School of Mathematics
University of Minnesota


A Quadratic Approximation to Budyko’s Ice-Albedo Feedback Model with Ice Line Dynamics

Richard McGehee and Esther Widiasih

SIAM Journal on Applied Dynamical Systems 13 (2014) 518-536. doi: 10.1137/120871286


Abstract.  The classical Budyko model of ice-albedo feedback describes Earth's ice cap location as an equilibrium solution of an integro-differential equation. The traditional interpretation is that the ice line adjusts to perturbations or parameter changes much more rapidly than does the surface temperature. Widiasih recently introduced some specific ice line dynamics and showed, under the assumption that the ice line changes much more slowly than surface temperature, that the resulting infinite dimensional dynamical system could be reduced to a one-dimensional system using invariant manifold theory. Here we introduce an approximation to the original Budyko model whereby the integro-differential equation reduces to a single ordinary differential equation describing the dynamics of the ice line under the assumption of instantaneous ice line adjustment. Adding an e quation incorporating Widiasih's approach leads to a system of two ordinary differential equations. These equations contain a parameter which at one extreme reduces to the traditional Budyko model while at the other extreme reduces to Widiasih's equation.

Electronic Copies

The paper is available for subscribers on the publisher's Web site:
doi: 10.1137/120871286

An early versions of this paper was posted on this Web site in 2012:
McGehee & Widiasih 2012


Last update: May 26, 2018 ©2018 Richard McGehee