Earth system models (ESMs) are commonly used for simulating the climate–carbon (C) cycle and for projecting future global warming. While ESMs are most often applied to century-long climate simulations, millennium-long simulations, which have been conducted by other types of models but not by ESM because of the computational cost, can provide basic fundamental properties of climate–C cycle models and will be required for estimating the carbon dioxide (CO₂) concentration and subsequent climate stabilization in the future. This study used two ESMs (the Model for Interdisciplinary Research on Climate, the Earth system model version (MIROC-ESM) and the MIROC Earth system version 2 for long-term simulation (MIROC-ES2L)) to investigate millennium-scale climate and C cycle adjustment to external forcing. The CO₂ concentration was doubled abruptly at the beginning of the model simulations and kept at that level for the next 1000 or 2000 years; these model simulations were compared with transient simulations where the CO₂ was increased at the rate of 1% year⁻¹ for up to 140 years (1pctCO2). Model simulations to separate and evaluate the C cycle feedbacks were also performed. Unlike the 1pctCO2 experiment, the change in temperature–cumulative anthropogenic C emission (∆T–CE) relationship was non-linear over the millennium time-scales; there were differences in this nonlinearity between the two ESMs. The differences in ∆T–CE among existing models suggest large uncertainty in the ∆T and CE in the millennium-long climate-C simulations. Ocean C and heat transport were found to be disconnected over millennium time-scales, leading to longer time-scale of ocean C accumulation than heat uptake. Although the experimental design used here was highly idealized, this long-lasting C uptake by the ocean should be considered as part of the stabilization of CO₂ concentration and global warming. Future studies should perform millennium time-scale simulations using a hierarchy of models to clarify climate-C cycle processes and to understand the long-term response of the Earth system to anthropogenic perturbations.

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二氧化碳倍增浓度下气候-碳循环的千年时标实验

地球系统模型（ESM）通常用于模拟气候-碳（C）循环并预测未来的全球变暖。尽管ESM最常用于百年气候模拟，但由于其他类型的模型（但由于计算成本原因而未由ESM进行）的千年模拟可以提供气候C循环模型的基本特征，并且将需要估算二氧化碳（CO ₂）的浓度并在将来稳定气候。这项研究使用了两个ESM（气候跨学科研究模型，用于长期模拟的地球系统模型版本（MIROC-ESM）和MIROC地球系统版本2（MIROC-ES2L））来研究千年尺度的气候和C周期调整到外部强迫。一氧化碳在模型仿真开始时，_2的浓度突然加倍，并在接下来的1000或2000年中保持在该水平；这些模型模拟与瞬态模拟进行了比较，在瞬态模拟中，CO ₂以每年^-1％的速度增长长达140年（1pctCO2）。还进行了模型仿真以分离和评估C周期反馈。与1pctCO2实验不同，温度-人为累积C排放量（ΔT-CE）关系的变化在千年时间尺度上是非线性的。两个ESM之间的非线性之间存在差异。现有模型之间∆T–CE的差异表明，在长达一千年的气候C模拟中，∆T和CE的不确定性很大。发现海洋碳和热传输在千年时间尺度上是断开的，从而导致海洋碳积累的时间尺度比热量吸收更长。尽管此处使用的实验设计高度理想化，但海洋对C的持久吸收应被视为稳定CO _{2的一部分}集中和全球变暖。未来的研究应使用模型层次结构执行千年时间尺度的模拟，以阐明气候-C循环过程并了解地球系统对人为扰动的长期响应。