Integration of Passive Tracers in a Three-Dimensional Ice Sheet Model - Towards an Interdisciplinary Approach in Earth System Science - page 153

(a) (b) (c)

Fig. 4 a Antarctic present day topography (m) and b modeled equilibrium ice sheet elevation after
50,000 years of PD atmospheric forcing, c anomalies. Ice shelves are shown in black/dark blue.
While most of the small circumantarctic ice shelves turned into grounded ice, the large ice shelves
are reasonably well represented

The Lagrangian advection assumes the particle-perspective, which means that the
particle is followed along its trajectory through the model grid. In contrast to the
Lagrangian approach the Eulerian tracer advection solves the advection equation

r t A ¼ @ t A þ u @ x A þ v @ y A þ w @ z A ¼ 0 ð 2 Þ

at every grid point covering the whole model domain, with the advantage of pro-
ducing information at every grid point. A is the advected property with absolute and
partial derivatives with respect to time and space ( r t ;@ xyz ). The drawback of the

Euler approach lies within the numerical diffusion arising from solving the
advection equation in a

finite differences environment. Furthermore it is impossible
to trace back the trajectories of single tracers from their origin. This is a valuable
feature of the Lagrangian transport, allowing detailed transport studies of any
passive tracer object. The disadvantage of the Lagrangian transport lies in the sparse
coverage of the model domain, which might be even reduced by dispersive fl ow as

is the case in the lower parts of an ice sheet.

2.2.1 Validation of Tracer Modules

To ensure the capability of the tracer modules of reproducing realistic transport
processes, tests are carried out in controlled model environments. The EISMINT
project provides the perfect testing ground for this purpose. Both Lagrangian and
Euler transport schemes are applied to simulations of spherical ice domes with
radial accumulation pattern on flat bedrock. The ice sheet is run into equilibrium

and subsequently the transport module is activated. The simulated age-depth rela-
tionship of both transport schemes is compared at the ice divide. Additionally both
transport schemes are compared to the analytical age-depth distribution for a Nye-
Vialov ice sheet, which is characterized as a radially symmetric ice dome with
relatively steep

fl

fl flanks (see Fig. 5 ).