Derivation of delay equation climate models using the Mori-Zwanzig formalism.
Derivation of delay equation climate models using the Mori-Zwanzig formalism.
复制标题
使用 Mori-Zwanzig 形式推导延迟方程气候模型。
DOI：
10.1098/rspa.2019.0075
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Falkena SKJ
中科院分区：
文献类型：
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作者：
Falkena SKJ
包含延迟的模型经常用于理解气候变率现象，但延迟通常是通过随机物理推理引入的，例如波的传播时间。在本文中，Mori-Zwanzig形式主义作为一种系统地从偏微分方程系统推导出延迟模型的方法，从而为使用这些延迟型模型提供了更好的理由。Mori-Zwanzig技术给出了一个正式的重写系统使用一组解决的变量，其中重写的系统包含一个内存项的投影。该记忆项的计算需要求解正交动力学方程，该方程表示未解决的动力学。对于非线性系统，通常不可能获得正交动力学的解析解，需要找到近似解。在这里，我们展示了厄尔尼诺南方涛动（ENSO）两条模式的Mori-Zwanzig技术，并探索解决正交动力学的方法。由此产生的非线性延迟模型包含一个额外的长期相比，以前proposedad的概念模型。这个新的术语导致了更大的ENSO周期，这更接近于观测中看到的。
Models incorporating delay have been frequently used to understand climate variability phenomena, but often the delay is introduced through anad hocphysical reasoning, such as the propagation time of waves. In this paper, the Mori-Zwanzig formalism is introduced as a way to systematically derive delay models from systems of partial differential equations and hence provides a better justification for using these delay-type models. The Mori-Zwanzig technique gives a formal rewriting of the system using a projection onto a set of resolved variables, where the rewritten system contains a memory term. The computation of this memory term requires solving the orthogonal dynamics equation, which represents the unresolved dynamics. For nonlinear systems, it is often not possible to obtain an analytical solution to the orthogonal dynamics and an approximate solution needs to be found. Here, we demonstrate the Mori-Zwanzig technique for a two-strip model of the El Niño Southern Oscillation (ENSO) and explore methods to solve the orthogonal dynamics. The resulting nonlinear delay model contains an additional term compared to previously proposedad hocconceptual models. This new term leads to a larger ENSO period, which is closer to that seen in observations.