2. Data and Methods
2.1. Last Millennium Global Mean Surface Temperature Data
We derived GMST records for the last millennium from a collection of 18
GCMs (Supplemental Table 2). Our ensemble spans multiple model
generations because of the relatively low number of modeling centers
that have published past1000/past2k simulations as a part of
Paleoclimate Model Intercomparison Projects 3 and 4 (PMIP3, Braconnot et
al., 2011; Braconnot et al., 2012 and PMIP4, Jungclaus et al., 2017;
Kageyama et al., 2018). Ten of the GCMs assessed here come from CMIP5
(Taylor et al., 2012), seven come from CMIP6 (Eyring et al., 2016), and
another stems from non-CMIP activities (CESM1-LME, Otto-Bliesner et al.,
2016). For each GCM, GMST from the past1000 scenario (850-1849) was
stitched with that of the historical scenario (1850-1999) to form a
1150-year timeseries. Model-based GMST anomalies were computed
separately relative to either the 1800-1849 baseline (for simulation
years before 1850) or the 1850-1899 baseline (for simulation years after
1850) to reduce any discontinuities between past1000 and historical
experiments. For one model (MPI-ESM1-2-LR, Mauritsen et al., 2019), a
past2k experiment was run instead of past1000. However, for consistency,
we only consider the 850-1849 from the past2k experiment. For another
model (FGOALS-gl; Zhou et al., 2018), we only consider the years that
were simulated, 1000-1999.
To assess temperature variability in the GCMs over the past millennium,
we leveraged an ensemble of Common Era GMST reconstructions published by
the PAGES 2k consortium (PAGES 2k Consortium, 2019) and based on a
global collection of temperature-sensitive proxies covering all or parts
of the Common Era (PAGES 2k Consortium, 2017). Seven statistical methods
were used to reconstruct GMST, such as the principal component
regression (PCR) method shown in Figure 2, and 1000 realizations are
available for each method to sample the uncertainty space. From these
reconstructions, we sub-selected the years 850-1999 to match model
output. We used 1800-1899 as a climatological baseline to compute the
reconstruction based GMST anomaly so that the record would be easily
compared to model output.
From 850-1849, the most dramatic external forcing stems from volcanic
eruptions, which have a substantial cooling effect on GMST due to their
abundant stratospheric aerosol emissions (PAGES 2k Consortium, 2019).
These eruptions are also notoriously poorly represented in last
millennium climate simulations, leading to potential systemic biases
which can distort the emergent relationship (Eyring et al., 2019). To
reduce the impact of major volcanic eruptions on GMST variability, we
regressed the timeseries generated in Section 2.1 against the volcanic
forcing profiles corresponding to each past1000 experiment (Crowley,
2000; Crowley et al., 2008; Gao et al., 2008; Toohey & Sigl, 2017). We
then used the resulting residuals to compute temperature variability.
This intervention substantially improved the strength of the emergent
relationship with ECS, increasing the correlation coefficient from
r=0.51 to r=0.62 for \(\psi\) and from r=0.42 to r=0.59 for\(\sigma_{b}\) (Supplemental Figure 1), so we used these residuals in
our analysis (Figure 2b, 3, 4) instead of the original GMST timeseries
(Figure 2a).
Historical external forcing is dominated by anthropogenic sources, which
have a persistent, strong warming effect. Anthropogenic forcing has been
shown to potentially impact the emergent relationship between
interannual temperature variability (\(\psi\)) and ECS (Brown et al.,
2018; Po-Chedley et al., 2018; Rypdal et al. 2018). To test the impact
of anthropogenic forcing on our analysis, we modified records to exclude
the historical (1850-1999) experiment and recomputed the emergent
relationship. Doing so had minimal impact on the emergent relationship
(Supplemental Figure 2). Therefore, we chose to include historical
records in our overall analysis to reduce sampling uncertainty in the
variability metric.
2.2. Calculating Temperature Variability Metrics and Equilibrium Climate
Sensitivity
We computed interannual (\(\psi\), 2) and decadal trend (\(\sigma_{b}\),
3) temperature variability for each timeseries generated in Section 2.1.
Observational uncertainty in each case was approximated as the standard
deviation across the seven available reconstruction methods, while the
observation mean was taken as the average of these methods (Supplemental
Figure 3bd). Temperature variability metrics computed using the PAGES 2k
reconstructions showed close agreement with those computed using the
HadCRUT4 dataset (Morice et al., 2012) over the 1850-1999 period
(Supplemental Figure 3ac). We removed volcanic forcing from
reconstruction output via linear regression against the evolv2k version
3 volcanic forcing profile before computing both metrics (Toohey &
Sigl, 2017).
The ECS values associated with each GCM were taken from Zelinka et al.
(2020), which uses model output from the abrupt-4xCO2 experiment and the
Gregory method (Gregory et al., 2004) to estimate ECS. In the case that
Zelinka et al. (2020) did not calculate ECS for a GCM in our ensemble,
we took ECS directly from publications pertaining to that model (Meehl
et al., 2013; Phipps et al., 2012; Randall et al., 2007; Zhang et al.,
2013). For each GCM, these values and their sources are listed in
Supplemental Table 2.
2.3. Constraining Equilibrium Climate Sensitivity:
To infer possible values of ECS suggested by the emergent constraint, we
employed the Hierarchical Emergent Constraint statistical framework
(Bowman et al., 2018). This method offers a more comprehensive approach
to constraining ECS compared to traditional techniques, as it accounts
for the emergent constraint’s reliance on the signal-to-noise ratio and
the correlation strength.