The North Atlantic Oscillation (NAO) index, a measure of sea-level atmospheric pressure variability, holds significant influence over weather patterns in North America and Northern Europe. A negative (positive) NAO value signifies increased cold air outbreaks and storm occurrences (reduced occurrences) in these regions. NAO, a product of multiple climate factors, demonstrates intricate dynamics with sea surface temperature (SST) and sea ice extent (SIE). In this study, we adopt a data-driven approach to explore the complex interplay between NAO, SST, and SIE, revealing a critical instability rooted in positive feedback loops among these climate variables. Our statistical machine learning methodology examines the impacts of melting Arctic SIE and rising SST on NAO, thereby understanding the weather patterns across the North Atlantic region. The skewness analysis yields a negative skewness in NAO across various time intervals -- daily, weekly, and monthly. This skewness, coupled with NAO's mean zero stationary nature, accentuates system instability. To capture these dynamics, we formulate a Bayesian Granger-causal dynamic linear model, which effectively updates the predictor-dependent variable relationship over time. The findings underscore an impending critical instability, indicative of more frequent occurrences of intensely cold climates in eastern North America and northern Europe, theory signifies a notable climate shift. By delving into the intricate feedback mechanisms of NAO, SST, and SIE, our study enhances our comprehension of climate variability, fostering a more informed perspective on the imminent climate changes that lie ahead.

翻译：北大西洋涛动（NAO）指数作为海平面大气压力变率的度量指标，对北美和北欧的天气模式具有重要影响。负（正）NAO值预示着这些区域冷空气爆发和风暴发生频率的增加（减少）。NAO作为多重气候因素的产物，与海表温度（SST）及海冰范围（SIE）呈现出复杂的动态关联。本研究采用数据驱动方法探究NAO、SST与SIE之间的复杂相互作用，揭示了根植于这些气候变量间正反馈循环的关键不稳定性。我们通过统计机器学习方法考察了北极海冰消融与海温上升对NAO的影响，从而解析北大西洋区域的天气模式。偏度分析显示NAO在日、周、月等不同时间尺度上均呈现负偏态特征。这种偏态特性与NAO均值为零的平稳性质相结合，加剧了系统不稳定性。为捕捉这些动态特征，我们构建了贝叶斯格兰杰因果动态线性模型，该模型能有效更新预测变量与因变量随时间演变的关系。研究结果突显了迫近的关键不稳定性，预示着北美东部与北欧地区将更频繁地出现极端寒冷气候，该理论标志着显著的气候转变。通过深入探究NAO、SST与SIE之间复杂的反馈机制，本研究深化了对气候变率的理解，为认知即将到来的气候变化提供了更科学的视角。