Identifying the possible driving mechanisms in Precipitation-Runoff relationships with nonstationary and nonlinear theory approaches

•A Driving index for Precipitation-Runoff relationships with the nonStationary theory approach (DPRS) is proposed to identify the driving levels and directions under nonstationary circumstances.•A Driving index for Precipitation-Runoff links with the nonLinear theory approach (DPRL) is further developed based on mutual information technique to quantify the nonlinear nature of their associations.•Following the quantitative assessment of candidate influencing factors in the precipitation-runoff relationships within nonstationary and nonlinear hydrological processes, the possible driving mechanisms for these relationships are investigated based on diverse catchment response elements. Climate change and complex anthropogenic activities have raised significant concerns regarding Precipitation-Runoff Relationships (PRR). Traditional methods, assuming stationary and linear conditions, often fail to adequately capture these intricate links. To address the limitations, we proposed an integrated framework, employing the Driving indices for Precipitation-Runoff relationships within the nonStationary and nonLinear theory approaches (DPRS and DPRL) to identify the possible driving mechanisms in PRR. The framework is validated across five sub-basins (WRB1-WRB5) within the Wei River Basin, known for its high spatiotemporal variability and intense anthropogenic activities. Spatiotemporal dynamics, nonstationary processes, and nonlinear interactions among various factors are assessed, including climate forcing, groundwater, vegetation dynamics, and anthropogenic influences. DPRS and DPRL assessments revealed that baseflow significantly influences PRR but with high uncertainty. Potential evapotranspiration plays a dominant role in driving negative PRR changes in WRB5 (weakening the correlation between precipitation and runoff), while vegetation dynamics negatively affect PRR with lower uncertainty. Anthropogenic influences represented by Impervious Surface Ratio (ISR), Night-Time Light (NTL), and population density (POP) exhibit varying driving levels, with ISR having the strongest and direct impact, closely linked to urbanization processes and scale within the study cases. The mutual validation of DPRS and DPRL confirms the dominance of baseflow in the Wei River Basin, with urbanization contributing to high ISR, NTL, and POP driving levels in WRB2 and WRB3. Afforestation policies intensify vegetation dynamics’ impact in WRB4 and WRB5. This framework extends its utility to