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Recent work has identified complex perennial supraglacial stream and river networks in areas of the Greenland Ice Sheet (GrIS) ablation zone. Current surface mass balance (SMB) models appear to overestimate meltwater runoff in these networks compared to in-channel measurements of supraglacial discharge. Here, we constrain SMB models using the hillslope river routing model (HRR), a spatially explicit flow routing model used in terrestrial hydrology, in a 63 km 2 supraglacial river catchment in southwest Greenland. HRR conserves water mass and momentum and explicitly accounts for hillslope routing (i.e., flow over ice and/or firn on the GrIS), and we produce hourly flows for nearly 10 000 channels given inputs of an ice surface digital elevation model (DEM), a remotely sensed supraglacial channel network, SMB-modeled runoff, and an in situ discharge dataset used for calibration. Model calibration yields a Nash–Sutcliffe efficiency as high as 0.92 and physically realistic parameters. We confirm earlier assertions that SMB runoff exceeds the conserved mass of water measured in this catchment (by 12 %–59 %) and that large channels do not dewater overnight despite a diurnal shutdown of SMB runoff production. We further test hillslope routing and network density controls on channel discharge and conclude that explicitly including hillslope flow and routing runoff through a realistic fine-channel network (as opposed to excluding hillslope flow and using a coarse-channel network) produces the most accurate results. Modeling complex surface water processes is thus both possible and necessary to accurately simulate the timing and magnitude of supraglacial channel flows, and we highlight a need for additional in situ discharge datasets to better calibrate and apply this method elsewhere on the ice sheet. [ABSTRACT FROM AUTHOR]