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).