fair-calibrate v1.4.1: calibration, constraining, and validation of the FaIR simple climate model for reliable future climate projections

Simple climate models (also known as emulators) have re-emerged as critical tools for the analysis of climate policy. Emulators are efficient and highly parameterised, where the parameters are tunable to produce a diversity of global mean surface temperature (GMST) response pathways to a given emission scenario. Only a small fraction of possible parameter combinations will produce historically consistent climate hindcasts, a necessary condition for trust in future projections. Alongside historical GMST, additional observed (e.g. ocean heat content) and emergent climate metrics (such as the equilibrium climate sensitivity) can be used as constraints upon the parameter sets used for climate projections. This paper describes a multi-variable constraining package for the Finite-amplitude Impulse Response (FaIR) simple climate model (FaIR versions 2.1.0 onwards) using a Bayesian framework. The steps are, first, to generate prior distributions of parameters for FaIR based on the Coupled Model Intercomparison Project (CMIP6) Earth system models or Intergovernmental Panel on Climate Change (IPCC)-assessed ranges; second, to generate a large Monte Carlo prior ensemble of parameters to run FaIR with; and, third, to produce a posterior set of parameters constrained on several observable and assessed climate metrics. Different calibrations can be produced for different emission datasets or observed climate constraints, allowing version-controlled and continually updated calibrations to be produced. We show that two very different future projections to a given emission scenario can be obtained using emissions from the IPCC Sixth Assessment Report (AR6) (fair-calibrate v1.4.0) and from updated emission datasets through 2022 (fair-calibrate v1.4.1) for similar climate constraints in both cases. fair-calibrate can be reconfigured for different source emission datasets or target climate distributions, and new versions will be produced upon availability of new climate system data.