Bayesian History Matching and Uncertainty Analysis in Atmospheric Modelling

Earth System Models (ESMs), integrating atmosphere, ocean, land, ice, and biosphere, are vital in climate science to study drivers of climate change; quantify uncertainties in future climate projections; and to guide policy decisions. This often entails the analysis of Perturbed Parameter Ensembles (PPEs) formed by evaluating an ESM over a carefully constructed design of input parameter combinations. However, ESMs exhibit a complex structure, possess high-dimensional input and output, including spatial-temporal fields, and have long evaluation times. Further challenges arise due to model stochasticity and the numerous sources of uncertainty inherent within the modelling process. Combined, these severely inhibit the direct analysis of ESMs and the size of PPEs which may be constructed. Bayesian statistical and uncertainty analysis methodology are employed to overcome these limitations.

In this research a PPE for the UK Met Office UKESM1 model is used to investigate natural and anthropogenic aerosol emission interactions with clouds, which yields large Effective Aerosol Radiative Forcing (ERF; the temporal change in Earth’s energy balance due to aerosols) induced uncertainty in historical climate change. ERF is unobservable, thus model-observation comparison to calibrate ESMs is essential to robustly constrain ERF uncertainty. Moreover, ERF is key to accurately predicting future climate, yet research has resulted in little uncertainty reduction in over 30-years of IPCC reports.

Bayesian history matching, an efficient procedure for model-observation comparison, is performed to resolve parametric uncertainty and obtain all parameter combinations which produce ESM output consistent with observation data. This yields a greater constraint on ERF uncertainty. An efficient global parameter search is enabled by Bayesian emulators; fast statistical approximations for ESM outputs, providing both predictions at new parameter settings, along with a corresponding statement of the uncertainty, which are built for a carefully selected set of model outputs. These are embedded within an uncertainty quantification framework which includes structural model discrepancy linking ESM and the real-world, as well as representation and observation errors. In addition, the Bayesian paradigm enables the interrogation of how prior beliefs and uncertainties propagate through history matching, including discerning and evaluating implicit prior beliefs within studies.