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.