ALBERT

Description: We review the theory of the Earth's elastic and gravitational response to a surface disk load. The solutions for displacement of the surface and the geoid are developed using expansions of Legendre polynomials, their derivatives and the load Love numbers. We provide a matlab  function called diskload that computes the solutions for both uncompensated and compensated disk loads. In order to numerically implement the Legendre expansions, it is necessary to choose a harmonic degree, n max , at which to truncate the series used to construct the solutions. We present a rule of thumb (ROT) for choosing an appropriate value of n max , describe the consequences of truncating the expansions prematurely and provide a means to judiciously violate the ROT when that becomes a practical necessity.

Description: SUMMARY We study the implications of a recently published mass balance of the Greenland ice sheet (GrIS), derived from repeated surface elevation measurements from NASA’s ice cloud and land elevation satellite (ICESat) for the time period between 2003 and 2008. To characterize the effects of this new, high-resolution GrIS mass balance, we study the time-variations of various geophysical quantities in response to the current mass loss. They include vertical uplift and subsidence, geoid height variations, global patterns of sea level change (or fingerprints), and regional sea level variations along the coasts of Greenland. Long-wavelength uplifts and gravity variations in response to current or past ice thickness variations are obtained solving the sea level equation, which accounts for both the elastic and the viscoelastic components of deformation. To capture the short-wavelength components of vertical uplift in response to current ice mass loss, which is not resolved by satellite gravity observations, we have specifically developed a high-resolution regional elastic rebound (ER) model. The elastic component of vertical uplift is combined with estimates of the viscoelastic displacement fields associated with the process of glacial-isostatic adjustment (GIA), according to a set of published ice chronologies and associated mantle rheological profiles. We compare the sensitivity of global positioning system (GPS) observations along the coasts of Greenland to the ongoing ER and GIA. In notable contrast with past reports, we show that vertical velocities obtained by GPS data from five stations with sufficiently long records and from one tide gauge at the GrIS margins can be reconciled with model predictions based on the ICE-5G deglaciation model and the ER associated with the new ICESat-derived mass balance.

Description: SUMMARY We study the implications of a recently published mass balance of the Greenland ice sheet (GrIS), derived from repeated surface elevation measurements from NASA’s ice cloud and land elevation satellite (ICESat) for the time period between 2003 and 2008. To characterize the effects of this new, high-resolution GrIS mass balance, we study the time-variations of various geophysical quantities in response to the current mass loss. They include vertical uplift and subsidence, geoid height variations, global patterns of sea level change (or fingerprints), and regional sea level variations along the coasts of Greenland. Long-wavelength uplifts and gravity variations in response to current or past ice thickness variations are obtained solving the sea level equation, which accounts for both the elastic and the viscoelastic components of deformation. To capture the short-wavelength components of vertical uplift in response to current ice mass loss, which is not resolved by satellite gravity observations, we have specifically developed a high-resolution regional elastic rebound (ER) model. The elastic component of vertical uplift is combined with estimates of the viscoelastic displacement fields associated with the process of glacial-isostatic adjustment (GIA), according to a set of published ice chronologies and associated mantle rheological profiles. We compare the sensitivity of global positioning system (GPS) observations along the coasts of Greenland to the ongoing ER and GIA. In notable contrast with past reports, we show that vertical velocities obtained by GPS data from five stations with sufficiently long records and from one tide gauge at the GrIS margins can be reconciled with model predictions based on the ICE-5G deglaciation model and the ER associated with the new ICESat-derived mass balance.

