The arbitrary adoption of cell center to represent the whole cell is a compromise to the grid structure of the digital elevation models (DEMs), which greatly limits the accuracy of estimating flow distance and width functions. This study uses the triangulation with linear interpolation (TLI) method to approximate the missing flow distance values within a cell except for the cell center. A new flow distance algorithm (D∞-TLI) is proposed to improve the flow distance estimation by using a two-segment-distance strategy. The first segment distance from a cell center to a crossing point at the local 3 × 3 window boundary is modeled by the D∞ method. The second segment distance souring from the crossing point is estimated by the TLI using the flow distance values assigned for the two closest downstream cell centers, while these values have been assigned by iterating from lowest to highest cells. Then, using the continuous flow distance field approximated over a cell region, this cell can be divided into multiple equidistant belts (MEB) to estimate the width function. Four numerical terrains and two real-world terrains are used for assessments. The results demonstrate that D∞-TLI outperforms nine existing flow distance algorithms over any numerical terrains, and it is overall optimal for real-world terrains. Meanwhile, MEB extracts the width function which is less affected by unreasonable artificial fluctuation than the previous method. Hence, MEB combined with D∞-TLI can obtain a high-accuracy estimation of hydro-geomorphological attributes that may be conducive to the application of hydrologic modeling.

The naturally-existing diffusive flow makes the multiple flow direction (MFD) algorithm for digital elevation models with revisited values. However, owing to a generally accepted hypothesis, i.e., flow over a grid cell is uniformly distributed ignoring the micro-topography and the inflow direction/position, nearly no existing MFD algorithms can simultaneously force the flow along the exact dispersive path, and provide highly accurate hydrological/geomorphological parameters. In this study, an improvement Triangular Form-based Multiple Flow Algorithm called iTFM is proposed to limit the arbitrary dispersion caused by the conventional hypothesis through considering the nonuniform flow domain within a cell. In the new algorithm, each facet flow and its inflow direction/position are considered to route the flow along the local aspect over partial areas to downstream facets or cells. Facets with or without inflow can behave quite nonuniformly in contributing areas, namely flow domains. This procedure is adopted to generalize the nonuniformity and route the flow to the exact downstream facets. Quantitative assessments using artificial terrains show that iTFM suppresses the artificial dispersion effectively and extracts the flow paths highly consistent with the exact ones. Compared with previous algorithms, iTFM provides the most accurate total contributing areas. In addition, vector split and area split strategies are compared for flow split within a facet which is a necessary step in both TFM and iTFM, and the results prove that area split is more efficient. Hence, it can be concluded that the iTFM algorithm combined with the area split strategy can better define the dispersion flow path.