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Farrell and Clark, ; Mitrovica and Milne, ; Spada and Stocchi, ; Spada, , and hence we briefly restate the main form of the equation here, starting with a definition of relative sea level. Here, S is relative sea level or water depth; N is absolute sea level, defined as the height of the sea surface above the centre of mass of the solid Earth, and U is the height of the seafloor, again defined relative to the centre of mass of the solid Earth. From Eq. Deformation of these two surfaces occurs in response to ice and ocean load changes, as calculated within the sea-level equation.
The first two terms on the right-hand side of Eq. The first term on the right-hand side of Eq. Today, it is used to describe the relationship between global ice volume change and global mean sea-level change, but the conversion is not straightforward Milne et al. By accounting for the time dependence of ocean area in Eq.
Inclusion of this dynamic effect, along with consideration of rotational feedback Sect. The final two terms of Eq. These final terms must be subtracted because although the mean of the spatially varying terms will be zero when integrated over the whole of Earth's surface, the mean will not necessarily be zero when integrated over the ocean; hence, a uniform shift is applied to conserve mass.
The following two sections describe recent extensions to the sea-level equation and outline how it has been used to provide confirmation of several global-scale processes that were hypothesized during the 19th and early 20th centuries. First, since the ocean is not typically bounded by vertical cliffs, a rise or fall in sea level at a particular location will result in onlap or offlap and hence an increase or decrease in the area of the ocean, respectively.
Secondly, during past glacial periods all the major ice sheets grew beyond the confines of the continent on which they were initially situated, expanding into the ocean and forming large areas of marine-grounded ice. Temporal variations in the extent of a marine-grounded ice sheet will alter the ocean area over which meltwater can be redistributed. In the near field of a melting ice sheet, rebound results in local sea-level fall, causing the shoreline to migrate offshore offlap. In the far field of a melting ice sheet, sea-level rise causes the shoreline to migrate onshore onlap.
An additional extension to the sea-level equation involves the treatment of rotational feedback Fig. It is clear that since GIA alters the distribution of mass throughout the Earth system, this will perturb the magnitude and direction of Earth's rotation vector e. Nakiboglu and Lambeck, ; Sabadini et al. These changes will, in turn, affect a number of processes associated with GIA: changing the Earth's rotation vector will instantaneously alter the shape of the sea surface, i. Over both timescales these mechanisms result in a long-wavelength change in the distribution of water across the ocean, and this will excite additional solid Earth deformation, thus further altering the rotational state of the Earth.
Temporal variations in water depth arise due to changes in the total mass of the ocean as described by Croll, and the shape of its two bounding surfaces; the sea surface as proposed by Woodward, and the solid Earth as proposed by Jamieson, , and Gilbert, b. Observations of relative sea-level change therefore require careful interpretation, particularly if they are to be used to determine changes in global ice volume.
Relative sea level rises and falls in opposing quadrants of the Earth. The magnitude of sea-level change in the far field of the major ice sheets has long been used to constrain changes in global ice volume e. Fairbanks, ; Fleming et al. It is clear that sea-level change in the near field of an ice sheet will reflect perturbations to the shape of the geoid and the solid Earth due to the presence, and loading effect, of the evolving ice sheet as well as changes in total ocean mass e.
Shennan et al. The most important of these processes are outlined below. Meltwater fingerprints building on theory developed by Woodward, : sea-level change associated with the addition of meltwater to the ocean will be spatially variable Milne et al. Consequently, the increase in water depth far from the melting ice sheet will be greater than the global mean. Ocean syphoning originally hypothesized by Nansen, : in the same way that rebound in response to ice mass loss can persist for many thousands of years, subsidence of peripheral bulge regions also continues long after the ice sheets have melted.
These peripheral bulge regions surround the former ice sheets and are typically located offshore, and hence their collapse acts to increase the capacity of the ocean basins Fig. In the absence of significant changes in ocean volume, peripheral bulge collapse will result in a fall in absolute sea level the height of the sea surface relative to the centre of the Earth even though global mean water depth will be unchanged.
This ocean syphoning effect explains why mid-Holocene sea-level highstands are observed across many equatorial regions Mitrovica and Peltier, b; Mitrovica and Milne, , and it must also be accounted for when interpreting contemporary measurements of global sea-level change derived from satellite altimetry Tamisiea, At sites located on a subsiding peripheral bulge, relative sea-level rise will occur throughout an interglacial period, even if global ice volumes remain roughly constant Lambeck et al.
Continental levering: during the LGM lowstand many continental shelves were sub-aerially exposed. Loading by the ocean during the subsequent sea-level rise will have caused the newly submerged continental shelves to be flexed downwards and the margins of the continents to be flexed upwards Walcott, In particular, it should be noted that coastlines orientated perpendicular to the continental shelf break will experience differential amounts of uplift e.
Lambeck and Nakada, ; Clement et al. In order to calculate the solid Earth response to surface load change over glacial timescales the Earth is commonly assumed to be a linear Maxwell viscoelastic body Peltier, , although a number of studies alternatively adopt a power-law approach Wu, The spatially variable, time-dependent response of a Maxwell body to surface load change can be calculated using viscoelastic Love numbers building on the work of Love, , which define the response of a spherically symmetric, self-gravitating, viscoelastic sphere to an impulse point load Peltier, ; Wu, ; Han and Wahr, The Love numbers reflect the assumed viscosity profile of the mantle, which must be defined a priori.
Alternatively, if a power-law approach is used, the problem becomes non-linear and the Love number approach cannot be used. Instead, the effective viscosity of the mantle will depend on the stress field throughout the mantle, which depends on surface load change. The non-linear stress—strain relationships that form the basis of the power-law approach are based on the results of laboratory experiments that seek to understand the controls on deformation within the mantle Hirth and Kohlstedt, For both approaches the elastic and density structure throughout the Earth must be defined e.
