Partitioning the contributions of glacier melt and precipitation to the 1971–2010 runoff increases in a headwater basin of the Tarim River

•The glacier covered area and glacier mass in the KRB have decreased from 1971 to 2010.•On average, the contributions to total runoff from rainfall, glacier melt and snow melt are 61%, 28% and 11%, respectively.•The largest monthly contribution of glacier melt to runoff occurs in August; while the maximum monthly rainfall is in July.•In terms of the increase in runoff, rainfall and glacier melt are the primary causes in response to the warmer and wetter climate over the study period.•Snow melt has a negative influence due to the downward trend.