  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.
