  In [SIAM J. Appl. Dyn. Sys., 12(4):2068--2092, 2013], Widiasih proposed and
analyzed a deterministic one-dimensional Budyko-Sellers energy-balance model
with a moving ice-line. In this paper, we extend this model to the stochastic
setting and analyze it within the framework of stochastic slow-fast systems. We
derive the dynamics for the ice line in the limit of a small parameter as a
solution to a stochastic differential equation. The stochastic approach enables
the study of co-existing (metastable) climate states as well as the transition
dynamics between them.
