A simple and robust river network scaling algorithm (NSA) is presented to rescale fine-resolution networks to any coarser resolution. The algorithm was tested over the Danube River basin and the European continent. Coarse-resolution networks, at 2.5, 5, 10, and 30 min resolutions, were derived from higher-resolution gridded networks using NSA and geomorphometric attributes, such as river order, shape index, and width function. These parameters were calculated and compared at each resolution. Simple scaling relationships were found to predict decreasing river lengths with coarser-resolution data. This relationship can be used to correct river length as a function of grid resolution. The length-corrected width functions of the major river basins in Europe were compared at different resolutions to assess river network performance. The discretization error in representing basin area and river lengths at coarser resolutions were analyzed, and simple relationships were found to calculate the minimum number of grid cells needed to maintain the catchment area and length within a desired level of accuracy. This relationship among geomorphological characteristics, such as shape index and width function (derived from gridded networks at different resolutions), suggests that a minimum of 200--300 grid cells is necessary to maintain the geomorphological characteristics of the river networks with sufficient accuracy. ¿ 2001 American Geophysical Union