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Climate science employs a hierarchy of models, trading the tractability ofsimplified energy balance models (EBMs) against the detail of GlobalCirculation Models. Since the pioneering work of Hasselmann, stochastic EBMshave allowed treatment of climate fluctuations and noise. However, it hasrecently been claimed that observations motivate heavy-tailed temporal responsefunctions in global mean temperature to perturbations. Our complementaryapproach exploits the correspondence between Hasselmann's EBM and the originalmean-reverting stochastic model in physics, Langevin's equation of 1908. Wepropose mapping a model well known in statistical mechanics, the Mori-KuboGeneralised Langevin Equation (GLE) to generalise the Hasselmann EBM. Ifpresent, long range memory then simplifies the GLE to a fractional Langevinequation (FLE). We describe the corresponding EBMs that map to the GLE and FLE,briefly discuss their solutions, and relate them to Lovejoy's new FractionalEnergy Balance Model.

On Generalized Langevin Dynamics and the Modelling of Global Mean Temperature