Dziewonski and Anderson, , and the deformation of the whole Earth must be considered if the sea-level equation is to be solved recall that the sea-level equation solves for global meltwater distribution. In a GIA model the lithosphere is typically represented by an elastic layer or a viscoelastic layer with viscosity high enough to behave elastically on the timescale of a glacial cycle tens of thousands of years e. Kuchar and Milne, The thickness of this layer influences the wavelength of deformation Nield et al. It therefore follows that the rheological properties of the Earth may be inferred from observations Fig.
However, in reality, poor data coverage, uncertainties associated with the ice load history, and spatial variations in Earth rheology make it difficult to uniquely determine an optimal solution for Earth properties such as lithosphere thickness or mantle viscosity. To overcome this, some studies consider multiple geodynamic processes when seeking to constrain mantle rheology e. Mitrovica and Forte, , while others use independent data sets to define the rheological properties of the Earth. As an example, seismic wave speeds can be related to the temperature distribution in the mantle, which in turn may be related to mantle viscosity Ivins and Sammis, This approach is discussed in more detail in Sect.
When considering a spherically symmetric Earth with linear rheology, the sea-level equation is most commonly solved using a pseudo-spectral approach e.
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Mitrovica and Peltier, b; Mitrovica and Milne, ; Kendall et al. However, finite-element e. Wu and van der Wal, ; Zhong et al. Martinec, ; Tanaka et al. Latychev et al. The equations used to represent solid Earth deformation may differ between these approaches, and in particular the finite-element approach was originally developed to permit consideration of power-law rheology Wu, A description of the different methods used to determine the response of the solid Earth to surface loading is given in the GIA benchmarking study of Spada et al. In all cases, an iterative approach is required to determine a gravitationally self-consistent solution to the sea-level equation since the time-dependent change in ocean loading is not known a priori.
A number of studies have sought to model the solid Earth component of GIA without solving the sea-level equation. These are often regional studies, where the focus is on determining the solid Earth response to local ice load change e. Auriac et al. Focusing on a regional rather than a global domain allows the surface load to be modelled at high resolution e. Nield et al. Kaufmann et al. In a few cases GIA models have been extended to explore the potential for GIA-related stress change to trigger earthquakes e.
Spada et al. Steffen et al. The majority of these studies use either a 2-D or 3-D finite-element approach that includes an elastic upper layer and a viscoelastic mantle. Within the model, the stress field associated with GIA is combined with the background tectonic stress field and a Coulomb failure criterion is implemented on pre-existing fault planes to identify faulting events. Models have been used to calculate the likely magnitude and timing of slip on a range of different orientations of faults in response to different ice-sheet sizes R.
A fundamental component of GIA modelling is the use of data to constrain unknown factors associated with the ice history and Earth rheology Fig. Different data have different roles. For example, dated geomorphological evidence for past ice extent can be used to define the surface load history, while observations relating to solid Earth deformation, such as relative sea-level indicators or GPS data, can be used to tune the rheological model.
There exist strong trade-offs between the timing and the magnitude of past surface load change Fig. One way to address this non-uniqueness is to independently constrain ice history and Earth rheology outside the confines of the GIA model. Alternatively, data sets that are sensitive to both factors, such as observations relating to past sea-level change, provide very powerful constraints on the coupled problem e. Future work should focus on collecting new data from locations that are optimally sensitive to the details of ice history or Earth rheology Wu et al. In all cases where data are used to tune a GIA model, it is important to assess whether there are unmodelled processes reflected in the data that may bias the results, and care must be taken to assign realistic errors.
The key data sets used in studies of GIA are briefly described below. A sea-level indicator is a piece of evidence that provides information on past sea level. In order to be compared with GIA model output, the age and current elevation of a sea-level indicator must be known including associated uncertainties , as well as the relationship between the sea-level indicator and mean sea level. Past relative sea-level change will be preserved in the geological record as a change in the position of the shoreline or a change in water depth. Past shoreline change can be reconstructed by identifying the time at which a particular location was inundated by, or isolated from, the ocean Fig.
Such information can be derived from microfossil analysis of the sediment contained within isolation basins lakes that were previously connected to the ocean, or former lakes that are now drowned e. Watcham et al. In some cases, sea-level indicators may only indicate whether a particular location was previously above or below sea level. For example, archaeological artefacts typically provide an upper bound on contemporaneous sea level, while the presence of any type of in situ marine material provides a lower bound on past sea level. More specifically, if a fossil shell or coral is found still in its growth position either above or below present sea level and its living-depth range is known, this can be used to determine past water depths e.
Deschamps et al. Although, note that temporal variations in local conditions, e.
At higher latitudes, reconstructions of salt marsh environments have proved very useful for determining not only past changes in water depth but also more subtle information relating to whether the sea level was rising or falling in the past Barlow et al. Finally, if past shorelines can be continuously reconstructed over length scales of a few kilometres or more, then the subsequent warping of these contemporaneous surfaces provides a powerful constraint on GIA McConnell, Church and White, Much of the observed spatial variation will be due to steric changes, but if this can be accounted for, then the remaining pattern of sea-level change provides information on both past and present ice-sheet change Hay et al.
Data relating to past ice extent, thickness, and flow direction all contribute useful information to ice-sheet reconstructions, with the latter providing an indication of past ice-sheet dynamics, and hence the location of former ice domes e. Margold et al. Terrestrial and marine geomorphological features that must have formed at the margin of a former ice sheet, such as moraines, grounding zone wedges, or deposits relating to ice-dammed lakes, can be used to build a picture of past ice extent if the age of the features can be precisely dated.
Indeed, a series of snapshots of past ice-sheet extent have been constructed from geomorphological data for the Laurentide, British—Irish, and Fennoscandian ice sheets Dyke et al. In contrast, determining past ice thickness over large spatial scales is more difficult. Field-based reconstructions of past ice thickness typically rely on cosmogenic exposure dating to determine when, and to what depth, mountain ranges in the interior of a former ice sheet were last covered by ice Ballantyne, Care must be taken when interpreting such information because complex topography will perturb the local ice flow, with the result that local ice thickness fluctuations may not represent regional-scale ice-sheet thickness change.
