A SIMPLE PROOF OF THE
SLOPE STABILITY THEOREM FOR
ENERGY BALANCE CLIMATE MODELS

SAMUEL SHEN AND GERALD NORTH

Abstract. In this paper a simple proof of the slope stability theorem for energy balance climate models is given. Mathematically, this is an interfacial free boundary value problem of a feedback reaction diffusion equation. The subtle technique of implicit differentiation in studying the stability of a regular turning point bifurcation problem is utilized and makes the proof of the slope stability theorem simpler than the existing proofs. The proof method and the derived results are useful in studying the sensitivity of the global climate to external forcings.