Uncertainty quantification in palaeoclimate reconstruction

Studying the dynamics of the palaeoclimate is a challenging problem. Part of the challenge lies in the fact that our understanding must be based on only a single realisation of the climate system. With only one climate history, it is essential that palaeoclimate data are used to their full extent, and that uncertainties arising from both data and modelling are well characterised. This is the motivation behind this thesis, which explores approaches for uncertainty quantification in problems related to palaeoclimate reconstruction. We focus on uncertainty quantification problems for the glacial-interglacial cycle, namely parameter estimation, model comparison, and age estimation of palaeoclimate observations. We develop principled data assimilation schemes that allow us to assimilate palaeoclimate data into phenomenological models of the glacial-interglacial cycle. The statistical and modelling approaches we take in this thesis means that this amounts to the task of performing Bayesian inference for multivariate stochastic differential equations that are only partially observed. One contribution of this thesis is the synthesis of recent methodological advances in approximate Bayesian computation and particle filter methods. We provide an up-to-date overview that relates the different approaches and provides new insights into their performance. Through simulation studies we compare these approaches using a common benchmark, and in doing so we highlight the relative strengths and weaknesses of each method. There are two main scientific contributions in this thesis. The first is that by using inference methods to jointly perform parameter estimation and model comparison, we demonstrate that the current two-stage practice of first estimating observation times, and then treating them as fixed for subsequent analysis, leads to conclusions that are not robust to the methods used for estimating the observation times. The second main contribution is the development of a novel age model based on a linear sediment accumulation model. By extending the target of the particle filter we are able to jointly perform parameter estimation, model comparison, and observation age estimation. In doing so, we are able to perform palaeoclimate reconstruction using sediment core data that takes age uncertainty in the data into account, thus solving the problem of dating uncertainty highlighted above