Mathematical modeling of river ice processes

River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes. River ice research has largely been driven by engineering and environmental problems that concern society, including ice effects on flooding, hydropower, navigation, ecology, and the environment. Important findings on river ice research before 1980 have been summarized by Ashton (1986) and Donchenko (1987). Significant progress has been made in river ice research in the last three decades. Mathematical modeling has been an essential part of this progress. Mathematical models have been developed for various river ice processes. They not only helped to advance understanding of the physical processes by complementing field and laboratory studies, but also provided tools for planning and design of engineering projects. In this paper, models of various river ice processes during the winter, from freeze-up to breakup, are reviewed after a brief overview of river ice phenomena. Following the discussion of these ‘component’ models, a discussion on ‘comprehensive’ models and an analytical framework which links all river ice processes in a coherent manner is presented.