  Climate science employs a hierarchy of models, trading the tractability of
simplified energy balance models (EBMs) against the detail of Global
Circulation Models. Since the pioneering work of Hasselmann, stochastic EBMs
have allowed treatment of climate fluctuations and noise. However, it has
recently been claimed that observations motivate heavy-tailed temporal response
functions in global mean temperature to perturbations. Our complementary
approach exploits the correspondence between Hasselmann's EBM and the original
mean-reverting stochastic model in physics, Langevin's equation of 1908. We
propose mapping a model well known in statistical mechanics, the Mori-Kubo
Generalised Langevin Equation (GLE) to generalise the Hasselmann EBM. If
present, long range memory then simplifies the GLE to a fractional Langevin
equation (FLE). We describe the corresponding EBMs that map to the GLE and FLE,
briefly discuss their solutions, and relate them to Lovejoy's new Fractional
Energy Balance Model.
