Model-based changes in global annual mean surface temperature change (Delta T_g) and radiative forcing due to land ice albedo changes (Delta R_[LI]) over the last 5 Myr, supplementary material@en

It is still an open question how equilibrium warming in response to increasing radiative forcing – the specific equilibrium climate sensitivity S – depends on background climate. We here present palaeodata-based evidence on the state dependency of S, by using CO2 proxy data together with a 3-D ice-sheet-model-based reconstruction of land ice albedo over the last 5 million years (Myr). We find that the land ice albedo forcing depends non-linearly on the background climate, while any non-linearity of CO2 radiative forcing depends on the CO2 data set used. This non-linearity has not, so far, been accounted for in similar approaches due to previously more simplistic approximations, in which land ice albedo radiative forcing was a linear function of sea level change. The latitudinal dependency of ice-sheet area changes is important for the non-linearity between land ice albedo and sea level. In our set-up, in which the radiative forcing of CO2 and of the land ice albedo (LI) is combined, we find a state dependence in the calculated specific equilibrium climate sensitivity, S[CO2,LI], for most of the Pleistocene (last 2.1 Myr). During Pleistocene intermediate glaciated climates and interglacial periods, S[CO2,LI] is on average ~ 45 % larger than during Pleistocene full glacial conditions. In the Pliocene part of our analysis (2.6–5 Myr BP) the CO2 data uncertainties prevent a well-supported calculation for S[CO2,LI], but our analysis suggests that during times without a large land ice area in the Northern Hemisphere (e.g. before 2.82 Myr BP), the specific equilibrium climate sensitivity, S[CO2,LI], was smaller than during interglacials of the Pleistocene. We thus find support for a previously proposed state change in the climate system with the widespread appearance of northern hemispheric ice sheets. This study points for the first time to a so far overlooked non-linearity in the land ice albedo radiative forcing, which is important for similar palaeodata-based approaches to calculate climate sensitivity. However, the implications of this study for a suggested warming under CO2 doubling are not yet entirely clear since the details of necessary corrections for other slow feedbacks are not fully known and the uncertainties that exist in the ice-sheet simulations and global temperature reconstructions are large.当前，辐射强迫（radiative forcing）增强所引发的平衡升温——即特定平衡气候敏感度（specific equilibrium climate sensitivity, S）——如何随背景气候变化，仍是一个悬而未决的学术问题。本研究借助二氧化碳代理数据（CO2 proxy data），以及基于三维冰盖模型（3-D ice-sheet-model）重建的过去5百万年（Myr）陆地冰反照率（land ice albedo）情况，提供了关于S的状态依赖性的古数据证据。研究发现，陆地冰反照率强迫随背景气候呈非线性变化，而二氧化碳辐射强迫的非线性特征则取决于所采用的二氧化碳数据集。由于此前的近似方法较为简化——当时将陆地冰反照率辐射强迫视为海平面变化的线性函数——这类类似研究迄今尚未考虑到该非线性特征。冰盖面积变化的纬度依赖性，对陆地冰反照率与海平面之间的非线性关系至关重要。在本研究的设置中，我们将二氧化碳与陆地冰反照率（LI）的辐射强迫相结合，结果显示，在更新世（Pleistocene，过去2.1百万年）的大部分时段内，计算得到的特定平衡气候敏感度S[CO2,LI]存在状态依赖性。在更新世的中等冰川气候与间冰期（interglacial periods）时段，S[CO2,LI]的平均值较全冰川期（full glacial conditions）条件下高出约45%。在本研究分析的上新世（Pliocene）时段（距今2.6至5百万年），由于二氧化碳数据存在不确定性，无法对S[CO2,LI]进行可信度较高的计算，但研究结果表明，在北半球（Northern Hemisphere）无大规模陆地冰盖的时期（例如距今2.82百万年之前），特定平衡气候敏感度S[CO2,LI]较更新世的间冰期更低。因此，本研究为此前提出的‘北半球广泛出现冰盖后气候系统发生状态转变’这一假说提供了支持依据。本研究首次指出，陆地冰反照率辐射强迫中存在迄今未被关注的非线性特征，这一点对基于古数据计算气候敏感度的类似研究具有重要意义。不过，本研究关于二氧化碳倍增下气候变暖的相关推论尚未完全明确，原因在于其他慢反馈（slow feedbacks）所需修正的细节尚未完全明晰，且冰盖模拟与全球温度重建中仍存在较大不确定性。