On the Budyko-Sellers energy balance climate model with ice line coupling
Abstract
Over 40 years ago, M. Budyko and W. Sellers independently introduced low-order climate models that continue to play an important role in the mathematical modeling of climate. Each model has one spatial variable, and each was introduced to investigate the role ice-albedo feedback plays in influencing surface temperature. This paper serves in part as a tutorial on the Budyko-Sellers model, with particular focus placed on the coupling of this model with an ice sheet that is allowed to respond to changes in temperature, as introduced in recent work by E. Widiasih. We review known results regarding the dynamics of this coupled model, with both continuous (``Sellers-type") and discontinuous (``Budyko-type") equations. We also introduce two new Budyko-type models that are highly effective in modeling the extreme glacial events of the Neoproterozoic Era. We prove in each case the existence of a stable equilibrium solution for which the ice sheet edge rests in tropical latitudes. Mathematical tools used in the analysis include geometric singular perturbation theory and Filippov's theory of differential inclusions.
Repository Citation
Walsh, James, and Christopher Rackauckas. 2015. "On the Budyko-Sellers energy balance climate model with ice line coupling." Discrete and Continuous Dynamical Systems - Series B 20(7): 2187-2216.
Publisher
American Institute of Mathematical Sciences
Publication Date
9-1-2015
Publication Title
Discrete and Continuous Dynamical Systems - Series B
Department
Mathematics
Document Type
Article
DOI
https://dx.doi.org/10.3934/dcdsb.2015.20.2187
Keywords
Climate modeling, Ice-albedo feedback, Singular perturbations, Differential inclusions
Language
English
Format
text