Another issue that must be taken into consideration is the fact that often only evidence relating to the last glacial advance will be preserved, with evidence relating to earlier fluctuations typically having been destroyed due to the erosive nature of ice. The task of determining the history of an ice sheet that is still present is more difficult, since any evidence relating to a smaller-than-present ice sheet will be obscured.
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Such a configuration can be inferred if moraines are truncated by the current ice sheet or if contemporary ice-sheet retreat exposes organic material that has been preserved beneath the ice — such material can be dated to determine when it was overrun by ice Miller et al. An alternative approach that should be pursued is the recovery of geological samples from beneath the current ice sheets; a number of techniques e. Finally, sampling of ice cores extracted from the ice sheet can provide an indication of past ice thickness, via the analysis of either the gas bubbles preserved in the ice or the isotopic composition of the ice itself Parrenin et al.
Simpson et al. See Sects. A number of geodetic data sets are used to quantify surface deformation associated with GIA King et al. These data must be corrected for signals associated with the global water cycle, atmospheric effects, and local processes associated with tectonics or sediment compaction King et al. In areas where non-GIA signals are well constrained and there is a dense network of measurements, such as across North America Sella et al. Milne et al. However, in regions where contemporary ice mass change also contributes to present-day solid Earth deformation, it becomes difficult to disentangle contributions from past and present ice-sheet change Thomas et al.
Horizontal GPS rates are often more precise than vertical rates by an order of magnitude King et al. This is non-trivial, since neither plate motion nor GIA are perfectly known King et al. It has long been known that horizontal deformation in response to surface loading can be strongly perturbed by the presence of lateral variations in Earth rheology Kaufmann et al. Steffen and Wu, Geodetic information is typically provided on a reference frame whose origin is located at the centre of mass of the entire Earth system e.
ITRF; Altamimi et al. Reference frame differences must therefore be accounted for when comparing model output with GPS data, along with uncertainties associated with the realization of the origin of the reference frame King et al. Between and , repeat measurements of the Earth's gravity field by the Gravity Recovery and Climate Experiment GRACE satellites allowed temporal variations in the distribution of mass throughout the cryosphere, the atmosphere, the oceans, and the solid Earth to be quantified e.
Wouters et al. Tamisiea et al. Root et al. Paulson et al. However, in areas where an ice sheet is still present, variations in the local gravity field will reflect the solid Earth response to both past and present ice mass change, as well as contemporary changes to the mass of the ice sheet itself Wahr et al.
In this situation, a joint approach to solving for GIA and contemporary ice mass change is necessary, often via the combination of GRACE data with other data sets see Sect. Sasgen et al. On a more local scale, absolute gravity measurements have been used to study GIA e.
Global sea level change signatures observed by GRACE satellite gravimetry
Peltier, ; Steffen et al. Wahr et al. The rheology of the mantle and the thickness of the lithosphere are often inferred by comparing GIA model output with observations that reflect past and present rates of solid Earth deformation, such as GPS time series or records of past relative sea-level change e.
However, GIA model predictions will be sensitive to the assumed ice history, and therefore it can be useful to draw on independent information to constrain properties of the solid Earth. Lithosphere thicknesses can be inferred from inversions of gravity or seismic data or via thermal modelling, although it should be noted that the apparent thickness of the lithosphere will depend on the timescale of the loading Watts et al. Finally, mantle viscosities can be independently estimated via a number of approaches, including consideration of processes associated with mantle convection e.
Mitrovica and Forte, or via the conversion of seismic velocity perturbations into mantle viscosity variations e. Ivins and Sammis, ; Wu and van der Wal, ; Latychev et al. If these processes can be quantified e. Gross and Vondrak, ; Cheng and Tapley, , they can be used to place constraints on lower mantle viscosity e. However, it should be noted that these large-scale processes will also be affected by contemporary surface mass redistribution, for example, associated with melting of the polar ice sheets Adhikari and Ivins, Unloading of the solid Earth during deglaciation alters the regional stress field and can trigger glacially induced faulting Arvidsson, ; Lund, However, it is not straightforward to infer past changes in surface loading from the regional faulting history because although deglaciation can trigger faulting, GIA-induced stress changes are probably only capable of triggering slip on pre-existing faults R.
Glacial loading is thought to promote fault stability Arvidsson, ; R. The timing of faulting can therefore provide some insight into the timing of ice unloading and potentially also the rheological properties of the mantle Brandes et al. It is more difficult to draw conclusions about the spatial history of the ice sheet from the distribution of faulting because modelling suggests that only small stress changes are required to trigger seismicity R.
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Finite-element modelling of glacially induced faulting indicates that the magnitude of fault slip is primarily governed by shallow Earth properties and fault geometry R. Key results are briefly outlined below. GIA modelling is one of the principle approaches used to determine mantle viscosity. Mitrovica, ; Lambeck et al.
It is generally agreed that the viscosity of the lower mantle is greater than that of the upper mantle, but the magnitude of the increase across this boundary continues to be the subject of significant discussion e. Mitrovica and Forte, ; Lau et al. GIA modelling can be used to solve for the depth-dependent viscosity profile of the mantle, but it is important to assess the resolving power of the constraining data sets when considering the accuracy and uniqueness of the results Mitrovica and Peltier, a; Milne et al. GIA modelling has been used to infer past global ice volumes, primarily via the comparison of low latitude relative sea-level records with GIA model output.
Estimates of global ice volume during three key periods are summarized below. Peltier, ; Lambeck et al. Small magnitude ice volume changes subsequent to this time are less well constrained Lambeck et al. Combining GIA modelling with a probabilistic approach, Kopp et al. Uncertainty associated with the interpretation and dating of sea-level indicators Rovere et al. Considering even earlier warm periods, Raymo et al. However, in order to reconstruct global ice volumes at this time, the complicating effects of tectonics, dynamic topography, and sediment compaction must be accounted for Rovere et al.
