The case for forward modelling in proxy-based palaeoclimate reconstruction

## Abstract

Now that so much interest in palaeoclimate research focuses on reconstruction of climate on large spatial scales, there is an increasing need to combine proxy-based reconstructions from many spatial locations. We struggle to do this, however, because most proxy-based reconstructions provide only limited assessment of the associated uncertainties. Without reliable uncertainty assessments even comparison is difficult. For example, we cannot tell whether apparent differences between reconstructions are important, and thus interpretable, or of little interpretable value given the nature and scale of the uncertainties.

In this talk I will make the case that uncertainty quantification is important and that we cannot do it reliably using the statistical methods most commonly adopted for proxybased

palaeoclimate reconstruction because so many of the sources of uncertainty cannot be accounted for within them. I will then argue that we can solve this by tailoring the statistical methods we use to the problem we are trying to solve. To do this, we start by creating a causal or forward model that represents the link between climate and the proxy. Such models are typically joint (across time, space and/or climate variables) and stochastic, thus capturing the uncertainties at each step of the causal pathway.

I will explain that this task is made tractable by statistical modelling of conditionally independent 'modules' within the climate-proxy system. The statistical inference is then made by inversion of the forward model and so, given actual proxy data, identifying a collection of likely past climates which together capture reconstruction uncertainties as well as trends. Increasingly standard statistical techniques exist for such inversions and I will discuss the advantages, current progress and limitations of using this framework and also look to future research.