On the definition of the flow width for calculating specific catchment area patterns from gridded elevation data

Specific catchment area (SCA) patterns are commonly computed on grids using flow direction algorithms that treat the flow as coming from a point source at the pixel centre. These algorithms are all ambiguous in the definition of the flow width to be associated with a pixel when computing the SCA. Different methods for computing the flow width have been suggested, without giving an objective reason. In the few cases where this issue has been specifically discussed, the flow width is derived from subjective analysis and incorrect conceptualizations. This paper evaluates alternative approaches for defining the flow width when computing SCA patterns using the D infinity and D8 algorithms, by comparing theoretical and computed SCA patterns on sloping planes, inward and outward cones. Two new methods of defining the flow width are also analysed for both the D infinity and D8 algorithms. The performances of the different methods are discussed in relation to two dimensionless parameters: (1) the global resolution, defined as the ratio of a characteristic length of the study area to the grid size and (2) the upslope area resolution, defined as the ratio of the theoretical SCA to the grid size. The optimal methods are identified by specific threshold values of these dimensionless parameters. We conclude that assuming the flow width invariant and equal to the grid size is generally the best approach in most practical circumstances, both for the D infinity and D8 algorithm. Copyright (c) 2005 John Wiley & Sons, Ltd.