Modeling climate change effects on river ice thickness in the Northern Hemisphere

River ice is a pivotal element in cryosphere hydrology, ecology, and engineering, influencing water resource management and ecological conservation, particularly in the context of global climate change. This study employs the Stefan and Ashton equations to simulate historical river ice thickness across the Northern Hemisphere from 1972 to 2022 and assesses the effects of winter mean temperature (WMT) and winter mean snow depth (WMSD) on maximum river ice thickness (MRIT). The results indicate that the Stefan equation has good fitting performance at most stations, achieving higher accuracy in simulating river ice thickness. Although the Ashton equation generally underestimates river ice thickness, it still demonstrates excellent performance in capturing variability in certain stations. Over time, MRIT has generally declined, with most stations showing annual variation rates between 0 and 0.004 m/yr, although localized rates can reach up to 0.032 m/yr. The WMT increases at an average rate of 0.05 °C per year, and a 1 °C rise in WMT corresponds to an average reduction of 0.03 m in MRIT, according to the analysis. River ice shows increased temperature sensitivity in warmer climates. Additionally, for every 0.1 m increase in WMSD, the MRIT can decrease by up to 0.34 m. Under conditions of low temperature and snow depth, the sensitivity of MRIT to changes in snow depth is significantly higher. These insights provide a foundation for predicting future river ice trends and offer key insights for sustainable water resource and ecosystem management in cryosphere regions.