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Generalised Langevin Equations and the Climate Response Problem
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  • Nicholas Watkins,
  • sandra chapman,
  • Rainer Klages,
  • Aleksei Chechkin,
  • Ian Ford,
  • david stainforth
Nicholas Watkins
CATS, LSE, London, UK

Corresponding Author:nickwatkins62@fastmail.com

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sandra chapman
University of Warwick
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Rainer Klages
QMUL London UK
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Aleksei Chechkin
Akhiezer Institute, Ukraine
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Ian Ford
UCL, London, UK
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david stainforth
Grantham Institute, LSE, UK
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There can be few greater scientific challenges than predicting the response of the global system to anthropogenic disruption, even with the array of sensing tools available in the “digital Anthropocene”. Rather than depend on one approach, climate science thus employs a hierarchy of models, trading off the tractability of Energy Balance Models (EBMs) [1] against the detail of Global Circulation Models. Since the 70s Hasselmann-type stochastic EBMs have allowed treatment of climate fluctuations and noise. They remain topical, e.g. their use by Cox et al to propose an emergent constraint on climate sensitivity [2]. Insight comes from exploiting a mapping between Hasselmann’s EBM and the original stochastic model in physics, the Langevin equation of 1908. However, it has recently been claimed that the wide range of time scales in the global system may require a heavy-tailed response [3,4] to perturbation, instead of the familiar exponential. Evidence for this includes long range memory (LRM) in GMT, and the success of a fractional Gaussian model in predicting GMT [5]. Our line of enquiry is complementary to [3-5] and proposes mapping a model well known in statistical mechanics, the Green-Kubo “Generalised Langevin Equation” (GLE) to generalise the Hasselmann EBM [6]. If present LRM then simplifies the GLE to a fractional Langevin equation (FLE). As well as a noise term the FLM has a dissipation term not present in [3,4], generalising Hasselmann’s damping constant. We describe the corresponding EBM [7] that maps to the FLE, discuss its solutions, and relate it to existing models. References: [1] Ghil M (2019) Earth and Space Sciences, in press. [2] Cox P et al. (2018) Nature 553: 319-322 [3] Rypdal K. (2012) JGR 117: D06115 [4] Rypdal M and Rypdal K (2014) J Climate 27: 5240-5258. [5] Lovejoy et al (2015) ESDD 6:1–22 [6] Watkins N W (2013) GRL 40:1-9 [7] Watkins et al, to be submitted.