Abstract Motivated by a recent active period of Tropical Instability Waves (TIWs) that followed the extreme 2015/2016 El Niño, we developed a stochastically forced linear model for TIWs with its damping rate modulated by the annual cycle and El Niño Southern Oscillation (ENSO). The model’s analytical and numerical solutions capture relatively well the observed Pacific TIWs amplitude variability dominated by annual and ENSO timescales. In particular, our model reproduces the seasonal increase in TIWs variance during summers and falls and the nonlinear relationship with the ENSO phase characterised by a suppression, respectively increase of TIW activity during El Niño, respectively La Niña. A substantial fraction of TIWs amplitude modulation emerges from the deterministic nonlinear interaction between ENSO and the annual cycle. This simple mathematical formulation allows capturing the nonlinear rectifications of TIWs activity onto the annual cycle and ENSO through, for instance, TIWs-induced ocean heat transport. Moreover, our approach serves as a general theoretical framework to quantify the deterministic variability in the covariance of climate transients owing to the combined modulation of the annual cycle and ENSO.

中文翻译：

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ENSO和年周期调制热带不稳定波的简单理论

摘要 受 2015/2016 年极端厄尔尼诺现象之后热带不稳定波 (TIW) 的近期活跃期的启发，我们开发了 TIW 的随机强制线性模型，其阻尼率受年度周期和厄尔尼诺南方涛动 (ENSO) 调制. 该模型的分析和数值解相对较好地捕捉了观测到的由年度和 ENSO 时间尺度主导的太平洋 TIW 振幅变化。特别是，我们的模型再现了夏季和秋季 TIW 方差的季节性增加以及与 ENSO 阶段的非线性关系，其特征是在厄尔尼诺和拉尼娜期间分别抑制或增加 TIW 活动。TIW 幅度调制的很大一部分来自 ENSO 和年周期之间的确定性非线性相互作用。这种简单的数学公式允许通过 TIW 引起的海洋热传输等方式捕捉 TIW 活动对年循环和 ENSO 的非线性修正。此外，我们的方法作为一个通用的理论框架来量化由于年周期和 ENSO 的组合调制而导致的气候瞬变协方差的确定性变异。