EGU22-3962, updated on 27 Mar 2022
EGU General Assembly 2022
© Author(s) 2022. This work is distributed under
the Creative Commons Attribution 4.0 License.

Beyond Hasselmann and Leith: The challenge of non-Markovian and fractional stochastic climate modelling

Nicholas Wynn Watkins1,2,3, Raphael Calel8, Sandra Chapman1,4, Aleksei Chechkin5, Ian Ford6, Rainer Klages7, and David Stainforth1,2
Nicholas Wynn Watkins et al.
  • 1CFSA, University of Warwick, Coventry, United Kingdom of Great Britain – England, Scotland, Wales (
  • 2GRI, London School of Economics and Political Science, London, UK
  • 3STEM, Open University, Milton Keynes, UK
  • 4UIT, Tromso, Norway
  • 5Akhiezer Institute for Theoretical Physics, Kharkov, Ukraine
  • 6Physics Department, University College London, London, UK
  • 7School of Mathematical Sciences, QMUL, London, UK
  • 8McCourt School of Public Policy, George Washington University, Washington DC, USA

The stochastic energy balance models (SEBMs) pioneered by  Hasselmann and  Mitchell [1] 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 last year’s Nobel Prize to Hasselmann, shared with Manabe and Parisi [1].

The earliest univariate SEBMs were, however, built around the simplest linear and Markovian stochastic process, and researchers have very intentionally exploited their equivalence to the Langevin equation of 1908. Although multivariate SEBMs have now been extensively studied [1,2] and provide one important route to incorporating non-Markovian memory effects into climate dynamics, my presentation will discuss the continuing value of univariate SEBMs, especially when coupled to other models. I  will also highlight how we and others (e.g. [4,5]) are going beyond the first SEBMs to incorporate more general models of temporal dependence, motivated by 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 [3] on using a Hasselmann-type EBM to study the economic impacts of climate change and variability and our other ongoing work [6, and its updated version, 7] on  generalised (and in particular fractional) Hasselmann univariate SEBMs. I will compare our model [6,7] with Lovejoy and co-workers' FEBE [5], and discuss what the requirements are in order for such non-Markovian SEBMs to exhibit fluctuation-dissipation relations, which have been debated in the  SEBM field since the early work of Leith in the 1970s.

[1] Scientific background on the Nobel prize in physics 2021, Nobel Committee, Royal Swedish Academy of Sciences.

[2] Franzke and O’Kane, eds. Nonlinear and Stochastic Climate Dynamics, CUP, 2017.

[3] Calel et al, Nature Communications, 2020.

[4] Rypdal et al, Climate, 2018.

[5] Lovejoy et al, QJRMS, 2021.

[6] Watkins et al, On Generalized Langevin Dynamics and the Modelling of Global Mean Temperature, 2021,

[7] Watkins et al, arXiv:

How to cite: Watkins, N. W., Calel, R., Chapman, S., Chechkin, A., Ford, I., Klages, R., and Stainforth, D.: Beyond Hasselmann and Leith: The challenge of non-Markovian and fractional stochastic climate modelling, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-3962,, 2022.


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