceptionally high amplitudes can be observed along the major river channels. As the horizontal resolution of global hydrological models is typically limited to 0.5° × 0.5°, the generalized model drainage network leads to simulated river mass distributions that are not necessarily collocated with the real courses of the rivers. Moreover, the spreading of locally concentrated surface water on the coarse model grids leads to substantially underestimated amplitudes of simulated hydrologically induced surface displacements. We therefore develop a relocation procedure to improve such hydrological loading estimates, especially at locations near the river banks. We separate the water masses stored in the modeled river network from the total water storage and relocate them on a georeferenced river map with higher resolution. Applying the relocated river masses, simulated hydrological loading amplitudes increase by 0.2–5 mm for the vertical load‐induced surface displacement along the major rivers, at the Amazon even up to additional 15 mm. The amplitudes for the horizontal load‐induced surface displacements are slightly increased, up to maximum 3 mm. Besides changes in the distance to the mass loads, the horizontal displacement fields is also heavily affected by significant changes in the directions to the relocated river mass load. The comparison of modeled hydrologically induced surface displacement time series with Global Positioning System observations shows a significantly improved fit for stations in close proximity to larger rivers when applying the relocation procedure.
Plain Language Summary
Variations in terrestrial surface water loads cause an elastic deformation of the Earth's lithosphere of several millimeters in the vertical direction. Locally, strong signals with exceptionally high amplitudes can be observed along the channels of large river like the Amazon, Nile, or Lena. In order to predict such hydrology‐induced surface displacements, mass distributions from global hydrological models are employed. Due to the limited resolution of such modeled mass loads, typically only 0.5°, the outspread and dislocated river mass distributions lead underestimated displacement amplitudes at even wrong locations. We therefore develop a relocation procedure to improve such hydrological loading estimates, especially at locations near the river banks. Water stored in model's river network is mapped onto a georeferenced river map with higher spatial resolution. Simulated hydrological loading amplitudes calculated from the refined river storage estimates significantly improve along the world's major rivers when compared to displacement time series as observed with Global Positioning System.
Key Points
The relocation procedure maps river storage from the 0.5 degrees model representation onto a 0.125 degrees river map
After applying the relocation procedure to modeled river storage data, the estimated hydrology‐induced surface displacements significantly improve
The relocation function can be generated automatically from the model river network
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