Description: 〈span〉〈div〉SUMMARY〈/div〉Glacial Isostatic Adjustment (GIA) modelling has recently seen a significant development, stimulated by the need of understanding past, current and future sea level variations and geodetic signals associated with climate change. Our main motivation is that albeit its importance is well recognized within the climate science community, the problem of classifying and quantifying GIA modelling uncertainties has so far received little attention. Here, we consider two possible ways of defining and evaluating these uncertainties. The first is associated with limited knowledge of input model parameters (e.g. the viscosity profile of the Earth’s mantle or the deglaciation history), once it is assumed that the ice margins are known and a unique set of relative sea level (RSL) data are used to constrain the model. We also discuss a second and more problematic source of uncertainty, associated with structural differences in GIA models, stemming from distinct eustatic curves and ice margins geometries, different RSL constraints, non-identical input parameters and different numerical solution schemes. By analysing the present-day ‘GIA fingerprints’ of relative and absolute sea level change, and exploring the GIA contribution to secular sea level rise and to the time-variations of the Earth’s gravity field, here we evaluate the two types of uncertainty showing that they are (i) of significant amplitude and (ii) of comparable importance.〈/span〉

Description: The geodetic rates for the gravity variation and vertical uplift in polar regions subject to past and present-day ice-mass changes (PDIMCs) provide important insight into the rheological structure of the Earth. We provide an update of the rates observed at Ny-Ålesund, Svalbard. To do so, we extract and remove the significant seasonal content from the observations. The rate of gravity variations, derived from absolute and relative gravity measurements, is –1.39 ± 0.11 μGal yr –1 . The rate of vertical displacements is estimated using GPS and tide gauge measurements. We obtain 7.94 ± 0.21 and 8.29 ± 1.60 mm yr –1 , respectively. We compare the extracted signal with that predicted by GLDAS/Noah and ERA-interim hydrology models. We find that the seasonal gravity variations are well-represented by local hydrology changes contained in the ERA-interim model. The phase of seasonal vertical displacements are due to non-local continental hydrology and non-tidal ocean loading. However, a large part of the amplitude of the seasonal vertical displacements remains unexplained. The geodetic rates are used to investigate the asthenosphere viscosity and lithosphere/asthenosphere thicknesses. We first correct the updated geodetic rates for those induced by PDIMCs in Svalbard, using published results, and the sea level change due to the melting of the major ice reservoirs. We show that the latter are at the level of the geodetic rate uncertainties and are responsible for rates of gravity variations and vertical displacements of –0.29 ± 0.03 μGal yr –1 and 1.11 ± 0.10 mm yr –1 , respectively. To account for the late Pleistocene deglaciation, we use the global ice evolution model ICE-3G. The Little Ice Age (LIA) deglaciation in Svalbard is modelled using a disc load model with a simple linear temporal evolution. The geodetic rates at Ny-Ålesund induced by the past deglaciations depend on the viscosity structure of the Earth. We find that viscous relaxation time due to the LIA deglaciation in Svalbard is more than 60 times shorter than that due to the Pleistocene deglaciation. We also find that the response to past and PDIMCs of an Earth model with asthenosphere viscosities ranging between 1.0 and 5.5 x 10 18 Pa s and lithosphere (resp. asthenosphere) thicknesses ranging between 50 and 100 km (resp. 120 and 170 km) can explain the rates derived from geodetic observations.

Description: 〈span〉〈div〉Summary〈/div〉Glacial Isostatic Adjustment (GIA) modelling has recently seen a significant development, stimulated by the need of understanding past, current and future sea-level variations and geodetic signals associated with climate change. Our main motivation is that albeit its importance is well recognised within the climate science community, the problem of classifying and quantifying GIA modelling uncertainties has so far received little attention. Here we consider two possible ways of defining and evaluating these uncertainties. The first is associated with limited knowledge of input model parameters (〈span〉e.g.〈/span〉, the viscosity profile of the Earth’s mantle or the deglaciation history), once it is assumed that the ice margins are known and a unique set of Relative Sea Level (RSL) data is used to constrain the model. We also discuss a second and more problematic source of uncertainty, associated with structural differences in GIA models, stemming from distinct eustatic curves and ice margins geometries, different RSL constraints, non-identical input parameters and different numerical solution schemes. By analysing the present-day “GIA fingerprints” of relative and absolute sea-level change, and exploring the GIA contribution to secular sea-level rise and to the time-variations of the Earth’s gravity field, here we evaluate the two types of uncertainty showing that they are 〈span〉i)〈/span〉 of significant amplitude and 〈span〉ii)〈/span〉 of comparable importance.〈/span〉