License . Climate of the Past Reply to Henriksson et al . ’ s comment on “ Using multiple observationally - based constraints to estimate climate sensitivity ” by Annan and Hargreaves ( 2010 )

Henriksson et al. (2010), hereafter HALTL10, criticize Annan and Hargreaves (2006a) (AH06) primarily on the grounds that we assumed that different sources of data were conditionally independent given the climate sensitivity. While we consider this approximation to have been a reasonable one under the circumstances (and provided arguments to justify this approach), we also acknowledged its importance in our original paper and performed several sensitivity analyses. The alternative calculations presented by HALTL10 appear to strengthen rather than contradict our conclusion. HALTL10 additionally criticize Annan and Hargreaves (2009) (AH09) for proposing a Cauchy type prior (as an alternative to the use of a uniform prior, which was widespread up to that time) " without sufficient support " , and further claim that anticipated economic damages were used as a means of selecting the prior. We are surprised by these claims, especially considering that the proposed prior was justified at some length both on the basis of both the " Char-ney report " (National Research Council, 1979) and basic physical arguments, and also in light of our elementary demonstration of the pathological failings of the most commonly-used alternative. Thus, these claims are factually incorrect. 1 Overview We are pleased to see that HALTL10 explicitly acknowledge that by combining information from various sources, a more precise estimate of the climate sensitivity should be obtained. This is merely a special case of a well-known theorem of probability (e.g. Lindley, 1956). Therefore, it is virtually assured that those analyses which ignore relevant information by focussing only on one or two summary indicator variables and periods when attempting to form probabilistic estimates of climate sensitivity will have unrealistically high uncertainty (long tails), when compared to a more comprehensive calculation. This was of course the main point of AH06. It is, therefore, unclear to us how HALTL10 can justify their endorsement of previous research that suffers from this limitation , and indeed they do not explain this apparent contradiction. We now address their specific criticisms in detail. 2 Independence HALTL10 criticized the way that multiple lines of evidence were combined in AH06 under the assumption that they could be considered conditionally independent given the climate sensitivity. We note that the assumption of independence , in combining different constraints, was not in itself a particular novelty of AH06. In fact, such an approximation has been often used in other work, sometimes implicitly , without attracting particular criticism (e. …