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Mountain precipitation is often strongly underestimated as observations are scarce, biased toward lower-lying locations and prone to wind-induced undercatch, while topographical heterogeneity is large. This presents serious challenges to hydrological modeling for water resource management and climate change impact assessments in mountainous regions of the world, where a large population depends on water supply from the mountains. The headwaters of the Tarim River, covering four remote and highly glacierized Asian mountain ranges, are vital water suppliers to large agricultural communities along the Taklamakan Desert, northwest China. Assessments of future changes to these water towers have been hampered because of the large precipitation uncertainties. In this study, six existing precipitation datasets (observation-based reanalysis datasets, satellite observation datasets, and the output of high-resolution regional climate models) were compared over five headwaters of the Tarim River. The dataset incorporating the highest observation density (APHRODITE) is then corrected by calibrating the glacio-hydrological model Soil and Water Integrated Model-Glacier Dynamics (SWIM-G) to observed discharge, glacier hypsometry, and modeled glacier mass balance. Results show that this form of inverse modeling is able to inform the precipitation correction in such data-scarce conditions. Substantial disagreement of annual mean precipitation between the analyzed datasets, with coefficients of variation in catchment mean precipitation of 68% on average, was found. The model-based precipitation estimates are on average 1.5-4.3 times higher than the APHRODITE data, but fall between satellite-based and regional climate model results. [ABSTRACT FROM AUTHOR]