Expanding scales: Achieving prediction of van Genuchten model hydraulic parameters in deep profiles by incorporating broad in situ soil information in pedotransfer functions

Soil hydraulic parameters (SHPs) are essential for evaluating soil ecosystem services. Yet direct measurements are costly, making pedotransfer functions (PTFs) a valuable alternative. Given the scale-dependent nature of soil hydrological processes and increasing importance of deep soil water cycling under global change, PTF research needs to be expanded both vertically and horizontally. Yellow River Basin (YRB) provides a representative region with its vast area (795,000 km²), strongly demanding accurate SHPs. Therefore, we conducted a field sampling at 475 sites up to 5 m depth across YRB, identifying the factors influencing deep SHPs, developing corresponding PTFs, and predicting SHP spatial distributions. Vertically, the heterogeneity of bulk density (BD), residual water content (θr), and shape parameter n of van Genuchten model increased generally, while that of shape parameter α decreased from 0 to 5 m. Horizontally, the order of variability was α > θr > θs > n > BD. Geostatistical analysis indicated moderate (BD, θs, and n) to strong (θr) spatial dependence above 1 m and strong dependence for all SHPs in deeper layers. Deep SHPs were primarily influenced by soil texture, organic carbon, depth, and topography. The new PTFs had higher accuracy than existing classical PTFs with R² ranging from 0.32 to 0.64 (except for α). This study developed the first set of PTFs for deep SHPs in YRB. The new PTFs with extended soil information further support the expansion of deep soil hydrological research, serving the soil and hydrological process quantification and regulation in YRB and similar regions globally.