A minimal dispersion flow algorithm

Over the past four decades numerous dispersive (multiple flow direction) flow algorithms have been proposed. Dispersive algorithms are often preferred for applications because they overcome the limitations of the main non-dispersive method, D8, specifically the unnatural appearing extensive straight/parallel flow patterns and the abundance of artifact source cells (ASCs). An ASC is a cell in a flow-direction (FD) raster that has no inflowing cells but is not situated at a summit within the digital elevation model. They represent locations where a flow line has been truncated in the upslope direction, disconnecting the flow line from its starting peak. Attempts to address the unnatural flow patterns of D8 using alternate non-dispersive flow algorithms have resulted in more abundant ASCs. Dispersive flow algorithms can yield more natural appearing flow patterns than D8 while reducing or eliminating ASCs. However, some researchers have argued that dispersion has little physical basis in the definition of upslope area and should be minimized in the formulation of these methods. It seems that a fundamental compromise in flow-path modelling exists between natural-looking flow patterns, the abundance of ASCs, and the need for dispersion. A new minimal dispersion flow algorithm (MDFA) is presented in this paper. MDFA restricts dispersion to locations where it is necessary to resolve ASCs in a non-dispersive path-corrected FD raster. A case study is presented, comparing flow algorithms for the prevalence of ASCs and the amount of dispersion in various non-dispersive and dispersive methods. Findings show that MDFA can produce the natural appearing flow patterns of a path-corrected non-dispersive flow algorithm, eliminates ASCs entirely, while requiring the least number of cells with multiple outflowing neighbors and the lowest average overall dispersion of any of the tested dispersive methods.