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Meltwater and runoff from glaciers in High Mountain Asia is a vital freshwater resource for one fifth of the Earth's population. Between 13% and 36% of the region's glacierized areas exhibit surface debris cover and associated supraglacial ponds whose hydrological buffering roles remain unconstrained. We present a high-resolution meltwater hydrograph from the extensively debris-covered Khumbu Glacier, Nepal, spanning a seven-month period in 2014. Supraglacial ponds and accompanying debris cover modulate proglacial discharge by acting as transient and evolving reservoirs. Diurnally, the supraglacial pond system may store >23% of observed mean daily discharge, with mean recession constants ranging from 31 to 108 hours. Given projections of increased debris-cover and supraglacial pond extent across High Mountain Asia, we conclude that runoff regimes may become progressively buffered by the presence of supraglacial reservoirs. Incorporation of these processes is critical to improve predictions of the region's freshwater resource availability and cascading environmental effects downstream.