A benchmark study for glacial isostatic adjustment codes

Spada, Giorgio; Barletta, V; Klemann, Volker; Riva, Riccardo; Martinec, Z.; Gasperini, Paolo; Lund, Björn; Wolf, Detlef; Vermeersen, L. L. A.; King, Matt

doi:10.1111/j.1365-246x.2011.04952.x

Cited by 120 publications

(160 citation statements)

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“…The other viscous amplitudes denoted by A i in Spada et al (2011) are shown to vanish identically. For Heaviside loading (f(s) = 1/s), the inverse Laplace transform of eq.…”

Section: Numerical Results For Polar Motionmentioning

confidence: 99%

“…Under assumption (91), Vermeersen et al (1994), Sabadini & Vermeersen (2004) and Spada et al (2011) showed that the time relaxation of the polar motion m(t) is characterized only by the rotational frequencies a i . This fact is expressed by eq.…”

Section: Downloaded Frommentioning

confidence: 99%

“…is the Laplace-transformed polar-motion transfer function representing the displacement of the rotation axis of the instantaneous configuration κ(t) with respect to the co-rotating frame O(x 1 , x 2 , x 3 ) for a unit surface-mass loading excitation (Spada et al 2011). The objective of this section is to compare the polar-motion function m(t) calculated by the LD method with that resulting from the TD method (presented in Section 5).…”

Section: T H E L Ov E -N U M B E R a P P Roa C H F O R P O L A R M O mentioning

confidence: 99%

“…(88) can be arranged as (e.g. Wu & Peltier 1984;Vermeersen et al 1997;Sabadini & Vermeersen 2004;Spada et al 2011) …”

Section: T H E L Ov E -N U M B E R a P P Roa C H F O R P O L A R M O mentioning

confidence: 99%

“…That is why we will not consider the rotational feedback on the sea level equation, but our surface load model will be defined by a simple spherical cap used by Spada et al (2011) for a benchmark study of the numerical performance of GIA computational codes. This provides the rotational amplitudes and the rotational relaxation times of the M3L70V01 model (Spada et al 2011) for the case where the rotational-feedback mechanism is included, which may then serve as a benchmark for other GIA computational codes. A full exploitation of the rotational-feedback effect on the complete suite of GIA-related observables, including the rotational feedback on the sea level equation, is the next step for future study.…”

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confidence: 99%

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The rotational feedback on linear-momentum balance in glacial isostatic adjustment

Martinec

Hagedoorn

2014

Geophysical Journal International

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S U M M A R YThe influence of changes in surface ice-mass redistribution and associated viscoelastic response of the Earth, known as glacial isostatic adjustment (GIA), on the Earth's rotational dynamics has long been known. Equally important is the effect of the changes in the rotational dynamics on the viscoelastic deformation of the Earth. This signal, known as the rotational feedback, or more precisely, the rotational feedback on the sea level equation, has been mathematically described by the sea level equation extended for the term that is proportional to perturbation in the centrifugal potential and the second-degree tidal Love number.The perturbation in the centrifugal force due to changes in the Earth's rotational dynamics enters not only into the sea level equation, but also into the conservation law of linear momentum such that the internal viscoelastic force, the perturbation in the gravitational force and the perturbation in the centrifugal force are in balance. Adding the centrifugal-force perturbation to the linear-momentum balance creates an additional rotational feedback on the viscoelastic deformations of the Earth. We term this feedback mechanism, which is studied in this paper, as the rotational feedback on the linear-momentum balance.We extend both the time-domain method for modelling the GIA response of laterally heterogeneous earth models developed by Martinec and the traditional Laplace-domain method for modelling the GIA-induced rotational response to surface loading by considering the rotational feedback on linear-momentum balance. The correctness of the mathematical extensions of the methods is validated numerically by comparing the polar-motion response to the GIA process and the rotationally induced degree 2 and order 1 spherical harmonic component of the surface vertical displacement and gravity field. We present the difference between the case where the rotational feedback on linear-momentum balance is considered against that where it is not. Numerical simulations show that the resulting difference in radial displacement and sea level change between these situations since the Last Glacial Maximum reaches values of ±25 and ±1.8 m, respectively. Furthermore, the surface deformation pattern is modified by up to 10 per cent in areas of former or ongoing glaciation, but by up to 50 per cent at the bottom of the southern Indian ocean. This also results in the movement of coastlines during the last deglaciation to differ between the two cases due to the difference in the ocean loading, which is seen for instance in the area around Hudson Bay, Canada and along the Chinese, Australian or Argentinian coastlines.Key words: Sea level change; Geopotential theory; Earth rotation variations. I N T RO D U C T I O NThe redistribution of ice and water over the Earth's surface during glaciation and deglaciation cycles due to changes in climate induces 3-D crustal motion, gravity-field variations and changes in sea level, which is known collectively as glacial isostatic adjustment (GIA). The surface-m...

