Dimension reduction in the Bayesian analysis of a numerical climate model

Abstract

We present a prediction of the strength of the meridional overturning circulation (MOC) in the Atlantic Ocean during the 21st century, and a quantitative estimate of its uncertainty. The MOC has been suggested as a potential source of abrupt climate change, with the ability to alter the climate of the North Atlantic on a short time-scale. The prediction takes the form of a calibrated uncertainty analysis, combining observations of the MOC, an ensemble of runs from a climate model, and expert knowledge, in a Bayesian fashion.
Uncertainty in model behaviour due to the model structure and forcing is explored by running an ensemble of the Earth system model of intermediate complexity GENIE-1. Input parameters representing physical constants, simplified processes, and forcings are varied across the ensemble in a designed computer experiment. We develop quantitative and qualitative methods to compare observational data of the MOC with corresponding output from the ensemble, to learn about plausible input configurations of the model. Dimension reduction is used to express patterns of variation in model behaviour across the ensemble in a low-dimensional form. The ensemble is used to train an emulator; a fast statistical approximation to the expensive model, that includes an estimate of uncertainty due to the limited size of the ensemble. By training the emulator using the low-dimensional representations of the output, we are able to predict high-dimensional model output at input configurations not tested in the original ensemble. This allows a more complete expression of the uncertainty in the evolution of the MOC throughout the 21st century.

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