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

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，辐射强迫增强所引发的平衡增温——即特定平衡气候敏感性S（equilibrium climate sensitivity）——如何依赖于背景气候这一问题，仍是一个尚未解决的开放议题。本文依托古气候数据（palaeodata），结合CO₂代用资料与近500万年（Myr）来基于三维冰盖模型（ice-sheet-model）重建的陆地冰反照率（land ice albedo，LI）数据，探究了S的状态依赖性。研究发现，陆地冰反照率强迫与背景气候呈非线性关系，而CO₂辐射强迫（radiative forcing）的非线性特征则取决于所采用的CO₂数据集。此前由于采用了更为简化的近似方法，即假定陆地冰反照率辐射强迫为海平面变化的线性函数，这类相似研究尚未考虑到这一非线性特性。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。在我们的研究框架中，将CO₂与陆地冰反照率（LI）的辐射强迫相结合，我们发现在更新世（Pleistocene，过去210万年）的大部分时段内，计算得到的S[CO₂,LI]存在状态依赖性。在更新世中等冰川气候与间冰期（interglacial periods）时段，S[CO₂,LI]的平均值较完整冰期（glacial conditions）条件下高出约45%。在本次分析的上新世（Pliocene）时段（距今260万至500万年BP），由于CO₂数据的不确定性，无法对S[CO₂,LI]进行可靠的计算，但研究结果表明，在北半球（Northern Hemisphere）无大规模陆地冰覆盖的时段（例如距今282万年前），S[CO₂,LI]较更新世的间冰期更小。因此，本研究为此前提出的“随着北半球广泛出现冰盖，气候系统发生状态转变”的假说提供了实证支撑。本研究首次指出，陆地冰反照率辐射强迫中存在此前被忽视的非线性特性，这对于采用类似古气候数据方法计算气候敏感性的研究具有重要意义。不过，本研究针对CO₂倍增下的预估增温所得出的结论仍不完全明确，因为其他慢反馈（slow feedbacks）所需校正的细节尚未完全明晰，且冰盖模拟（ice-sheet simulations）与全球温度重建（global temperature reconstructions）中存在较大的不确定性。