Assessment and prediction of the effects of Arctic river flows on ocean circulation and climate are hindered by lack of knowledge about the terrestrial water balance. This study quantifies the components of the annual water budget (precipitation, streamflow, and evapotranspiration) and their uncertainty for a large Russian river basin. Over long periods, assuming negligible change in storage, inputs and outputs should balance. However, measurement limitations and errors lead to nonzero water balance closure (WBC). The variance of WBC, computed by summing the component variances, quantifies uncertainty in the water budget. The component terms and their uncertainty are calculated from independent observations and physically-based modeling. For the analysis period, the WBC is negative. The computed uncertainty is large, but not sufficient to conclude that WBC could be zero. Because current assessments do not completely account for the water budget, statements about the effects of climate change must be done cautiously.