Variability Characteristics of Sea Ice Durations in the Bohai and Northern Yellow Seas: A Fourier Series Expansion-Augmented Stationarity Test and Long-Term Trend Analysis

Modulated by diverse climatic and oceanic forcing factors, the sea ice durations in the nearshore waters of the Bohai and northern Yellow Seas exhibit complex fluctuations on interannual and interdecadal timescales. Systematically analyzing the oscillatory patterns and trend stationarity of long-term sea ice duration series provides robust theoretical and practical guidance for coastal ice disaster early warning, marine industrial safety, and coastal economic sustainability. This study analyzes annual sea ice duration series recorded over 59 winters (1966–2024) at six representative coastal marine stations spanning the full spatial gradient of regional ice regimes across the Bohai and northern Yellow Seas. Isolated missing values were filled by linear interpolation, and the Ljung–Box Q test confirmed that the residual series do not follow a white-noise process. Two categories of stationarity tests—conventional unit root tests and Fourier series expansion-augmented stationarity tests—are adopted to quantify the stationary properties, nonlinear trend transitions, and smooth structural breaks of sea ice durations at each station. The results reveal marked spatial differences in interannual volatility and evolutionary trends among stations: two smooth transitional shifts are identified for Bayuquan (BYQ) and Qinhuangdao (QHD), whereas the remaining stations each exhibit a single shift. Long-term trends range from multistage declining patterns to a rising pattern for Donggang (DGG), while Zhimaowan (ZMW) shows a statistically insignificant trend. This work provides quantitative statistical evidence for sea ice risk evaluation and coastal structural safety protection across the Bohai and northern Yellow Seas, and offers actionable decision-making references for climate change adaptation and integrated coastal zone governance in ice-affected coastal zones worldwide.