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Sponsored by the Divisions of Mathematical Sciences (DMS), Atmospheric Sciences (ATM), Earth Sciences (EAR) and Ocean Sciences (OCE), National Science Foundation
Michael Ghil (Department of Atmospheric Sciences and Institute of Geophysics and Planetary Physics, University of California) http://www.atmos.ucla.edu/tcd/ ghil@atmos.ucla.edu
Hilbert Problems for Earth's Fluid Envelope in the Next Decades
The scientific problems posed by Earth's fluid envelope - its atmosphere, oceans, and the land surface that interacts with them - are central to major socio-economic and political concerns of this turn of the 20th into the 21st century. It is natural, therefore, that a certain impatience should prevail in attempting to solve these problems. The point of this review talk is that one should proceed with all diligence, but not excessive haste: "festina lente," as the Romans said two thousand years ago, i.e., "hurry in a measured way."
The talk traces necessary progress through the solution to ten problems:
A unified framework is proposed to deal with these problems in succession, from the shortest to the longest time scale, i.e., from weeks to centuries and millennia. The framework is that of dynamical systems theory, with an emphasis on successive bifurcations and the ergodic theory of nonlinear systems. The main ideas and methods are outlined and the concept of a modeling hierarchy is introduced. The methodology is applied, across the modeling hierarchy, by sketching ways of solving Problems 1-4.
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