Bayesian Additive Regression Trees for Multi-Depth Soil Moisture Modeling

Soil moisture content (SMC) is a key variable in hydrology, irrigation, and land-atmosphere interactions, yet continuous monitoring remains constrained by sensor limitations and site heterogeneity. This study evaluated Bayesian Additive Regression Trees (BART) for estimating daily SMC at 10, 30, and 50 cm depths in the Arta plain, northwestern Greece, using combinations of in situ soil moisture observations from other depths together with Sentinel-2-derived NDVI and NDMI. BART was trained with 2020–2021 data and evaluated using 2022 observations. Model performance was generally high, with Nash–Sutcliffe efficiency often exceeding 0.90 and RMSE remaining below nominal sensor uncertainty. The best results were obtained when soil moisture from two additional depths was used as predictor information, confirming the strong vertical dependence of profile moisture dynamics. NDVI and NDMI did not systematically improve point prediction accuracy but provided complementary information by improving the estimation of predictive uncertainty and generating more reliable credible intervals within the probabilistic formulation. Residuals were normally distributed and showed no evident systematic bias. Preliminary external validation at an independent site showed moderate skill, with most cases still producing errors below nominal sensor accuracy. Finally, a comparison between BART and Multiple Linear Regression (MLR) showed that BART outperformed MLR, particularly in cases where both machine learning models performed weakly. Overall, BART proved to be a robust framework for multi-depth soil moisture estimation.