In addition to constraining global ice volumes, comparison of GIA model output with a range of data sets has been used to reconstruct the past configuration of individual ice sheets, including the Fennoscandian Lambeck et al. Due to a lack of constraining data, there are often large discrepancies between different ice-sheet reconstructions. Global ice-sheet reconstructions also exist Peltier, ; Peltier et al. Finally, improved quantification of the geodetic signal associated with past ice-sheet change has led to recent improvements in the accuracy of contemporary estimates of ice mass balance, as derived from GRACE or altimetry data King et al.
Understanding the rate, magnitude, and spatial pattern of past, present, and future sea-level change and linking these changes to climate forcing is one of the most important questions facing modern society IPCC, Important results that have been derived using GIA modelling include. Clark et al. Kopp et al. Riva et al. Mitrovica et al. All of these results draw on the complex relationship between ice-sheet change and spatially variable sea-level change, as described by the sea-level equation.
Significant advances in our understanding of sea-level and ice-sheet change have come about due to improvements in data availability and GIA modelling capability during the last decade, but persistent uncertainties associated with the GIA correction that must be applied when interpreting gravity, altimetry, tide gauge, or GPS data Tamisiea, and ongoing ambiguity associated with the interpretation of palaeo-data mean than future progress will require input from a diverse range of disciplines.
Over the past decade there have been rapid advances in our understanding of how GIA processes can influence other dynamic systems and an increased awareness of additional factors that must be considered when seeking to constrain or tune a GIA model using independent data sets. New approaches of isolating the GIA signal have also been devised. Four of the most important recent advances are briefly described in this section. However, it is only recently that glaciologically consistent ice-sheet reconstructions, i.
Tarasov and Peltier, ; Tarasov et al. A crucial boundary condition that must be defined when modelling the evolution of a marine-grounded ice sheet is the water depth of the surrounding ocean. This water depth determines where the ice sheet begins to float, a point known as the grounding line. More importantly, it determines the rate at which ice flows across the grounding line and into the ocean because ice flux depends on ice thickness; Schoof, Numerical ice-sheet models are typically run assuming that sea-level change adjacent to an ice sheet will track global mean sea-level change.
Far-field ice melt will indeed cause near-field sea-level rise Fig. The decreased gravitational attraction of the melting ice sheet also acts to reduce local water depths. Modelling both effects, Gomez et al. Spatially variable water depth boundary conditions were first used in conjunction with a numerical ice-sheet model, for the purposes of reconstructing past ice-sheet change, by Whitehouse et al. Subsequently, Gomez et al. If the coupled model results are robust this makes it difficult to account for the global mean sea-level lowstand during the LGM Clark and Tarasov, This has a stabilizing effect on the ice sheet and results in grounding line advance.
Considering future ice-sheet change, Adhikari et al. A crucial factor in determining the stability of an ice sheet is the resistance provided by the surrounding floating ice shelves. If rebound is fast enough for the ice shelves to re-ground on submerged topographic highs, forming ice rises Matsuoka et al. Uncertainties associated with the bathymetry and the upper mantle viscosity beneath the Antarctic and Greenland ice sheets currently present the greatest barriers to accurately quantifying the degree to which GIA-related feedbacks have the potential to limit future ice loss from these regions.
GIA models traditionally assume the Earth behaves as a linear Maxwell viscoelastic body with a viscosity profile that varies in the radial direction only and stays constant with time e. Peltier et al. A number of studies have made use of a bi-viscous Burgers rheology within a radially varying framework, in which mantle deformation is dominated by the behaviour of two viscosities linearly relaxing over different timescales Yuen et al. However, an increasing number of studies are making use of a framework that can accommodate three-dimensional variations in mantle viscosity e.
Ivins and Sammis, ; Martinec, ; Latychev et al. The effect of including plate boundaries Klemann et al. It is important to question whether such increased model complexity is necessary. Whitehouse et al. Since solid Earth deformation depends on both the surface load history and Earth rheology, non-uniqueness is a problem when solving for these two unknowns.
For example, past ice thickness change is likely to be overestimated in regions where the local mantle viscosity is weaker than assumed by the model Fig. Similarly, global ice volumes may be incorrectly inferred if viscosity variations are ignored at far-field sea-level sites Austermann et al. If the past ice history of a region has been independently determined then neglect of lateral variations in Earth structure will lead to bias in predictions of the GIA signal and hence bias in estimates of contemporary ice-sheet mass balance, potentially on the order of tens of gigatons per year van der Wal et al.
Furthermore, models that consider the coupled evolution of the ice-sheet—solid Earth system see Sect. The net redistribution of mass solid Earth and sediment will also change the shape of the geoid and hence local sea level. A range of approaches are used to define spatial variations in Earth rheology, but most rely on deriving a temperature field from a seismic velocity model e.
Ritsema et al. Ivins and Sammis, ; Latychev et al. This derivation is not straightforward, and in particular, compositional effects must be accounted for when interpreting seismic velocity perturbations in terms of temperature perturbations Wu et al. If a power-law approach is used, grain-scale deformation of mantle material is described by diffusion and dislocation creep through the use of a non-linear relationship where the strain rate depends on stress to some power. This power is thought to be 1 for diffusion creep — i. This has implications for the inferred viscosity of the mantle: if dislocation creep is important, i.
Inputs to the power-law relationship include grain size, water content, and melt content, as well as temperature, although a lack of direct observational data for most of these parameters mean that values derived in laboratory experiments are often adopted Hirth and Kohlstedt, ; Burgmann and Dresen, ; King, Significant further work is needed to better quantify the viscosity distribution throughout the mantle and to determine the spatial resolution at which viscosity variations must be resolved to accurately reflect the global GIA process Steffen and Wu, The isostatic response to sediment erosion and deposition, on glacial and longer timescales, has long been considered in studies of onshore and offshore crustal deformation, associated with both fluvial and glacial systems.
