The response and coupling coordination of soil moisture to vegetation in the Yellow River’s primary tributaries: a multi-source data analysis of the Wanchuan River Basin

The results reveal a distinct spatial pattern of lower moisture in the northern part and higher moisture in the southern part, with no significant variation across soil depths. A comprehensive vegetation index (VEG) integrating net primary productivity (NPP), leaf area index (LAI), and atmosphere-resistant vegetation index (ARVI) was found to be most suitable for this region. Overall vegetation conditions improved annually, with interannual variation following a normal distribution. Significant interaction between vegetation and soil moisture was observed, with the area of statistically significant positive correlation substantially exceeding that of negative correlation, indicating a synergistic relationship between the two variables. Coupling coordination analysis showed notable seasonal differences: in summer, coordination between SM and VEG was significantly divergent (coordinated in the south, uncoordinated in the north), while in other seasons, the relationship was characterized as marginally coordinated. This suggests a need for continuous structural optimization, with marginal coordination representing the predominant state of the soil moisture- vegetation system in the basin.Variable importance screening using the Giniindex- enhanced random forest algorithm identified land surface temperature and potential evapotranspiration as the dominant factors influencing the soil moisture-vegetation coupling coordination degree. These findings provide valuable data and theoretical support for understanding the synergistic mechanisms between soil, water, and vegetation in the Gansu section of the Yellow River, contributing to more effective ecosystem management strategies in the Loess Plateau region.