Model Complexity of Global Climate: Could Arrhenius have Foreseen the Hiatus?

Abstract:

Recent interest in model complexity of complex systems is motivated by opacity of complex models and overfitting leading to low skill. In this work we explore a notion of model complexity of global climate as measured by a suitable function of number of parameters, granularity of relevant data, and targeted forecasting skill (certainty of prediction).

In this notion each dataset is associated with typically one to three parameters. Data is coarsened by low-pass filtering. Forecasting skill is assessed by fitting the model to available data up to various values of year Y and comparing its predictions between Y and now with what actually happened.

At one extreme we achieve very low model complexity using one parameter relating 60-year-smoothed CO2 to temperature data and a goal of high skill. To maintain skill when data is refined to 20-year smoothing we model the influence of length of day on climate using three parameters, two of which however cannot be separated by the data and hence can be coalesced to one without loss of skill. Further refinement to 10 years is necessary in order to account for the recent hiatus, accomplished with heliomagnetic field data collected by Gauss and others since 1835, which we fit with three parameters.

The primary conclusion is that high skill, at least up to the present, is possible with surprisingly simple yet physically plausible models. Using additional data not needed for the foregoing, such as volume of the oceanic mixed layer, we explore circumstances under which the apparent promise of high skill might not be realized in future due to departures from regularities to date such as the RCP8.5 concentration pathway. Of secondary interest, for Y = 1925, 2 years before Arrhenius died, temperature up to the present is significantly underestimated (low temperature skill) but exhibits a hiatus accurately matching today's in both year of onset and duration (high timing skill).

Further details at http://clim.stanford.edu/modcomp/