Hybrid Sensitivity Analysis of Soil Hydraulic Parameters in Nature-Based Solution Coupling Hydrus-1D Simulations with Data-Driven Interpretation

Abstract This study proposes an integrated predictive framework for analysis of substrates’ hydrological response in urban nature-based solutions (NBS), combining numerical modeling with HYDRUS-1D, probabilistic techniques, and advanced tools of statistical analysis and machine learning. The aim is to quantify the influence of Van Genuchten’s hydraulic parameters on flow generation and identify critical factors for optimized green infrastructures’ design. Monte Carlo simulations were carried out on eight parameterized families of NBS substrates, each represented by about 1,000 combinations of hydraulic parameters derived from laboratory analysis. The results show that the most influential parameters are saturated hydraulic conductivity ( Ksat ), parameter α (retention curve position), and, in some cases, parameter n (curve slope). The simulations returned average annual outflow values ranging from − 4,096 mm (less efficient substrate) to − 4,336 mm (more draining substrate), with standard deviations between 1.2 mm (high stability) and 188 mm (high instability). Among the analyzed substrates, through regression analysis, the coarse-textured T5, T6, and T7 (sand- and gravel-rich growing media with high hydraulic conductivity) showed the best overall performance, combining high drainage efficiency, robust model predictability, and a dominant influence of the α parameter. The parameters α and Ksat have emerged as dominant drivers in the most draining substrates, while θ s (saturated water content) and n are critical in substrates with intermediate retention capacity. The methodology also integrates correlation analysis (Pearson, Spearman), partial dependence plot, and nonparametric bootstrap, providing a robust and multiperspective diagnosis of hydraulic sensitivity. The results identify the most stable and predictable substrate configurations and provide practical guidance for NBS design and calibration in complex urban scenarios.