Chang, K-L; (2016) Calibration of Computer Models with Global-Scale Outputs. Doctoral thesis , UCL (University College London).

Abstract

Modelling in spatial statistics is usually speci ed through the covariance function for the data or the latent eld. Covariance models for data distributed on the sphere present additional challenges compared to covariance models for data over an Euclidean space. The rst topic of this research is devoted to constructing spherical correlation structures through the stochastic partial di erential equation (SPDE) approach (Lindgren et al., 2011). This method is illustrated by using total column ozone data over the globe. This work proved that using the spherical correlation estimated by SPDE can outperform the currently used spatial kriging in terms of approximation of the total column ozone. Maps over the globe are more precise and the uncertainties are also more accurately estimated. The second topic is devoted to Bayesian calibration of complex computer model with spherical and nonstationary outputs. The basic formulation of Bayesian calibration has proven to be e ective in a wide range of applications (Kennedy and O'Hagan, 2001). However, the size of the climate model output leads to computational challenges in implementing this framework. To overcome this challenge, we reduce the dimensionality of the outputs by employing spherical harmonics in a Bayesian setting where we assume that both the simulator and the discrepancy with observations can be represented by a Gaussian Process over the reduced input space. This reduction allows us to solve e ciently the inverse problem of nding the posterior densities of input parameters by comparing outputs to observations. In a second stage, we model the outputs as a nonstationary Gaussian eld on the sphere. Since nonstationary Gaussian elds with Mat ern covariance functions can be obtained as the solution to a nested SPDE, we propose to include spatially-varying coe cients associated with precision and scale in the SPDE into our calibration framework, nally considering applications to the Whole Atmosphere Community Climate Model.

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