SIAM News Blog

Math of Planet Earth at EGU 2018

In 1990, Kirk Maasch and Barry Saltzman introduced a three-dimensional dynamical system to explain central features of the glacial cycles observed in the climate record of the Pleistocene Epoch. The model incorporates interactions between the Earth’s oceans, atmosphere, and cryosphere, emphasizing the role of atmospheric carbon dioxide. 

At a session on Mathematics of Planet Earth at the European Geosciences Union (EGU) General Assembly to be held in Vienna, Austria in April, Hans Engler, Hans Kaper, Tasso Kaper, and Theodore Vo will present a dynamical systems approach to the Pleistocene climate. 

Their work demonstrates that, in most parameter regimes, the long-term system dynamics occur on certain intrinsic two-dimensional invariant manifolds in the three-dimensional state space. These invariant manifolds are slow manifolds when the characteristic time scales for the total global ice mass and the volume of the North Atlantic Deep Water are well separated, and they are center manifolds when these characteristic time scales are comparable. In both cases, the reduced dynamics on these manifolds can be examined with unfolding techniques for multi-parameter bifurcation problems. The resulting bifurcation curves organize the parameter regions in which the model exhibits limit cycles of different types. In addition, knowledge of the reduced systems and their bifurcations is useful for understanding the effects of slowly varying parameters, which cause passage through Hopf bifurcations, and of orbital (Milankovitch) forcing. Both are central to the mechanism proposed by Maasch and Saltzman for the mid-Pleistocene transition.

The EGU, which is the European analog of the American Geophysical Union, is Europe's premier geosciences union, dedicated to the pursuit of excellence in the Earth, planetary, and space sciences for the benefit of humanity, worldwide.  


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