Since Hasselmann and Leith, stochastic Energy Balance Models (EBMs) have allowed treatment of climate fluctuations, and at least the possibility of fluctuation-dissipation relations. However, it has recently been argued that observations motivate heavy-tailed temporal response functions in global mean temperature. Our complementary approach (arXiv:2007.06464v2[cond-mat.stat-mech]) exploits the correspondence between Hasselmann’s EBM and Langevin’s equation (1908). We propose mapping 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 EBMs that correspond to the GLE and FLE, and relate them to Lovejoy et al’s FEBE [NPG Discussions, 2019; QJRMS, to appear, 2021].
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Watkins et al. (2021) studied this question.