An Improved Triangular Form-Based Multiple Flow Direction Algorithm for Determining the Nonuniform Flow Domain Over Grid Networks

The naturally existing diffusive flow provides revisited values for the multiple flow direction (MFD) algorithm for digital elevation models. However, since the flow is uniformly distributed over a grid cell, existing MFD algorithms can hardly force the flow to propagate within a finite region without arbitrary dispersion. In this study, an improved Triangular Form-based Multiple Flow Algorithm called iTFM is proposed to limit the arbitrary dispersion by considering the nonuniform flow domain in a cell. In the new algorithm, flow is routed between facets rather than cells and drained to at most two downstream facets, which forces the flow to propagate over partial subregions of a cell, so that different facets in the cell may have different contributing areas. In addition, two alternative strategies including vector split (VS) and area split (AS) are evaluated to determine the flow split ratio for the two downstream facets in this study. Then, the algorithms combining different split strategies (i.e., iTFM-VS, iTFM-AS) are compared with eight existing algorithms over four numerical terrains and one physical terrain. The visual and quantitative assessment results show that iTFM-AS can provide accurate total contributing areas and predicted flow domains for numerical terrains with resolutions ranging from 1 to 20 m. Moreover, the flow domains predicted by iTFM-AS are in high agreement with the observed domains over the physical terrain with practical resolutions. Therefore, it can be concluded that the iTFM-AS algorithm can better and more robustly define the dispersive flow domain.