Review of algorithms and parameterizations to determine unfrozen water content in frozen soil

Unfrozen water plays an important role in a number of processes, including water and heat transfer, frost heave, thaw settlement and simulations for the hydro-thermo-mechanical interactions in frozen soil. Past studies have demonstrated that considering the unfrozen water content in cold regions can significantly improve accuracy in coupling heat and water transfer modeling in frozen soil. However, differences between experimental data and theoretical understanding have resulted in discrepancies between parameterizations. To address this, we presented the first study to synthesize the algorithms and parameterizations used for unfrozen water content; we also discussed influential factors on unfrozen water content in frozen soil. We then provided a comprehensive discussion of the progress in algorithms and parameterizations regarding unfrozen water content and summarized them into four categories, which were calculated using soil temperature, specific surface area of soil particles, soil water curve, and different types of water. Selected unfrozen water content parameterizations were then evaluated based on those previous results as well as the data collected from our field observation station in permafrost region on the Qinghai-Tibet Plateau (QTP). These results revealed that empirical parameterizations were useful for calculating unfrozen water content. In addition, the physical parameterizations had higher accuracy for calculating unfrozen water content, but they were more complicated and difficult to use in practical applications. Unfrozen water content parameterizations were influenced by many factors, and the warming and cooling processes were especially important when calculating unfrozen water content. Finally, future research should aim to improve our theoretical understanding and to develop simple parameterizations that couple land surface processes models in cold regions. It is expected that this review will provide a sound theoretical basis for the further study of the unfrozen water content in frozen soil and its subsequent effects on hydrothermal transfer processes in cold regions.