Progess in non-Markovian (and Fractional) StochasticClimate Modelling: A GLE-based perspective

The mathematical stochastic energy balance models (SEBMs) pioneered by Hasselmann and Mitchell  have long been known to climate scientists to be important aids to gaining both qualitative insight and quantitative information about global mean temperatures. SEBMs are now much more widely visible, after the award of the 2021 Physics Nobel Prize to Hasselmann,  Manabe and Parisi. The earliest univariate SEBMs were, however, built around the simplest linear and Markovian stochastic process, enabling Hasselmann and his successors to exploit their equivalence to the Langevin equation of 1908. Multivariate SEBMs have now been extensively studied  but this presentation focuses on the continuing value of univariate SEBMs, especially when coupled to economic models, or when used to study longer-ranged memory than the exponential type seen in Hasselmann's Markovian case.

I will highlight how we and others are now going beyond the first SEBMs to incorporate more general temporal dependence, motivated by increasing evidence of non-Markovian, and in particular long-ranged, memory in the climate system. This effort has brought new and interesting challenges, both in mathematical methods and physical interpretation. I will highlight our recent paper [Calel et al, Nature Communications, 2021] on using a Markovian Hasselmann-type EBM to study the economic impacts of climate change and variability and our other ongoing work on generalisations (in particular fractional ones) of Hasselmann SEBMs.

This presentation updates our preprints [Watkins et al, arXiv; Watkins et al, in preparation for submission to Chaos] to show how the overdamped generalised Langevin equation can be mapped onto an SEBM that generalises Lovejoy et al's FEBE and I will give a progress report on this work. I will also briefly discuss  the relation of such non-Markovian SEBMs to fluctuation-dissipation relations.