A comparison of Eulerian and Lagrangian methods for dating in numerical ice sheet models

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Rybak, O. and Huybrechts, P. (2002): A comparison of Eulerian and Lagrangian methods for dating in numerical ice sheet models , International Symposium on Physical and Mechanical Processes in Ice in relation to Glacier and Ice-sheet modelling, Chamonix (F)August 2002. .
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The Antarctic ice sheet contains a record of palaeoclimatic data over at least the last half a milllionyears. Much of this information, such as age and a wealth of chemical and physical properties, migratesthrough the ice sheet together with the particle it was deposited with. To correctly attribute theseconservative properties to a sample of ice requires to estimate its age, location of origin, or moregeneral, its trajectory. The problem consists of locating an ice particle in the time-dependent threedimensionalvelocity field, which in turn depends on a set of parameters such as climatic conditions(changing in time and space), non-uniform distribution of the basal sliding and the basal melting rates,etc.Eulerian computational schemes are not well suited due to the necessity of having to introduce newartificial terms describing diffusion. On the contrary, the Lagrangian approach enables to obtain keyparameters of a particle in a much more correct way. In general, the methodology consists of followinga limited ensemble of Lagrangian particles, which migration is traced while the model runs. Piece-wiselinear approximations are used to compute intermediate tracer transportation in a generally nonstationarythree-dimensional velocity field.We use results from a thermomechanical model of the Antarctic ice sheet coupled with simple modelsof climatic variations to demonstrate the methodology. Notwithstanding that only a limited number oftracers can be introduced into a computational scheme due to objective limitations of computationalcapacity, it is demonstrated that the approach is rather effective to be applied to trace back the age,place of origin, and isotopic content of a tracer. We will in particular compare the results for age toother methods being used to estimate this quantity to discuss the merits and shortcomings of theLagrangian scheme. Interpretation of the results obtained in terms of isotope content, on the other hand,requires a much higher degree of accuracy. Its variability together with the extremely low diffusioncoefficient of ice makes its real distribution to have a very fine structure. The way of overcoming thisobstacle is also discussed as well as the applicability of different computational schemes.

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