概念气候模式中内部弛豫振荡的渐近分析
Asymptotic analysis of internal relaxation-oscillations in a conceptual climate model
摘要：
在KCG（Källén，Crafoord，Ghil）概念气候模式的基础上，建立了一个包含冰-冰-温度反馈和降水-温度反馈的动力系统。此外，我们分类的稳定性的各种临界点的系统，并确定一个参数的变化产生的Hopf分岔。这就产生了一个稳定极限环周围的物理有趣的临界点。此外，根据一般理论，周期轨道表现出松弛振荡，这是更新世冰期的一个特征。我们提供了一个渐近分析他们的行为，并得出一个公式的期间随着几个估计。反过来，他们是在一个体面的协议与古气候数据，是独立的任何参数化使用。因此，我们简单但强大的模型表明，气候可能会表现出内部弛豫振荡，没有任何外部强迫和广泛的参数。
英文摘要：
We construct a dynamical system based on the KCG (Källén, Crafoord, Ghil) conceptual climate model which includes the ice-albedo and precipitation-temperature feedbacks. Further, we classify the stability of various critical points of the system and identify a parameter which change generates a Hopf bifurcation. This gives rise to a stable limit cycle around a physically interesting critical point. Moreover, it follows from the general theory that the periodic orbit exhibits relaxation-oscillations which are a characteristic feature of the Pleistocene ice-ages. We provide an asymptotic analysis of their behaviour and derive a formula for the period along with several estimates. They, in turn, are in a decent agreement with paleoclimatic data and are independent of any parametrization used. Whence, our simple but robust model shows that a climate may exhibit internal relaxation-oscillations without any external forcing and for a wide range of parameters.
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