Site-specific soil water characteristic curve prediction with extremely scarce data using data-driven hierarchical Bayesian model

Abstract

The soil-water characteristic curve (SWCC) is fundamental for understanding the hydro-mechanical behavior of unsaturated soils and is widely applied in various fields. However, determining the SWCC through laboratory experiments is time-consuming. As a result, developing efficient prediction models for SWCC is highly valuable for timely decision-making. Existing methods face fundamental limitations: Bayesian approaches rely on predefined empirical models that may fail to fully capture soil–water interactions, while current data-driven machine learning models struggle to handle extremely sparse measurements, incomplete inputs and uncertainty quantification. To address these challenges, this study introduces a data-driven hierarchical Bayesian model (HBM) that integrates an indirect database with extremely sparse site-specific measurements (e.g., fewer than four data points) to reliably predict the SWCC. The HBM operates in two stages where hyperparameters are first estimated from the database to establish a prior model, and then in the inference stage, the prior model is refined through transfer learning to generate a quasi-site-specific posterior model. Through conjugate priors and Gibbs sampling, this approach enables robust SWCC predictions with severely limited data and/or incomplete soil parameters. A comprehensive drying SWCC database with ten essential soil parameters is compiled to train and validate the model through three case studies and leave-one-site-out cross-validation. The results show that the HBM outperforms widely used machine learning models, such as Artificial Neural Networks and Extreme Gradient Boosting, offering a robust solution for SWCC prediction under site-specific data constraints.