Machine learning-based pseudo-continuous pedotransfer function for predicting soil freezing characteristic curve

• Pedotransfer function for soil freezing characteristic curve (SFCC) is proposed. • Quantitatively understanding the variation of unfrozen water with temperature. • Influential mechanisms of dominant factors characterizing SFCCs are determined. Unfrozen water plays a crucial role in thermophysical processes occurring in frozen ground. Measurement difficulties require approximate approaches to describe the relationship between unfrozen water content ( θ ) and soil temperature, known as soil freezing characteristic curve (SFCC). Despite significant progress, model characteristics, freezing-thawing hysteresis, and phase equilibrium remain challenging. This study developed an alternative approach to estimate θ using a pedotransfer function (PTF) implemented with extreme gradient boosting (XGB). The XGB-PTF model was trained using SFCC data available in the literature, and cooperative game theory was utilized to assess potential impacts on θ predictions. The performance of the XGB-PTF was rigorously evaluated and compared with two high-performance empirical models. Significant reductions in root mean square error and mean absolute error of 42% and 55%, respectively, demonstrated the superiority of the XGB-PTF. The XGB-PTF’s usability was also verified by experimental validation. A notable advantage of the proposed model is its capacity to provide a credible range containing the actual θ with a 95% confidence level. Coupling the XGB-PTF with game theory indicated that the primary factors influencing the SFCC were in order of porosity ( n ), initial saturation degree ( S r ), and clay fraction ( F clay ) for fine-grained soils, while for coarse-grained soils, the order is F clay , n , and S r . Furthermore, insights derived from game theory aligned with previous experimental studies concerning the phase transition of pore water across various temperature ranges. The proposed XGB-PTF, with its straightforward predictors, efficiency, and transparency, is expected to serve as a versatile tool for advancing SFCC studies.