Efficient Bayesian analysis of long memory processes applied to climate

Abstract

Temperature fluctuations can be described by a persistent correlation structure known as long-range dependence (LRD). This is a phenomenon which implies that the autocorrelation function follows a power-law decay and that observations may still be significantly correlated even if the temporal or spatial distance between them is large. Moreover, temperature is known to be influenced by radiative forcing, or how much of the solar radiation is absorbed by the earth. This is affected by factors such as solar variation and emission of climate gases.

The topic of this thesis is to develop efficient statistical methodology to obtain Bayesian inference for global and local climatic time series data. This is achieved using the general hierarchical modeling framework of latent Gaussian models. Bayesian analysis can be performed efficiently using the methodology of integrated nested Laplace approximation (INLA), utilising the sparse structure of the inverse covariance matrix of the latent Gaussian field. Obtaining inference for LRD processes using INLA is inefficient on account of their dense inverse covariance matrix.

Paper I demonstrates how stationary Gaussian LRD processes with memory governed by a single-parameter can be approximated with great accuracy using a mixture of four first-order autoregressive processes. This approximation ensures that the LRD model retains conditional independence and that inference can be obtained in linear time and memory.

Paper II details how this methodology can be used to design a Bayesian model for global mean surface temperature (GMST) that reflects climate dynamics by incorporating radiative forcing data. This model is available as the R-package INLA.climate and is used to estimate the transient climate response and to predict temperature response to future forcing scenarios. Paper III uses the GMST model to estimate equilibrium climate sensitivity, and paper IV applies the same methodology to gridded local time series.