Principal Investigator Kurt Lambeck Project n55

Department of Geodynamics, Machine VP

Research School of Earth Sciences

Co-Investigators A P Purcell, C Smither and D Zwartz

Department of Geodynamics, Research School of Earth Sciences

Mantle Viscosity, Glacial Rebound and Sea-Level Change

When a large ice sheet melts, its meltwater is added to the world's oceans, changing the distribution of water and ice over the earth's surface, causing the surface to deform to come to equilibrium with the changing load. These deformations are preserved in the form of sea-level records and are functions of both the rheological properties of the earth and the load distribution through time. An analysis of post-glacial sea-levels therefore yields constraints on both the rheology of the earth and the melting history of the late Holocene ice sheets which in turn is an important constraint on the earth's climatological history.

What are the basic questions addressed?

Accurate modelling of the change in sea-level that results from the melting of a large ice sheet requires calculation of several factors: the total volume of meltwater added to the oceans by the melting of the ice sheet, the viscoelastic deformation of the surface as a result of both loading by the newly added meltwater and unloading due to removal of the ice sheet, the effect of the removal of the gravitational attraction of the ice sheet and the gravitational self-attraction of the meltwater, and changes in the shape of the geoid due to the redistribution of mass in the earth's interior compensating for the new load distribution. These calculations are complicated by changes in the geometry of the ocean basins through time.

What are the results to date and the future of the work?

Recent work has focused on developing high resolution models for the history of the Holocene ice sheets. Emphasis has focussed on the Barents Sea ice sheet, where most of the geomorphological indicators of the extent and thickness of the ice sheet are now submerged so that the constraints derived from numerical modelling, particularly the time and rate of retreat of the ice sheet, are valuable climatological indicators. A comprehensive model of the Barents ice over the past 20,000 years has been developed and is currently being tested against new geological data.

Other work has focussed on the sea-level evolution of the North Sea over the past 20,000 years. This will be extended further back in time to the Last Interglacial at about 125,000 years ago. The purpose of these models is to provide the framework for understanding coastal evolution processes. Similar work has also been initiated for the Mediterranean Sea and the Persian Gulf.

We intend to continue our development of high resolution variants of the spherical harmonic procedure currently used. We will also continue our development of high resolution models of the Holocene ice sheets and their melting history. Further work will also be devoted to investigating whether post-glacial rebound data may be used to determine the nature of rheological variations in the earth's interior.

What computational techniques are used and why is a supercomputer required?

Taking the earth to be a Maxwell solid we invoke the correspondence principle and take a Laplace transform in the time domain. We then solve the viscoelastic problem indirectly by solving an associated series of elastic problems in the Laplace domain and inverting to get the time dependent solution. Accurate modelling of the geometry of shorelines and ice sheets requires that the spherical harmonic calculations be carried to a very high degree, greatly increasing the computational cost of the procedure. The dependence of sea level change on the time-dependent geometry of the ocean basins, the gravitational self-attraction of the water, and the loading of the ocean basins by the added meltwater results in the governing integral equation being implicit so that numerical solutions require several iterations to get accurate results. The supercomputer environment allows the problem to be solved with sufficient accuracy in a reasonable amount of time, and the VP is well-suited to the spherical harmonic techniques most commonly applied to the problem.


Constraints on the late Weichselian ice sheet over the Barents Sea from observations of raised shorelines, K Lambeck, Quaternary Science Reviews (1994), in press.

Glacial isostasy and water depths in the Late Devensian and Holocene on the Scottish shelf west of the Outer Hebrides, K Lambeck, J. Quaternary Sci. (1994), in press.

Late Devensian and Holocene shorelines of the British Isles and North Sea from models of glacio-hydro-isostatic rebound, K Lambeck, J. Geol. Soc. Lond. (1995), in press.

Glacial rebound of the British Isles, K Lambeck, Geophys. J. Int., 115, 941-959 and 960-990 (1993).

Late Pleistocene and Holocene sea level change in Greece and southwestern Turkey, K Lambeck, Geophys. J. Int. (1995), in press.