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Streamflow Q estimation in ungauged catchments is one of the greatest challenges facing hydrologists. Observed Q from 3000 to 4000 small-to-medium-sized catchments (10-10 000 km2) around the globe were used to train neural network ensembles to estimate Q characteristics based on climate and physiographic characteristics of the catchments. In total, 17 Q characteristics were selected, including mean annual Q, baseflow index, and a number of flow percentiles. Testing coefficients of determination for the estimation of the Q characteristics ranged from 0.55 for the baseflow recession constant to 0.93 for the Q timing. Overall, climate indices dominated among the predictors. Predictors related to soils and geology were relatively unimportant, perhaps because of their data quality. The trained neural network ensembles were subsequently applied spatially over the entire ice-free land surface, resulting in global maps of the Q characteristics (at 0.125° resolution). These maps possess several unique features: they represent observation-driven estimates, they are based on an unprecedentedly large set of catchments, and they have associated uncertainty estimates. The maps can be used for various hydrological applications, including the diagnosis of macroscale hydrological models. To demonstrate this, the produced maps were compared to equivalent maps derived from the simulated daily Q of four macroscale hydrological models, highlighting various opportunities for improvement in model Q behavior. The produced dataset is available online (). [ABSTRACT FROM AUTHOR]