Publications by Author: Ghil, Michael

1983
Ghil, Michael, and John Tavantzis. “Global Hopf Bifurcation in a Simple Climate Model.” Siam Journal on Applied Mathematics 43, no. 5 (1983): 1019–1041. Publisher's Version Abstract
The mathematical structure of a simple climate model is investigated. The model is governed by a system of two nonlinear, autonomous differential equations for the evolution in time of global temperature $T$ and meridional ice-sheet extent $L$. The system's solutions are studied by a combination of qualitative reasoning with explicit calculations, both analytical and numerical. For plausible values of the physical parameters, a branch of periodic solutions obtains, which is both orbitally and structurally stable. The amplitude of the stable periodic solutions in $T$ and $L$ correspond roughly to that obtained from proxy records of Quaternary glaciation cycles. The period of these solutions increases along the branch, until it becomes infinite, while the amplitude of the limiting solution is finite. The limiting solution is a homoclinic orbit formed by the reconnecting separatrix of a saddle. The exchange of stability between the branch of periodic solutions and the steady solution from which it arises is studied by a slight simplification of known methods [20], [21].
1981
Ghil, Michael, S. Cohn, John Tavantzis, K. Bube, and Eugene Isaacson. “Applications of estimation theory to numerical weather prediction.” In Dynamic meteorology: Data assimilation methods, 139–224. Springer, 1981.
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Ghil, Michael, and H. Le Treut. “A climate model with cryodynamics and geodynamics.” Journal of Geophysical Research 86 (1981): 5262–5270. Publisher's Version
Ghil, Michael, J. Tavantzis S. Coho, K. Bube, and E. Isaacson. “Dynamic Meteorology: Data Assimilation Methods.” In Applied Mathematical Sciences, edited by L. Bengtsson, Michael Ghil, and E. Källén, 36:139–224. Dynamic Meteorology - Data Assimilation Methods. Springer-Verlag, 1981.
Ghil, Michael, J. Tavantzis S. Coho, K. Bube, and E. Isaacson. “Dynamic Meteorology: Data Assimilation Methods.” In Applied Mathematical Sciences, edited by L. Bengtsson, Michael Ghil, and E. Källén, 36:139–224. Dynamic Meteorology - Data Assimilation Methods. Springer-Verlag, 1981.

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