GIS approach to scale issues of perimeter-based shape indices for drainage basins

Shape indices have been in use for several decades to describe the characteristics and hydrological properties of drainage basins. Due to the fractal behaviour of the basin boundary, perimeter-based shape indices depend on the scale at which they are determined. Therefore, these indices cannot objectively compare drainage basins across a range of scales and basin sizes. This paper presents an objective GIS-based methodology for determining scale-dependent shape indices from gridded drainage basin representations. The scale effect is addressed by defining a representative scale at which the indices should be determined, based on a threshold symmetric difference between two grids representing the drainage basin at different resolutions.