Comparing the views of the driven climate system through the lenses of statistical time series analysis and stochastic EBMs: Apparent absence of mean reversion can be evidence of anthropogenic driving.

Connecting the different levels of the hierarchy of complexity in which climate models operate, and comparing the assumptions that apply at each level, has led to much progress in climate science. A particularly notable success was Klaus Hasselmann’s use of Brownian motion to inspire his linear Markovian stochastic energy balance model (EBM), the history of which was recently summarised by Watkins [2024]. Another informative, but lateral, connection and comparison is that between either studying climate through the lens of stochastic physical models or doing so via statistical methods. This presentation showcases how comparing these approaches can sometimes surprise us.

It has been asserted that because the Hasselmann stochastic EBM has a mean-reverting term due to feedbacks, this property must also be detected in global mean temperature time series by statistical models such as the well-known Box-Jenkins ARIMA family. Conversely its absence has been taken as an indication of fundamental difficulties with anthropogenic driving. By fitting Hasselmann models, with and without anthropogenic driving, to an ARFIMA model with automatically selected parameters we show that in fact the absence of a prominent autoregressive term has precisely the opposite meaning, and is, rather, a clear indication of strong driving.

We will also report preliminary findings about the extent to which the presence of long range memory due to the multiple time scales present in the coupled ocean-atmosphere can affect the above conclusions, updating  the work summarised by Watkins et al [2024]. We thank Nick Moloney for many insightful suggestions.

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).