Methods developed to process raster digital elevation models (DEM) automatically in order to delineate and measure the properties of drainage networks and drainage basins are being recognized as potentially valuable tools for the topographic parameterization of hydrological models. All of these methods ultimately rely on some form of overland ¯ow simulation to de®ne drainage courses and catchment areas and, therefore, have diculty dealing with closed depressions and ¯at areas on digital land surface models. Some fundamental assumptions about the nature of these problem topographic features in DEM are implicit in the various techniques developed to deal with them in automated drainage analysis. The principal assumptions are: (1) that closed depressions and ¯at areas are spurious features that arise from data errors and limitations of DEM resolution; (2) that ¯ow directions across ¯at areas are determined solely by adjacent cells of lower elevation; and (3) that closed depressions are caused exclusively by the underestimation of DEM elevations. It is argued that while the ®rst of these assumptions is reasonable, given the quality of DEMs generally available for hydrological analysis, the others are not. Rather it seems more likely that depressions are caused by both underand overestimation errors and that ¯ow directions across ¯at areas are determined by the distribution of both higher and lower elevations surrounding ¯at areas. Two new algorithms are introduced that are based on more reasonable assumptions about the nature of ¯at areas and depressions, and produce more realistic results in application. These algorithms allow breaching of depression outlets and consider the distribution of both higher and lower elevations in assigning ¯ow directions on ¯at areas. The results of applying these algorithms to some real and hypothetical landscapes are presented.