Variational formulation of Budyko-Sellers climate models

Creators: North, Gerald R.; Howard, Louis; Pollard, David; Wielicki, Bruce

Abstract

A class of simple climate models including those of the Budyko-Sellers type are formulated from a variational principle. A functional is constructed for the zonally averaged mean annual temperature field such that extrema of the functional occur when the climate satisfies the usual energy-balance equation. Local minima of the functional correspond to stable solutions while saddle points correspond to unstable solutions. The technique can be used to construct approximate solutions from trial functions and to carry out finite-amplitude stability analyses. A spectral example is given in explicit detail.

Additional Information

© 1979 American Meteorological Society. Manuscript received 16 August 1978, in final form 10 October 1978. The authors would like to express their thanks to the 1976 Geophysical Fluid Dynamics Summer Program at the Woods Hole Oceanographic Institution for its hospitality during the course of completion of this work. The 1976 GFD program was supported in part by grants from the Office of Naval Research and the National Science Foundation. The authors further wish to acknowledge helpful discussions with Prof. A. Ingersoll and Prof. C. Rooth. One of us (G.R.N.) was supported in part by a research grant from the Office for Climate Dynamics of the National Science Foundation and in part by funds from Goddard Laboratory for Atmospheric Sciences, National Aeronautics and Space Administration.

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