Quantifying the effects of driving factors and runoff sensitivity on runoff variation based on the Budyko equation

• The change of the runoff sensitivity coefficients should be considered in runoff attribution analysis. • The causes of runoff change from two aspects was quantified: runoff sensitivity coefficients and driving factors. • The sensitivity of runoff to driving factors had gradually increased since the abrupt change in streamflow. • The change of runoff sensitivity coefficients was the dominant factor of streamflow change in most watersheds. Changes in driving factors can directly impact runoff variation and indirectly alter it through the runoff sensitivity coefficients. This study has broken through the problem of ignoring the dynamic change of runoff sensitivity coefficients in previous studies, and attributed the runoff change to runoff sensitivity coefficients and driving factors. The contribution rate of runoff sensitivity coefficients to runoff change was quantified based on the improved Budyko equation. The results showed that: (1) From 1960 to 2022, the annual runoff of the main rivers in Gansu Province decreased from the southeast to the northwest, with a range of 9.1 mm- 309.6 mm. The number of significantly reduced rivers accounted for 75 %. The mutation years of annual runoff were mainly concentrated between 1970 and 2010. (2) From 1960 to 2022, the annual precipitation decreased from southeast to northwest, the annual potential evapotranspiration increased from southeast to northwest, and the annual temperature decreased from northeast to southwest. Land use conversion was frequent between 1980 and 2020, with a total conversion area of 30 %. (3) The runoff sensitivity coefficients had spatial and temporal heterogeneity. Precipitation and the characteristic parameters of the underlying surface were the main driving factors for the change of runoff sensitivity coefficients in most rivers. (4) In addition to the Dang River, Shiyang River, and Datong River, the primary factor contributing to the alteration in runoff in the remaining nine rivers was the impact of runoff sensitivity coefficients. Human activities were the main reason for the change of runoff in other rivers except for the Shule River, Dang River, and Heihe River Basin. The findings contribute to grasping the response of streamflow alterations to the driving factors and offer a new insight to effectively understand the mechanism of runoff variation under the changing environments.