However, the impact of sediment redistribution on Earth's gravitational and rotational fields, and the consequent effect on sea-level, has only recently been considered. Dalca et al. The resulting theory has been used to demonstrate that the impact of sediment erosion and deposition, associated with both fluvial and glacial systems, can alter relative sea level by several metres over the course of a glacial cycle and rates of present-day deformation by a few tenths of a millimetre per year Wolstencroft et al. Although the magnitude of the perturbation due to sediment loading is small, it is greater than the precision of modern geodetic methods and hence has the potential to bias contemporary estimates of sea-level change Ferrier et al.
Perhaps the most important finding of these preliminary studies is the observation that in order for relative sea-level indicators to be used to constrain past global ice volumes, they must first be corrected for the effects of both glacial and sedimentary isostasy Ferrier et al. As an example, if sediment loading has caused a sea-level indicator to subside subsequent to its formation, this will lead to an overestimation of the magnitude of sea-level rise since the formation of the sea-level indicator.
Sedimentary isostasy is not the only sediment-related process that affects sea level. Wolstencroft et al. To address this Ferrier et al. Water depth changes associated with sediment redistribution and compaction can vary over short spatial scales, and therefore care is needed to interpret individual sea-level indicators, but the modelling approaches described above are well-suited to studying the large-scale impact of sediment redistribution.
In conclusion, both sediment loading and sediment compaction have been demonstrated to have a non-negligible effect on relative sea-level change, and this has far-reaching implications for the interpretation of relative sea-level indicators within the framework of a GIA model see Sect. Both effects should be accounted for in future GIA models, although better constraints on the timing and distribution of erosion and deposition, over the last glacial cycle and beyond, are needed before past global ice volumes can be robustly inferred from global sea-level records.
The primary motivation for the recent focus on developing GIA models for Greenland and Antarctica has been to permit the accurate interpretation of GRACE data, partitioning the mass change time series into contributions from GIA and contemporary ice mass change King et al. This is possible because the two data sets have a different sensitivity to GIA. The basic premise of the method is that the GRACE satellites detect the spatial pattern of mass change, which is attributed to the redistribution of ice and solid Earth mass after accounting for atmospheric and oceanic mass change , whereas altimetry satellites such as ICESat measure the spatial pattern of surface elevation change, which is attributed to a combination of solid Earth deformation and ice volume change.
This method of simultaneously solving for ice mass change and GIA was originally suggested by Wahr et al. Further advances were made by Martin-Espanol et al. The advantage of using data inversion to isolate the contemporary GIA signal Eq. In this final section a number of emerging areas of research are outlined. It is now clear that GIA should be considered within future Earth system modelling efforts, and some of the most exciting developments will come as GIA modelling becomes even better integrated with a range of disciplines.
A central component of GIA modelling has always been the use of independent data sets to either prescribe model inputs, tune model parameters, or test model outputs. As the accuracy and coverage of these data sets improves, along with our understanding of the processes they record, it is important to be aware that it will not be possible to honour all of the constraints provided by the data. A strategy is therefore needed in which the available data are used to develop the most accurate GIA model possible and assign a level of uncertainty to the resulting model output.
Many of the data sets that record GIA processes also record competing processes. Changes in oceanic or atmospheric circulation will alter the dynamic topography of the ocean surface, while changes in the tidal regime or ocean conditions acidity, temperature, opacity can alter the habitat distribution of species that are used to infer the position of the shoreline. When seeking to reconstruct past ice extent it is important to acknowledge that a change in local ice flow or wind direction can alter the height of the ice-rock contact, while changes in ice surface elevation, as recorded by ice cores, will reflect changes in both ice thickness and the height of the underlying bed Bradley et al.
Finally, land motion, as recorded by GPS, will reflect the solid Earth response to contemporary surface mass redistribution ice, water, sediment as well as tectonics and sediment compaction. Once a suitable data set has been identified, it can be used to determine an optimal GIA model.
Due to data gaps and uncertainties there are often trade-offs between the magnitude and timing of the surface loading history and Earth rheology that can explain the observations Fig. Using data assimilation or statistical emulation, in combination with large ensemble modelling, it should be possible to determine a suite of GIA solutions that provide a reasonable fit to all available constraints.
Such an approach has already been pioneered for ice-sheet modelling Briggs et al. When applied to GIA modelling, decisions will have to be made on: how to weight different data types, the length scale over which each is relevant, how to treat uncertainties in age and elevation, whether to use raw data or statistical reconstructions e. Khan et al. The uncertainty on the resulting GIA estimate should directly reflect uncertainties in the constraining data. In order to optimize the search through the parameter space associated with ice history and Earth rheology a number of approaches could be taken.
When determining the past evolution of the global ice sheets, a previously used method involves taking an existing global reconstruction and scaling the thickness of each ice sheet in turn e. Caron et al. However, building on new understanding of the feedbacks between ice dynamics and GIA Sect. When determining the optimal Earth model, it will be important to allow for the possibility that different regions are characterized by different viscosity profiles, guided by independent constraints on mantle viscosity variations Sect.
There will always be some parts of the parameter space that cannot be constrained. A useful exercise is to determine the locations in which it would be most beneficial to have new data constraints e. Wu et al. For example, it would be very useful to know the rate of solid Earth rebound beneath the present-day ice sheets and across the ocean floor although research is underway in this area; see Honsho and Kido, ; it would be useful to know the past thickening history of the ice sheets as well as their thinning history; and it would be useful to know how sea level has changed at locations distal from current and past shorelines.
