Evaluating soil freezing characteristic curve models for predicting unfrozen water content in freezing soils

Frozen soil is widely distributed around the world, and the phase change and migration of ice and water contribute to various engineering and agricultural challenges. The Soil Freezing Characteristic Curve (SFCC), which elucidates the relationship between water and temperature in permafrost, serves as a crucial tool for studying permafrost and forms the foundational equation for coupled numerical simulations involving permafrost water-heat-force. Different choices of SFCC result in variations in the predicted values of unfrozen water, thereby affecting the accuracy of other issues or numerical simulations. Moreover, there is a lack of studies on the performance of SFCC models under diverse conditions. Therefore, we review and classify some existing SFCC models, selects 14 SFCC models according to functional form, derivation process, physical significance etc., and evaluates these models through published data and statistical indicator RMSE, R2adj and BIC. The effects of functional form, soil type, cooling stage and initial water content on each model were analyzed using cluster analysis and other means. It is concluded that the SFCC model is affected by the function form, and the power and exponential functions need to be modified by more parameters. The nested soil water characteristic curve model also needs to be modified for the low water content section. Meanwhile, each model also shows sensitivity to the characteristics of datasets, and the performance under different conditions is not the same. Some models may not fit data features under certain conditions. Therefore, it is necessary to reasonably select the SFCC model in different use backgrounds and conditions.