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Climate stability for a Sellers-type modelWe study a diffusive energy-balance climate model governed by a nonlinear parabolic partial differential equation. Three positive steady-state solutions of this equation are found; they correspond to three possible climates of our planet: an interglacial (nearly identical to the present climate), a glacial, and a completely ice-covered earth. We consider also models similar to the main one studied, and determine the number of their steady states. All the models have albedo continuously varying with latitude and temperature, and entirely diffusive horizontal heat transfer. The diffusion is taken to be nonlinear as well as linear. We investigate the stability under small perturbations of the main model's climates. A stability criterion is derived, and its application shows that the 'present climate' and the 'deep freeze' are stable, whereas the model's glacial is unstable. A variational principle is introduced to confirm the results of this stability analysis. For a sufficient decrease in solar radiation (about 2%) the glacial and interglacial solutions disappear, leaving the ice-covered earth as the only possible climate.
Document ID
19760039518
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Ghil, M.
(New York University; NASA, Goddard Institute for Space Studies, New York, N.Y., United States)
Date Acquired
August 8, 2013
Publication Date
January 1, 1976
Publication Information
Publication: Journal of the Atmospheric Sciences
Volume: 33
Subject Category
Meteorology And Climatology
Accession Number
76A22484
Funding Number(s)
CONTRACT_GRANT: AT(11-1)-3077
CONTRACT_GRANT: NSG-5034
CONTRACT_GRANT: AF-AFOSR-74-2728
Distribution Limits
Public
Copyright
Other

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