大西洋年代际振荡的延迟方程模式
A Delay Equation Model for the Atlantic Multidecadal Oscillation
摘要：
基于Mori-Zwanzig形式主义，利用一种新的从偏微分方程系统导出延迟模型的方法，导出了大西洋年代际振荡的延迟差分方程模型。Mori-Zwanzig形式主义给出了一个重写的原始方程组，其中包含一个记忆项。该记忆项可以与所得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，但空间扩展，大西洋年代际振荡模型。由此产生的延迟差分模型与用于描述厄尔尼诺-南方涛动的延迟差分模型是不同类型的。除了这个模型，它也可以通过集成沿特征，误差项的平滑近似的模型已来自Mori-Zwanzig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。
英文摘要：
A new technique to derive delay models from systems of partial differential equations, based on the Mori-Zwanzig formalism, is used to derive a delay difference equation model for the Atlantic Multidecadal Oscillation. The Mori-Zwanzig 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 Atlantic Multidecadal Oscillation. 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 Mori-Zwanzig 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.
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