# Solution to the paradox of climate sensitivity

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## Abstract

Most countries endorse a limit of either 2°C or 1.5°C global warming above pre-industrial levels. However, for several reasons, there is still a significant uncertainty in the climate sensitivity parameter, which relates greenhouse gas concentration (or other forcings) to steady-state temperature. One key source of uncertainty is the disagreement about the appropriate prior for Bayesian estimation. A common choice is the uniform distribution, often thought to contain no information. However, when used to estimate sensitivity it leads to paradoxical results, which have been interpreted as revealing an inherent indeterminacy in the prior of choice. If this were the case, part of the uncertainty would be irreducible. Here I develop an objective Bayesian approach to this problem. I show that both Jaynes’ invariant groups criterion and a new criterion based on information theory lead to the conclusion that there is a uniquely defined non-informative prior of climate sensitivity, which is distinct from the uniform and solves the paradox. This prior distribution is the log-uniform. Furthermore, this result is supported empirically by the observation that other comparable non-equilibrium parameters display a scale-invariant, log-uniform-like frequency distribution. Rather than advocating a direct use of this prior, I recommend to refine it with a limited use of expert elicitation or other methods. A sound prior is a key ingredient in the process to reach a consensus low-uncertainty estimate of climate sensitivity to inform climate policy.

## Keywords

Electronic Supplementary Material Probability Density Function Mutual Information Prior Distribution Climate Sensitivity## Notes

### Acknowledgements

I am grateful for the useful comments by J. Ballester, X. Rodó, M. Oppenheimer, G. Yohe and three anonymous referees. I thank Bill Shipley for calling my attention on the paper by Baker and Christakos (2007).

## Supplementary material

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