Integration of Passive Tracers in a Three-Dimensional Ice Sheet Model - Towards an Interdisciplinary Approach in Earth System Science - page 150

Fig. 1 Physical components of RIMBAY. The 3D ice sheet model RIMBAY, used in this study,
represents all major physical components of Antarctica, such as ice shelves, subglacial hydrology,
ice streams as well as including external forcings such as sea level and ocean temperatures as well
as topographic and hydrologic features like nunataks and subglacial lakes

where n is the exponent found in the Glen flow law (Cuffey and Paterson 2010 ) set

to the empirical value of 3 (some ice sheet models use n as a variable parameter for
tuning purposes. For the sake of simplicity, here the empirical value is chosen),
A ðh Þ

and g
are density of ice (910 kgm − 3 ) and gravitational force constant (9.81 ms − 2 ). The
integral is evaluated from the bedrock (b) underneath the ice to ice surface (s). This
approximation is valid for ice sheets with a small depth-to-width relationship,
which applies to the interior of Greenland and Antarctica but not to the margins,
where ice shelves and fast

is a temperature dependent flow rate factor and u b the basal velocity, q

flowing ice streams govern ice dynamics. In the shallow
shelf approximation basal friction is omitted while lateral velocities are assumed to
be constant throughout the depth of the shelf ( @ u

@ z ; @ v @ z ¼

0). Figure 2 illustrates the

different stress field domains within the model domain.

Since tracer advection models simply utilize the velocity output of the under-
lying model, realistic velocity patterns are required for the reconstruction of age-
depth distributions. To this end, model runs with present day boundary conditions
where carried out to achieve an equilibrium ice sheet state comparable to the present
day surface topography and mass balance. This approach involves the underlying
postulate, that under PD-conditions the Antarctic ice sheet is close to equilibrium.
Even though this is not the case it is a reasonable

first estimate.

2.1 Present Day Control Run

One of the main drivers of ice sheet evolution in Antarctica (next to the surface
mass balance), is the ocean-ice shelf interaction. The inflow of warm water masses