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The use of emergent constraints to quantify uncertainty for key policyrelevant quantities such as Equilibrium Climate Sensitivity (ECS) has becomeincreasingly widespread in recent years. Many researchers, however, claim thatemergent constraints are inappropriate or even under-report uncertainty. Inthis paper we contribute to this discussion by examining the emergentconstraints methodology in terms of its underpinning statistical assumptions.We argue that the existing frameworks are based on indefensible assumptions,then show how weakening them leads to a more transparent Bayesian frameworkwherein hitherto ignored sources of uncertainty, such as how reality mightdiffer from models, can be quantified. We present a guided framework for thequantification of additional uncertainties that is linked to the confidence wecan have in the underpinning physical arguments for using linear constraints.We provide a software tool for implementing our general framework for emergentconstraints and use it to illustrate the framework on a number of recentemergent constraints for ECS. We find that the robustness of any constraint toadditional uncertainties depends strongly on the confidence we can have in theunderpinning physics, allowing a future framing of the debate over the validityof a particular constraint around the underlying physical arguments, ratherthan statistical assumptions.

How are emergent constraints quantifying uncertainty and what do they leave behind?