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“…The other viscous amplitudes denoted by A i in Spada et al (2011) are shown to vanish identically. For Heaviside loading (f(s) = 1/s), the inverse Laplace transform of eq.…”

Section: Numerical Results For Polar Motionmentioning

confidence: 99%

Section: Downloaded Frommentioning

confidence: 99%

Section: T H E L Ov E -N U M B E R a P P Roa C H F O R P O L A R M O mentioning

confidence: 99%

“…(88) can be arranged as (e.g. Wu & Peltier 1984;Vermeersen et al 1997;Sabadini & Vermeersen 2004;Spada et al 2011) …”

Section: T H E L Ov E -N U M B E R a P P Roa C H F O R P O L A R M O mentioning

confidence: 99%

mentioning

confidence: 99%

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The rotational feedback on linear-momentum balance in glacial isostatic adjustment

Martinec

Hagedoorn

2014

Geophysical Journal International

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A mascon approach to assess ice sheet and glacier mass balances and their uncertainties from GRACE data

Schrama

Wouters

Rietbroek³

2014

JGR Solid Earth

117

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The purpose of this paper is to assess the mass changes of the Greenland Ice Sheet (GrIS), Ice Sheets over Antarctica, and Land glaciers and Ice Caps with a global mascon method that yields monthly mass variations at 10,242 mascons. Input for this method are level 2 data from the Gravity Recovery and Climate Experiment (GRACE) system collected between February 2003 and June 2013 to which a number of corrections are made. With glacial isostatic adjustment (GIA) corrections from an ensemble of models based on different ice histories and rheologic Earth model parameters, we find for Greenland a mass loss of −278 ± 19 Gt/yr. Whereas the mass balances for the GrIS appear to be less sensitive to GIA modeling uncertainties, this is not the case with the mass balance of Antarctica. Ice history models for Antarctica were recently improved, and updated historic ice height data sets and GPS time series have been used to generate new GIA models. We investigated the effect of two new GIA models for Antarctica and found −92 ± 26 Gt/yr which is half of what is obtained with ICE-5G-based GIA models, where the largest GIA model differences occur on East Antarctica. The mass balance of land glaciers and ice caps currently stands at −162 ± 10 Gt/yr. With the help of new GIA models for Antarctica, we assess the mass contribution to the mean sea level at 1.47 ± 0.09 mm/yr or 532 ± 34 Gt/yr which is roughly half of the global sea level rise signal obtained from tide gauges and satellite altimetry.

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Vertical land motion as a key to understanding sea level change and variability

Wöppelmann

Marcos

2016

Reviews of Geophysics

301

280

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Vertical land motions are a key element in understanding how sea levels have changed over the past century and how future sea levels may impact coastal areas. Ideally, to be useful in long-term sea level studies, vertical land motion should be determined with standard errors that are 1 order of magnitude lower than the contemporary climate signals of 1 to 3 mm/yr observed on average in sea level records, either using tide gauges or satellites. This metrological requirement constitutes a challenge in geodesy. Here we review the most successful instrumental methods that have been used to determine vertical displacements at the Earth's surface, so that the objectives of understanding and anticipating sea levels can be addressed adequately in terms of accuracy. In this respect, the required level of uncertainty is examined in two case studies (global and local). A special focus is given to the use of the Global Positioning System (GPS) and to the combination of satellite radar altimetry with tide gauge data. We update previous data analyses and assess the quality of global satellite altimetry products available to the users for coastal applications. Despite recent advances, a near-plateau level of accuracy has been reached. The major limitation is the realization of the terrestrial reference frame, whose physical parameters, the origin and the scale factor, are beyond the scope of a unique technique such as the GPS. Additional practical but nonetheless important issues are associated with the installation of GPS antennas, such as ensuring that there is no unknown differential vertical motion with the tide gauge.

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A benchmark study for glacial isostatic adjustment codes

Cited by 120 publications

References 110 publications

The rotational feedback on linear-momentum balance in glacial isostatic adjustment

The rotational feedback on linear-momentum balance in glacial isostatic adjustment

A mascon approach to assess ice sheet and glacier mass balances and their uncertainties from GRACE data

Vertical land motion as a key to understanding sea level change and variability

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