Assessing uncertainty in past ice and climate evolution: overview, stepping-stones, and challenges

Abstract. In the geosciences, complex computational models have become a common tool for making statements about past earth system evolution. However, the relationship between model output and the actual earth system (or component thereof) is generally poorly specified and even more poorly assessed. This is especially challenging for the paleo sciences for which data constraints are sparse and have large uncertainties. Bayesian inference offers a self-consistent and rigorous framework for assessing this relationship as well as a coherent approach to combining data constraints with computational modelling. Though “Bayesian” is becoming more common in paleoclimate and paleo ice sheet publications, our impression is that most scientists in these fields have little understanding of what this actually means nor are they able to evaluate the quality of such inference. This is especially unfortunate given the correspondence between Bayesian inference and the classical concept of the scientific method. Herein, we examine the relationship between a complex model and a system of interest, or in equivalent words (from a statistical perspective), how uncertainties describing this relationship can be assessed and accounted for in a principled and coherent manner. By way of a simple example, we show how inference can be severely broken if uncertainties are erroneously assessed. We explain and decompose Bayes Rule (more commonly known as Bayes Theorem), examine key components of Bayesian inference, offer some more robust and easier to attain stepping stones, and provide suggestions on implementation and how the community can move forward. This overview is intended for all interested in making and/or evaluating inferences about the past evolution of the Earth system (or any of its components), with a nominal focus on past ice sheet and climate evolution during the Quaternary.