### Lagrangian method for the calculation of age and isotopic composition of ice in a 3D Antarctic ice-sheet model

#### O.O. Rybak^{1,2}, Ph. Huybrechts^{2,3}

^{1}Sochi Scientific Research Centre RAS, 354000, Sochi, Teatralnaya str., 8a, Russia, snic@sochi.ru

^{2}Alfred Wegener Institut für Polar- und Meeresforschung, Postfach 120161, D-27515, Bremerhaven, Germany

^{3}Departement Geografie, Vrije Universiteit Brussel, Pleinlaan 2, B-1050, Brussels, Belgium
Two basic approaches exist for describing advection in the ice sheet model. We proceed with comparing traditional Eulerian approach with a rather new in glaciological applications Lagrangian one. Particle tracing in the ice sheet is required to deal with such problems as detailed ice dating, establishing its isotopical composition, or distribution of any other conservative characteristic, which is advected with the ice flow. Within the frame of the Particle-in-Cell (PIC) algorithm, a particle’s trajectory is constructed by numerical interpolation as it moves through an evolving ice sheet within a regular 3D grid. The algorithm is conceptually straightforward, but demanding in terms of its practical implementation. The main advantage of the algorithm as compared to a pure Eulerian approach is that it is diffusion free, which makes it much more accurate in the lower part of the ice sheet. Application of PIC immediately yields the trajectories of the particles, which is important for reconstruction of the flow peculiarities and the distribution of transported properties on isochronous surfaces. To implement it in the most effective way it is necessary to follow accurate balance between computational overhead and designed accuracy.

Ice sheet, ice chronology, isotopic composition, mathematical model, Antarctica