Comparison of different rheological approaches and flow direction algorithms in a physically based debris flow model for data scarce regions

Abstract. A debris flow simulation model was proposed for data-scarce regions. The model couples a one-dimensional explicit solution for a monophasic sediment-water mixture with flow direction algorithms for debris flow routing. We investigate the effects of different multiple flow direction algorithms (D8, D∞, and Freeman’s Multiple Flow Direction (MFD)) and multiple rheology approaches (Newtonian, Bingham, Herschel-Bulkley, and dilatant) for the one-dimensional flow on the debris flow simulations. The model was tested by simulating debris flows triggered by an extreme rainfall in the Mascarada river basin in southern Brazil. We conducted two separate sets of simulations: one focused on the effects of flow directions, considering multiple DEM resolutions, and another to compare rheology approaches. A third simulation was conducted for multiple debris flows concurrently, utilizing optimal parameters derived from the results of the two simulation sets. D8 proved to be unsuitable for debris flow routing, whereas MFD performed better for high-resolution DEM (1 m pixel size) and D∞ for coarser resolutions (2.5, 5, and 10 m). In terms of affected area, the difference between the rheology approaches was less impactful than the difference between flow direction algorithms. The lack of velocity estimates and deposition depths for the simulated debris flow hindered a detailed comparison of which rheology had a more accurate result. Nevertheless, we found MFD and dilatant fluid to perform slightly better and utilize the optimal parameters to simulate three other debris flows, reaching true positive ratios of 58 % up to 83 %.