Study on automated detection methods of shallow surface soil water content based on GPR signal level

This paper addresses automated, uncertainty-aware estimation of shallow surface soil water content (SWC) from ground-penetrating radar (GPR) at the A-scan signal level, overcoming the reliance of conventional workflows on manually picked interfaces and empirical dielectric–moisture curves. Refined gradient soil boxes of sandy and clayey soils (0–30 % gravimetric SWC in 1 % steps) are constructed, 2 GHz GPR and TDR permittivity data are acquired, an effective time window is defined by consistency between travel-time inferred permittivity and TDR, and three physically interpretable attributes—time delay, envelope amplitude area (AEA) and centroid frequency (CF)—are extracted as candidate predictors. Attribute analysis reveals that AEA and CF behave as global indicators that are highly sensitive to SWC in sandy soil, whereas the local delay feature responds more strongly and monotonically in clayey soil because of its higher specific surface area, stronger bound-water effects and slower saturation. Single-indicator regressions already achieve high coefficients of determination (R² up to 0.98 for delay in sand and not less than 0.80 for the remaining indicators), but also expose soil-dependent bias and instability. To exploit the complementary information content of the three attributes, a three-indicator SWC model is built whose weights are obtained by multiplicatively fusing random forest importance with grey relational degree, thereby balancing direct predictive power with dynamic trend consistency. Model comparison shows that, for sandy soil, the three-indicator formulation reduces mean squared error (MSE) by more than 80 % relative to AEA- or CF-only models and remains comparable to delay-only regression, while for clayey soil it lowers MSE by approximately 27 %, 30 % and 51 % with respect to delay-, CF- and AEA-based models, respectively. Bayesian linear and nonlinear regression, combined with Monte Carlo sampling, is further employed to infer posterior distributions of model parameters and observation noise. The resulting credible intervals demonstrate that both model and data uncertainties remain within controllable ranges across the calibrated three-indicator space, with delay exhibiting particularly high predictive reliability. Building on the near-consistent predictions of the delay-only and three-indicator models, an error-recursive optimisation framework is proposed for fully automated SWC inversion. For each A-scan, an initial SWC is assumed, mapped to a travel time via the delay model, and used to recompute AEA and CF within the corresponding time gate; the discrepancy between the two SWC estimates is iteratively minimised until a strict convergence criterion is satisfied. The framework is implemented in dedicated software and validated on independent gradient-box samples and a 1.6 m field transect, where GPR-derived SWC profiles agree well with TDR yet avoid the low-moisture underestimation and high-moisture overestimation characteristic of TDR plus Topp/Roth mixing models. In terms of practical performance, the automated scheme markedly reduces manual interaction, maintains smooth SWC gradients even under 3 % step changes, and remains robust to mixing-induced heterogeneity in clayey samples. Overall, the study demonstrates a technically rigorous pathway toward highly automated, high-resolution GPR monitoring of shallow SWC with explicit quantification of predictive uncertainty.