The middle Pleistocene transition as a generic bifurcation on a slow manifold
The middle Pleistocene transition as a generic bifurcation on a slow manifold
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DOI：
10.1007/s00382-015-2501-9
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发表时间：
2015-11-01
期刊：
影响因子：
4.6
通讯作者：
Ditlevsen, Peter
中科院分区：
文献类型：
--
作者：
Ashwin, Peter;Ditlevsen, Peter
第四纪的特点是一系列周期性的冰川作用，这是由于地球绕太阳轨道的变化引起的日射量（入射太阳辐射）的变化。气候记录中的谱功率与轨道强迫的谱功率有很大的不同：在1000 kyr之前，目前大部分谱功率在41 kyr波段，而从那时起，功率一直在100 kyr波段。这种变化定义了中更新世过渡（MPT）。MPT没有显示出轨道强迫的任何明显差异。因此，气候对日照的响应远不是线性的，在MPT前后似乎存在结构上的不同。本文提出了一个受Milankovitch强迫的多能级弛张振子的冰盖振荡动力学的低阶概念模型。该模型展示了三种不同气候状态之间的平滑过渡; Paillard提出的间冰期（i），温和冰期（g）和深冰期（G）（Nature 391：378-381，1998）。该模型提出了一个动态的解释，在一个缓慢的歧管的结构观察到的允许和“禁止”之间的三个气候状态的过渡。在该模式下，天文强迫对气候振荡的控制是通过弛豫振荡的相位重置机制实现的，即强迫对振荡的内相位产生影响。尽管它作为一个强迫常微分方程很简单，但该模式不仅能够再现一般特征，而且能够再现气候记录中观测到的振荡的许多细节。一个特别的新奇是，它包括一个缓慢的漂移的形式的慢流形，再现观察到的动态变化的MPT。我们解释了这种变化的跨临界分叉在快速动态变化的慢变量，这种分叉可以引起周期和振幅的突然变化，我们认为，这是与一个分支的“鸭式振荡”，出现在一个小范围的参数。该模型在模拟MPT之前，期间和之后的气候记录方面非常稳健。尽管概念模型没有指出具体的机制，但物理含义是，气候对轨道强迫的反应的重大重组并不一定意味着环境条件发生了重大变化。
The Quaternary period has been characterised by a cyclical series of glaciations, which are attributed to the change in the insolation (incoming solar radiation) from changes in the Earth's orbit around the Sun. The spectral power in the climate record is very different from that of the orbital forcing: prior to 1000 kyr before present most of the spectral power is in the 41 kyr band while since then the power has been in the 100 kyr band. The change defines the middle Pleistocene transition (MPT). The MPT does not indicate any noticeable difference in the orbital forcing. The climate response to the insolation is thus far from linear, and appears to be structurally different before and after the MPT. This paper presents a low order conceptual model for the oscillatory dynamics of the ice sheets in terms of a relaxation oscillator with multiple levels subject to the Milankovitch forcing. The model exhibits smooth transitions between three different climate states; an interglacial (i), a mild glacial (g) and a deep glacial (G) as proposed by Paillard (Nature 391:378-381, 1998). The model suggests a dynamical explanation in terms of the structure of a slow manifold for the observed allowed and "forbidden" transitions between the three climate states. With the model, the pacing of the climate oscillations by the astronomical forcing is through the mechanism of phase-resetting of relaxation oscillations in which the internal phase of the oscillation is affected by the forcing. In spite of its simplicity as a forced ODE, the model is able to reproduce not only general features but also many of the details of oscillations observed in the climate record. A particular novelty is that it includes a slow drift in the form of the slow manifold that reproduces the observed dynamical change at the MPT. We explain this change in terms of a transcritical bifurcation in the fast dynamics on varying the slow variable; this bifurcation can induce a sudden change in periodicity and amplitude of the cycle and we suggest that this is associated with a branch of "canard oscillations" that appear for a small range of parameters. The model is remarkably robust at simulating the climate record before, during and after the MPT. Even though the conceptual model does not point to specific mechanisms, the physical implication is that the major reorganisation of the climate response to the orbital forcing does not necessarily imply that there was a big change in the environmental conditions.