In this thesis, we provide the Uncertainty Quantification (UQ) tools to assist automatic and robust calibration of complex computer models. Our tools allow users to construct a cheap (statistical) surrogate, a Gaussian process (GP) emulator, based on a small number of climate model runs. History matching (HM), the calibration process of removing parameter space for which computer model outputs are inconsistent with the observations, is combined with an emulator. The remaining subset of parameter space is termed the Not Ruled Out Yet (NROY). A weakly stationary GP with a covariance function that depends on the distance between two input points is the principal tool in UQ. However, the stationarity assumption is inadequate when we operate with a heterogeneous model response. In this thesis, we develop diagnostic-led nonstationary GP emulators with a kernel mixture. We employ diagnostics from a stationary GP fit to identify input regions with distinct model behaviour and obtain mixing functions for a kernel mixture. The result is a continuous emulator in parameter space that adapts to changes in model response behaviour. History matching has proven to be more effective when performed in waves. At each wave of HM, a new ensemble is obtained to update an emulator before finding an NROY space. In this thesis, we propose a Bayesian experimental design with a loss function that compares the volume of the NROY space obtained with an updated emulator to the volume of the “true” NROY space obtained using a “perfect” emulator. We combine Bayesian Design Criterion with our proposed nonstationary GP emulator to perform calibration of climate model
