Studying the response of a climate system to perturbations has practical significance. Standard methods in computing the trajectory-wise deviation caused by perturbations may suffer from the chaotic nature that makes the model error dominate the true response after a short lead time. Statistical response, which computes the return described by the statistics, provides a systematic way of reaching robust outcomes with an appropriate quantification of the uncertainty and extreme events. In this paper, information theory is applied to compute the statistical response and find the most sensitive perturbation direction of different El Ni\~no-Southern Oscillation (ENSO) events to initial value and model parameter perturbations. Depending on the initial phase and the time horizon, different state variables contribute to the most sensitive perturbation direction. While initial perturbations in sea surface temperature (SST) and thermocline depth usually lead to the most significant response of SST at short- and long-range, respectively, initial adjustment of the zonal advection can be crucial to trigger strong statistical responses at medium-range around 5 to 7 months, especially at the transient phases between El Ni\~no and La Ni\~na. It is also shown that the response in the variance triggered by external random forcing perturbations, such as the wind bursts, often dominates the mean response, making the resulting most sensitive direction very different from the trajectory-wise methods. Finally, despite the strong non-Gaussian climatology distributions, using Gaussian approximations in the information theory is efficient and accurate for computing the statistical response, allowing the method to be applied to sophisticated operational systems.

翻译：研究气候系统对扰动的响应具有实际意义。传统的基于轨迹偏差的扰动响应计算方法可能受混沌特性影响，导致模型误差在短期预报后主导真实响应。统计响应通过计算由统计量描述的回报，提供了一种系统性方法，能够合理量化不确定性和极端事件，从而获得稳健结果。本文应用信息论计算统计响应，并针对不同厄尔尼诺-南方涛动（ENSO）事件，确定其对初值和模型参数扰动最敏感的扰动方向。最敏感扰动方向取决于初始相位和时间尺度：海表温度（SST）和温跃层深度的初值扰动分别在短期和长期范围内引起最显著的SST响应，而纬向平流的初始调整对于引发约5-7个月的中期强统计响应至关重要，尤其在厄尔尼诺与拉尼娜之间的过渡阶段。研究还表明，由外部随机强迫扰动（如风爆发）触发的方差响应通常主导均值响应，使得所得最敏感扰动方向与基于轨迹的方法显著不同。最后，尽管气候态分布呈现强非高斯特征，信息论中采用高斯近似在计算统计响应时仍高效且准确，使该方法可应用于复杂的业务化系统。