The El Ni{~n}o-Southern Oscillation (ENSO) exerts profound influence on global climate variability, yet its prediction remains a grand challenge. Recent advances in deep learning have significantly improved forecasting skill, but the opacity of these models hampers scientific trust and operational deployment. Here, we introduce a mathematically grounded interpretability framework based on bounded variation function. By rescuing the "dead" neurons from the saturation zone of the activation function, we enhance the model's expressive capacity. Our analysis reveals that ENSO predictability emerges dominantly from the tropical Pacific, with contributions from the Indian and Atlantic Oceans, consistent with physical understanding. Controlled experiments affirm the robustness of our method and its alignment with established predictors. Notably, we probe the persistent Spring Predictability Barrier (SPB), finding that despite expanded sensitivity during spring, predictive performance declines-likely due to suboptimal variable selection. These results suggest that incorporating additional ocean-atmosphere variables may help transcend SPB limitations and advance long-range ENSO prediction.

翻译：厄尔尼诺-南方涛动（ENSO）对全球气候变率具有深远影响，但其预测仍是一项重大挑战。深度学习的最新进展显著提升了预报技巧，但这些模型的不透明性阻碍了科学信任和业务化应用。本文提出基于有界变差函数的数学可解释性框架，通过将"死亡"神经元从激活函数的饱和区中恢复，增强了模型的表达能力。分析表明ENSO可预测性主要源于热带太平洋，印度洋和大西洋亦有贡献，这与物理认知一致。控制实验证实了方法的鲁棒性及其与传统预报因子的一致性。值得注意的是，我们探究了持续的春季可预报性障碍（SPB），发现尽管春季敏感性增强，但预报性能反而下降——这很可能源于次优的变量选择。这些结果表明，引入更多海气变量可能有助于突破SPB限制，推动ENSO的长期预测发展。