In the near future, advances will come through the application of novel analytical techniques in regions where sea-level reconstructions have so far proved challenging, e. Significant advances in understanding GIA have often stemmed from a cross-disciplinary approach. The gravitational theory developed by the mathematician Woodward in the late 19th century came about as the result of a question posed by geologists Gilbert and Chamberlin Woodward, More recently, observations of a mid-Holocene highstand throughout the low latitudes led to recognition of the ocean syphoning process Mitrovica and Milne, , while disparate observations relating to the magnitude of the Pliocene highstand led to advances in the modelling of GIA over multiple glacial cycles Raymo et al.
Sea-level observations, and more recently GPS observations, have often been the motivation for developing new hypotheses relating to the history of the major ice sheets e. Bradley et al. Pollard et al. Future progress is likely to be made by fully integrating a number of different disciplines, i. Coupled ice-sheet—GIA modelling has already been discussed in Sect. Gomez et al. This will be computationally challenging, and careful experiment design will be needed to ensure an efficient, yet sufficient, search of the parameter space.
The impacts of GIA, i. Perturbations to the seafloor due to the growth and decay of submerged peripheral bulges Fig. Similarly, changes in surface topography due to solid Earth deformation will affect atmospheric circulation patterns and consequently precipitation patterns.
This latter factor has clear implications for the mass balance of an ice sheet and has been proposed as an explanation for hysteresis within glacial cycles Abe-Ouchi et al. Additional land bridges will have existed, with direct implications for migration pathways and ocean circulation, and in the Northern Hemisphere the additional land mass may have facilitated ice-sheet expansion or inception. GIA is also able to provide insight into the timing, magnitude, and source of freshwater inputs to the ocean during deglaciation. In order to accurately model the palaeo-circulation of the ocean and the atmosphere, some factors associated with GIA should be incorporated into future modelling efforts.
GIA-related solid Earth deformation during the last glacial cycle will have affected the routing of palaeo-drainage systems Wickert et al. Accounting for GIA-related factors such as changes to the shape of the land surface and changes to the position of the base level within landscape evolution models will lead to a more complete understanding of Earth surface processes. The full impacts of GIA, including spatially variable sea-level change and changes to the shape of Earth's gravitational field, should be accounted for in future studies that seek to understand the isostatic response to glaciation, erosion, and sedimentation e.
Mey et al. GIA potentially plays a role in modulating climate cycles. Postglacial rebound acts to reduce the pressure in the mantle, and this has been implicated in promoting terrestrial volcanism Sigmundsson et al. But postglacial rebound is not the only GIA-related process that affects the rate of CO 2 release: as the ice sheets wax and wane this alters the global sea level, and the resulting stress changes are thought to be sufficient to perturb rates of volcanism Kutterolf et al.
It was originally assumed that mid-ocean ridge volcanism would be suppressed during periods of sea-level rise i. However, the evidence suggests that there is actually a significant delay in the response of the mid-ocean ridge system to a change in seafloor pressure. This can be deduced from records of hydrothermal and magmatic activity along mid-ocean ridges Crowley et al. The magnitude of the lag depends on a number of factors, including the plate spreading rate and the rate of sea-level change, so it is not a simple task to quantify the time-dependent net effect of terrestrial and marine volcanic processes on atmospheric CO 2.
The CO 2 perturbations described here are triggered by GIA processes, and there is clear scope for further exploration of the feedbacks between the spatially variable isostatic response to surface load changes including the response to changes in sediment loading; Sternai et al.
A number of glaciated regions — Alaska, Iceland, the northern Antarctic Peninsula, and Patagonia — are situated on active or recently active plate boundaries. Sato et al. Glaciated low-viscosity regions are exciting places to study GIA, but the issues listed above complicate attempts to separate the geodetic signal into a response to past and contemporary change.
It is typically assumed that GIA is a linear background signal that reflects the viscous response to long-past ice-sheet change and any departure from the linear trend reflects the elastic response to contemporary ice-sheet change. However, in a low-viscosity region the short relaxation time of the mantle means that the solid Earth response to historical ice mass change, i. Furthermore, the geodetic response to contemporary ice mass change may contain both an elastic and a viscous signal Nield et al.
The problem becomes more tractable if the viscosity of the mantle can be absolutely determined, for example, via careful analysis of GPS time series in response to known surface mass change, permitting more reliable predictions of the time-varying elastic and viscous components of deformation.
The low-viscosity values inferred from GIA for regions such as Iceland and Alaska are similar to the values determined in studies of post-seismic deformation Arnadottir et al. There is the additional complication that afterslip must be accounted for in post-seismic studies Ingleby and Wright, , but in general, the changing deformation rates observed during an earthquake cycle suggest that the Earth either follows a power-law rheology Freed and Burgmann, ; Freed et al. Is there a single rheological law that can explain GIA, post-seismic deformation, intra-plate deformation, and deformation in response to sediment or lake loading Gilbert, ; Dickinson et al.
It is clear that the Earth behaves differently over different timescales Burgmann and Dresen, ; Watts et al. With the rapid development of cross-disciplinary science in the last 2 decades, the field of GIA has expanded beyond geodynamics, incorporating important developments from geodesy, glaciology, and seismology, whilst embracing new results from the fields of geology and geomorphology. Likely areas of future research are summarized below. GIA modelling is a tool that can be used to reconstruct past ice-sheet change, but there remain large uncertainties on past global and regional ice volumes.
We invite contributions dealing with 1 using geodetic data to characterize, analyse, and understand current climate change, 2 evaluating climate models against geodetic data, 3 using these data to constrain and improve climate projections, 4 creating long and consistent geodetic time series, 5 climate modelling of geodetically observable variables, and 6 the prospects of future missions. Ionosphere, plasmasphere and thermosphere are manifestations of space weather; its impacts and risks are gaining more and more importance in politics and sciences, since our modern society is highly depending on space-borne techniques, e.
Stratosphere and troposphere and their constituents are essential for life on our planet, and tropospheric water vapour is source of clouds and of precipitation, which in turn affect the large-scale circulation through heat transfer. The synergistic use of different instruments and modelling is leading to major advances in the understanding of our climate. This symposium invites contributions on advances in observing and understanding our atmosphere — from troposphere to magnetosphere. Specific topics are:. As the climate continues to warm, it is important to precisely measure sea level changes and its different components at both global and regional scales.
