The challenge of non-Markovian energy balance models in climate

背景(考古学) 能量平衡 平衡(能力) 布朗运动 统计物理学 随机建模 等级制度 朗之万方程 简单(哲学) 数学 物理 认识论 经济 哲学 热力学 生物 古生物学 统计 神经科学 市场经济
作者
N. W. Watkins,Raphael Calel,S. C. Chapman,Aleksei V. Chechkin,Rainer Klages,David A. Stainforth
出处
期刊:Chaos [American Institute of Physics]
卷期号:34 (7) 被引量:2
标识
DOI:10.1063/5.0187815
摘要

We first review the way in which Hasselmann’s paradigm, introduced in 1976 and recently honored with the Nobel Prize, can, like many key innovations in complexity science, be understood on several different levels. It can be seen as a way to add variability into the pioneering energy balance models (EBMs) of Budyko and Sellers. On a more abstract level, however, it used the original stochastic mathematical model of Brownian motion to provide a conceptual superstructure to link slow climate variability to fast weather fluctuations, in a context broader than EBMs, and led Hasselmann to posit a need for negative feedback in climate modeling. Hasselmann’s paradigm has still much to offer us, but naturally, since the 1970s, a number of newer developments have built on his pioneering ideas. One important one has been the development of a rigorous mathematical hierarchy that embeds Hasselmann-type models in the more comprehensive Mori–Zwanzig generalized Langevin equation (GLE) framework. Another has been the interest in stochastic EBMs with a memory that has slower decay and, thus, longer range than the exponential form seen in his EBMs. In this paper, we argue that the Mori–Kubo overdamped GLE, as widely used in statistical mechanics, suggests the form of a relatively simple stochastic EBM with memory for the global temperature anomaly. We also explore how this EBM relates to Lovejoy et al.’s fractional energy balance equation.

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