Modeling the ice age: the finite-element method in glaciology

To comprehend the Earth´s climatic system we develop more and more complex models of its atmosphere, hydrosphere, cryosphere (the icy regions), and even biosphere to understand the interactions that control climate. Ice sheet modeling is tied intrinsically to the understanding of past and future climatic change. Many climate models behave well in recreating present conditions, but we must test them against different climates of the past to see if they are predictive. One time period with a reasonably well understood and yet very different climate was the most recent ice age, late in the Pleistocene Epoch, climaxing approximately 18000 years ago. How do we recognize a good theoretical framework, or model, within which to interpret experimental data? In glaciology, the model must describe as completely as possible the physical processes connecting different aspects of the data. Computers have allowed scientists to apply numerical methods to equations that were not amenable to analytic evaluation, and thus obtain approximate solutions without restrictive assumptions or simplified domains. One such numerical technique, the finite element method, can be used to solve differential equations that arise when we deal (as we do in glaciology) with conserved quantities, that is, mass, momentum, and energy. Having applied this technique to model glaciers and ice sheets, this approach is a robust alternative to traditional numerical techniques.<>