This IAG-led Joint Symposium JG6 symposium invites contributions from studies that monitor and observe sea level changes on multiple scales employing satellite altimetry, GNSS at tide gauges, GNSS reflectometry, airborne laser scanning, satellite gravimetry and in-situ measurements. A range of important geological processes occur beneath volcanic belts. Subsurface fluxes of magma and hydrothermal fluids have generated both the continental and oceanic crust and formed many mineral deposits.
A force that shapes our planet / GOCE / Observing the Earth / Our Activities / ESA
However, the crustal structure of volcanic belts is not fully understood. This symposium seeks to advance this research area by gathering researchers studying the subsurface structure of active volcanic systems. We welcome all contributions that present a geophysical studies of volcanic belts and b geological studies that seek to interpret geophysical models in terms of laboratory experiments, c Geodetic measurements, imaging and topography of volcanic belts, and d multidisciplinary studies on volcanic belts.
Earth systems are complex and public awareness is critical for balancing societal demands for minerals and water with sound environmental practices, as well as building resilience to natural hazards and a changing climate. Strong partnerships between scientists, data scientists, teachers and non-academic communities are critical for successfully guiding such citizen scientist and educator use of these data products.
Such approaches are important for both recruiting the geophysicists of the future and for developing critical skills for our future generations. Key among these skills is the ability to assess and recheck claims made about environmental issues by interested parties, thus enabling evidence-based decision-making processes.
This symposium invites contributions from scientists, educators, communicators and those who design, facilitate, fund or deliver such programs. This symposium seeks contributions covering from core to mantle, including observations, material properties, structure and dynamics. In the mantle, composition, rheology, density, electric and magnetic properties are required to define the dynamical evolutionary path through space-time. Models of mantle convection and the interaction with lithospheric plates and subducted relics use these data as input to define the models in greater detail.
Geodetic and seismic data provide inputs necessary for constraining possible stable layers in the outer core, with high resolution models of the geomagnetic field required to make further progress in our understanding of core dynamics and dynamo generation. Seismology and mineral physics continue to work in tandem to further our understanding of inner core structure and dynamics.
We also welcome studies concerning global-scale coupling, including the dynamical interaction between the inner, outer core, the mantle and earth rotation. Data assimilation has become a valuable tool for improving our understanding of the Earth and its different dynamical layers, such as the core, mantle, oceans, atmosphere and magnetosphere.
By merging sparse observations, complex physical models and their respective errors, data assimilation attempts to unveil hidden features of a given system as well as predicting its evolution. Although its long-term development in the field of meteorology has led to a well-established framework, data assimilation methodologies still bear considerable challenges. Amongst those we can cite the numerical stability of ensemble-based methods such as the Ensemble Kalman Filter, the identification and handling of model errors and biases, the hybridization of variational and sequential approaches, and the usage of multi-model ensembles for parameter estimation.
Moreover, in many fields of application, such as core and mantle dynamics, as well as volcanism and space weather, data assimilation remains fairly exploratory. However, these novel applications can provide a platform for further analysis of the aforementioned challenges. This symposium aims at promoting a constructive dialogue between the different geophysical communities with a shared interest in the development of innovative strategies in data assimilation.
We therefore particularly encourage the participation of contributions connected to emerging research fields of geophysical data assimilation, as well as the development of libraries, testbeds and computationally efficient data assimilation schemes. This symposium aims to bring together a wide range of investigations related to paleomagnetism, magnetic anisotropy, gravimetry, seismic, volcanologic and other geophysical studies intended to unveil tectonic and geodynamic processes at different scales and their links to Earth Dynamics.
Thus, presentations may include:. We encourage contributions pertaining to recent progress in the effective incorporation of data into space weather modeling and prediction at any point along the chain from sun to planets. Moreover, we welcome approaches that are less traditional in the space weather community but possess potential for significant progress in forecasting and understanding space weather, and that draw upon "lessons learned" or "best practices" from applications to non-space-weather problems.
Together these initiatives make it possible for users to easily access huge archives of disparate geoscience data and metadata in a secure and reliable manner, a task that was complex and time consuming before these initiatives were available. Clear licensing of geoscience data gives users clarity over how they can use and share the data, protects the rights of data providers and promotes integrated research.
Data publication and citation will benefit data suppliers by giving them proper credit, professional recognition and rewards for their works, in a similar manner to the way that publication of scientific results benefits scientific researchers. Licensing, publication and citation of data are becoming a requirement for contribution to geoscience infrastructures.
The system of licensing, producing, publishing, and citing of geoscience data is a structure for persistent intellectual content identification and management as well as for connection of users with content suppliers. This symposium solicits contributions presenting actual practices and future plans of data licensing, producing, publication, and citation of scientific data, and possible related topics.
These include the magnetic and gravity field, electromagnetic induction, heat flow and seismological data. The lithospheric magnetic field reflects properties like composition and temperature and carries information about tectonic, chemical, and thermal alterations that magnetized rocks have undergone throughout their history. Gravity field, apart from information on composition, reveals information about mass exchange mechanisms related to dynamic processes like sea level rise, glacial retreat, and lithospheric flexure.
Seismological methods including receiver functions map the location of major interfaces like the Moho and the Lithosphere-Asthenosphere Boundary. Seismic velocities can be inverted for density and temperature, and seismic attenuation and seismic anisotropy are correlated with temperature and strain, respectively.
In this respect, we welcome contributions from studies focusing on data collection and processing, global or regional modeling and interpretation of data and models in terms of tectonic, geological or geophysical implications. With climate change and decreasing water availability per capita being one of the crucial challenges for society in the 21st century, there is the urgent need to develop and initiate adaptation measures.
