3. Results
3.1. Last Millennium Global Mean Surface Temperature Anomalies
Temperature variability over the past 1150 years is illustrated by Figure 2. The magnitude of model-generated GMST anomalies greatly varies across our ensemble (blue shading) due to differing sensitivities to internal variability, aerosols, and greenhouse gases (GHGs). The multi-model mean closely tracks reconstructed GMST anomalies from the PAGES 2k dataset over the study period (consistent with PAGES 2k Consortium, 2019), although agreement is noticeably weaker in earlier years and during periods of high volcanic activity (which manifest in the timeseries as sharp, transient, negative anomalies). We chose to illustrate only the Principal Component Regression (PCR) in Figure 2 as an example. Taken together, the ensemble of temperature reconstruction methods accurately represents both interannual and decadal variability over the observed period of 1850-1999 (Figure 2ab). We consider all reconstruction methods with equal weight in our emergent constraint analysis (Figure 3, 4).
3.2. Emergent Relationship between Temperature Variability and ECS
Next, we examine the proposed emergent relationships from Figure 1 in the context of our paleoclimate model ensemble. In Figure 3, we show a statistically significant, positive relationship between ECS and both temperature variability metrics over the last millennium (850-1999). The variability metrics are calculated with a reduced influence of major volcanic eruptions according to the procedure outlined in Section 2.1. The correlation with ECS is slightly stronger in the case of \(\psi\) (r = 0.62) than for \(\sigma_{b}\) (r = 0.59). Importantly, when the ensemble is broken down by model generation, we find that correlations are positive and similar in magnitude for both PMIP3-CMIP5 and PMIP4-CMIP6, although weaker for PMIP4-CMIP6 (Figure 3), consistent with prior studies (Figure 1).
Observational estimates of temperature variability from the PAGES 2k ensemble are low relative to model spread (Figure 3). Mean estimates from these reconstructions are insensitive to both the influence of volcanic forcing and period of analysis (Supplemental Table 3).
3.3 Constraining ECS
Using the statistical framework described in Section 2.3, we constrain model uncertainty in ECS for both emergent relationships shown in Figure 3, resulting in two separate estimates of ECS. The interannual temperature variability metric (\(\psi\)) yields a central estimate of 2.6K, with a 66% confidence interval of 1.8-3.3K. The decadal trend variability metric (\(\sigma_{b}\)) yields a central estimate of 2.8K, with a 66% confidence interval of 2.0-3.4K. Both central estimates are lower than that of the unconstrained past1000/past2k ensemble (3.3K). The estimated intervals overlap with the IPCC likely range for ECS, which is 2.5-4.0K (IPCC, 2021). They are also consistent with the mean estimate generated by Cox et al. (2018a), although the uncertainty attributed to our estimates is slightly larger (see Methods). While the ‘likely’ ranges from our study have widths of 0.8K (for both \(\psi\)and \(\sigma_{b}\)), the Cox et al. (2018a) ‘likely’ range has a width of 0.6K when recalculated using the statistical framework described in Section 2.3 (Bowman et al., 2018).