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.

一种基于Mori-Zwanzig（MZ）形式主义的，从偏微分方程系统中导出延迟模型的新技术，用于为大西洋多年代际振荡（AMO）导出延迟差分方程模型。MZ形式主义重写了包含记忆项的原始方程组。该存储项可以与所得延迟方程中的延迟项相关。在这里，该技术应用于AMO的理想化但空间扩展的模型。所得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的类型不同。除了该模型（也可以通过沿特征进行积分而获得）之外，还从MZ形式主义中得出了用于模型平滑近似的误差项。