History of climate modeling

The history of climate modeling begins with conceptual models, followed in the 19th century by mathematical models of energy balance and radiative transfer, as well as simple analog models. Since the 1950s, the principal tools of climate science have been computer simulation models of the global general circulation. From the 1990s to the present, a trend toward increasingly comprehensive coupled models of the entire climate system has dominated the field. Climate model evaluation and intercomparison is changing modeling into a more standardized, modular process, presenting the potential for unifying research and operational aspects of climate science. WIREs Clim Change 2011 2 128–139 DOI: 10.1002/wcc.95 For further resources related to this article, please visit the WIREs websitePeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79438/1/95_ftp.pd

Computing the Maximum Volume Inscribed Ellipsoid of a Polytopic Projection

We introduce a novel scheme based on a blending of Fourier-Motzkin elimination (FME) and adjustable robust optimization techniques to compute the maximum volume inscribed ellipsoid (MVE) in a polytopic projection. It is well-known that deriving an explicit description of a projected polytope is NP-hard. Our approach does not require an explicit description of the projection, and can easily be generalized to find a maximally sized convex body of a polytopic projection. Our obtained MVE is an inner approximation of the projected polytope, and its center is a centralized relative interior point of the projection. Since FME may produce many redundant constraints, we apply an LP-based procedure to keep the description of the projected polytopes at its minimal size. Furthermore, we propose an upper bounding scheme to evaluate the quality of the inner approximations. We test our approach on a simple polytope and a color tube design problem, and observe that as more auxiliary variables are eliminated, our inner approximations and upper bounds converge to optimal solutions