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.

中文翻译：

---

基于机器学习的伪连续 pedotransfer 函数预测土壤冻结特性曲线


未冻结的水在冻土中发生的热物理过程中起着至关重要的作用。测量困难需要近似方法来描述未冻结水分含量 （θ） 和土壤温度之间的关系，称为土壤冻结特性曲线 （SFCC）。尽管取得了重大进展，但模型特性、冻融滞后和相位平衡仍然具有挑战性。本研究开发了一种使用极端梯度提升 （XGB） 实现的 pedotransfer 函数 （PTF） 估计 θ 的替代方法。XGB-PTF 模型使用文献中可用的 SFCC 数据进行训练，并利用合作博弈论来评估对 θ 预测的潜在影响。对 XGB-PTF 的性能进行了严格评估，并与两个高性能经验模型进行了比较。均方根误差和平均绝对误差分别显著降低 42% 和 55%，证明了 XGB-PTF 的优越性。XGB-PTF 的可用性也通过实验验证得到了验证。所提出的模型的一个显着优点是它能够提供一个包含实际 θ 的可靠范围，置信度为 95%。将 XGB-PTF 与博弈论耦合表明，影响 SFCC 的主要因素对于细粒土壤，按孔隙度 （n）、初始饱和度 （Sr） 和粘土分数 （Fclay） 的顺序排列，而对于粗粒土壤，顺序为 Fclay、n 和 Sr。此外，从博弈论得出的见解与之前关于孔隙水在不同温度范围内相变的实验研究一致。拟议的 XGB-PTF 具有简单的预测因子、效率和透明度，有望成为推进 SFCC 研究的多功能工具。