  The use of emergent constraints to quantify uncertainty for key policy
relevant quantities such as Equilibrium Climate Sensitivity (ECS) has become
increasingly widespread in recent years. Many researchers, however, claim that
emergent constraints are inappropriate or even under-report uncertainty. In
this paper we contribute to this discussion by examining the emergent
constraints 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 framework
wherein hitherto ignored sources of uncertainty, such as how reality might
differ from models, can be quantified. We present a guided framework for the
quantification of additional uncertainties that is linked to the confidence we
can have in the underpinning physical arguments for using linear constraints.
We provide a software tool for implementing our general framework for emergent
constraints and use it to illustrate the framework on a number of recent
emergent constraints for ECS. We find that the robustness of any constraint to
additional uncertainties depends strongly on the confidence we can have in the
underpinning physics, allowing a future framing of the debate over the validity
of a particular constraint around the underlying physical arguments, rather
than statistical assumptions.
