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

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 (Sr), and clay fraction (Fclay) for fine-grained soils, while for coarse-grained soils, the order is Fclay, n, and Sr. 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.