Testing the assumptions in emergent constraints: Why does the 'Emergent constraint on equilibrium climate sensitivity from global temperature variability' work for CMIP5 and not CMIP6?

Abstract. It was shown that a theoretically derived relation between annual global mean temperature variability and climate sensitivity held in the (then latest) state-of-the-art CMIP5 climate model ensemble (Cox et al (2018), hereafter CHW18). This so called emergent relationship was then used with observations to constrain the value of equilibrium climate sensitivity (ECS) to about 3 °C. Since this study was published, CMIP6, a newer ensemble of climate models has become available. Schlund et al (2020) showed that many of the emergent constraints found in CMIP5 were much weaker in the newer ensemble including that of CHW18. As the constraint in CHW18 was based on a relationship derived from reasonable physical principles it is of interest to find out why it got weaker in CMIP6. Here, we look in detail at the assumptions made in deriving the emergent relationship in CHW18 and test them for CMIP5 and CMIP6 models. We show one assumption, that of low correlation and variation between the internal variability parameter and ECS, while true for CMIP5 is not true for CMIP6. When accounted for, an emergent relationship appears once again in both CMIP ensembles implying the theoretical basis is still applicable although the original assumption in CHW18 does not. Unfortunately however, we are unable to provide an emergent constraint in CMIP6 as observational estimates of the internal variability parameter are too uncertain.