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。由于混沌特性，标准方法在计算扰动引起的轨迹偏差时，可能会在短期预报后因模型误差主导真实响应而失效。统计响应通过计算统计量描述的回报，为量化不确定性和极端事件提供了系统性方法，从而获得稳健结果。本文应用信息论计算统计响应，并确定不同厄尔尼诺-南方涛动（ENSO）事件对初始值和模型参数扰动的最敏感扰动方向。取决于初始相位和时间尺度，不同状态变量对最敏感扰动方向贡献各异。尽管海表温度（SST）和温跃层深度的初始扰动分别在短期和长期范围内引起SST最显著响应，但纬向平流的初始调整可能在中尺度（约5-7个月）触发强烈统计响应，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）引发的方差响应往往主导平均响应，导致最敏感方向与轨迹方法截然不同。最后，尽管存在强非高斯气候分布，信息论中采用高斯近似计算统计响应既高效又准确，使该方法可应用于复杂业务系统。