In this paper we introduce a Bayesian framework, which is explicit about prior assumptions, for using model ensembles and observations together to constrain future climate change. The emergent constraint approach has seen broad application in recent years, including studies constraining the equilibrium climate sensitivity (ECS) using the Last Glacial Maximum (LGM) and the mid-Pliocene Warm Period (mPWP). Most of these studies were based on ordinary least squares (OLS) fits between a variable of the climate state, such as tropical temperature, and climate sensitivity. Using our Bayesian method, and considering the LGM and mPWP separately, we obtain values of ECS of 2.7 K (0.6–5.2, 5th–95th percentiles) using the PMIP2, PMIP3, and PMIP4 datasets for the LGM and 2.3 K (0.5–4.4) with the PlioMIP1 and PlioMIP2 datasets for the mPWP. Restricting the ensembles to include only the most recent version of each model, we obtain 2.7 K (0.7–5.2) using the LGM and 2.3 K (0.4–4.5) using the mPWP. An advantage of the Bayesian framework is that it is possible to combine the two periods assuming they are independent, whereby we obtain a tighter constraint of 2.5 K (0.8–4.0) using the restricted ensemble. We have explored the sensitivity to our assumptions in the method, including considering structural uncertainty, and in the choice of models, and this leads to 95 % probability of climate sensitivity mostly below 5 K and only exceeding 6 K in a single and most uncertain case assuming a large structural uncertainty. The approach is compared with other approaches based on OLS, a Kalman filter method, and an alternative Bayesian method. An interesting implication of this work is that OLS-based emergent constraints on ECS generate tighter uncertainty estimates, in particular at the lower end, an artefact due to a flatter regression line in the case of lack of correlation. Although some fundamental challenges related to the use of emergent constraints remain, this paper provides a step towards a better foundation for their potential use in future probabilistic estimations of climate sensitivity.

中文翻译：

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贝叶斯紧急约束框架：PMIP对气候敏感性的案例研究

在本文中，我们介绍了一个贝叶斯框架，该框架对于先前的假设是明确的，用于一起使用模型集合和观测值来约束未来的气候变化。近年来，涌现约束方法得到了广泛应用，包括使用末次冰期最大值（LGM）和上新世中期暖期（mPWP）来限制平衡气候敏感性（ECS）的研究。这些研究大多数基于普通最小二乘（OLS）在气候状态变量（例如热带温度）与气候敏感性之间的拟合。使用我们的贝叶斯方法，并分别考虑LGM和mPWP，使用LGM的PMIP2，PMIP3和PMIP4数据集和2.3 K（0.5-4.4）获得的ECS值为2.7 K（0.6-5.2、5-95％） ）以及mPWP的PlioMIP1和PlioMIP2数据集。限制集成仅包含每个模型的最新版本，使用LGM可获得2.7 K（0.7-5.2），使用mPWP可获得2.3 K（0.4-4.5）。贝叶斯框架的一个优点是可以假设两个周期是独立的，从而将两个周期合并，从而使用受限的集合获得2.5 K（0.8–4.0）的更严格约束。我们已经在方法中探索了对假设的敏感性，包括考虑结构不确定性以及模型的选择，这导致95％的气候敏感性概率大部分在5 K以下，并且在单个且最不确定的情况下仅超过6 K假设存在较大的结构不确定性。该方法与其他基于OLS，卡尔曼滤波方法和备选贝叶斯方法的方法进行了比较。这项工作的一个有趣的含义是，基于ECS的基于OLS的紧急约束会产生更严格的不确定性估计，尤其是在较低端，这是在缺乏相关性的情况下由于回归线更平坦而造成的假象。尽管仍然存在与使用紧急约束相​​关的一些基本挑战，但本文为在将来对气候敏感性的概率估计中潜在使用它们的基础上提供了迈出的一步。