Nondispersive Drainage Direction Simulation Based on Flexible Triangular Facets

Abstract

A new eight-direction algorithm (iFAD8) for the simulation of drainage directions on grid digital elevation models (DEMs) is presented. In this algorithm, a flexible triangular facet construction technique (ND∞) is developed to provide local drainage directions ranging continuously from 0°to 360°. Subsequently, a flow aggregation technique using global deviations of local drainage directions is proposed to simplify the flow paths into a nondispersive format. Another algorithm (FAD8) accompanying the iFAD8 is also presented, which uses the D∞ directions as the local drainage directions. Then FAD8, iFAD8, and three existing algorithms are compared on 10 abstract terrains including nine basic terrains and a Himmelblau terrain. The algorithms are tested to reproduce exact slope lines and specific catchment areas derived from the terrain functions. The results show that iFAD8 has better performance than FAD8. Both iFAD8 and FAD8 outperform existing algorithms in most cases. The flow aggregation technique is shown to be an excellent choice for nondispersive drainage direction simulation based on infinite directions. The ND∞ direction based on flexible triangular facets is also an improvement to the local infinite direction of D∞. We conclude that the iFAD8 algorithm can provide better definitions of drainage directions.Plain-language Summary Overland movement of water and soil plays an important role in hydrological cycle and geomorphologic evolution. Analysis and modeling of these processes rely on drainage direction information. Through digitalizing and discretizing a continuous terrain into a mass of grid cells, drainage direction can be assigned to each cell. The accuracy of drainage directions may have a tremendous impact on the hydrologic and geomorphologic modeling. So an advanced algorithm for determination of drainage direction is required. Many algorithms have been proposed for this purpose. But there are some shortcomings in the existing algorithms. Here we present a new algorithm named iFAD8 to provide single drainage direction for each topographic cell. Two newly developed techniques are adopted in iFAD8 to improve both local drainage directions and global flow paths. iFAD8 partly optimizes the shortcomings of existing algorithms in theory and has a better performance on various terrains. Finally, iFAD8 will benefit hydrologic and geomorphologic modeling.

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

“…The Ed s of iFAD8 for these three cells are lower than any other algorithms. Meanwhile, D8 drains flow to the direction deviating from the theoretical direction (Figure 13a), because D8 does not consider the deviations between the selected and the theoretical direction (Wu et al., 2020). All the MFD algorithms produce excessive artificial dispersion on the plane, and their Ec equal to zero can be ignored again.…”

“…The cells with the same elevation can be processed according to the order in which they are searched from the DEM, but this is not forced because there is no flow transport between two neighboring cells with the same elevation. This sorting process is also adopted by several existing algorithms (e.g., Orlandini et al., 2003; Wu et al., 2020), and a data structure called Priority‐Queue can order the cells efficiently (Barnes, 2016).…”

“…The neglect of this problem will direct the partial flow to false downstream cells and lead to artificial dispersion. Several SFD algorithms take this problem into account and have made effective improvements (Orlandini et al., 2003; Shin & Paik, 2017; Wu et al., 2020). However, only a few methods try to solve the problem by MFD algorithms, including DEMON (Costa‐Cabral & Burges, 1994) and D∞‐LTD (Orlandini & Moretti, 2009).…”

“…To reproduce the dispersive areas of flow domains over the DEM, multiple flow direction (MFD) schemes assigning a cell with multiple drainage directions and presetting ratios for different downstream flows are widely adopted in scientific community (Freeman, 1991; Quinn et al., 1991). On the contrary, the single flow direction (SFD) algorithms route the flow to only one neighboring cell (e.g., Fairfield & Leymarie, 1991; Lea, 1992; O'Callaghan & Mark, 1984; Orlandini et al., 2003; Paik, 2008; Shin & Paik, 2017; Wu et al., 2020). MFD algorithms have been shown to outperform SFD algorithms by providing parameters varying smoothly and continuously (Wilson et al., 2007; Zhou & Liu, 2002).…”

“…Most of the mathematical models adopt numerical approximations of the topography and the grid digital elevation model (DEM) is used most widely (Li et al., 2021). The DEM discretizes a continuous terrain into a mass of grid cells, and the flow domain is estimated for every cell (Wu et al., 2020). Besides, the flow originating from different points within a grid may reach different neighboring grid cells along respective slope lines owing to the grid structure and the micro‐relief over soil surface (Costa‐Cabral & Burges, 1994; Moore & Grayson, 1991).…”