Gaussian Process Emulation: Theory and Applications to the Problem of Past Climate Reconstruction

The dynamics of complex systems are commonly explored via the use of computer simulators. To ensure an understanding of the phenomena they model, simulators are usually run at a sequence of inputs, to explore different scenarios. This, however, often requires a prohibitive amount of time and computational resources. In such a case, the Bayesian framework of Gaussian process emulation allows to build a fast and reliable statistical surrogate of the simulator, called an emulator. This provides not only predictions of the simulator outputs, but also information on the uncertainty of these predictions. This work investigates the framework of Gaussian process emulation, and provides two separate examples of application to climate problems. In Part I of the thesis, Gaussian process emulation is introduced and investigated in depth. We employ a formal probabilistic setting, allowing us to see the derivation as an example of Bayesian analysis in an infinite-dimensional space, and to recover the formulas commonly used as a limit case. Further analyses are carried out, and the case of a chaotic simulator is investigated. In relation to the problem of emulating climate simulators, we also propose a dimension-reduction technique that accounts for the Earth’s spherical geometry. In Part II of the thesis, we employ the emulation framework to tackle problems of past climate reconstruction, key to understanding the dynamics and potential consequences of current global warming. In a first application, we explore the mismatch between simulated mid-Pliocene ocean temperatures and geological records. By sampling from the emulator trajectories, we reproduce the way records are extracted and account for orbitally-induced changes in temperature. In a second application, we explore the morphology of the Greenland ice sheet during the last Interglacial, to locate areas prone to melting under warm temperatures. The context provides an example of non-standard emulation setting, where the emulator input space consists of ice shapes.