Coupled models of glacial isostasy and ice sheet dynamics

This thesis deals with the incorporation of isostatic processes into realistic models of ice sheet dynamics. A viscoelastic half-space model of isostatic adjustment is developed, and as an initial exercise is coupled to a model of the Antarctic ice sheet simulating the last glacial cycle. The ice sheet model is a three dimensional, time-dependent model originally formulated by Jenssen (1977) where the driving input data are net accumulation of snow and eustatic sea level change. This allows examination of the sensitivity of the ice sheet simulation to changes in the parameters of the isostatic model. In general, the maximum ice volume generated over a glacial cycle decreases with increasing mantle viscosity and increasing lithospheric rigidity. To obtain realistic values for the isostatic parameters of mantle viscosity and lithospheric rigidity the retreat of the Northern Hemisphere ice sheets and the subsequent isostatic adjustment since the last ice age is simulated. The isostatic parameters are adjusted until the overall model provides the best match to relative sea level data, with the eustatic component of the relative sea level change prescribed. (The maximum value of the amplitude of the prescribed sea level change is 130 m as determined from the Huon Peninsula in Papua New Guinea). Initially the simulation and matching procedure is performed using a simple ice sheet model whose time dependent extent is set by the ICE4G dataset (Peltier, 1994) and whose thickness and volume is set on the assumption of a parabolic profile of thickness. From these trials the model parameters that most realistically reproduce the observed isostatic adjustment associated with the retreat of the Laurentide ice sheet are 3 x 1021 Pa s for lower mantle viscosity, 2 x 1021 Pa s for upper mantle viscosity and 1 x 1025 N m for lithospheric rigidity. For the Fennoscandian ice sheet the corresponding parameter values are 6 x 1021 Pa s, 4 x 1021 Pa s and 6 x 1024 N m. The trials are then repeated with the parabolic profile ice sheet assumption replaced by generation of ice sheet thickness using the Jenssen ice sheet model. For the Laurentide ice sheet the same earth model parameters are recovered. For the Fennoscandian ice sheet the use of the Jenssen model to simulate ice thickness produces earth model parameters of 1.3 x 1021 Pas for both the lower and upper mantle viscosity and 2 x 1025 N m for the lithospheric rigidity. A problem with the analysis is that the maximum volume of the combined ice sheets corresponds only to 50 m of eustatic sea level change in the case of the parabolic profile simulation and to 40 m when using the Jenssen model. The sensitivity of the Antarctic ice sheet to regional variations in lithospheric rigidity is examined. Using a range of simple relations between crustal thickness (for which there exists data on geographic distribution) and lithospheric thickness, it is determined that the main effect of non-uniform lithospheric thickness is on the extent of the Ronne and Amery ice shelves. The constraint of prescribed eustatic sea level change since the last ice age is removed by linking the Laurentide, Fennoscandian and Antarctic ice sheet models via the common sea level change determined by the deglaciation of the combined ice sheets. The constraint on Northern Hemisphere ice sheet extent is also removed by allowing the ice sheet model (the Jenssen model) t determine its own extent when driven by climatology and the Milankovitch cycles of solar input. This overall model produces a realistic eustatic sea level change since the last ice age (130 m), but unrealistic changes in relative sea level. In some locations the calculated relative sea level changes are too large by 200 m. The problem of obtaining a consistent simulation of both eustatic and relative sea level change is not resolved. There are three possible explanations. First there may have been an extensive ice sheet over Siberia, which has not been accounted for in this or any other analysis. Second the calculations here assume linearity between isostatic ·disequilibrium and rate of adjustment. This may not be the case. Third, significant changes in ice volume may have occurred before the relative sea level record was laid down in the geological record.