Drainage basin perimeters: a fractal significance

Abstract

Drainage basin boundaries are irregular curves with many scales of crenulation, defying precise measurement of basin perimeter. Richardson “divider” analysis of six drainage basin outlines from southern Indiana, and of an additional six from larger U.S. basins, suggests that basin boundaries are fractal or near-fractal shapes. Although the basins differ significantly in physiography, the fractal dimension values obtained fit within the narrow range 1.06–1.12, indicating that while basins may differ greatly in overall shape, they are very similar in terms of smaller-scale boundary irregularity. Techniques of measuring basin perimeter should be modified in recognition of these facts. The consistent fractal or near-fractal geometric characteristics of basin boundaries give a basis for extrapolation of perimeter values to appropriate levels of resolution. For most basin morphometry applications, however, the objective should be to make comparison among basins using measurements taken at the same degree of resolution relative to basin size, rather than identical resolution.