A three-dimensional thermomechanical ice sheet model coupled to a climate model - theory, model test and application to the northern Hemisphere ice sheets
by R. Calov
The thermomechanics is implemented into an existing vertically integrated ice sheet model. Applying the shallow ice approximation to the balance equations and the flow law of ice in sperical coordinates leads to a fully three-dimensional ice sheet model. The model equations are expressed in spherical stretched σ-coordinates. The improved model now includes an evolution equation of the ice temperature, the 3-d velocity, basal sliding and temperature-velocity coupling using the Arrhenius relation according to Paterson (1981).
The new thermomechanical ice sheet model is applied successfully to the artificial ice sheet of the EISMINT model intercomparison project. The resulting temperature field is in good agreement with other models. Furthermore, steady state computations for the Greenland ice sheet with the thermomechanical model and prescribed measured snowfall and surface temperature are performed. Taking into account the coarse spatial resolution of 0.7 × 0.7 degrees - the grid is defined for the whole northern Hemisphere - the resulting surface topography corresponds surprisingly well with the measured one. The modelled basal temperature distribution is in good aggreement with that of other thermomechanical models.
Numerous computations of the northern Hemisphere ice sheets through the last glacial-interglacial cycle show the advantages as well as the disadvantages of the 3-d model. For these transient calculations the 3-d (latitude, longitude and altitude) ice sheet model is coupled asychronously to the zonally averaged (latitude and altitude) LLN-climate model driven by astronomical forcing. We compare results of the vertically integrated with those of the thermomechanical ice sheet model. It is shown that the deformation of the ice is crucial for the temporal development of the northern Hemisphere ice distribution. In the thermomechanical model the deformation properties of ice depends on the temperature within the ice and the enhancement factor; the latter accounts for the different flow properties of Pleistocene and Holocene ice due to varying dust content. The computations with the thermomechanical model show that the growth and decay of the northern Hemisphere ice sheets can be modelled with a common enhancement factor for all ice sheets; the vertically integrated model applies different enhancement factors for the different ice sheets. Two topography data sets are used for the calculations: The CLIMAP topography (CLIMAP, 1981) with Greenlands ice thickness from Radok et al. (1982) as well as the ETOPO 5 surface topography (ETOPO 5, 1986) where Greenland's surface elevation and ice thickness from Letréguilly et al. (1990) is merged in for our computations. It is shown that there are model set-ups for the thermomechanical model yielding temporal developments of total ice volume comparable to the vertically integrated model using the CLIMAP topography as well as the ETOPO-5 topography. To show the further advantages of the thermomechanical model for paleoclimatic simulations additional computations must be carried out, e.g. sensitivity runs with varying geothermal heat and sliding parameter. This could elucidate the question how sophisticated the ice sheet model should be for paleo runs or whether a proper representation of surface mass balance through time with a climate model is sufficient.
