Evolving Bayesian Emulators for Structured Chaotic Time Series, with application to large climate models

Abstract

We develop Bayesian dynamic linear model Gaussian processes for emulation of time series output for computer models that may exhibit chaotic behavior, but where this behavior retains some underlying structure. The statistical technology is particularly suited to emulating the time series output of large climate models that exhibit this feature and where we want samples from the posterior of the emulator to evolve in the same way as dynamic processes in the computer model do. The methodology combines key features of good uncertainty quantification (UQ) methods such as using complex mean functions to capture large-scale signals within parameter space, with dynamic linear models in a way that allows UQ to borrow strength from the Bayesian time series literature. We present an MCMC algorithm for sampling from the posterior of the emulator parameters when the roughness lengths of the Gaussian process are unknown. We discuss an interpretation of the results of this algorithm that allows us to use MCMC to fix the correlation lengths, making future online samples from the emulator tractable when used in practical applications where online MCMC is infeasible. We apply this methodology to emulate the Atlantic Meridional Overturning Circulation (AMOC) as a time series output of the fully coupled non–flux-adjusted atmosphere-ocean general circulation model HadCM3.