# History matching for exploring and reducing climate model parameter space using observations and a large perturbed physics ensemble

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## Abstract

We apply an established statistical methodology called history matching to constrain the parameter space of a coupled non-flux-adjusted climate model (the third Hadley Centre Climate Model; HadCM3) by using a 10,000-member perturbed physics ensemble and observational metrics. History matching uses emulators (fast statistical representations of climate models that include a measure of uncertainty in the prediction of climate model output) to rule out regions of the parameter space of the climate model that are inconsistent with physical observations given the relevant uncertainties. Our methods rule out about half of the parameter space of the climate model even though we only use a small number of historical observations. We explore 2 dimensional projections of the remaining space and observe a region whose shape mainly depends on parameters controlling cloud processes and one ocean mixing parameter. We find that global mean surface air temperature (SAT) is the dominant constraint of those used, and that the others provide little further constraint after matching to SAT. The Atlantic meridional overturning circulation (AMOC) has a non linear relationship with SAT and is not a good proxy for the meridional heat transport in the unconstrained parameter space, but these relationships are linear in our reduced space. We find that the transient response of the AMOC to idealised CO_{2} forcing at 1 and 2 % per year shows a greater average reduction in strength in the constrained parameter space than in the unconstrained space. We test extended ranges of a number of parameters of HadCM3 and discover that no part of the extended ranges can by ruled out using any of our constraints. Constraining parameter space using easy to emulate observational metrics prior to analysis of more complex processes is an important and powerful tool. It can remove complex and irrelevant behaviour in unrealistic parts of parameter space, allowing the processes in question to be more easily studied or emulated, perhaps as a precursor to the application of further relevant constraints.

## Keywords

Bayesian uncertainty quantification History matching Implausibility Observations NROY space## Notes

### Acknowledgments

This research was funded by the NERC RAPID-RAPIT project (NE/G015368/1), and was supported by the Joint DECC/Defra Met Office Hadley Centre Climate Programme (GA01101). We would like to thank the CPDN team, in particular Andy Bowery, for their work in submitting our ensemble to the CPDN users. We’d also like to thank Richard Allan for helpful discussions regarding precipitation estimates, and all of the CPDN users around the world who contributed their spare computing resource as part of the generation of our ensemble. Finally, we’d like to thank both referees for their thoughtful and detailed comments.

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