Conventional and Bayesian approach to climate-change detection and attribution

The conventional multi-variate, multi-fingerprint theory of climate-change detection and attribution, expressed in terms of existing frequency distributions, is reviewed and generalized to a Bayesian approach based on subjective probabilities. Bayesian statistics enable a quantitative determination of the impact of climate-change detection tests on prior subjective assessments of the probability of an externally forced climate change. The Bayesian method also provides a potentially powerful tool for enhancing statistical detection and attribution tests by combining a number of different climate-change indicators that are not amenable to standard signal-to-noise analyses because of inadequate information on the associated natural-variability statistics. The relation between the conventional and Bayesian approach is illustrated by examples taken from recent conventional analyses of climate-change detection and attribution for three cases of climate-change forcing by increasing greenhouse-gas concentrations, increasing greenhouse-gas and aerosol concentrations, and variations, in solar insolation. The enhancement of detection and attribution levels through a joint Bayesian anal:lsis of a number of different climate-change indices is demonstrated in a further example. However, this advantage of the Bayesian approach can be achieved only within the framework of a subjective rather than objective analysis. The conventional and Bayesian approach both exhibit specific advantages and shortcomings, so that a parallel application of both methods is probably the most promising detection and attribution strategy.