4. Discussion and Conclusions
We examined the relationship between climate sensitivity and global
temperature variability and its potential to constrain uncertainty in
ECS. Prior work characterizing temperature variability over the
historical period was criticized for a variety of reasons, including the
short span of the historical record, the presence of external forcing,
and the dependency of the relationship on selection of models (Brown et
al., 2018; Po-Chedley et al., 2018; Rypdal et al. 2018). Thus, we
analyzed temperature variability over an extended record that includes
the pre-industrial climate of the Common Era (850-1999), offering a new
line of evidence supporting the goal of constraining climate
sensitivity.
From a last-millennium perspective, we can effectively address
significant questions posed by the research community regarding prior
endeavors to constrain ECS via temperature variability. Notably, it was
previously suggested that the instrumental record is too brief to
accurately measure global temperature variability for the purposes of
constraining ECS and cannot be used alone to constrain climate
sensitivity (Annan et al., 2020). We find that while the observed
estimate of interannual temperature variability is weakly sensitive to
the period of analysis (Supplemental Table 3), individual GCMs can
exhibit meaningful differences in estimates of \(\psi\) produced when
calculated over the past millennium (Supplemental Figure 2). This
illustrates the added value of a much longer timeseries, which allows us
to reduce sampling uncertainty. It was also suggested that external
(especially anthropogenic and volcanic) forcing in the climate system
would impact the constraints’ validity. The presence of external forcing
is a major concern because it can violate the stationary climate
assumption that is fundamental to the theoretical basis for the proposed
constraint. However, we found that excluding periods of substantial
anthropogenic forcing (ex: GMST from 1850 to 1999) from our analysis did
not substantially affect the strength of the proposed emergent
relationship or the resulting constraint on ECS (Supplemental Figure 2).
We also removed major sources of volcanic eruptions and showed that the
emergent constraint improved (Supplemental Figure 1). Therefore, our
work suggests that the potentially deleterious effects of external
forcing can be appropriately handled over the past millennium.
To build our model ensemble, we used as many publicly available GCM
simulations of the Common Era as we could find. As a result, most
(12/18) of the models in our ensemble were also analyzed in prior
studies (Cox et al., 2018a; Nijsse et al., 2019; Schlund et al., 2020),
meaning that the GCMs are not necessarily “out of sample”. However,
our analysis does utilize new, longer model experiments and forcing
profiles. Additionally, because our ensemble is limited to the models
which carried out past1000 or past2k experiments, it is a pseudo-random
combination of models which also provides a degree of independence from
prior research. Our findings are in line with those of past CMIP5
studies, which have found the emergent relationship between GMST
variability and ECS to be strong.
Taken together, these improvements over prior work add value to the
efforts behind accurately estimating ECS through emergent constraints
and point to the potential value of the last millennium climate for
constraining uncertainty in other aspects of future climate change.
However, there are still some limitations to this approach. Given the
relatively small sample size (n=18), one outlier model can degrade the
emergent relationships (Supplemental Figure 4). As newer model
generations become available, along with additional past1000 and past2k
experiments from existing models, we will gain more empirical evidence
for or against the proposed emergent constraint. Subsequent
investigations will also be crucial in further examining the resilience
of the emergent relationship to changes in future climate feedbacks such
as interactions between warming and cloudiness that could drive future
ECS (Zelinka et al., 2020), and the behavior behind potential outlier
models, thereby enhancing our understanding of this methodology.
Another caveat to our approach is that GMST reconstructions of the past
millennium may underestimate variability altogether via spatiotemporal
sampling (F. Zhu et al., 2020), regression dilution (Tingley et al.,
2012), and the nonlinearity of some proxy systems (Evans et al., 2014),
resulting in an artificially low estimate of ECS. There are two main
reasons to be skeptical of the preservation of GMST variance in the
PAGES 2k GMST estimates: (a) data attrition back in time, which weakens
the signal to noise ratio and amplifies regression dilution (Frost &
Thompson, 2000) as the proxy data become sparser earlier in the Common
Era; (b) age uncertainties compound back in time, resulting in variance
losses from composite metrics (e.g. GMST) derived from multivariate
proxy compilations (Comboul et al., 2014). This caveat contributes to
the uncertainties in the emergent constraint derived from the
reconstructed GMST statistics. We investigate these possibilities using
pseudoproxy experiments (Supplemental Figure 5; F. Zhu et al., 2023),
which suggest that there would be great value in increasing the quality
and spatial coverage of paleoclimate proxies over the Common Era,
perhaps according to optimal sampling protocols (Comboul et al., 2015).
Finally, recent studies have produced mixed results constraining ECS
through temperature variability. While a strong linear relationship was
found within the CMIP5 ensemble, this relationship evaporated in CMIP6
(Schlund et al., 2020). Unfortunately, our analysis does not fully
resolve this difference because of a lack of available simulations,
highlighting the need for more resources to be committed to last
millennium experiments (ex: past1000 and past2k). While we explored the
use of piControl experiments to potentially augment our ensemble, we
found that their temperature variability is not strongly correlated with
that of past1000 experiments (Supplemental Figure 6). The lack of a
strong relationship between temperature variability in past1000 and
piControl experiments is likely primarily due to a lack of common
external forcing variability. While the past1000 experiment is forced by
multiple external sources (volcanic, solar, orbital), the piControl
experiment is not forced by any external sources (except for seasonal
solar variability, which is smoothed out on annual scales). This finding
is reinforced by the results of prior studies, which have shown that the
comparison of temperature variability between piControl experiments and
externally forced experiments is not trivial (Cox et al., 2018b) and
could require multiple realizations for each model to subtract out the
forced response (Nijsse et al., 2019).
Our constraints, which imply an ECS between 2.6 +/- 0.8K (for \(\psi\))
and 2.8 +/- 0.8K (for \(\sigma_{b}\)), are slightly lower than the
IPCC’s central estimate of 3K, but substantially overlap with the IPCC’s
likely range. The ability of temperature variability to constrain ECS on
its own has been shown to be limited, especially in cases where climate
sensitivity is greater than 2.5K (Annan et al., 2020). Therefore,
instead of viewing our study as fully capable of constraining ECS on its
own, we contend that our estimates and their associated uncertainties
should be regarded as an additional source of knowledge within the
existing body of work to generate the most accurate ECS estimate
(Sanderson et al., 2021). While this study has exclusively used
paleoclimate simulations and reconstructions from the Common Era, there
are multiple other past intervals that could be brought to bear on
estimates of ECS, including warmer and colder intervals (Renoult, 2022;
Tierney et al., 2020; J. Zhu et al., 2020). Combined with additional
sources of evidence (e.g. Sherwood et al., 2020), we hope that this
work, will contribute to tighter constraints on ECS.