The provision of state of the art climate- and hydrology information for services has been initiated for different regions worldwide in order to approach the manifold demands of stakeholders, particularly in water management, agriculture, energy production or civil protection. This symposium invites for abstracts that address the challenges faced in both climate- and hydrological service provision when bridging from science to practice and finally to the derivation of adaptation measures. This comprises particularly contributions on 1 provisions of high-quality real-time and historical data from national and international databases, 2 hydrometeorological forecasts and particular subseasonal to seasonal predictions, 3 high resolution downscaling efforts of global climate scenarios, 4 development of bias-correction techniques for provided hydrometeorological fields, 5 solutions for digital and open data access, 6 development of methods to overcome limitations due to limited observation data density or —quality, 7 efforts to improve structure and parameterization of models, 8 improved ways to communicate scientific results and uncertainty to decision makers to increase chances of uptake, 9 examples and descriptions of case studies and initiatives worldwide, including the role of local and national legislations that help the adaptation process.
This symposium focuses on the impact of natural emissions, such as those from volcanoes, and anthropogenic fluxes on atmospheric composition, chemical transformation, dynamics and climate. In this context we welcome contributions from. The symposium will be open to any aspect of the science or history of the tides of the ocean, solid earth and atmosphere and of lakes and planets. The science will include the present accuracy of coastal, regional and global ocean tide models, tidal dissipation and its role in geophysics, internal tides and their role in mixing the ocean and in the global ocean circulation, secular changes in tides, new techniques for measuring tides and analysing the data, the role of tides in the origin of life on earth and palaeotides.
It will also be open to presentations on earth and atmospheric tides, the tides of lakes and planets and many other aspects of tidal science. The symposium will provide a fitting mark of the th anniversary of the Liverpool Tidal Institute which led to many advances in tidal science in the 20th century. However, our understanding of the processes governing these changes are hindered by a lack of observations with sufficient temporal and spatial resolution, in these generally remote landscapes. Fortunately, many of the cryospheric processes of interest produce ground vibrations.
Analysis of these seismic signals can yield insight into the relationship between environmental forcings and the response of ocean - cryosphere - solid earth systems. The properties of these systems, such as mantle rheology or till thickness, can also be inferred from both passive and active studies. Continuous study of their time and space variability informs our understanding of climate change. We encourage contributions treating the observation and modeling of seismic signals involving dynamics of ice sheets, sea ice, icebergs and glaciers, as well as changes to the thermal and physical structure of permafrost and snow.
Damaging phenomena related to a variety of geo-hazards constantly threaten people, the built environment and its vulnerable infrastructure on a global scale. These phenomena depend on the type of underlying geologic process and may unfold across different spatial and temporal scales. The increasing urbanization and subsequent socio-economic development continuously raise the bar for the Civil Protection authorities and decision makers striving to control and reduce the associated risk.
The development of Early Warning systems has been often proposed as a technological solution for mitigating the impact of geo-hazards. The development and implementation of such systems depends on understanding, modelling and monitoring the underlying natural processes. The Symposium aims at bringing together scholars and practitioners with mutual interest in modelling, computational and experimental methods and technological advances from the design to the practical implementation of early warning systems for a broad range of geo-hazards.
The symposium encourages original research, benchmark studies and practical examples with particular emphasis on open questions, unsolved issues and societal impact. The overall goal is to foster a holistic, multi-disciplinary discussion addressing the key challenges for the design and development of next generation early warning systems in the context of the Sendai Framework for Disaster Risk Reduction. Topics of interest include but are not limited to: Multi-source real-time data collection, sensors fusion; dynamic, evolutionary process modelling; decision-making strategies; rapid response and performance-driven approaches; from forecasting to nowcasting to early warning; industrial and mission-critical applications; Near real-time risk mitigation; Cost-benefit analysis and socio-economic impact; practical case studies.
Subduction zones encompass a range of significant processes contributing to the long-term evolution of the Earth. Megathrust earthquakes along subduction margins define a major geohazard capable of catastrophic damages, as evidenced by the Japan and Indian Ocean earthquakes, that are stark reminders of what is likely in store for Cascadia.
However, our understanding of subduction zone processes and ultimately characterization of geohazards is hampered by a lack of observations, in particular offshore. For Cascadia, this data gap lies directly above the seismogenic zone and its downdip transition to slow earthquake phenomena, where material properties evolve due to hydro-mechanical variations and metamorphic reactions.
In recent years, improvements to permanent monitoring networks and dense temporary deployments have focused on a 4D characterization of stress, strength and fluid pressure evolution in subduction zones. In the past two decades, space geodetic techniques such as GNSS and InSAR have provided a detailed image of lithospheric deformation caused by earthquakes. Accumulating geodetic data, including those associated with recent giant earthquakes in Sumatra, Chile and Japan, have manifested peculiar deformation patterns that occur at different stages in an earthquake cycle.
Studies based on such a wide variety of deformation data as well as terrestrial and satellite gravity data have dramatically improved insights on earthquake rupture process, seismicity modulated by small stress perturbations, rheology of lithosphere and asthenosphere and frictional property and fluid migration in a fault zone. In this interdisciplinary symposium, we welcome presentations of new results on geodetic and seismological measurements and modeling related with fast and slow earthquakes, postseismic transients, interseismic elastic strain accumulation and permanent inelastic deformation.
Probabilistic and statistical approaches to modeling different types of Geoscience data have become more popular in the last years, partly due to advances in methodological approaches and algorithms, and also due to increasing computing power. Papers from the session will be considered for publication in the journal of Mathematical Geosciences. Studying a changing world needs long series of data. Those old data are in analogue form and, many times, are contained in unique documents.
Historical information may also be retrieved from documentary evidence such as narrative sources and legal-administrative institutional documentation e. Techniques and methodologies for preservation, dissemination, interpretation, homogenisation and use of such data, as well as for their present scientific use are important topics for advancing of our understanding of the changing Earth and of past extreme events.
Different approaches have been devised to deal with different data and problems.