What do we learn from looking at the Hasselmann model through 2 lenses ? Stochastics meets statistics

Connecting the different levels of the hierarchy of mathematical and conceptual complexity at which climate models operate, and comparing the assumptions that apply at each level, and the results produced, 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) and its successors . Another informative, but lateral, connection and comparison is that between either studying climate through the lens of stochastic physical models and 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 ARIMA model with automatically selected parameters I will show that in this instance the absence of a prominent autoregressive term can have quite the opposite meaning and  instead be a clear indication of strong driving. I will present results of our ensemble study which is examining the ability of automatic fitting to correctly infer ARIMA parameters on EBMs with realistic values of heat capacity and other system variables. Progress in extending the study to fractional EBMs and to ARFIMA models will be discussed.