ALBERT

Description: Understanding the response of the Earth to the waxing and waning ice sheets is crucial in various contexts, ranging from the interpretation of modern satellite geodetic measurements to the projections of future sea level trends in response to climate change. All the processes accompanying Glacial Isostatic Adjustment (GIA) can be described solving the so-called Sea Level Equation (SLE), an integral equation that accounts for the interactions between the ice sheets, the solid Earth, and the oceans. Modern approaches to the SLE are based on various techniques that range from purely analytical formulations to fully numerical methods. Here we present the results of a benchmark exercise of independently developed codes designed to solve the SLE. The study involves predictions of current sea level changes due to present-day ice mass loss. In spite of the differences in the methods employed, the comparison shows that a significant number of GIA modellers can reproduce their sea-level computations within 2% for well defined, large-scale present-day ice mass changes. Smaller and more detailed loads need further and dedicated benchmarking and high resolution computation. This study shows how the details of the implementation and the inputs specifications are an important, and often underappreciated, aspect. Hence this represents a step toward the assessment of reliability of sea level projections obtained with benchmarked SLE codes.

Description: The choice of the physical model of postglacial rebound plays a decisive role to derive information about the mantle rheology and viscosity from observed data. In models for the mantle rheology, an incompressible Maxwell material is often assumed in spite of seismic observations showing that the Earth's mantle is composed of compressible material. In this study, in order to assess the influence of compressibility on glacial isostatic adjustment (GIA), the spectral-finite element approach proposed by Martinec is extended to incorporate the effect of compressibility. Using this approach, the present-day velocity field is computed for Peltier's ICE5G/VM2 earth-model/glaciation-history combination considering the sea level equation in the formulation of Hagedoorn et al. The results show that the effect of compressibility on the vertical displacement rate is small whereas the horizontal rates are markedly enhanced. For example, the rate around Fennoscandia and Laurentide becomes twice as large when compressibility is considered. This large difference between the compressible and incompressible models can be reduced by adjusting the elastic rigidity of the incompressible model so that the flexural rigidity becomes approximately the same as that in the compressible model. However, differences of ∼1 mm yr−1 still remain for wavelengths longer than 8000 km. These findings show that when modelling horizontal motion induced by GIA, the influence of compressibility cannot be neglected.

Description: 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.