A delay equation model for the Atlantic Multidecadal Oscillation
A delay equation model for the Atlantic Multidecadal Oscillation
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DOI：
10.1098/rspa.2020.0659
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发表时间：
2020-08
期刊：
影响因子：
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通讯作者：
Swinda K. J. Falkena;C. Quinn;J. Sieber;H. Dijkstra
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文献类型：
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作者：
Swinda K. J. Falkena;C. Quinn;J. Sieber;H. Dijkstra
基于Mori-Zwanzig（MZ）形式主义，提出了一种从偏微分方程组导出延迟模型的新方法，并用于导出大西洋年代际振荡（AMO）的延迟-差分方程模型。MZ形式主义给出了一个重写的原始系统的方程，其中包含一个记忆项。该记忆项可以与所得到的延迟方程中的延迟项相关。在这里，该技术被应用到一个理想化的，但空间上扩展，模型的AMO。由此产生的延迟差模型与用于描述厄尔尼诺南方涛动的延迟微分模型是不同类型的。除了这个模型，这也可以通过积分沿着特性，误差项的平滑近似模型已从MZ形式主义。我们的新方法，从空间扩展模型推导延迟模型有很大的潜力，使用延迟模型来研究一系列的气候变率现象。
A new technique to derive delay models from systems of partial differential equations, based on the Mori–Zwanzig (MZ) formalism, is used to derive a delay-difference equation model for the Atlantic Multidecadal Oscillation (AMO). The MZ formalism gives a rewriting of the original system of equations, which contains a memory term. This memory term can be related to a delay term in a resulting delay equation. Here, the technique is applied to an idealized, but spatially extended, model of the AMO. The resulting delay-difference model is of a different type than the delay differential model which has been used to describe the El Niño Southern Oscillation. In addition to this model, which can also be obtained by integration along characteristics, error terms for a smoothing approximation of the model have been derived from the MZ formalism. Our new method of deriving delay models from spatially extended models has a large potential to use delay models to study a range of climate variability phenomena.