Bayesian statistics incorporate prior knowledge, along with a given set of current data, to make statistical inferences. Lemoine developed a hierarchical Bayesian framework that explicitly represents sources of uncertainty in climate models such as common biases and unknown and unmodeled feedbacks.

The framework uses models’ estimates of albedo, carbon cycle, cloud, and water vapor-lapse rate feedbacks to generate posterior probability distributions for feedback strength and equilibrium temperature change. The posterior distributions are especially sensitive to prior beliefs about models’ shared structural biases, Lemoine notes. Nonzero probability of shared bias moves some probability mass towards lower values for climate sensitivity even as it thickens the distribution’s positive tail.

Obtaining additional models of these feedbacks would not constrain the posterior distributions as much as would narrowing prior beliefs about shared biases or, potentially, obtaining feedback estimates having biases uncorrelated with those impacting climate models, he writes.

The CO₂ concentration needed to meet a 2 °C target relative to pre-industrial levels depends strongly on risk tolerance and on prior beliefs about shared model biases and about model completeness. If models are unrealistically assumed to be complete and to lack shared biases (prior combination 5), then CO₂ concentrations could stabilize at 410 ppm (slightly above present levels) and still have less than a 5% chance of exceeding the 2 °C target.

If, on the other hand, models are believed to possibly have shared biases and omissions (prior combination 3), then, before accounting for the effects of non-CO₂ GHGs or of aerosols, even stabilizing CO2 concentrations at current levels leaves a 10% chance of exceeding the 2 °C target.

—Derek Lemoine

In contrast to many previous studies, Lemoine’ proposed hierarchical Bayes methods recognize the possibility of structural biases shared across models, which limits the information gain from an unbounded increase in the number of models. This statistical framework also includes uncertainty about climate models’ completeness and about the similarity of the present and future higher-GHG world to the worlds represented by past climate observations.

The method Lemoine elaborates is extensible. Further work could incorporate more complex representations of model dependencies, could explore alternate types of prior beliefs, and could refine prior beliefs about shared structural biases and about unknown and unmodeled feedbacks. Further work could also develop temperature change distributions for planned emission pathways by including uncertainty about the operation of CO₂ sinks in response to changing CO2 concentrations and uncertainty in monitoring negotiated emission allocations, Lemoine says.

A robust Bayesian approach may help to address the difficulty in choosing the “right” prior distribution for feedbacks and shared biases, and this paper’s use of multiple priors could complement an ambiguity aversion framework for decision-making. Finally, to make them more useful for adaptation work and impacts assessments, these probability distributions should be extended to consider transient climate change by including uncertainty about heat uptake by oceans, uncertainty about emission paths, and uncertainty about the timescales over which feedbacks operate.

—Derek Lemoine

Resources

• Derek M. Lemoine (2010) Climate sensitivity distributions depend on the possibility that models share biases. Journal of Climate doi: 10.1175/2010JCLI3503.1