Energy Balance Models: interdisciplinary history, statistical fitting, stochastic modelling and long range memory | Nick Watkins
Nick Watkins will be presenting the paper ‘Energy Balance Models: Interdisciplinary History, Statistical Fitting, Stochastic Modelling and Long Range Memory.’
Abstract
Although the phrase “climate model” frequently suggests a large deterministic code like a GCM, stochastic energy balance models (EBMs) continue to have a role to play, and indeed his part in their development was one reason for the award of the Nobel Prize in 2021 to Klaus Hasselmann. The first part of my talk will draw on my recent introduction [Watkins, 2024] to his 1976 Tellus paper reprinted in the Santa Fe Institute’s “Foundational Papers in Complexity Science”. I will recount how his work exemplified an interdisciplinary approach to climate science, and how he used his familiarity with the mathematics of Brownian motion to provide a unified framework for slow climate and fast weather fluctuations.
Hasselmann’s work continues to inspire us and I will summarise how Calel et al [2020] combined a stochastic EBM of Hasselmann type with models of economic damage to explore a policy relevant question. I will also present work in progress with Dave Stainforth using Hasselmann’s EBM. This is a response to the contention, expressed for example by Mills [2019], that the finding that global mean temperature can be fitted by an ARIMA(0,1,q) statistical model invalidates any theory that posits an equilibrium to which temperature returns. By fitting Hasselmann stochastic models, with and without anthropogenic driving, to an ARIMA statistical model with automatically selected parameters we find that in fact the absence of a prominent autoregressive term in the fitted ARIMA model can have an opposite implication. It can, instead, be a clear indication of strong driving in a physical system which would otherwise be able to equilibrate.
I will conclude by talking about how the presence of long range memory due to the multiple time scales present in the coupled ocean-atmosphere may affect the above conclusions, and will summarise the recent review paper of Watkins [2024].
Calel, R., Chapman, S.C., Stainforth, D.A. et al. Temperature variability implies greater economic damages from climate change. Nature Communications. 11, 5028. DOI:10.1038/s41467-020-18797-8 (2020)
Mills, T, Applied Time Series Analysis, Academic Press (2019)
Watkins, N. W., “Brownian motion as a mathematical superstructure to organise the science of climate and weather”, In Foundational Papers in Complexity Science, Volume 3, pp. 1481–1510. Edited by David C. Krakauer. Santa Fe, NM: SFI Press. DOI:10.37911/9781947864542.51 (2024).
Watkins, N. W., R. Calel, S. C. Chapman, A. Chechkin, R. Klages and D. Stainforth, The Challenge of Non-Markovian Energy Balance Models in Climate. Chaos. 34, 072105 . DOI:10.1063/5.0187815 (2024)
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