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A new geographic information system (GIS) numerical framework (NF), called CUENCAS, for flows in river networks is presented. The networks are extracted from digital elevation models (DEMs). The program automatically partitions a basin into hillslopes and channel links that are required to correspond to these features in an actual terrain. To investigate the appropriate DEM resolution for this correspondence, we take a high-resolution DEM at 10-m pixel size, and create DEMs at eight different resolutions in increments of 10 m by averaging. The extracted networks from 10-30 m remain about the same, even though there is a tenfold reduction in the number of pixels. By contrast, the extracted networks show increasing distortions of the original network from 40-90 m DEMs. We show the presence of statistical self-similarity (scaling) in the probability distributions of drainage areas in a Horton-Strahler framework using CUENCAS. The NF for flows takes advantage of the hillslope-link decomposition of an actual terrain and specifies mass and momentum balance equations and physical parameterizations at this scale. These equations are numerically solved. An application of NF is given to test different physical assumptions that produce statistical self-similarity in spatial peak flow statistics in a Horton-Strahler framework.